SIMPOZIONUL NAŢIONAL DE ELECTROTEHNICĂ TEORETICĂ

SNET‘09

27 noiembrie 2009

Universitatea “Politehnica” din Bucureşti, Facultatea de Inginerie Electrică

Dedicat Profesorilor Cezar Flueraşu şi Mihai Vasiliu cu ocazia

împlinirii vârstei de 70 de ani

Universitatea “Politehnica” din Bucureşti CATEDRA DE

ELECTROTEHNICĂ

Asociaţia Inginerilor ElectricieniŞi Electronişti Din România

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Preşedinte: Prof.dr.ing. Florin CONSTANTINESCU Preşedinţi de onoare: Prof.dr.ing. Andrei ŢUGULEA, membru titular al Academiei Române Prof.dr.ing. Augustin MORARU Comitetul ştiinţific: Prof. dr. ing. Cezar FLUERAŞU, U.P.B. Prof. dr. ing. Mihai VASILIU, U.P.B.Prof. dr. ing. Horia ANDREI, U. Târgovişte Prof. dr. ing. Oszkár BÍRÓ, T.U. Graz Prof. dr. ing. Constantin BALA, U.P.B. Prof. dr. ing. Costin CEPIŞCĂ, U.P.B. Prof. dr. ing. Ioan CIRIC, U. Manitoba, FIEEE, membru al Academiei de Electromagnetism, MIT Prof. dr. ing. Paul CRISTEA, membru corespondent al Academiei Române Prof. dr. ing. Toma DORDEA, membru titular al Academiei Române Prof. dr. ing. Radu ENACHE, H.P.-România Prof. dr. ing. Alexandru FRANSUA, U.P.B. Prof. dr. ing. Horia GAVRILĂ, U.P.B. Prof. dr. ing. Constantin GHIŢĂ, U.P.B. Prof. dr. ing. Vasile IANCU, U.T.Cluj-Napoca Prof. dr. ing. Valentin IONIŢĂ, U.P.B. Prof. dr. ing. Mihai IORDACHE, U.P.B. Prof. dr. ing. Antonios KLADAS, N.T.U. Athena Prof. dr. ing. Teodor LEUCA, U. Oradea Prof. dr. ing. Gheorghe MÂNDRU, U.T.Cluj-Napoca Prof. dr. ing. Marlene MARINESCU, U.Wiesbaden Prof. dr. ing. Dan MICU, U.T.Cluj-Napoca Prof. dr. ing. Alexandru MOREGA, U.P.B. Prof. dr. ing. Radu MUNTEANU, U.T.Cluj-Napoca Prof. dr. ing. Claudia POPESCU, U.P.B. Prof. dr. ing. Mihai O. POPESCU, U.P.B. Dr. ing. Vergil RACICOVSCHI, I.C.P.E.-S.A. Prof. dr. ing. Costel RĂDOI, U.P.B. Prof. dr. ing. Alecsandru SIMION, U.T.Iaşi Prof. dr. ing. Emil SIMION, U.T.Cluj-Napoca Prof. dr. ing. Fănică SPINEI, U.P.B. Prof. dr. ing. Florin Teodor TĂNĂSESCU, C.E.R. Prof. dr. ing. Dumitru TOADER, U.P.Timişoara Prof. dr. ing. Vasile ŢOPA, U.T.Cluj-Napoca Prof. dr. ing. Nicolae VASILE, I.C.P.E.-S.A.

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Comitetul de organizare: Prof. dr. ing. Claudia POPESCU, decanul Facultatii de Inginerie Electrica, Prof. dr. ing. Miruna NIŢESCU, Ş.l. dr. ing. Mihai MARICARU, Drd. ing. Alexandru GHEORGHE, Conf. dr. ing. Viorel MARIN, Dr. ing. Mihaela MATEESCU, Drd. ing. Marian VASILESCU, Drd. ing. Bogdan VĂRATICEANU, Drd. ing. Aurelian FLOREA, S.l. dr. ing. George PALTANEA, Cătălin MOICEANU

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CUPRINS

Prezentări în plen

1. Cezar Flueraşu, UPB, O Cooperare Ştiinţifică Fructuoasă UPB – EDF, pp. 7-12

2. Paul Svasta, Ciprian. Ionescu, Norocel Dragos Codreanu, UPB, Investigation of Solder Joints by Thermographical Analysis, pp. 13-20

Secţiunea 1

Câmp electromagnetic şi dispozitive electromagnetice - prezentări orale

moderatori: Alecsandru Simion, Micu Ovidiu Dan

1. Adrian Munteanu, Alecsandru Simion, Leonard Livadaru, UT Gh. Asachi Iasi, Evaluation and

Performance Analysis of a Dual-Rotor Hybrid Synchronous Machine, pp. 21-26

2. Alecsandru Simion, UT Gh. Asachi Iasi, Analysis of Induction Machine Operating under Unsymmetrical Condition by Using Symmetrical Components, pp. 27-32

3. Liviu Emil Petrean, Mircea Horgos, Olivian Chiver, Universitatea de Nord Baia Mare, Unele Aspecte Privind Distributia Potentialului la Instalatiile de Legare la Pamânt din Staţii Electrice Exterioare, pp. 33-38

4. Micu Ovidiu Dan, Vlaicu Popescu, Dan D. Micu, Adriana Micu, UT Cluj Napoca, Precizia Unor Formule Aproximative Folosite la Calculul Prizelor de Pamânt, pp. 39-44

5. Dan-Cristian Popa, Vasile Iancu, UT Cluj Napoca, Particularities of the Design of the Variable Reluctance Linear Machine in Modular Construction, pp. 45-50

6. Augustin Moraru, Gabriel Preda, Ioan Florea Hantila, Mihai Maricaru, UPB, Metoda integrala de solutionare a problemlor de camp magnetic in structuri 3D cu medii feromagnetice, pp. 51-57

7. Ilona Plesa, Florin Ciuprina, Petru V. Notingher, UPB, Dielectric Spectroscopy of Polypropylene with and without Inorganic Nanofillers, pp. 58-63

8. Marilena Stănculescu, Stelian Marinescu, Dan Răducanu, UPB, Data Base Construction for Flaw Shape Reconstruction, pp. 64-68

Secţiunea 2

Circuite electrice şi aplicaţii - prezentări orale

moderatori: Mircea V. Nemescu, Gabriela Ciuprina 1. Alexandru Lazăr, Radu Popescu, Gabriela Ciuprina, Daniel Ioan, UPB, Parallel iterative

techniques for the extraction of line parameters of interconnects, pp. 69-74

2. Mircea V. Nemescu, Mitica Temneanu, UT Gh. Asachi Iasi, Oscilatii Lente în Circuite Electrice Prezentând Rezonanţă cu Salt şi Amortizare Neliniară, pp. 75-80

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3. Ion Voncilă, Cristian Munteanu, Universitatea „Dunarea de Jos” Galaţi, Evaluarea Performanţelor Acţionărilor Electrice Moderne pe Baza Determinării Dimensiunii Fractale a Curbelor de Regim Cvasistaţionar, pp. 81-86

4. Alexandru Bujor, Mihai Iordache, UPB, Linear Circuit Synthesis Using Matlab, pp. 87-92

5. Alexandru Gabriel Gheorghe, Florin Constantinescu, UPB, Rezolvarea numerică a circuitelor rezistive care conţin modele companion, pp. 93-98

6. Marin Constantin Viorel, Gheorghe Alexandru, UPB, Test Frequency Selection in Fault Dictionary Approach, pp. 99-105

Sectiunea 3

POSTER

moderator: Marin Mihalache 1. Ana-Maria Dumitrescu, Melania Naumof, Razvan Magureanu, Mihaela Albu, UPB, Estimation

of the Measurement Uncertainities in the Control Loop of Active Filters. Part I., pp. 106-110

2. Ana-Maria Dumitrescu, Melania Naumof, Razvan Magureanu, Mihaela Albu, UPB, Estimation of the Measurement Uncertainities in the Control Loop of Active Filters. Part II., pp. 111-115

3. Luminiţa Barote, Corneliu Marinescu, Ioan Şerban, Transilvania University Brasov, Stand-Alone Wind Energy System Using a Lead Acid Battery For Energy Storage, pp. 116-121

4. Maria Daniela Orban, Marius Daniel Marcu, Florin Popescu, University of Petrosani, Simulation software for static rectifiers and static switch controllers, pp. 122-127

5. Marin Mihalache, UPB, Vectorul Poynting si Tratarea Unitara a Problemelor de Dimensionare a Convertoarelor Electromagnetice Partea I - Convertoare Electromagnetice Statice, pp. 128-133

6. Marin Mihalache, UPB, Vectorul Poynting si Tratarea Unitara a Problemelor de Dimensionare a Convertoarelor Electromagnetice Partea II - Convertoare Electromagnetice Rotative, pp. 134-139

7. Dan Răducanu, Virgil Dulgheru, Marilena Stănculescu, Adrian Alexei, UPB, A Change Detection Algorithm for Cartographic Raster Images, pp. 140-145

8. Nicolae Badea, Ion Voncila, Nelu Cazacu, Universitatea “Dunarea de Jos” Galati, Studiul Influenţei Instalaţiilor de Răcire Asupra Eficienţei Energetice Totale a Sistemelor CCHP Rezidenţiale cu Pile de Combustie, pp. 146-151

9. Teofil Ovidiu Gal, Diana Popovici, Ovidiu Popovici, Lucian Marius Velea, Luminita Camelia Porumb, Universitatea din Oradea, A specific study of art gallery lighting, pp.152-156

10. Teodor Leuca, Livia Bandici and Paula Palade, University of Oradea, Aspects Regarding the Processing of Boxthorn Fruits in a Microwave Electromagnetic Field, pp. 157-162

11. Sonia Degeratu, Nicu George Bizdoaca, Anca Petrisor, University of Craiova, Performance Evaluation of a Class F Electrical Insulation System for Three Phase Induction Motors, pp.163-168

12. Sonia Degeratu, Rotaru Petre, Nicu George Bizdoaca, Horia Octavian Manolea, Universitatea din Craiova, Thermal Characterization and Design of an Actuator based on a Shape Memory Alloy Wire working against a steel spring, pp. 169-175

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13. Catalin Petrea Ion, Corneliu Marinescu, Universitatea Transilvania Brasov, Single-phase operation of a three-phase induction generator, pp.176-181

14. Dorin Cismasiu, Universitatea Lucian Blaga Sibiu, Active Power Factor Correction, pp. 182-185

15. R. Stanescu, A. Duca, M. Rebican, UPB, Neural Network Cracks classifier for NDET inverse problems, pp. 186-191

16. Teodor Leuca, Claudiu Mich-Vancea, Ştefan Nagy, Mariana Tamaş and Radu Cărăban, University of Oradea, About the Electrothermal Systems and Numerical Modelling of the Induction Heating, pp. 192-197

17. Lucian Gabriel Petrescu, Aurel Chirilă, UPB, Modeling of an electromagnetic device with hysteretic materials, pp. 198-202

18. Aurelian Florea, Olivier Llopis*, Miruna Nitescu, Florin Constantinescu, UPB, *LAAS Toulouse France, Measurement of nonlinear effects in power BAW resonators, pp. 203-208

19. Oana Mihaela Drosu, Florea Ioan Hantila, Evangelos Hristoforou, Mihai Maricaru, UPB, Au-Fe Nannospheres-Assisted Delivery in Breast Tumour IR Thermography, pp. 209-211

20. Emil Cazacu and Iosif Vasile Nemoianu, UPB, Calculation on a static horizontal diamagnetic levitation setting for permanent magnets, pp. 212-217

21. Lucian Marius Velea, Diana Popovici, Ovidiu Popovici, Zahei Podea, University of Oradea, Measurement and Control Systems with Programmable SMC- PLC Automation Systems, pp. 218-223

22. Iulia Dumitrescu, Ileana Calomfirescu, Mihaela Ionita, UPB, Analiza Pspice a oscilatoarelor de tip Van der Pol cuplate, pp. 224-228

23. Cristina Stancu, Petru Notingher, Constantin Stoica, Mihai Plopeanu, Petru Notingher jr, UPB, Influence of Dimensions and Density of Water Trees on Residual Electric Field in Polymeric Power Cables Insulations, pp. 229-234

24. Cristian Barz, Constantin Oprea, Olivian Chiver, Universitatea de Nord Baia Mare, Influenţa Materialelor Nemagnetice la Analiza Tridimensională a Câmpului Electromagnetic la Alternatorul cu Poli Gheară, pp. 235-240

25. Catalin Adrian Brinzei, Iulian Ursac, UPB, Power mixer for conversion from low to high frequency CMOS, pp.241-246

26. Iulian Ursac, Catalin Adrian Brinzei, UPB, Sintetizor de Frecvenţă cu Oscilator Comandat Digital, pp. 247-252

27. Gheorghe Mulec*, Emil Cazacu **, *University Politehnica of Timisoara, **UPB, Energy consumption in Wireless LAN according to different models of encryption, pp.253-258

28. Ştefan Nagy, Teodor Leuca, Claudiu Mich and Adrian Nagy, University of Oradea, Numeric analysis of the thermal field in the controlled solidification casting processes, pp. 259-264

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O COOPERARE ŞTIINłIFICĂ FRUCTUOASĂ UPB – EDF.

Cezar FLUERAŞU Universitatea “Politehnica” din Bucureşti, Spl. IndependenŃei 313, 060042, Bucureşti;

cfluerasu@ing.pub.ro

Abstract. Cooperarea ştiinŃifică dintre Universitatea Politehnica din Bucureşti (UPB), reprezentată în principal prin catedra de Electrotehnică şi Societatea NaŃională Electricité de France (EDF) s-a desfăşurat într-o perioadă de peste 20 de ani. Rezultatele obŃinute au fost apreciate atât în Ńară cât şi în străinatate, conferind colectivului de cercetare o prioritate într-un domeniu de mare importanŃă, care a acoperit mai multe teme. În cele ce urmează, se face o prezentare succintă a principalelor teme abordate, din perspectiva unuia dintre participanŃi, fără a avea pretenŃia la o prezentare exhaustivă.

1 Introducere

Catedra de Electrotehnică din Universitatea Politehnică din Bucureşti s-a dezvoltat în jurul unor mari personalităŃi ale lumii academice. Dacă ne limităm la ultima jumătate de secol, trebuie să evocăm în primul rând pe Academicianul Remus RăduleŃ, adevărat creator de şcoală în domeniul electrotehnicii teoretice. Profesorul RăduleŃ a fost preşedinte al Comisiei Electrotehnice InternaŃionale (CEI), cu care ocazie a valorificat rigoarea care l-a caracterizat şi prestigiul pe care l-a dobândit, ceea ce a sporit prestigiul şcolii româneşti de electrotehnică teoretică şi a constituit amorsa unor cooperări ştiinŃifice de mare amploare şi prestigiu. Alte mari personalităŃi, cum ar fi profesorii I.S. Antoniu şi C. Mocanu s-au ilustrat prin cercetări valoroase în domeniul ingineriei electrice.

Programul de cercetări care face obiectul prezentării care urmează a reprezentat, fără a exagera, principala cale prin care realizările din şcoala noastră s-au impus pe plan internaŃional într-o perioadă dificilă. La acestă cooperare au participat numeroşi membri ai catedrei, ceea ce constituit o oportunitate de deschidere către lume. Cooperarea a implicat un mare volum de muncă, dar s-a tradus prin relativ puŃine publicaŃii, din cauza, pe de o parte, a unor dificultăŃi de natură ne-ştiinŃifică, dar şi a unor clauze impuse de colaborarea cu producători de echipamente.

2 Principale domenii de cooperare

Pierderi suplementare şi fenomene asociate din zonele frontale ale turbogeneratoarelor de putere mare.

Cooperarea ştiinŃifică dintre catedra de Electrotehnică din UPB şi Electricité de France (EDF) a fost iniŃiată în jurul unui subiect de mare actualitate în perioada dezvoltării construcŃiei de centrale electrice nucleare, în FranŃa dar şi în alte Ńări, printre care şi România.

Odată cu intrarea în exploatare a primelor turbogeneratoare de puteri mari (de sute până la mii de MW), proiectate conform metodologiilor uzuale în perioada respectivă, s-au constatat fenomene noi, capabile să pericliteze integritatea acestor utilaje extrem de scumpe, sau să le limiteze destul de sever specificaŃiile. Unul dintre aceste fenomene este cel al supraîncălzirii pachetelor de tole de extremitate a statorului, constatate în cazul funcŃionării în regimuri cu absorbŃie de putere reactivă (cum ar fi funcŃionarea conectate la linii electrice în gol).

Cauza a fost identificată şi au fost lansate, pe lângă soluŃii constructive adecuate adoptate de principalii constructori, studii teoretice ale fenomenului.

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Fig.1: Supraîncălzirea pachetelor de tole de extremităŃi ale statorului turbogeneratoarelor, în funcŃiune de regimul de funcŃionare.

Fig.2: Câmpul magnetic de dispersii în zona frontală a unui turbogenerator

Din cauza faptului că aceste generatoare au întrefieruri relativ mari, la extremitatea statorului câmpul magnetic prezintă un important „efect de capăt”, concretizat printr-un flux magnetic parazit care pătrunde în primele pachete de tole perpendicular pe planul tolelor şi care poate induce curenŃi turbionari în planul acestora.

Profitând de prezenŃa profesorului Alexandru Timotin, în stagiu la EDF, s-a iniŃiat o cooperare ştinŃifică cu această temă, având ca finalitate elaborarea unui model teoretic şi a unor metodologii de proiectare care să fie adoptate de către constructori. Această cooperare a debutat în anul 1972 şi a continuat până în 1991, cu toate dificultăŃile inerente perioadei pe care ni le mai amintim.

Studiile efectuate au implicat mulŃi membri ai catedrei şi au reprezentat, în vremea respectivă, un element important pentru deschiderea catedrei către lume.

Având în vedere noutatea problemei, primul pas a consistat în realizarea unor modele experimentale, atât în FranŃa, cât şi în Romania, la parteneri interesaŃi. Pe baza experienŃei dobândite, s-a trecut la etapa superioară, de elaborare a uor modele teoretice şi a unor programe de calcul specifice. Fiind vorba de anii 1972-1974, „evantaiul” disponibil era relativ redus. S-a început cu programe elaborate pentru sistemele „mainframe”, cu toate dificultăŃile inerente, mai ales din cauza faptului că la Politehnică nu existau încă echipamente adecuate. Prin urmare, s-a facut apel la echipamente puse la dispoziŃie de colaboratori externi, în fond membri ai catedrei care aveau şi alte funcŃiuni. Din pacate, transferul aplicaŃiilor între UPB şi EDF punea mari probleme de compatibilitate, deşi furnizorul de echipamente şi de programe era acelaşi.

Având în vedere perspectiva dezvoltării sectorului energetic nuclear în România, în principal în cooperarea prevăzută cu EDF, în program s-au înscris şi alŃi parteneri din România (Ministerul Energiei Electrice, Icemenerg, Centrala Industrială de ReŃele Electrice, IMGB). În paralel, s-a lansat o campanie de încercări experimentale asupra unor generatoare aflate în exploatare în sistemul energetic francez, ca şi în Ńara noastră.

Ulterior, s-a decis, de comun acord, să se achiziŃioneze pentru ambii parteneri echipamente similare, în particular sisteme de calcul de ultimă generaŃie pentru acel moment (calculatoare HP9845 şi periferice). Cu toate dificultăŃile de natură legală, echipamentul a sosit la UPB. El a constituit, pentru destul de mulŃi ani, singurul echipament de calcul din dotarea catedrei.

Coordonarea generală, ca şi elaborarea elementelor princiale ale modelului teoretic pentru calcul câmpului magnetic în interiorul statorului, a revenit profesorului Alexandru Timotin, iar elaborarea programului de calcul, în varianta definitivă a fost realizată de către Alexandru Timotin, Augustin Moraru şi Cezar Flueraşu.

Modelul teoretic pentru calculul pierderilor prin curenŃi turbionari produse în pachetele de tole a fost elaborat de către prof. Andrei ługulea, care a participat şi la elaborarea modului respectiv din programul de calcul, împreună cu Cezar Flueraşu.

Programul de calcul al încălzirii pachetelor de tole a fost elaborat de către Cezar Flueraşu.

Q (generata) (absorbita)

Θ max. stator

P

Rotor

Stator

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Un element fundamental al aplicaŃiei dezvoltate a consistat în eleborarea unui program de mare complexitate destinat calculului câmpului magnetic în zona capetelor de bobină ale statorului, realizată integral de către prof. Augustin Moraru. De asemenea,în acelaşi context, prof. Moraru a elaborat o altă aplicaŃie, pentru determinarea unor parametri fundamentali ai maşinii (reactanŃe, etc) în funcŃiune de regimul de funcŃionare al maşinii.

La elaborarea aplicaŃiei globale, au mai contribuit, prin studii auxiliare, alŃi membri (actuali şi foşti) ai catedrei, printre care F.M.G. Tomescu. Al. Nicolae, Cornelia Ionescu, N. Cristea, G. Costache.

De asemenea, au contribuit cercetători din afara catedrei, în special la realizarea unor încercări experimentale de mare acurateŃe.

Cercetarea s-a concretizat prin realizarea unei aplicaŃii informatice de mare complexitate, denumită INT. Una dintre condiŃiile impuse aplicaŃiei a fost cea de a se baza doar pe datele constructive ale maşinii, disponibile încă din faza de proiect, ca şi pe datele de material uzuale.

AplicaŃia realizată, elaborată atât în varianta Fortran,pentru sistemele „mainframe”, cât şi pentru sistemele HP9845, cuprinde mai multe module, integrate într-o logică unitară.

1. Program auxiliar REGIME pentru determinarea unor parametri principali ai maşinii (cum ar fi reactanŃele xd, xq, δ, caracteristicele unghiulare) în funcŃiune de regimul de funcŃionare (tensiunea U, puterile activă şi reactivă P şi Q).

2. Programul EXT pentru calculul câmpului magnetic în zona capetelor de bobină. Acest program, de mare complexitate, pleacă de la datele furnizate de modulul precedent, de la structura reală a zonei şi de la sursele câmpului magnetic (curentul rotoric, curentul statoric), Ńinând seama de saturaŃia fierului statoric, prin pânze de curent echivalente. Deoarece aceste pânze de curent nu sunt cunoscute înaintea rezolvării problemei interioare, sunt necesare iteraŃii între această etapă şi cea care urmează. Acelaşi program poate fi folosit şi pentru determinarea altor mărimi, cum ar fi forŃele exercitate asupra capetelor de bobină, în special în cazul unor regimuri de avarii (cum ar fi scurt-circuitele). Programul foloseşte metoda diferenŃelor finite şi potenŃialul magnetic scalar, într-o variantă capabilă să Ńină seama, printr-un sistem complex de „tăieturi”, de curenŃii din conductoare.

3. Programul MAGINT pentru calculul câmpului magnetic în interiorul pachetelor de tole frontale. CondiŃiile la limită sunt furnizate de către modulul precedent. Aceste condiŃii sunt ajustate printr-o procedură iterativă între primeşe două module, prin care se corectează condiŃiile la limită în funcŃiune de saturaŃia fierului statoric (iteraŃiile „mari”). Problema tridimensională este redusă la o problemă bidimensională, prin considerarea unui singur dinte statoric (ales în funcŃiune de solicitarea sa) şi prin utilizarea de valori medii pe un pas dentar. SaturaŃia fierului implică iteraŃii în cadrul acestui modul (iteraŃiile „mici”). Metoda folosită e ea a „volumelor finite”, bazată pe formele integrale ale legilor (într-o perioadă în care o astfel de metodă nu fusese încă prezentată).

4. Programul PERT, pentru calculul pierderilor în tolele pachetelor frontale, produse de câmpul magnetic radial (pierderi normale) sau axial (pierderi suplementare). Se foloseşte potenŃialul vector al curenŃilor şi dezvoltarea în serie Fourier, pentru estimarea pierderilor pe armonice. Programul Ńine seama de forma tolelor, ca şi de prezenŃa unor fante prevăzute în tole de către unii constructori, în scopul diminuării pierderilor suplementare.

5. Programul TERM pentru calculul încălzirii pachetelor de tole frontale, produse de către pierderile calculate în etapa precedentă. Programul Ńine seama, printr-o procedură iterativă, de variaŃia unor proprietăŃi de material în funcŃiune de tenperatură (conductivitatea termică, căldura specifică, coeficienŃii de convecŃie). De asemenea, se pot impune iteraŃii între PERT şi TERM în situaŃia în care conductivitatea electrică a tolelor variază mult în funcŃie de temperatură. Acest program foloseşte metode denumită în prezent a „volumelor finite”, bazată pe forma integrală a ecuaŃiei de bilanŃ termic.

Rezultatele au fost validate printr-un amplu program de experimentări. Ele au fost valorificate pe mai multe căi, cum ar fi: validarea soluŃiilor constructive preconizate de către producători încă din etapa de proiect, elaborarea de norme de exploatare a maşinilor în regimuri care le-ar periclita integritatea din punctul de vedere al solicitării zonelor frontale, studii asupra solicitării capetelor de bobină în regimuri de avarie, studii de stabilitate, şi altele.

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Transmiterea supratensiunilor tranzitorii între înfăşurările transformatoarelor electrice. O serie de incidente constatate în exploatare la EDF au fost explicate prin transmiterea

supratensiunilor tranzitorii între înfăşurărilor transformatoarelor, în special a celor conectate la generatoare. Unele supratensiuni s-au transmis în continuare în înfăşurarea rotorică a generatoarelor, periclitând integritatea componentelor electronice din circuitele de excitaŃie. S-a constatat că valorile transmise nu sunt legate în mod direct de raportul de transformare al transformatorului. ExplicaŃia propusă a fost aceea că supratensiunile sunt transmise în principal pe cale capacitivă, prin fereastra transformatorului. Modelele teoretice cunoscute nu permiteau explicarea corectă a fenomenelor.

Ca o consecinŃă a bunei cooperări în domeniul turbogeneratoarelor, EDF a propus această nouă temă. Deoarece s-au găsit şi parteneri romîni interesaŃi, s-a lansat un nou program multilateral.

Coordonarea echipei din catedră a fost realizată de ătre prof. Andrei ługulea. Din catedră, au mai participat profesorii Augustin Moraru, Ioan Daniel, F. M. G. Tomescu, Cezar Flueraşu, şi alŃii.

Într-o primă etapă, s-a elaborat un model bazat pe teoria câmpului electromagnetic pentru câmpul tranzitoriu din fereastră, în regimuri rapid variabile. În aceste regimuri, influenŃa fierului este relativ redusă, transmisia supratensiunilor având loc, în principal, pe cale capacitivă. Ca rezultat, a fost elaborat un circuit electric echivalent, de mare complexitate, capabil să modeleze corect fenomenele avute în vedere.

Complexitatea circuitelor echivalente propuse a impus găsirea unor mijloace care să permită analiza regimurilor tranzitorii. Programele disponibile în vremea respectivă prezentau mai multe inconveniente: erau puŃin performante, relativ rigide în ce priveşte configuraŃiile care puteau fi studiate şi, în plus, erau foarte oneroase (atât la cumpărare, la închiriere, ca şi pentru asistenŃa tehnică). În consecinŃă, s-a luat decizia de a realiza, cu forŃe proprii. astfel de programe.

De fapt, au fost realizate două programe diferite şi, în mare măsură, complementare. Un prim program, denumit DISTRIB, realizat de către prof. D. C. Ioan, bazat pe analiza

Fourier, permitea studiul regimurilor tranzitorii în circuitele liniare, cu parametri distribuiŃi sau concentraŃi.

Un al doilea program, denumit RESEL, realizat de către prof. Cezar Flueraşu, e bazat pe integrarea ecuaŃiilor în valori instantanee, printr-o metodă performantă, bazată pe folosirea tehnicilor specifice matricilor „rare”. Acest program permite studierea regimurilor tranzitorii în circuite electrice liniare sau neliniare.

De altfel, aceste programe au fost exploatate cu mult dincolo de cadrul în care ele au fost dezvoltate. Numeroase contracte ale catedrei, cu numeroşi beneficiari (din sectorul energetic, producători de echipamente, etc) au beneficiat de aceste mijloace. De asemenea, în cadrul EDF, programele au fost utilizate în cercetări de mare importanŃă, cum ar fi conceperea schemelor de încercare a echipamentelor, proiectarea unor componente ale legăturii în curent continuu între FranŃa şi Marea Britanie. În plus, producători francezi de echipamente au folosit aceste programe. Mai e important de adăugat că ele au fost folosite şi în scopuri didactice, în UPB şi în alte Ńări.

Studiul fenomenelor de ferorezonanŃă în reŃelele electrice. Acest studiu a constituit o urmare logică a celui precedent, prin valorificarea mijloacelor de

calcul dezvoltate cu acea ocazie. El a pornit de la o serie de incidente în exploatare constatate de către EDF, dar şi la noi în Ńară. Astfel, în situaŃiile în care transformatoarele funcŃionau cuplate la linii în gol, prezenŃa capacităŃilor liniilor în prezenŃa circuitului magnrtic neliniar poate conduce la fenomene care se încadrează în clasa mai largă a ferorezonanŃei. Pe lângă generarea de armonice, pot să apară şi subarmonice, cu frecvenŃe fracŃionare faŃă de cea fundamentală. Studiul teoretic este deosebit de dificil, din cauza prezenŃei elementelor neliniare. De aceea, s-a adoptat, în paralel,

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studiul prin simulare numerică. Programul RESEL s-a dovedit foarte bine adaptat unor astfel de studii, datorită caracteristicilor sale, varietăŃii de elemente de circuit, uşurinŃei în exploatare şi performanŃelor, cel puŃin comparabile cu cele ale altor programe de referinŃă (EMTP, etc). Au fost dezvoltate modele teoretice ale transformatoarelor, capabile să descrie aceste fenomene, modelele clasice fiind total insuficiente.

Rezultatele au fost utilizate şi în Ńară, la studii ample, cum ar fi cele legate de linia 750 kV dintre Ucraina şi Bulgaria, ca şi în numeroase alte studii.

Fenomenele de ferorezonanŃă pot fi amorsate pe mai multe căi. Una dintre acestea ar fi un scurt-circuit la bornele secundare ale transformatorului, urmată de acŃiunea protecŃiei. Exemplul alăturat provine dintr-un caz real, în care fenomenele s-au manifestat în mod foarte pronunŃat. Se constată că după acŃiunea protecŃiei, curentul şi tensiunea secundară prezintă o puternică subarmonică cu frecvenŃa de jumătate din frecvenŃa reŃelei.

Studiul circulaŃiei puterilor în reŃelele electrice în regimuri nesinusoidale. Acest subiect, deşi dezvoltat în afara cooperării cu EDF, a beneficiat din plin de experienŃa partenerilor în exploatarea reŃelelor electrice în regimuri nesinusoidale. Dezbaterea asupra definirii puterilor în regimuri nesinusoidale si-a găsit o rezolvare riguroasă, bazată pe teoreme de conservare a puterilor şi prin separarea din puterea (activă sau reactivă) totală a puterii utile (de pe armonica fundamentală) şi a reziduului deformant (suma puterilor pe armonicile superioare). Din aceste studii, decurg criterii noi de apreciere a calităŃii energiei electrice, ca şi principii noi de tarifare a energiei electrice [17, 18].

Elaborarea tezaurului de concepte al Comisiei Electrotehnice InternaŃionale (CEI). Ca urmare a experienŃei acumulate sub auspiciile Comisiei Electrotehnice InternaŃionale, în

1983 a aărut la Geneva „Dictionnaire CEI multilingue de l’électricité” cu 892 de pagini şi 20 000 de termeni sub coordonarea academicianului Remus RăduleŃ. Alexandru Timotin s-a ocupat de selectarea şi definitivarea conceptelor cu definiŃii multiple. În 1986 apare „Thesaurus CEI rationnel de l’électricité” elaborat de un grup de lucru al Comitetului Electrotehnic Român (CER) sub coordonarea profesorului Timotin (900 pagini, Geneva). În 1996, în Editura Tehnică a apărut „DicŃionarul terminologiei electrotehnice standardizate, Englez - Român şi Român – Englez, 1000 de pagini, sub coordonarea profesorilor Alexandru Timotin şi Florin Teodor Tănăsescu [19, 20].

Concluzii. Cele prezentate mai sus reprezintă o trecere în revistă succintă a unor subiecte de cercetare de mare importanŃă, care au concentrat, timp de peste 20 de ani, activitatea unui mare număr de membri ai catedrei şi au reprezentat o bună ocazie de afirmare pe plan internaŃional, în ciuda vicisitudinilor inerente epocii respective. Ele se înscriu în istoria, nu numai a catedrei noastre, dar şi a şcolii româneşti de electrotehnică teoretică şi merită a fi reamintite. ReferinŃe [1] Al. Timotin, A. ługulea: Pénétration du flux axial dans les zones frontales du stator des grands

turboalternateurs- Rapport no 1.11, Section no.1, Congrès Electrotechnique Mondial, Moscova, 1977. [2] R. RăduleŃ, A. Tugulea, Al. Timotin, C. Flueraşu: Pertes supplémentaires par courants de Foucault et

échauffements des dents frontales du stator des grandes machines synchrones. Congresul mondial al electricienilor, Moscova, 21-25/06/1977.

[3] R.RăduleŃ, A. Tugulea, Al. Timotin, C. Flueraşu: Pertes supplémentaires par courants de Foucault et échauffements des dents frontales du stator des grandes machines synchrones. Rev. Roum. Sci. Techn., Electrot. et Energ., 23, 1, Buc. 1978.

0 200 400 600-50

0

50U2

s

0 200 400 6000

1

2x 10

4f(U2)

Hz Fig. 3 Exemplu de ferorezonanŃă

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[4] Y. Colot, A. Coustére, Al. Timotin, A. ługulea, J. Barthélemy: Etude théorique et expérimentale des pertes par courants de Foucault créées dans les structures magnétiques feuilletées Note EDF;Etudes et Recherches; juin 1975 .

[5] A.Tugulea, J.Barthélémy, Al.Timotin, A.Cousterre: Pertes par courants de Foucault dans les conducteurs immobiles, non homogènes et anisotropes. Application au calcul des pertes engendrées dans les structures magnétiques feuilletée, RGE, 1978.

[6] Y. Colot, C. Flueraşu, Al. Timotin: Pénétration du flux magnétique axial, pertes locales et échauffements dans les dents d'extrémité du stator des turboalternateurs. Document no.2: Présentation de la châine de programme adaptée au cas des machines avec écrans a répulsion. Note EDF M16-629 YC/TPLD, 20/03/77.

[7] Y. Colot, C. Flueraşu: Pénétration du flux magnétique axial, pertes locales et échauffements dans les dents d'extrémité du stator des turboalternateurs. Document no.3: Calcul des pertes supplémentaires locales par la méthode des fonctions de Green et présentation du programme de calcul associé, dans le cas de la technique des écrans a répulsion de flux. Note EDF M16-652 YC/TPLD, 10/07/77.

[8] Y. Colot, C. Flueraşu: Pénétration du flux magnétique axial, pertes locales et échauffements dans les dents d'extrémité du stator des turboalternateurs. Document no.4: Calcul des échauffements locaux par la méthode des fonctions de Green et présentation du programme de calcul associé, dans le cas de la technique des écrans a répulsion de flux. Note EDF M16-653 YC-CF/TPLD-NG, 21/10/77.

[9] Y. Colot, C. Flueraşu, Al. Timotin, A. Tugulea: Pénétration du flux magnétique axial, pertes locales et échauffements dans les dents d'extrémité du stator des turboalternateurs. Présentation de la chaine de programme adaptée au cas des machines avec écrans a répulsion de flux. Note EDF M16-629 YC/TPLD, 20/05/77.

[10] C.Flueraşu, J.L. Duchateau, M. Orange: Pénétration de flux magnétique axial dans les dents d'extrémité des stators d'alternateur. Calcul des pertes et échauffements locaux. Note d'éxploatation du programme intérieur. Note EDF HM/16-1049, CF-JLD/MO-BT, 23/06/1983.

[11] A. Moraru: Determination of the magnetic field in the end region of turbogenerators. RRST-EE, Tome 24, No.1, 1979.

[12] A. Moraru: Determination of the electrodynamic forces on turbogenerator end windings. RRST-EE, Tome 24, No.3, 1979.

[13] A.Moraru: Calculation of the saturated parameters and operating characteristics of high-power turbogenerators. RRST-EE, Tome 25, No.1, 1980.

[14]A.Tugulea, C.D. Ioan, C. Flueraşu, Isabelle Hennebique: La transmission des surtensions entre les enroulements des transformateurs. Note EDF HM/15-888, IH/CBs, 2/12/1982.

[15] C.Fluerasu: RESEL – Simulation interactive sur ordinateur personnel des régimes transitoires dans les réseaux électriques. Première partie : Description du programme. Rev. Roum. Sci. Techn.., Energ. et Electrot., 35, 1, 1990

[16] C. Fluerasu: RESEL – Simulation interactive sur ordinateur personnel des régimes transitoires dans les réseaux électriques. Deuxième partie : Algorithmes principaux. Rev. Roum. Sci. Techn.., Energ. et Electrot., 36, 2, 1991

[17]A. Tugulea: Power flows under non-sinusoidal and non-symmetric periodic and almost-periodic steady-states of electrical power systems, 6th. Int.Conf. on Harmonics in Power Systems, (ICHPS VI), Bologna/Italy, 1994, proc.pp.388-395

[18] A.Tugulea: Criteria for the Definition of the Electric Power Quality and its Measurement Systems, ETEP, Vol.6, No.5, Sept/Oct, 1996

[19]Dictionnaire CEI multilingue de l’électricité (préparé sous la coordination du prof. R.Radulet, président 1980-1982 du CEI Terminologie), Bureau Central CEI, Genève, 1983, 892 p.

[20] Comité Électrotechnique Roumain: Thesaurus CEI rationnel de l’électricité (élaboré suite à l’initiative du prof. R.Radulet), Bureau Central CEI, Genève, 1986, 900 p.

[21] Comité Électrotechnique Roumain: IEC Thesaurus Concepts in Electricity (sample abstract), Bureau Central CEI, Genève, 1990, 45 p.

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Investigation of Solder Joints by Thermographical Analysis

Paul SVASTA, Ciprian. IONESCU, Norocel Dragos CODREANU University “Politehnica” of Bucharest, Center for Technological Electronics and Interconnection Techniques, Spl.

Independentei 313, 060042-Bucharest, Romania, Phone: (+40)21-316 9633; E-mail: ciprian.ionescu@cetti.ro

Detlef. BONFERT Fraunhofer Institute Reliability and Microintegration / IZM-M, Munich, Germany

Abstract. The present stage of development of electronics technology there is an increased interest in the study of new materials used as solder that replaces the already banned tin-lead alloy. Many investigations were done in direction of metallurgic compatibility between the printed circuit board finishing, component terminal finishing and solder itself. Other studies are taken in direction of mechanical characterization of lead free alloys. We propose a study from electrical point of view. So we will analyze the current capabilities of solder joints by thermographical investigations. The finite conductivity of the solder alloy will act as a dissipating media and will heat the adjacent region to the joint. In order to make this effect more pregnant it is necessary to dispose of very precise low-ohm resistors and to pass through them relatively high currents. Based on a high resolution infrared camera the temperature gradient will be better observed. The measured results are compared to the results derived from finite element modeling and simulation. In the simulations, the whole 3D structure of solder joint is modeled. It has practically a very complex shape and is difficult to be analyzed using other methods. Our tests will be realized on organic rigid substrates using a configuration that was intended to characterize the solder joint dissipation. The data derived from this analysis will be very useful in the design process of high power circuits that could be used in advanced electronic modules. Key words: solder joints, thermography, finite element analysis, coupled field modeling and simulation

1 Introduction

In actual stage of electronics the major attachment technique of components to printed circuit boards (PCB’s) is represented by the soldering technology. The various method for soldering electronic components include hand soldering, wave soldering, reflow soldering using infrared radiation or convection ovens. Due to the European RoHS regulations the vapor phase soldering process, although known for many years come in foreground for use in lead-free applications. Modern soldering techniques as laser soldering are also investigated. Regardless the soldering process a solder joint of a component has mechanical, thermal and electrical functions that must ensure the reliability of the electronic assembly. For our investigation we have decided to use SMD chip type components. The solder joint of rectangular type components is presented in figure 1. The significance of parameters from figure 1 is: Maximum Side Overhang -A , Maximum End Overhang- B, Minimum End Joint Width -C, Minimum Side Joint Length- D, Maximum Fillet Height- E , Minimum Fillet Height F, Solder Fillet Thickness G, Height of Termination- H, Minimum End Overlap J, Width of Land-P, Width of Termination –W. In our model we have tried to model accordingly to these drawings the solder parameters.

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Figure 1: Solder joint geometry for rectangular components according to IPC ref [3]

The IPC standards give intervals for these parameters not strictly values. Some parameters are noted to be correlated to the technology or the design. We have chosen a 2512 chip type geometry for the solder joints to be investigated.

2 Modeling for electric-thermal analysis

We have the intention to do a comparison between measured and simulated values in this solder joints study. To obtain the thermal solution, i.e. the temperature map, a coupled-field analysis is required. For this type of analysis the interaction (coupling) between two or more types of physical phenomena (fields) is considered. Such analyses may involve direct or indirect coupling of fields.

When performing a directly coupled analysis, the variables from both fields (e.g., heat generation rate and temperatures) are computed simultaneously. This method is necessary when the individual field responses of the model are strongly dependent upon each other. Directly coupled analyses are usually nonlinear since equilibrium must be satisfied based on multiple criteria. The finite element model requires more computational resources in this case.

An indirectly coupled analysis involves the solution of single-field models in a particular sequence. The results of one analysis are used as loads for the following analysis. This is also known as the sequential method of coupled analysis. This method of analysis is applicable when there is one-way interaction between fields.

In our case, for example, if we consider that the resistivity of conductive materials is not temperature dependent we could also apply this method. This method is usually more efficient than the direct method, and it does not require use of special coupled finite elements and no multiple iterations are required. We have used ANSYSTM software which supports both type of simulations.

Electric-Thermal coupling is presented in figure 2:

Thermal model

Electric model

Heat Generation

Temperature

Temperature dependent resistivities

Source for thermal field, Temperature dependent boundary conditions

Figure 2: Coupled field electric-thermal simulation

Only for one simulation scenario we have developed a different model using a different solving approach. This is called “Multi-field solver”. In this modeling technique there are created two overlapped solid models with different finite element types which may have different meshes. Each model and the associated parameters and boundary conditions is saved as a “field”. There is the need to define the interaction surface between the fields, in our case we have a transfer which

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occurs from the electrical domain to thermal domain as volumetric transfer and the transfer from thermal field to electrical field is done also inside the metallic conductive elements (change in resistivity). The solver converges more rapidly for this solver as in direct coupling, but there were no differences found in results up to the third decimal position. For the ease of model creation and the ease of parameters change we have realized the models using the first presented method, i.e. direct coupling using thermal-electric element called SOLID69. This permits us to combine mapped meshing where this was possible to be done with the free meshing using pyramids (tetrahedral elements)

3 Modeling considerations

A little simplification was necessary for the purpose of the analysis. In this direction, resistors constructive details were ignored as not important. The resistors were modeled as simple bricks.

The software that was used is ANSYS, a finite element analysis (FEA) software for which the modeling and simulation flow includes: building the solid model, defining and assigning material properties and proper finite elements, meshing the model, applying the loads and boundary conditions, and finally solving and postprocessing the results. A characteristic of the model is that the full 3D structure was modeled. In all cases parametric type model was built which permit us to realize a series of runs without to re-create the solid model.

A major problem in modeling planar structures, as the copper traces, is the large number of elements that can be generated by the very thin layers that model the conductive, dielectric or resistive depositions used in electronics. We have used a special modeling technique, which implies the building of the solid model by extrusion of areas along “z“ direction. In this way, hexahedral elements and not tetrahedral are built, and the number of finite elements can be dramatically reduced.

For our models presented here which include the large FR4 substrate, there were up to 1300000 elements, with 294000 nodes, a large number absolutely sufficient for the electrical field which requires a finer mesh than the thermal field. The running time for one data was about 2 hours. A model, for one structure, as seen in FEA program is presented in figure 3.

Figure 3: Solid model for one tested structure The boundary conditions involve the applying of heat transfer coefficients on the exterior

surfaces. For the convection coefficients we have chosen to take some result from literature and our previous papers. The board was hold suspended and there was also convection from the bottom side of the board. We have used temperature dependent film coefficients. The values were derived from values at room temperature with the assumption of variation according to ~(ΔT)0.25 relation.

Temperature dependent resistivities were used for copper and for solder alloy too. The parameters that were used in simulations are presented in table 1:

Table 1: Material properties used in analysis

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Mat. Nr. Material Thermal constant(W/mK)

Resistivity (Ω·m)

at 25°C 1 Copper 390 1.72e-8 2 FR4 0.3 ∞ 3 Solder Sn-Pb (63-37) 57.9 14.9 e-8

3* Solder Sn-Ag (96,5-3,5) 55.3 12.3e-8

The issues for determining the heat convection coefficients are presented in [5]. The source of heat is the electrical power dissipated in the volume of electrical components, copper traces, solder joints, resistors.

The loads are applied to the model as volume (body) loads, this means a heat generation rate (HGEN) or other named power density. These Joule heat generation has a specific distribution for a certain geometry and is difficult to be predicted without using software simulation tools.

4 Experimental vehicle

The test board was supposed to emphasize the heating of solder joints. Regarding this it is very difficult to emphasize only the heat produced by the current inside the joints because in a real assembly the current is supplied through relatively thin PCB traces. There is a trade-off in this study, one point is to apply large currents and to dissipate the energy in the joint and not in the resistor or in the electronic component. On the other side a good electrical contact means also a good thermal contact so the heat will be conducted away from the solder joint region.

We have used a structure with the intention to emphasize different the joint properties compared to copper track heating.

Figure 4: Test board for investigations

The structure presented in figure 4 has being used for comparative investigation of copper tracks and solder joints heating. In order from upper to lower side we have a) tracks with gap 0.75 mm, b) with gap 1.5 mm, c) copper necked track with 1 mm minimal width, d) One copper part like resistor type 2512, e) Two resistor similar to previous, f) one copper track with constant width of 1mm.

Three different substrate materials were tried, generally known as: ½ oz (17 μm), 1 oz (35 μm), 2 oz (70 μm) with laminate thickness of 0.5 mm, 0.8 mm and 1.5 mm respectively. For each of the six structures we have built parametric models. In figure 5 is a part of the model realized for structure 1.

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Figure 5: Finite element model for structure 1 (left). Detail of meshed model for structure 4(right) It presents a hemispherical solder joint, realized with the intention to read the temperature

distribution in it. In figure 5 a mesh detail for the solder fillet modeled for structures 4 and 5, is presented. For the measurement under load we have applied constant current through our probes.

5 Electrical characterization of solder joints

It is difficult to estimate by hand calculus the solder joint resistance especially because of the complex contact geometry between the component and the solder.

From the variety of SMD components we have chosen rectangular type components. This is because these have applications in power electronics, as power resistors. Our component is a bulk copper part with the dimensions corresponding to SMD 2512 resistor. Regarding the model of solder joint we have built a model based on IPC reference [3]. In order to approximate the real situation, the input current is applied through a very short PCB stub, as in figure 6.

Figure 6: Model used for electrical analysis

The electrical circuit for this assembly, which is very simple, is presented in Figure 7 Rc Rs1Rs2

Figure 7: Equivalent electric circuit of SMD chip resistor assembly

In the picture above Rs1 and Rs2 are the solder joint resistances and Rc is the resistance of the component. If we apply constant current to the structure and read the obtained potential we can read twice the solder joint resistance.

We have run the simulations for different material resistivities and for different type of solder joints geometries. The parameters that were changed are F and G from figure 1. Parameter F which determines the percentage of solder fillet that covers the height of resistor was changed to realize a cover percentage from 20% to 90 % of component height H. For parameter G three values were tried 0,1mm, 0.2 mm and 0.3 mm. For G=0.3 mm the obtained resistance of the structure for different fillet height (F parameter) was between 113.4μΩ and 115.9μΩ. It was observed a

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relatively stronger dependence on solder fillet thickness, as expected small values are more convenient.

In this case the analysis is pure electrical, no temperatures or other coupling was involved. From the potential values we can extract the resistance of the solder joint. We can examine also the Joule heat generation in the solder, but the relevance of this may be reduced in a real circuit. In this situation the temperature is the most important factor, not the heat generation rate.

Other possible results from the electrical simulation are the plots where the current densities in the circuit can be examined. In figure 8 two qualitative situations of current densities vector plot are presented. The size of the solder fillet for the two cases are 0.4 and 0.9 from component height.

Figure 8: Current distributions for different solder fillet height (not at the same scale)

6 Experimental setup

All the measurements were done using the boards presented in figure 3. A high current DC voltage source was used to supply the probes. The source was operating in constant current mode (current limiting). A low resistance shunt resistor made from parallel connected wirewound resistors was also used for precise reading of the current, the instrument front panel meters presenting a low accuracy. The shunt is necessary also to permit the operation of the power supply in a point with convenient voltage level, slightly higher than 0 V. We have stopped the measurements when the obtained temperature on the board becomes unusual hot.

Because the boards were not provided with coating material there were problems detected in measurement of bare copper tracks and solder joints. It is a well known issue of the infrared measurement that the shiny surfaces are difficult to measure. The observed phenomenon was that the temperature of the tracks seams to be higher than the rest of the board, although their emissivity is much lower. This is due to reflected heat from ambient. A solution possible to be tried in latter experiments will be to do the measurements in a closed (dark) box. We have decided to coat the boards with a mate dye, sprayed from a tube. This has given a picture with uniform temperatures at room temperature which means that the effects of ambient reflections were eliminated. The very thin painting is expected to not produce any change in the heat transfer distribution. The thermovision camera was placed at 30 cm above the board and the current was incremented in 1 ampere step. The measurements were taken according to IPC standards [2] at three minutes after a current supply change.

7 Sample results

We present the result of simulations and of measurements made on the structure 4 from figure 4. In figure 9, the FEA result in form of a thermal map is presented.

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Figure 9: Results from FEA at 10 A (left) and thermogram picture at 10A, structure 4

A thermogram picture captured in the measurement of the same structure is presented in figure 9.The result from measurement and from simulation are very closed one to each other, only for very high temperatures differences of about 2 degrees being observed, FEA showing a higher temperature that the real one. This can be due to the fact that radiation effects were included in the convection film coefficient.

From a deeper analysis it can be seen the heat generation takes place in the copper traces and in the solder joints. There is a uniformity effect of the PCB laminate and of the conducting copper traces, so the expected hot spot in the solder joint is not at all so obvious. Although the resistivity of the solder alloy can be up to ten times higher than the resistivity of copper, the relatively large dimensions of the solder joints section, compared to the copper traces leads to a low Joule heat generation in the joint itself.

In this direction we will be re-orienting toward the heat dissipated by the copper traces. Results from simulation, measurements and reference literature are presented in table 2. Table 2: Temperature in degree Celsius of a 1mm (40 mil) PCB copper track

Current (A) Data source 1/2 oz(18μm) 1 oz (35μm)

2 Measurement 45.6 33 FEA 47.1 35 Ref [2] 50 30

3

Measurement 76.1 46.7 FEA 77.2 47.4 Ref [2] 85 37

4

Measurement 122 67 FEA 124.3 67.8 Ref [2] 125 49

5

Measurement 178.5 92.6 FEA 180.2 94.2 Ref [2] N/A 65

6

Measurement N/A 131.4 FEA N/A 133.3 Ref [2] N/A 85

For the 35 μm copper thickness board, the results are plotted against the current, in figure 10.

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0 2 4 6 80

20

40

60

80

100

120

35 μm Cu thickness (1 oz)

IPC Standards Thermography FEA

Tem

pera

ture

rise

abo

ve 2

5 de

gree

s (°

C)

Current (A) Figure 10: Temperature rise above 25 °C from IPC standard compared to measurements and

simulation on our test board From the graph we see the very good agreement between simulation and measurements

results and a large difference from the values presented by IPC. It is possible to obtain such different results because in the IPC standard the clad laminate thickness is not clearly shown. According to different sources [1] the current carrying capabilities of the copper traces on PCB depend on the copper thickness and material type and thickness (epoxy or phenolic) laminate.

Anyhow, the IPC graphs are intended to be used backwards, this means to determine the current for a given track cross-section. Also the graphs have already applied some de-rating derived from practical experience.

8 Conclusions

The investigation started in order to characterize the solder joints have been re-oriented towards investigations on PCB copper traces. In order to characterize from thermal point of view only the heating of solder joints, a new test structure must be developed using a spatial structure not a PCB. From the simulations, but also from thermographical measurements it has resulted that the limiting factor for high power applications is not the solder joint itself, but the PCB copper track. The measurement of self-heating PCB traces has shown large differences between the IPC standard values and the measurements/simulations based on the test structure from figure 4.

Regarding the electrical behavior, the resistance of the solder joint depends not only on the material and geometry of the solder alloy itself, but depends also on the configuration of the PCB assembly including PCB traces and geometry of component. The reason for this is the different field distribution on solder edges, or briefly saying the entry and the exit surfaces of the current. The current distribution on the surface of the solder is in this sense, determined by the “exterior” circuit.

References [1] ****, IPC-2221, “Generic Standard on Printed Board Design”, pp. 38.

[2] ***, IPC/EIA J-STD-001C, “Joint Industry Standard”. [3] ANSYS 6.1, “Theory Reference Manual”, 2002. [4] W. M. Rohsenow, J. P. Hartnett, Young I. Cho (eds.). Handbook of heat transfer, 3rd edition,

McGraw-Hill, 1998. [5] K. Puttlitz, K. Stalter (editors). Handbook of Lead-Free Solder Technology for Microelectronic

Assemblies, Marcel Dekker, New York, 2004

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UNELE ASPECTE PRIVIND DISTRIBUŢIA POTENŢIALULUI LA INSTALAŢIILE DE LEGARE LA

PǍMÂNT DIN STAŢII ELECTRICE EXTERIOARE

Liviu Emil PETREAN, Mircea HORGOŞ, Olivian CHIVER Universitatea de Nord din Baia Mare, Str.Dr. Victor Babeş, 62/A,430083, Baia Mare;

petreanliviu@yahoo.com,lpetrean@ubm.ro, mircea.horgos@ubm.ro, olivian.chiver@ubm.ro

Abstract. În această lucrare se prezintă unele aspecte privind distribuţia potenţialului în jurul prizelor de pământ ale staţiilor electrice exterioare de înaltă tensiune. Se prezintă rezultate ale măsurătorilor efectuate, situaţii de neconformitate cu prescripţiile în vigoare privind valorile tensiunilor de pas în exteriorul staţiei cât şi propuneri de modificare a prescripţiilor privind realizarea instalaţiilor de legare la pământ pentru eliminarea gradienţilor de potenţial ridicaţi. Se evaluează influenţa reciprocă a prizelor de pământ în cazul unor rapoarte mari între rezistenţele de dispersie ale celor două prize. Se prezintă şi unele rezultate obţinute pe modele simple de analiză a câmpului electrocinetic.

1 Introducere

Instalaţiile de legare la pământ se proiectează, execută şi verifică în conformitate cu prevederile prescripţiilor în vigoare [2 - 4] sau a unor norme tehnice interne. Valorile maxime admise ale tensiunilor de atingere şi de pas sunt cele care determină dacă o instalaţie de legare la pământ este corespunzătoare sau nu. Pentru efectuarea măsurătorilor este important să se determine corect zona de potenţial nul şi zonele de influenţă ale prizei măsurate şi prizei auxiliare. Acest lucru este destul de dificil, îndeosebi în cazul instalaţiilor de legare la pământ ale staţiilor exterioare de înaltă tensiune, care au o suprafaţă mare. Efectuarea unor calcule preliminare de modelare şi evaluare este utilă pentru a permite obinerea de rezultate corecte. Două dintre standardele de bază privind protecţia împotriva electrocutărilor [5,6] au fost anulate, iar revizuirea [7] a acestora nu a fost încă aprobată.

2 Măsurători şi rezultate

Măsurătorile s-au efectuat cu un aparat de măsurare specializat, de performanţă, cu afişaj digital [9]. Pentru efectuarea măsurătorilor s-a realizat o priză de pământ auxiliară PA situată la o distanţă de circa 500 m faţă de staţie, ca în Fig. 1. Iniţial rezistenţa prizei auxiliare a fost în jur de 80 Ω, iar ulterior s-a întărit priza auxiliară astfel încât rezistenţa acesteia a ajuns în final sub 8 Ω. Valoarea rezistenţei de dispersie a prizei PM măsurate, corectată în funcţie de starea de umiditate a solului a fost de 0.194 Ω, astfel că raportul dintre rezistenţa prizei auxiliare şi aceea a prizei măsurate a fost iniţial de 400, iar în final de 40. Această întărire a prizei auxiliare s-a realizat pentru ca raportul dintre rezistenţa prizei auxiliare şi aceea a prizei măsurate să nu fie prea mare, ceea ce poate conduce [2] la erori mari în determinarea rezistenţei de dispersie a prizei măsurate. Măsurătorile s-au efectuat iniţial pe aliniamentul PM – PA, iar apoi pe aliniamentul PM – S din Fig. 1. Pentru a stabili zona de potenţial nul s-a determinat distribuţia potenţialului în exteriorul staţiei pentru o valoare a curentului prin priza de pământ calculată pe baza valorii curentului de scurtcircuit monofazat pe barele de 110 kV ale staţiei. La măsurătorile efectuate pe aliniamentul PM – PA s-a constatat, chiar la distanţe mari faţă de priza auxiliară, o influenţă mare a acesteia asupra valorii rezistenţei de dispersie a prizei măsurate. Aceasta se explică prin faptul că, la o vaoare de 80 Ω a rezistenţei prizei auxiliare şi o zonă de potenţial nul

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Fig. 1 Amplasarea prizei auxiliare PA şi a sondei S faţă de staţia electrică

faţă de aceasta unde influenţa prizei auxiliare ar fi doar de 0.1 %, eroarea de determinare a rezistenţei de dispersie a prizei măsurate ar fi de peste 40 %. Diagrama de variaţie a potenţialului pe aliniamentul PM – S se prezintă ca în Fig. 2. Menţionăm că la aceste măsurători punctul de

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Fig. 2 Diagrama de variaţie a potenţialului în exteriorul staţiei, pe direcţia PM – S.

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lângă gardul staţiei era situat la 1 m spre nord faţă de colţul gardului. Se constată un gradient de potenţial mare în apropierea gardului staţiei, ceea ce determină o tensiune de pas de 247,9 V lângă gardul staţiei şi de 227.3 V la 1 m de gardul staţiei, valori care depăşesc valoarea maximă admisă de norme. Pentru a identifica extinderea faţă de colţul gardului staţiei a zonei cu gradienţi de potenţial ridicaţi s-au determinat distribuţiile potenţialului pe direcţii perpendiculare pe gardul staţiei astfel:

• la 2 m nord de colţul gardului, distribuţie prezentată în Fig. 3 prin curba 2 (), • la 4 m vest de colţul gardului, distribuţie prezentată în Fig. 3 prin curba 3 (),

precum şi pe direcţia prizei auxiliare la 4 m vest de colţul gardului, distribuţie prezentată de asemenea în Fig. 3 prin curba 4 (x). Tensiunile de pas corespunzătoare curbelor 2, 3 şi 4 sunt mai reduse şi corespund normelor, dar cele corespunzătoare curbei din Fig. 2, reluată prin curba 1 în Fig. 3 sunt mai mari decât limitele admise.

Variatia potentialului in apropierea gardului statiei

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entia

l [V

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La 2 m de coltul statiei

Pe directia perpendiculara fatade auxiliaraPe directia prizei auxiliare

Fig. 3 Distribuţia potenţialului în funcţie de distanţa faţă de gardul staţiei, pentru direcţii apropiate de

colţul gardului staţiei.

Conform normelor, priza de pământ a staţiei are o configuraţie dreptunghiulară şi este situată în interiorul staţiei la o distanţă de 1.5 m de gardul staţiei. În exteriorul staţiei, la 1.5 m de gardul staţiei se află o bandă metalică cu un profil de asemenea dreptunghiular, rolul acesteia fiind de a diminua tensiunile de pas din vecinătatea staţiei.

Explicaţia valorilor mari ale gradientului de potenţial în apropierea colţului gardului staţiei este aceea că la colţurile dreptunghiulare ale instalaţiilor de legare la pământ apar câmpuri electrocinetice de intensitate foarte mare. Se conturează soluţionarea situaţiei de neconformitate cu normele privind tensiunile de atingere şi de pas maxime admise prin rotunjirea colţurilor instalaţiilor de legare la pământ. Evident că aceasta presupune modificarea corespunzătoare a normelor referitoare la construcţia instalaţiilor de legare la pământ şi efectuarea unor calcule de câmpuri electrice pe modele corespunzătoare pentru a evalua corect raza de rotunjire necesară la colţurile prizelor.

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3 Rezolvarea numerică unor probleme de câmp electrocinetic asociate

Pentru a evalua prin calcul distribuţia câmpului electrocinetic în cazul unei instalaţii de legare la pământ s-au luat în considerare modele simple de calcul a distribuţiei câmpului electric echivalente unui sistem de prize de pământ. Ecuaţiile ce descriu distribuţia câmpului electrocinetic fiind similare cu cele ale câmpului electrostatic [1] modelele au fost analizate în ambele situaţii. Ecuaţiile de stare au fost rezolvate prin metoda elementelor finite cu ajutorul programului de calcul numeric specializat FEMM 4.2 [8] .

Pentru început s-a considerat un model format din două prize echivalente de formă clasică semisferică, una cu o rază de 80 m pentru priza măsurată şi cealaltă cu o rază de 0.2 m pentru priza auxiliară. S-a rezolvat problema de câmp prin metoda elementelor finite şi s-a determinat zona de potenţial nul corespunzătoare unei erori maxime datorate influenţei reciproce a celor două prize de 5% şi 2 %. Se prezintă în Fig. 4 a şi b zonele de potenţial nul corespunzătoare unei erori maxime de 5 %. Distanţa între cele două prize a fost de 500 m.

a) b)

Fig. 4 Distribuţia zonelor de potenţial nul pentru cazul unei prize auxiliare cu raza de a) 0.2 m, b) 8 m

Distribuţia zonelor de potenţial nul pentru o valoare maximă a erorii datorate influenţei dintre cele două prize de maxim 2% este similară, având corespunzător o extindere mult mai mică. Se constată la toate cazurile o lăţime extrem de mică a zonei de potenţial nul între priza măsurată şi cea auxiliară, dar o extindere amplă a acesteia de o parte şi de alta a aliniamentului celor două prize.

Al doilea caz studiat a fost acela în care priza măsurată s-a reprezentat printr-o placă metalică echivalentă de formă circulară cu diametrul de 120 m, situată la 1 metru adâncime în sol. Grosimea plăcii s-a considerat de 10 cm. Variaţia potenţialului la suprafaţa solului începând de la marginea plăcii se prezintă ca în Fig. 5 (curba placa). Pentru comparaţie, în aceeaşi figură se prezintă variaţia potenţialului pentru cazul unei prize semisferice (curba semisfera). Se constată variaţii similare ale potenţialului la distanţe mari faţă de cele două prize.

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Fig. 5 Variaţia potenţialului la suprafaţa solului pentru o semisferică metalică aflată la suprafaţa solului

şi o placă metalică circulară cu grosimea de 0.1 m situată la 1 m adâncime în sol.

Zona de potenţial nul (sub 2 %) începe de la o distanţă de numai 32 de ori mai mare decât raza plăcii spre deosebire de cazul prizei semisferice la care zona de potenţial nul (sub 2 %) începe de la o distanţă de 50 de ori mai mare decât raza sferei. De asemenea, în apropierea prizei, se constată o variaţie mai rapidă a potenţialului la suprafaţa solului în cazul plăcii decât aceea din cazul modelului unei prize semisferice. Ca urmare şi tensiunile de pas în vecinătatea prizelor sunt mai mari în cazul prizei în formă de placă.

Considerăm acum cazul unei prize de pământ singulare cu raza de 80 m situată într-un sol omogen cu o rezistivitate de 100 Ωm, având rezistenţa de 0.199 Ω şi al unei prize auxiliare singulare cu raza de 2 m, a cărei rezistenţă de dispersie este de 7.958 Ω.

Expresia simplă [1] a distribuţiei potenţialului în jurul unei prize semisferice singulare situată într-un sol omogen şi izotrop ne permite să facem următoarele observaţii:

• Dacă se consideră zonă de potenţial nul zona în care potenţialul solului a scăzut la 1 % din valoarea potenţialului prizei, atunci această zonă, pe care o numim zonă de potenţial nul 1 %, începe de la o distanţă de 100 de ori mai mare decât raza semisferei.

• Conform normelor se consideră că zona de potenţial nul începe de la distanţe de 3 – 5 ori mai mari decât diametrul prizei. La o distanţă de 3 ori mai mare decât diametrul prizei valoarea potenţialului este de 16.7 %, iar la o distanţă de 5 ori mai mare decât diametrul prizei valoarea potenţialului este de 10 %.

• Se constată că în cazul prizei semisferice la distanţa acceptată de norme ca fiind limită a zonei de potenţial nul erorile sunt mari, de 16.7 % respectiv 10 %.

• Pentru a avea erori de maxim 5 % se poate observa că zona de potenţial de 5 % începe de la distanţe de 20 de ori mai mari decât raza semisferei. Erorile maxime vor fi de 2 % începând de la o distanţă de 50 de ori mai mare decât diametrul prizei, adică 4000 m.

Dacă ne referim acum la o priză semisferică singulară echivalentă prizei auxiliare, care ar avea o rază de 0.2 m atunci constatăm următoarele:

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• Zona de potenţial nul de 5 % începe de la o distanţă de 4 m faţa de priza auxiliară, iar zona de potenţial nul de 2 % începe de la o distanţă de 10 m faţa de priza auxiliară,

• Raportul între rezistenţele de dispersie ale prizei auxiliare şi prizei este mare, de 400. Ca urmare raportul între valorile potenţialelor la limita zonelor de potenţial nul este şi el de 400, deci 2 % din valoarea potenţialului prizei auxiliare reprezintă 800 % din valoarea potenţialului prizei măsurate deci o eroare de influenţă foarte mare.

• Zona de potenţial nul a prizei auxiliare corespunzătoare unei valori de 2 % din potenţialul prizei măsurate înseamnă o zonă de potenţial nul cu o valoare maximă de 0.005 % din potenţialul prizei auxiliare. Această zona începe de la o distanţă de 20000 de ori mai mare decât raza prizei auxiliare, adică tot de 4000 m.

Rezumând, pentru ca zonele de potenţial nul ale celor două prize, considerate singulare, să nu se influenţeze cu o eroare mai mare de 2 % trebuie să avem între cele două prize o distanţă egală cu dublul distanţei de unde începe zona de potenţial nul a prizei măsurate, adică de 8000 m în aceste caz. Dacă se consideră cele două prize în interacţiune se constată, din Fig. 4 că între cele două prize există totdeauna o zonă de potenţial nul, dar extensia acestei zone este redusă pe axa ce uneşte cele două prize şi mai extinsă de o parte şi de alta a acestei axe.

4 Concluzii

a. Datorită profilului dreptunghiular al instalaţiilor de legare la pământ se constată gradienţi de potenţial ridicaţi în apropierea colţurilor prizelor care pot produce tensiuni de pas mai mari decât cele permise de norme. Se recomandă modificarea în acest sens a normelor în vigoare privind proiectarea şi execuţia instalaţiilor de legare la pământ.

b. Zona de potenţial nul dintre priza auxiliară şi priza măsurată are o extindere mai mare de o parte şi de alta a axei ce uneşte priza auxiliară cu cea măsurată. Se recomandă o evaluare atentă a acestei zone în cazul când raportul dintre rezistenţa prizei auxiliare şi aceea a prizei măsurate este mare.

c. Se recomandă efectuarea unor calcule preliminare de câmp electrocinetic pentru a putea aproxima unde se află zona de potenţial nul.

Referinţe [1] C. Şora. Bazele Electrotehnicii, Editura Didactică şi Pedagogică, Bucureşti, 1982. [2] ***. 1 RE-Ip 30/2004 Îndreptar de proiectare şi execuţie a instalaţiilor de legare la pământ [3] ***. STAS 2612-87 Protecţia împotriva electrocutărilor. Limite admisibile. [4] ***. STAS 12604 – 87 Protecţia împotriva electrocutării. Prescripţii generale. [5] ***. STAS 12604/4 – 89 Protecţia împotriva electrocutărilor. Instalaţii electrice fixe. Condiţii tehnice de calcul. [6] ***. STAS 12604/5 – 90 Protecţia împotriva electrocutărilor. Instalaţii electrice fixe. Prescripţii de proiectare, execuţie şi verificare. [7] ***. Revizuirea standardelor STAS 12604/4 – 89 şi STAS 12604/5 – 90, Contract nr.4/2006 între SIER şi SC ELECTRICA SA, Responsabil lucrare Ing. M. Sufrim., Standard neavizat încă de ASRO. [8] *** . Finte Element Method Magnetics, Version 4.2, User’s Manual, David Meeker, Sept, 2009 [9] *** . FLUKE 1625 Earth/Ground Tester, User’s Manual, January 2006, Fluke Corporation

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METODA INTEGRALA DE SOLUTIONARE A PROBLEMLOR DE CAMP MAGNETIC IN STRUCTURI

3D CU MEDII FEROMAGNETICE

Augustin Moraru, Gabriel Preda, Ioan Florea Hantila, Mihai Maricaru Catedra de Electrotehnica, Universitatea Politehnica Bucuresti

Rezumat. Lucrarea este dedicata unei metode integrale pentru solutionarea problemelor de camp magnetic in medii neliniare. Dezavantajele metodelor diferentiale in comparatie cu de metodele integrale si hibride justifica obiectivul acestei lucrari. Desi procedura a fost deja elaborata pentru structuri 2D, extinderea ei la structuri tridimensionale conduce la dimensiuni foarte mari ale matricei de influente si necesita, partial, integrarea numerica pentru calculul elementelor acestei matrice. Aceasta lucrare prezinta proprietati ale acestei matrice care permit reduceri spectaculoase ale efortului de calcul si de memorie. Procedura nu necesita solutionarea unui sistem de ecuatii ci doar constructia matricei de influente. Solutionarea numerica necesita doar discretizarea corpurilor feromagnetice in subdomenii, necunoscutele fiind asociate acestor subdomenii.

1. Introducere

Utilizarea programelor comerciale de element finit (FEM) are cateva dezavantaje importante. Reteaua de discretizare este construita in intreg domeniul de calcul, deci si in aer. La frontierele subdomeniilor, marimile campului electromagnetic au discontinuitati si, ca urmare, solutia numerica conduce la aparitia unor surse parazite. O prima consecionta este aparitia unor forte parazite pe aceste frontiere. Deoarece domeniul de calcul trebuie marginit, se adopta o frontiera artificiala care, la randul ei, poate influenta rezultatul. Daca frontiera este impinsa la distante prea mari, numarul de necunoscute creste foarte mult si apar probleme de solutionare a sistemelor de ecuatii. Generatoarele de retea pot conduce la solutii nepotrivite atunci cand in domeniul de calcul exista diferente mari de dimensiuni.

Dezavantajele de mai sus pot fi evitate daca reusim sa aplicam metode integrale de solutionare a problemelor de camp electromagnetic. Procedurile hibride element finit – element de frontiera (FEM-BEM) sunt o solutie, dar, in comparatie cu FEM, matricea sistemului pierde din proprietatile avantajoase la rezolvare. In aceasta lucrare, prezentam o metoda integrala bazate pe metoda polarizatiei, in care necunoscutele sunt polarizatiile magnetice din mediile feromagnetice. Solutionarea ecuatiei integrale se face iterativ, priontr-o metoda numerica a carei convergenta este dovefita. Mentionam ca procedura a fost deja aplicata la structuri plan paralele, unde elementele matricei de influenta pot fi calculate analitic si dimensiunile acestei matrice erau suficient de mici. 2. Ecuatia integrala a polarizatiei magnetice Se inlocuieste relatia constitutiva H=F(B) cu:

IHB += 0μ (1)

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unde )Q()F( BBBI =−= 0μ (2)

Se poate arata ca functia Q este contractie [1]:

)G()G( 21 BB − ≤ 21 BB −λ (3) pentru orice 1B , 2B , cu 1<λ . Norma este definita prin

U =

21

0

1

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛Ω⋅∫ ∫

Ω

T

fe

dtdT

UU (4)

In aer, polarizatia magnetica este nula. Avand o polarizatie arbitrara I, se rezolva probleme de camp electromagnetic in mediul liniar, cu caracteristica constitutiva (1). Inductia magnetica obtinuta se poate scrie sub forma:

)L(IBB += 0 (5) unde 0B este inductia magnetica datorata altor cauze, diferite de polarizatia I (de exemplu, curenti imprimati), iar L este functia liniara prin care se obtine componenta inductiei magnetice datorate polarizatiei I. Se poate arata ca functia L este neexpansiva [2], [3], [4] in cazul regimurilor stationare si cvasistationare. Relatiile (2) si (5) conduc la ecuatia neliniara:

))L(Q( IBI += 0 (6) In cazul in care operatorul L poate fi exprimat cu ajutorul functiei Green, relatia (6) devine

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛Ω+= ∫

ΩF

dIBI LQ 0 (7)

unde FΩ sunt domeniile corpurilor feromagnetice. Relatia (7) este o ecuatie integrala pe domeniile feromagnetice.

3. Rezolvarea ecuatiei integrale neliniare a polarizatiei Solutionarea numerica a ecuatiei (7) se poate face impartind domeniile corpurilor feromagnetice in subdomenii poliedrale kω , unde se considera inductia magnetic constanta, si anume valoare sa medie pe acest sudomeniu:

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∫ Ω=

k

dVk

kω

BB 1~ (8)

unde kV este volumul domeniului kω . Notam cu Y functia de aproximare prin valoarea medie. Func\ia Y este neexpansiv` (Anexa A). Atunci si polarizatia magnetica este constanta pe subdomenii. Rezolvarea ecuatiei integrale (7) se poate face iterativ, conform schemei:

KK )(L)(Q)(Y)(L)( ~ 11 +− ⎯→⎯⎯→⎯⎯→⎯⎯→⎯ nnnnn BIBBI , K,,21=k . (9) si, deoarece procedura iterativa consta in compunerea a doua functii neexpansive cu o functie contrativa, schema iterativa este o procedura Picard-Banach convergenta spre punctul fix al acestei compuneri de functii. Matriceal, avem:

•

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=

NB

BB

~...

~~

)B~( 21

, matricea valorilor medii ale inductiilor din subdomenii, iar N este numarul

de subdomanii in care se impart mediile feromagnetice.

•

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=

N0

2010

0

B

BB

~...

~~

)B~( este matricea valorilor medii ale inductiilor din subdomenii, produse de

surse.

• )(τ este matricea diagonala, cu elementele kV1

•

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=

)~(.....

.)~(

.)~(~(

NN B

BB

B

Q00

0Q000Q

)Q 2211

este operatorul diagonal neliniar ale carui

componente jjj IB =)~(Q dau polarizatiile magnetice jI pentru valoarea medie jB~ a

inductiei magnetice din subdomeniul jω . jQ difera, daca materialele din subdomenii au caracteristici B-H diferite.

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•

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=

NNNN

N

N

SSS

SSSSSS

S

.....

.

.

)(

21

22221

11211

este matricea coeficientilor de influenta, ale carei

componente dau integrala inductiei ImB~ pe subdomeniul mω , produsa de polarizatia iI din subdomeniul iω :

ImB~ =kV1 ∑

=

N

iimiS

1I (10)

unde, in cazul intregului spatiu R3;

( ) ( )∫ ∫

∂ ∂

−⋅≡

m i

immimimi dSdS

RI

Sω ω

πnnnn

41

= ( )( ) ( )∑ ∑∈ ∈

⎥⎦⎤

⎢⎣⎡ −⋅

,

mp iqqpqpqp IT nnnnσσ

π41 (11)

unde ( )minn este produsul diadic intre normalele la frontierele mω∂ si iω∂ ale subdomeniilor mω si iω si

( ) ∫ ∫≡

p qS Sqpqp dSdS

RSST 1, (12)

p si q fiind indici de fatete pe mω∂ si iω∂ . Astfel, schema iterativa (10) se scrie matriceal:

)~()())()(()~()~()( )()()()()( nnnnn QS BIIBBI =→+=→ −− 10

1 τ (13) Aparent, principalul dezavantaj al acestei metode este dimensiunea uriase a matricei S . Fiecare element al matrice este un tensor cu 9 componente in R3:

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

=

zzzyzx

yzyyyx

xzxyxx

kjkjkj

kjkjkj

kjkjkjkj

SSSSSSSSS

S (14)

Rezulta ca efortul de memorare al matricei )(S necesita retinerea a 9N2 numere in R3. Se poate arata (Anexa B) ca sunt valabile cateva proprietati deosebit de importante pentru reducerea acestui efort:

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a) Matricea )(S este simetrica: )(S = TS )( .

b) Elementele kjS ale matricei )(S sunt simetrice.

c) Urmele matricelor kjS au proprietatea: d)

⎩⎨⎧

=≠

=++jkVjk

SSSk

kjkjkj zzyyxx pentrupentru0

,,

(15)

Aceste propritati permit memorarea matricei S prin retinerea doar a )( 125

−NN elemente. In plus,

se mai pot face reduceri de memorie daca, pentru distante relativ mari intre subdomeniile jω si

kω , in locul memorarii componentei kjS , se calculeaza direct

kjkj V

S 1I = )()(

jjj

rrωσ

π ⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅−

533

41 IrrI

(16)

in cazul in care j=k, adaugandu-se si termenul kI . Vectorul r uneste centrele de greutata ale domeniilor jω si kω . Bibliografie 1. F. Hantila, “Mathematical models of the relation between B and H for nonlinear media”, Revue Roum.

Sci. Techn. Ser. Electrotechnique et Energ., no.3, 1974, p.429-448. 2. F. Hantila, “A method for solving stationary magnetic field in nonlinear media”, Revue Roum. Sci.

Techn. Ser. Electrotechnique et Energ., no.3, 1975, p.397-407, 3. F. Hantila, G .Preda, M. Vasiliu “Polarization Method for Static Fields“, IEEE Transaction on

Magnetics , vol.36, no.4, July 2000, p. 672-675, 4. I. Ciric, F. Hantila, “An Efficient Harmonic Method for Solving Nonlinear Time-Periodic Eddy-Current

Problems”, IEEE Transaction on Magnetics (ISI), no.4, vol.43, 2007, pp.1185-1188, 5. F. Hantila, E. Demeter, “Rezolvarea numerica a problemelor de camp electromagnetic”, Editor ARI

Press, Bucuresti, 1995.

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Anexa A

Functia de aproxinare Y este neexpansiva. Intr-adevar, in fiecare subdomeniu ωi , avem:

222

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡Ω== ∫∫

ii

dV

Vdvii

iiiiiωω

ννν BBB ~~

∫∫∫ Ω=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡Ω

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡Ω≤

iii

dddVi

i

ωωων

ν 22 BB

De unde rezult`:

∑ ∫∫= Ω

=≤=N

iii dvdv

i1

2222ν

ων νν BBBB

Anexa B

Proprietatile elementelor matricei )(S Fie B este un camp vectorial cu 0=⋅∇ B si H un camp vectorial cu 0=×∇ H . In plus,

cele doua campuri cu conditii de frontiera nule complementare. De exemplu, pentru simplitate, componenta tangentiala nula a lui H pe Ω∂⊂HS , presupusa simplu conexa, si componenta normala nula a lui B pe restul frontierei HB SS −Ω∂= . Atunci este valabila relatia de ortogonalitate:

∫Ω

⋅ dvHB = HB, =0 (b1)

i) Matricea )(S este simetrica: )(S = TS )( Fie kI si jI doua polarizatii arbitrare ce ocupa subdomeniile kω si jω si fie ),( kk HB ,

),( jj HB campurile magnetice produse de aceste polarizatii. Conform relatiei (b1) avem

0μjk H,B = j

jk IB,B − =0, de unde jk B,B = jk I,B . Asemanator,

kj B,B = kj I,B . Deoarece polarizatiile kI si jI sunt nule in afara subdomeniilor kω si

jω inductiile magnetice kjB si j

kB produse de aceste polarizatiile in subdomeniile jω si kω

verifica relatia:

jkj I,B = k

jk I,B (b2)

Sau kjkTj S II = jkjT

k S II = kTkjT

j S II . De unde, rezulta simetria matricei )(S

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ii) Elementele kjS ale matricei )(S sunt simetrice.

Sa aratam ca kjS -TskS =0. Deci

( )∫ ∫

∂ ∂k j

jkkj dSdS

Rω ω

nn-

( )∫ ∫

∂ ∂k j

jkjk dSdS

Rω ω

nn=0.

Inmultim aceasta relatie la stanga si dreapta cu vectorii arbitrari a si b. Avem:

∫ ∫∂ ∂

⋅⋅

k j

jkkj dSdS

Rω ω

)( bnna - ∫ ∫

∂ ∂

⋅⋅

k j

jkjk dSdS

Rω ω

)( bnna = ∫ ∫

∂

⋅∇⋅

k j

jkk dvdSR

ω ω

)( bna

- ∫ ∫∂

⋅∇⋅

k j

jkk dvdSR

ω ω

)( bna = ∫ ∫∂

⋅⋅

k j

jkk dvdSRω ω

3Rbn

a)(

- ∫ ∫∂

⋅⋅

k j

jkk dvdSRω ω

3)( Rbna =

∫ ∫∂

××

j k

jkk dvdSRω ω

3Rn

ba )( = ( )

∫ ∫∂

××⋅

j k

jkk dvdS

Rω ω3

)( baRn =

∫ ∫∂

⎟⎠⎞

⎜⎝⎛ ×

×∇⋅

j k

jkk dvdSR

ω ω

)( ban = 0

iii) Urmele matricelor kjS au proprietatea: ⎩⎨⎧

=≠

=++jkVjk

SSSk

kjkjkj zzyyxx pentrupentru0

,,

Se observa ca:

)( zzyyxx kjkjkj SSS ++π4 = ∫ ∫∂ ∂

⋅

k j

jkkj dSdS

Rω ω

nn = kjk dSdv

Rk j∫ ∫

∂ ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⋅

ω ω3

Rn

= ∫ ∫⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⋅

∂j k

jkk dvdSRω ω

3Rn

Cand j≠k, cantitatea din ultima paranteza este nula (3R

R⋅∇ =0). Cand j=k, se izoleaza punctul de

observatie cu o mica sfera in maniera din [5] si rezulta πω

43

=⋅

∫∂ k

kk dSR

Rn, fiind unghiul solid

sub care se vede suprafata inchisa kω∂ din orice punct de observatie din jω .

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DIELECTRIC SPECTROSCOPY OF POLYPROPYLENE WITH AND WITHOUT INORGANIC NANOFILLERS

Ilona PLESA, Florin CIUPRINA, Petru V. NOTINGHER

University Politehnica of Bucharest, Faculty of Electrical Engineering, ELMAT Laboratory, 313 Spl. Independentei, Bucharest, Romania, florin@elmat.pub.ro

Abstract. Study of electrical properties of polymer nanocomposites has known an important development in the last years. In the present work two dielectric properties – permittivity and tan delta – are analyzed by dielectric spectroscopy over a frequency range of 1 mHz – 1 MHz for plane samples made of three polypropylene (PP) nanocomposites obtained by using as filler particles of silica (SiO2), alumina (Al2O3) and titania (TiO2). For all the formulations the filler concentration was 5 wt.%. All the measurements were performed at a temperature of 300 K.

1 Introduction

In the last five years the research in the field of polymer nanocomposites with dielectric and electrical insulating properties has known a sharp increase, this being today a domain in which research teams from all over the world have focused their energies. The interest in nanodielectrics, as these polymer nanocomposite dielectrics are usually called, has become such important due to significantly improved electrical, mechanical and thermal behaviour of these new materials compared to the traditional polymer microcomposites. The research in the field of polymer nanocomposite dielectrics has as one of the main targets to obtain new materials with improved dielectric properties such as resistivity, dielectric strength, permittivity and dielectric losses. Until now several methods for processing and characterization have been tested, and some theories and models have been proposed for these materials having a huge nanofiller-polymer interface area which seems to be the main responsible for their unique properties. Despite the encouraging advances in this field we are still far from understanding and controlling the phenomena in these materials.

The most studied nanodielectrics are polymer nanocomposites defined as polymers with a small amount of nanofillers. Usually, the nanofillers are 1 to 100 nm in size, 1 to 10 wt.% in content, and should be homogeneously dispersed in the polymer matrix. Polymers such as polyamide (PA), polyethylene (PE), polypropylene (PP), ethylene vinyl acetate (EVA), epoxy resins and silicone rubbers are combined with nanofillers such as layered silicate (LS), silica (SiO2), titania (TiO2), and alumina (Al2O3) [1]. The properties of nanocomposites certainly depend on the kind of nanoparticle materials, physical and chemical conditions of their surfaces, the kind of coupling agents to bridge inorganic and organic substances chemically and physically, the kind and content of compatibilisers and/or dispersants, and the kind of polymer matrices. In the present work, the technique used to study the interaction between nanocomposites based on polypropylene and filled with inorganic nanoparticles and the applied electric fieldd was the frequency response dielectric spectroscopy.

Dielectric spectroscopy is based on the phenomena of electrical polarization and electrical conduction in materials. There are a number of different dielectric polarization mechanisms operating at the molecular and microscopic level. Each polarisation mechanism, either a relaxation or resonance processes, is centered on its particular characteristic frequency, which is the reciprocal time of the process and therefore separable in frequency (Figure 1) [2]. The most common mechanisms of polarization will occur at high frequencies (103 Hz - 1015 Hz), while at

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very low frequencies (10-3 Hz– 103 Hz), DC conduction will become significant. Thus dielectric spectroscopy is also well suited for the determination of DC conductivity of materials.

Figure 1. Dielectric permittivity spectrum over a wide range of frequencies [2].

Figure 2. Overview of the employed techniques and corresponding frequency ranges [3].

Various dielectric spectroscopy techniques and their associated frequency ranges are

summarized in Figure 2 [3]. The real part ( '

rε ) and the imaginary part ( ''rε ) of the complex dielectric permittivity

'''rrr εεε −= and the loss tangent

ωεεσ

εεδ

rr

r

0'

''

tan += (σ is the electrical conductivity of the

samples and ω is electric field angular frequency) depend on the nanocomposites structure, samples manufacturing and electric field frequency [4].

Figure 3. Principle of frequency response analyzer.

As shown in Figure 3, phase sensitive voltmeters are used to compare the voltage ( )1U ω and

( )2U ω (the latter proportional to ( )sI ω ). Commercial instruments often employ reference impedance RZ within the dielectric interface to facilitate accurate measurements. The complex impedance sZ of the sample can be calculated from the measured data by the equation:

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xs

ss Z

UU

IUZ

)()(

)()()(

2

1

ωω

ωωω −== (1)

where ω is the angular frequency. The complex relative permittivity can be then calculated from:

εεωω

ε ′′−′== jCZj s 0)(

1 (2)

provided that the geometric capacitance, 0C , of the sample is known [5]. In our previous studies the dielectric behaviour of polymer nanocomposites based on

polyethylene and PVC was analysed by using the same nanofillers (SiO2, TiO2 and Al2O3) [6, 7, 8]. In this paper we have studied the two dielectric properties – permittivity and tan delta – in PP nanocomposites, by using the frequency response dielectric spectroscopy in the range 10-3 Hz – 106 Hz.

2 Experimental

Systems investigated The nanocomposites tested in this study were polypropylene – SiO2, polypropylene – TiO2

and polypropylene – Al2O3. The content of nanofillers was 5 wt.%. The nanoparticles of SiO2 and TiO2 were of 15 nm diameter and the nanoparticles of Al2O3 had the diameter of 40 nm. The nanocomposites were manufactured by direct mixing method, using the installation shown in Figure 4.

Figure 4. Installation used for samples manufacturing [8].

For all the formulations the surface of the nanoparticles was treated with maleinized

polypropylene for a better compatibility between the nanofiller and the polymer matrix, and for a better dispersion of the nanoparticles. The nanocomposite samples for electrical tests performed in this study were plaques of square shape (10 x 10 cm2) having the thickness of 0.5 – 0.6 mm.

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Dielectric spectroscopy

The real part of the permittivity 'rε and the loss tangent ( δ tan ) were determined by

dielectric spectroscopy using a Novocontrol ALPHA-A Analyzer in combination with an Active Sample Cell ZGS (Figure 5), over the frequency range 10-3 – 106 Hz, at a temperature of 300 K. Four disks of 40 mm diameter were cut from one plaque of each formulation and tested by dielectric spectroscopy.

Figure 5. Setup for dielectric spectroscopy measurements (1 – PC; 2 – Control System; 3 – Modular Measurement System; 4 – Measurement Cell; 5 – Temperature Control System).

3 Results and discussion

In the following we present the preliminary results obtained on the analyzed samples.

a)

b) Figure 6. Relative permittivity rε ′ (a) and loss tangent δtan (b) as a function of frequency for

PP/inorganic nanoparticles samples. Figure 6 shows the dependences of the relative permittivity rε ′ (a) and of the loss tangent δtan (b) as a function of frequency for PP - TiO2, PP - SiO2 and PP - Al2O3 nanocomposites

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with 5 wt.% nanoparticles concentration. We remark a different dielectric behaviour of polypropylene nancomposites depending of the filler type, which is due to the contribution of studied inorganic nanofillers to the structure modifications of PP, especially in the region of the interface between the nanoparticles and the polymer matrix. Thus, it is observed that the inclusion of different types of nanoparticles leads to an increase of the permittivity of the nanocomposites compared with unfilled polypropylene. This increase in permittivity is more important when PP was filled with SiO2 nanoparticles, whose relative permittivity is about 4, than in the case when the filler was TiO2, which have a relative permittivity of about 90. This proves that the dominant effect of the presence of the nanoparticles on the relative permittivity of the nanocomposite is due to the polarization in the nanofiller - polymer interface region.

The δtan variation is a “classical” one, with the distinct separation of the parts ascribed mainly to polarization and conduction, with a peak at 102 Hz for PP - SiO2 and PP - TiO2 nanocomposites. These peaks correlate very well with the decrease of rε ′ noticed for about 102 Hz, which indicate a relaxation process associated to the interfacial polarization for both PP - SiO2 and PP - TiO2 nanocomposites. We have remarked this type of relaxation also for some polyethylene nanocomposites [7].

The presence of the filler for 5 wt.% content, determines an increase of the δtan values for all the tested nanocomposites compared with PP only.

4 Conclusions and perspectives

The preliminary results presented in this paper emphases different behaviour of the nanocomposites with polypropylene matrix and inorganic nanofillers, depending on the type of nanoparticles. In the frequency range analyzed in our experiments the real part of the permittivity and loss tangent decreases with the frequency for all formulation with 5 wt.% filler content.

The further steps of the research will extend the electrical characterization of the samples presented in this paper to ageing study and lifetime estimation under different stress factors (electric field, heat, humidity, radiation) and elaboration of models to correlate the results about properties with those of the nanostructure analysis.

References

[1] T.Tanaka, Dielectric Nanocomposites with Insulating Properties, IEEE Trans. Diel. and Electr.Insul., Vol.12, pp.914–928, 2005

[2] Tong Liu, John Forthergill, Steve Dodd, Ulf Nilsson, Dielectric spectroscopy measurements on very low loss cross-linked polyethylene power cables, Journal of Physics, Conference Series 183, 2009

[3] Tony Blythe, David Bloor, Electrical Properties of Polymers, Cambridge University Press, 2005.

[4] M.F. Frechette, C. Reed, H. Sedding, Progress, Understanding and Challenges in the Field of Nanodielectrics, IEEJ Trans. FM, Vol. 126, No. 11, pp.1031-1043, 2006.

[5] James P. Runt, John J. Fitzgerald, Dielectric Spectroscopy of Polymeric Materials: Fundamentals and Applications, American Chemical Society, 1999.

[6] Florin Ciuprina, Traian Zaharescu, Silviu Jipa, Ilona Plesa, Petru V. Notingher, Denis Panaitescu, Dielectric properties and thermal stability of γ -irradiated inorganic nanofiller

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modified PVC. Radiation Physics and Chem.(2009), Elsevier B.V, doi:10.1016/j.radphyschem.2009.08.018.

[7] F. Ciuprina, I.Plesa, P.V.Notingher, T.Tudorache, Dielectric Properties of Nanodielectrics with Inorganic Fillers, IEEE-Annual Report of CEIDP, ISBN 978-1-4244-2549-5, pp. 682-685, 2008

[8] Florin Ciuprina, Ilona Plesa, Jean César Filippini, Traian Zaharescu, Denis Panaitescu, Effects of Al2O3 Nanoparticles on Dielectric Properties and Thermal Stability of LDPE, in Proceedings of the Joint International Conference Materials for Electrical Engineering (ROMSC IEEE 2008 & MmdE 2008) , pp 301-306, 16th-17th June 2008, Bucharest, Romania.

Acknowledgments

The research activities have been partially performed in the frame of CEEX-PoNaDIP-234, project supported by National Authority for Scientific Research from Romania.

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Parallel iterative techniques for the extraction of line

parameters of interconnects

Alexandru LAZĂR, Radu POPESCU, Gabriela CIUPRINA, Daniel IOAN POLITEHNICA University of Bucharest. Splaiul Independenţei Nr. 313, Bucharest, Romania;

lmn@lmn.pub.ro

Abstract. Due to higher integration and increasing frequency-based effects, the tools used for forward-simulation of integrated circuits have to be adapted to meet the new demands. Full electromagnetic models are required, which yield large, sparse linear systems to be solved. This paper focuses on the parallelization of the Conjugate Gradient method used to solve the linear systems of algebraic equations that arise from the finite integration technique method applied to analyse an electrostatic field problem aiming to compute the line capacitance of interconnects.

1 Introduction

In the design of integrated circuits, the performance of interconnect performance has become important as millions of closely spaced interconnections in one or more levels connect various components on the integrated circuit [1]. In general, if on-chip interconnects are sorted with respect to their electric length, they may be categorized in three classes: short, medium and long. While the short interconnects have simple circuit models with lumped parameters, the extracted model of the interconnects longer than the wave length also has to consider the effect of the distributed parameters. Fortunately, the long interconnects have usually the same cross-sectional geometry along their extension. If not, they may be decomposed into straight parts connected by junction components (Fig.1). The former are represented as transmission lines (TLs) whereas the latter are modelled as common passive 3D components.

Figure 1: Examples of interconnect types.

At high frequencies, accurate values for the line parameters can be obtained only by modelling the electromagnetic field. Our approach consists of solving two complementary electromagnetic field problems. The first one is the computation of transversal parameters, using electro-quasi-static (EQS) field in dielectrics, considering the line wires as perfect conductors with a given voltage. The second one focuses on the longitudinal electric and generated transversal magnetic field, by solving a full-wave transversal magnetic problem. This approach is validated by experiments [2]. The EQS field problem leads to the solving of an algebraic system of linear equations, the coefficient matrix being a positive defined symmetrical matrix with complex entries. The EQS field problem can be analysed by separately solving the electrostatic (ES) field problem and the electric conduction problem. Solving the problems separately has the advantage that the coefficient matrices of the problems to be solved have real entries, they are diagonally dominant, thus, and thus well suited for the Conjugate Gradient (CG) method.

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2 Parallel approaches to solving linear systems of algebraic equations

It is well-known that the methods of solving linear systems of algebraic equations are classified as direct or iterative. Direct methods use a finite number of operations in order to compute the solution of a linear system. On an ideal computing system with no rounding errors, direct methods would deliver an exact solution. Iterative methods build the solution by computing a sequence of approximations. If the sequence is convergent, a satisfying precision can be obtained after a finite number of steps. The question is: what can we parallelize in order to speed up the solving process? Some of the steps of the algorithms do not depend on each other and can be executed in parallel. Direct solvers typically require the result of each step in order to progress with the solving process. This is called data dependency and it is an unwanted feature in parallel methods, because it requires the execution of most of the steps sequentially. Even so, a number of special algorithms can be devised for this, several parallel direct solvers being currently available [3], [4]. Some iterative methods, such as the Conjugate Gradient method, have a low data dependency. This makes it possible to execute some of the operations in parallel, obtaining a speed improvement over the sequential version of the same algorithm [5], [6]. An asymptotic estimation of the speed improvement is given by Amdahl’s law [7], which gives a heuristic estimation of the speed-up achievable by parallelizing a block of code as s = 1 / [(1 – P) + P / S], where P is the proportion of parallel code and S is the proportion of serial code. In practice, the speed improvement is lower than that obtained through this estimation. This is due to the various limitations of current computer architectures. In terms of computer architecture, there are three usual approaches to parallelism that are still used in practice: the vector model, the shared-memory model and the distributed-memory model. The vector model (also known as Single Instruction Multiple Data – SIMD) has a logical-arithmetical unit capable of executing a given instruction on several values at once. This approach is the oldest and still in use by General-Purpose Graphical Processing Units (GPGPUs). GPGPUs are powerful graphical cards which can expose their processing units, making them available for calculations not related to graphics. The advantage of these units is that they have an excellent cost/performance ratio: the processing units are not meant to be used for anything but raw mathematical operations, thus making it possible to build dedicated units with excellent performance at a fraction of the cost of a general-purpose CPU. The shared memory model exposes the main memory of the computer to several separate processors (Fig 2-left). Values in the main memory can only be accessed by one processor at a time, thus requiring careful use of each processor’s cache memory. The computations can be divided into several concurrent execution threads, each thread having access to the main memory, which makes programming fairly easy and does not require large communication costs like the distributed-memory model. However, the shared-memory model does not scale well due to the inherent limits of its architecture. [4].

Figure 2: Shared memory systems (left) and distributed memory systems (right).

Finally, the distributed memory model involves several independent nodes with one or more CPUs, each having its own main memory module (Fig. 2-right). In order for one node to use data

MEM 1

Computer 1

MEM 2

Computer 2

MEM 3

Computer 3

MEM N

Computer N

MEMORY Core1 Core2 Core3 CoreN

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stored on another, the data has to be copied, a typically costly operation which can be a disadvantage in some cases. However, some parallelization paradigms can be more cleanly implemented on distributed-memory systems, and there is virtually no limit to how far they can scale.

3 A shared-memory parallel version of the Conjugate Gradient Method

A well-known formulation of the Conjugate Gradient Method [5] is:

Figure 3: The conjugate gradient solver algorithm.

By profiling the serial implementation of this algorithm one can notice that most of the processing time is spent on the matrix-vector product (Table 1). This is the most complex operation which, unless some properties of the matrix can be exploited, will require O(n2) iterations. Therefore, we would like to direct our attention at achieving a good speed improvement of this procedure.

Table 1: Execution profile for one iteration on a 20228795x20228795 matrix

Function Time Matrix-vector product (line 13) 1.21 s Vector addition and subtraction 0.57 s Inner product 0.29 s

In the general case of a dense matrix, we expect this matrix-vector product to become dominant as the size of the system grows, whereas the other operations (such as inner product and vector scaling) become negligible. However, in our case, due to the very sparse block-diagonal structure of the matrix (Fig. 5-right), the proportion of these less complex operations is still significant enough to require some parallelization effort in order to obtain the best performance. Storing the matrix in the Compressed Column Storage (CCS) format allows for a general implementation. CCS is a widely-used format being also the default format used by MATLAB for manipulating sparse matrices. While CCS does not allow for an easy exploitation of the matrix' block-diagonal structure, it allows an implementation to be seamlessly extended to cover any type of matrix that meets the requirements of the Conjugate Gradient method. However, the CCS format only leaves room for a moderate performance gain in the matrix-

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vector product, as the total number of operations inside the inner loop is small. Since the matrix is symmetric, it is possible to decompose the matrix-vector product by rows rather than by columns and parallelize the outer loop. Nevertheless, even in this case, the small amount of operations and poor locality result in a significant cost of parallelization that only allows for some performance gain. Additional efficiency can be obtained by parallelizing the less complex operations, such as the inner products (which are inherently parallel).

The shared-memory implementation of the algorithm used the OpenMP platform. OpenMP allows one to explicitly delimit parallel regions of the code, according to the fork-join programming model (Fig. 4). Due to the fact that entering and exiting a parallel region has an associated cost, the implementation should focus on minimizing the number of parallel regions.

Figure 4: The fork-join programming model.

The speed-up which can be expected is difficult to evaluate using Amdahl's law. This law assumes an ideal implementation, which does not take into account the various additional time costs associated with a parallel program and architecture. In our case, the synchronization costs can become significant. This small loss of performance is tolerable because it yields an implementation that is easier to read and extend. Running one of the OpenMP benchmarks (such as EPCC [9] or NAS [10]) can offer an estimation of this performance penalty, allowing one to fine-tune the source code if required. These benchmarks suites can reveal how much time is spent on operations associated with managing execution threads, synchronization and other tasks associated with parallelism. It is therefore possible to identify and eliminate bottlenecks that occur due to the particularities of an OpenMP implementation or hardware architecture. Having these results at hand, one can improve the performance of a parallel program on a given platform.

4 Results

The test problem we considered arises from a the simulation of a four-layer structure similar to the one shown in (Fig. 5-left). The computing platform is one of the nodes of the ATLAS cluster (www.lmn.pub.ro/atlas) with two Quad-Core 2.3 GHz AMD Opteron processors with 2 MB of cache memory and 16 GB RAM. Our speed reference is MATLAB’s implementation of the CG method (on the same hardware test platform) which can be called through the pcg function, as this is a standard tool used in research and industry. In addition, we also compared our results against a serial implementation of the CG method.

PROGRAM

EXECUTION

SEQUENTIAL

AREA

SEQUENTIAL

AREA

PARALLEL AREA

PARALLEL AREA

thread thread thread thread

thread thread thread thread

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Figure 5: The configuration of the test problem used to validate the mode (left). The structure of the

coefficient matrix (right).

The shared-memory implementation yields a cost per iteration that is 1.8-2.1 times smaller than in Matlab. The speed-up for a large number of iterations can be expected to be slightly larger, as the time spent on synchronization and other associated costs becomes less and less significant compared to the total amount of computation. Compared to the serial implementation, parallel implementations yield an average improvement of 15-20%, due to the data structure’s poor exploitation of the block diagonal structure of the matrix. The most important performance gain can be obtained when moving from one thread to two concurrent threads. Using more execution threads does not allow for much performance gain, because the small number of operations in the inner loop of the matrix-vector product does not leave the thread scheduler much room for speed improvement. As can be seen in Fig. 6, the maximum speed improvement is obtained in a relatively narrow area, for matrices of sizes between 4 million and 10 million. Below this point, the poor exploitation of the matrix’ structure means that the computation effort of the calculations is still not optimum in relation to the parallelization-related costs. Past this point, the architectural limits become apparent, as efforts related to memory management, scheduling and cache misses increase.

Figure 6: Improvement in cost per iteration (left) and speed-up (right)

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Table 2: Comparison of execution speed

System size Cost of first iteration (s)

Matlab Serial 2 Threads 4 Threads 305887 0.73 0.42 0.40 0.39

3995807 0.95 0.62 0.53 0.52 6243243 1.68 0.97 0.82 0.82 8988519 2.63 1.68 1.27 1.25

20228795 5.49 3.15 2.69 2.67

5 Conclusions

VLSI circuit design and analysis can benefit greatly from using HPC techniques. A two-fold performance improvement over an industry-standard tool like MATLAB can be obtained even on the most general cases, without exploiting special properties of the problem. In this paper, a parallel implementation of the conjugate gradient solver on a shared memory system was used to solve large system arising from an electrostatic field formulation. There is an optimum number of threads that allow a maximum speed improvement. Using the current implementation of the solver, without fine tuning that would take away from the generality of the approach, using more than two threads does not does not come with any significant increase in speed. It should also be noted that the speed improvement does not vary greatly with the number of degrees of freedom. While small variations do exist, due to the properties of the hardware and compilers, the speed improvement is consistent for any large enough system.

References [1] A. K. Goel, High Speed VLSI Interconnections, Wiley Series in Microwave and Optical Engineering,

2007. [2] D. Ioan, G. Ciuprina, S. Kula, “Reduced Order Models for HF Interconnect over Lossy Semiconductor

Substrate”, Proc. of the 11th IEEE Workshop on Signal Propagation on Interconnects, pp.:233 – 236, 2007.

[3] PSPASES, www.cs.umn.edu/~mjoshi/pspases

[4] MUMPS, http://graal.ens-lyon.fr/MUMPS/ [5] Gene H. Golub, Charles F. Van Loan, “Matrix Computations”, Hopkins Fulfillment Service, 1996 [6] Youseef Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, 1996 [7] Mark D. Hill, Michael R. Marty, "Amdahl's Law in the Multicore Era," Computer, vol. 41, no. 7, pp.

33-38, July, 2008. [8] Barbara Chapman, Gabriele Jost, Ruud van der Paas, “Using OpenMP - Portable Shared Memory

Parallel Programming”, The MIT Press, 2008 [9] http://www.epcc.ed.ac.uk/research/openmpbench/ [10] http://www.nas.nasa.gov/Software/NPB/

Acknowledgments - The work described in this paper was done on the ATLAS cluster in the Numerical Methods Laboratory. The authors acknowledge the financial support of the following research projects: Tok4nEDA (FP6), IDEI/609 and IDEI/664 of 2009.

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OSCILAŢII LENTE ÎN CIRCUITE ELECTRICE PREZENTÂND REZONANŢĂ CU SALT ŞI

AMORTIZARE NELINIARĂ

Mircea V. NEMESCU, Mitică TEMNEANU Universitatea Tehnică“Gh. Asachi” din Iaşi, B-dul D. Mangeron 67, vnemescu@yahoo.com,

mitica_temneanu@yahoo.com

Abstract. Lucrarea îşi propune să prezinte apariţia şi existenţa oscilaţiilor lente în circuite electrice în care apare rezonanţa cu salt şi conţinând un element de amortizare neliniar.

1 Introducere

În literatura de specialitate există numeroase lucrări care prezintă fenomenul de rezonanţă cu salt [2], [3] ce poate să apară în circuite electrice neliniare la variaţia frecvenţei sau amplitudinii semnalului de excitaţie. În astfel de circuite pot să apară oscilaţii lente prin salturi rezonante, pentru un semnal armonic de amplitudine şi frecvenţă constante, dacă circuitul conţine un resistor neliniar a cărui rezistenţă variază inerţial la producerea saltului resonant.

2 Consideraţii teoretice

Fie circuitul electric dat în Fig.1a şi conţinând un bec cu filament metalic (Wolfram). Pentru o anumită valoare a tensiunii de excitaţie, în circuit poate să apară fenomenul de rezonanţă însoţit de creşterea prin salt a curentului. (a) (b)

Fig.1. Structura circuitului electric şi a celui echivalent Ca urmare, creşte rezistenţa rezistorului neliniar, ceea ce determină micşorarea curentului, ieşirea din rezonanţă a circuitului şi producerea saltului de curent către valori mici ale acestuia. Are loc răcirea filamentului becului, creşterea lenta a curentului şi producerea din nou a saltului resonant.În circuit are loc creşterea şi descreşterea succesivă a curentului prin salturi rezonante şi apariţia fenomenului de automodulaţie. Circuitul electric echivalent celui dat în Fig.1a este reprezentat în Fig.1b, în care R este rezistenţa echivalentă a ansamblului inductor-rezistor neliniar. Pentru circuitul echivalent dat în Fig.2, poate fi scrisă relaţia:

∫ =+⋅+ )()(1)()( tedttiC

tiRdt

tdψ (1)

Se consideră: )()()( 3 tntmti ψψ ⋅+⋅= (2) )sin()( ϕω += tEte m (3)

e(t)

B C

L i(t)

e(t)

R C

L i(t)

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cu care ecuaţia (1) devine:

)cos()()()())(31()( 32

2

2

ϕωωψψψψψ+=++++ tEt

Cnt

Cm

dttd

mtnRm

dttd

m (4)

Introducându-se variabilele normate,

0

)()(ψψ ttx = şi

0m

m

EE

K = (5)

cu 20

00 ω

ωψ mE

= (6)

şi Cm

=0ω (7)

Ecuaţia (4) poate fi pusă sub forma:

)cos()()()())(31(2)( 320

20

22

2

ϕωβωωβα +=++++ tKtxtxdt

tdxtxdt

txd (8)

în care:

2

mR=α , coeficient de amortizare (9)

m

n 20ψ

β = , coeficient de neliniaritate (10)

Din motive de stabilitate se consideră că: xtxxg ∀>+= ,0))(31()( 22

0 βω . Condiţie îndeplinită dacă:

0>β sau 0<β şi β3

1−

<x .

Pentru obţinerea unui rezultat mai general, se neglijează termenul )(3 2 txβ [2], cu care relaţia (8) devine:

)cos())(1)(()(2)( 2202

2

ϕωβωα +=+++ tKtxtxdt

tdxdt

txd (11)

Ecuaţia (11) este de tip Duffing şi nu are o soluţia analitică exactă. Ca urmare, pentru analiză, se foloseşte metoda liniarizării armonice. Se consideră soluţia de regim permanent tatx ωcos)( = (12) cu care ecuaţia (11) devine:

041sin)sin2(2cos)cos

43)(( 32

032

022

0 =+−−−+− atKatKaa βωωϕωαωϕβωωω (13)

Se neglijează în (13) termenul 3204

1 aβω şi se anulează coeficienţii funcţiilor tωsin şi tωcos .

Cu notaţiile:

0ωω

=u şi 0ωαλ = (14)

se obţine:

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04)431(),( 4

02

222222

20

=−++−=ω

λβω a

KuauaKF (15)

În planul ),( 20

aKω

reprezentarea ecuaţiei (15) se numeşte curbă de rezonanţă şi are aspectul din

Fig.2.

Fig.2. Curbele de rezonanţă pentru două valori ale lui λ.

Punctul de funcţionare al circuitului este dat de intersecţia dreptei 20

1

ωK cu curba de rezonanţă.

În punctele de tangenţă au loc salturile rezonante, când

0=∂∂

aF (16)

respectiv

0)1(21

89

40

2

22242 =−−+

ωββ

aKuaa (17)

În punctual A are loc creşterea prin salt a amplitudinii a, când

02

2

>∂∂

aF (18)

Această creştere determină creşterea rezistenţei lămpii, şi deci a coeficientului de amortizare. Variaţia coeficientului de amortizare este inerţială, ceea ce face ca valoarea λ2 să fie atinsă cu întârziere. Astfel, punctul de funcţionare se deplasează din C în B, are loc o micşorare a amplitudinii a, deci a curentului din circuit În punctual B este îndeplinită condiţia:

02

2

<∂∂

aF , (19)

ceea ce determină micşorarea prin salt a amplitudinii corespunzătoare punctului D Are loc o răcire a filamentului, micşorarea rezistenţei şi a coeficientului de amortizare. Ca urmare, punctual de funcţionare se deplasează lent din D în A, când se produce o nouă creştere prin salt a curentului. Ca urmare a acestui process, apare fenomenul de automodulaţie prin salturi rezonante. Înfăşurătoarea acestor oscilaţii constituie oscilaţii lente. Pentru lampa din circuit, poate fi scrisă relaţia pff dQdQdQ += (20) pbbpf dQdQdQ += (21) dtUIPdtdQ e== (22) unde:

20ω

K

20

1

ωK

a

1λ 12 λλ >A

B

C

D

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dQ = energia termică dezvoltată în filament [J]; P = puterea absorbită de lampă din reţea [W]; U = tensiunea la bornele lămpii [V]; eI = valoarea efectivă a curentului sinusoidal echivalent [1], egală cu valoarea efectivă a curentului real deformat:[A]

2

maxII e = (23)

ffff dcmdQ θ= (24)

fdQ = căldura necesară încălzirii filamentului [J]; fm = masa filamentului [kg]; fc = căldura specifică a materialului filamentului [J/kg grad]; fθ = temperatura filamentului [grad]. )( bfffpf AdQ θθα −= (25)

pfdQ = pierderi prin radiaţie între filament şi balon [J]; fα = coeficient de schimb de căldură prin radiaţie [W/m2 grad]; fA = suprafaţa filamentului [m2]; bθ = temperatura interioară a balonului [grad]. bbbb dcmdQ θ= (26)

bdQ = căldura necesară încălzirii balonului de sticlă [J]; bm = masa balonului de sticlă [kg]; bc = căldura specifică a sticlei balonului [J/kg grad]; bθ = temperatura balonului [grad]. )( abbbpb AdQ θθα −= (27)

pbdQ = căldura pierdută prin radiaţie şi convecţie între balon şi mediul ambient [J]; bα = coeficient de schimb de căldură prin convecţie şi radiaţie [W/m2 grad]; bA = suprafaţa balonului [m2]; aθ = temperatura mediului ambiant [grad]. Cu relaţiile (23)-(27), expresiile (20) şi (21) devin: dtAdcmdtUI bffffffe )( θθαθ −+= (28)

)()( abbbb

bbbfff Adt

dcmA θθα

θθθα −+=− (29)

Relaţiile (28) şi (29) pot fi scrise sub forma:

bff

ef

f

ff

ff

AUI

dtd

Acm

θα

θθ

α+=+ (30)

abbff

bbf

bbff

ffb

b

bbff

bb

AAA

AAA

dtd

AAcm

θαα

αθ

ααα

θθ

αα ++

+=+

+ (31)

Se fac notaţiile:

ff

fff A

cmT

α= ;

bbff

bbb AA

cmT

αα += ;

bbff

ff

AAA

Kαα

α+

=1 ;bbff

bb

AAA

Kαα

α+

=2 ;ff

e

AUIα

θ =1

Ecuaţiile (30) şi (31) pot fi scrise sub forma:

bff

f dtd

T θθθθ

+=+ 1 (32)

afbb

b KKdt

dT θθθθ

21 +=+ (33)

Făcând transformatele Laplace ale ecuaţiilor (32) şi (33) se obţine:

))()((1

1)( 1 sssT

s bf

f θθθ ++

= (34)

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)(1

)(1

)( 21 ssTKs

sTKs a

bf

bb θθθ

++

+= (35)

Înlocuind relaţia (35) în (34) rezultă

))(2

)(21

(1

)( 222

1221

2

sss

Ksss

sTK

s annnn

bnf θ

ωςωθ

ωςωω

θ++

+++

+−

= (36)

fb

n TTK11−

=ω ; fb

fbn TT

TT +=ςω2 ; (37)

Se observă din relaţia (36) că temperatura filamentului lămpii are o variaţie inerţială atât la variaţia curentului, prin 1θ , cât şi la variaţia temperaturii mediului ambiant, prin aθ . Variaţia rezistivităţii Wolframului este [4] 2,1

fTfT mθρ = (38) 11102.6 −⋅=m [ΩmK-1.2]; fTθ = temperatur [grade Kelvin]

Rezistenţa filamentului la temperatura T este

42d

lR fTfT πρ= (39)

unde: l = lungimea firului filament; d = diametrul firului filament. Rezultă din cele arătate că rezistivitatea şi rezistenţa au o variaţie inerţială şi neliniară. La valori mici ale curentului eI temperatura 1θ are valori scăzute, ceea ce face ca în regim staţionar, când

)(1

121

1af K

Kθθθ +

−= (40)

rezistivitatea şi rezistenţa să fie puternic influenţate de variaţiile temperaturii mediului ambiant aθ . Această influenţă face ca intervalul de timp în care punctul de funcţionare parcurge

segmentul DA, Fig.2, să fie mare, ca urmare oscilaţia să fie lentă.

3 Rezultate experimentale

Experimentul a fost efectuat pe un circuit RLC serie, Fig.1a. În Fig.3a este prezentată caracteristica ψ(i) a bobinei neliniare iar în Fig.3b sunt date variaţiile tensiunii de alimentare (preluată printr-un divizor 1/10) şi ale curentului din circuit (tensiunea pe o rezistenţă de 5Ω).

600m

-600m

-500m

-400m

-300m

-200m

-100m

0

100m

200m

300m

400m

500m

Time (s)08:37:53.308:37:53.005 08:37:53.105 08:37:53.205 08:37:53.305

(a) (b)

Fig.3. Caracteristica ψ(i) a bobinei neliniare, curentul şi tensiunea din circuit

i

ψ

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Becul B este cu filament de wolfram, având Pn=25 [W], Un=220 [V]. Condensatorul are valoarea C=7.2 [μF]. Tensiunea de alimentare a circuitului este E=55 [V], f=50 [Hz]. În fig.4a sunt prezentate oscilaţiile lente ce apar iar în Fig.4b este prezentată, în detaliu, creşterea şi descreşterea prin salt a curentului. Se observă că înfăşurătoarea este o oscilaţie lentă, în ambele situaţii. Aceasta este determinată de variaţia inerţială a rezistenţei filamentului la creşterea şi descreşterea prin salt a curentului de la 2 [mA] la 10 [mA], Fig.5 şi Fig.6.

600m

-600m

-500m

-400m

-300m

-200m

-100m

0

100m

200m

300m

400m

500m

Time (s)08:38:09.608:37:50.878 08:37:55.878 08:38:00.878 08:38:05.878

500m

-500m

-400m

-300m

-200m

-100m

0

100m

200m

300m

400m

Time (s)08:37:53.908:37:52.916 08:37:53.116 08:37:53.316 08:37:53.516 08:37:53.716

(a) (b)

Fig.4. Oscilaţiile lente obţinute şi detaliu

8.5

0

500m

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

Time (s)10:03:10.310:02:55.738 10:02:58.238 10:03:00.738 10:03:03.238 10:03:05.738 10:03:08.238

620m

300m

320m

340m

360m

380m

400m

420m

440m

460m

480m

500m

520m

540m

560m

580m

600m

Time (s)10:03:24.910:03:12.922 10:03:14.922 10:03:16.922 10:03:18.922 10:03:20.922 10:03:22.922

Fig.5. Variaţia inerţială a rezistenţei filamentului la creşterea prin salt a curentului

Fig.6. Variaţia inerţială a rezistenţei filamentului la scăderea prin salt a curentului

4 Concluzii

Lucrarea prezintă fenomenul de apariţie a oscilaţiilor lente în circuite neliniare prezentând rezonanţă cu salt şi o variaţie neliniară a amortizării. Consideraţiile teoretice făcute sunt confirmate de rezultatele experimentale. Referinţe [1] A. Timotin, V. Hortopan, A. Ifrim, M. Preda, Lecţii de bazele electrotehnicii, EDP, 1970 [2] E. Philippow, Nichtlineare Electrotechnik, Akademische Verlagsgeselschaft Gest und Portig, Leipzig, 1971 [3] Gh. Savin, H. Rosman, Circuite electrice neliniare şi parametrice, Ed. Tehnică, 1973 [4] P. Dinculescu, Surse de lumină, lampi cu incandescenţă, Ed. IPB, 1974 [5] M.V. Nemescu, D.D. Lucache, Slow oscillations in SISO nonlinear system described by Duffing equation type, 7-th IEEE International Conference on Methods and Models in Automation and Robotics, Poland, 2001, pp. 661-664.

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EVALUAREA PERFORMANŢELOR ACŢIONĂRILOR ELECTRICE MODERNE PE BAZA DETERMINĂRII

DIMENSIUNII FRACTALE A CURBELOR DE REGIM CVASISTAŢIONAR

Ion Voncilă, Cristian Munteanu

Universitatea „Dunărea de Jos” Galaţi, str. Domnească, nr. 47, 800008, Galaţi; Ion.Voncila@ugal.ro

Abstract. În cadrul lucrării este prezentată o metodă de analiză duală metodei analizei Fourier. Această metodă – bazată pe determinarea dimensiunii fractale a curbelor de regim cvasistaţionar din cadrul acţionărilor electrice cu motoare de curent alternativ – comandate prin intermediul convertoarelor statice – are drept scop caracterizarea gradului de neregularitate ale acestor curbe. Un grad ridicat de neregularitate al acestor curbe reliefează duritatea regimului deformant din reţea.

1 Introducere

Teoria fractalilor face apel la două definiţii foarte diferite ale dimensiunii [1], [3], [4]: dimensiunea topologică, pe de o parte, şi dimensiunea fractală, de cealaltă parte. Dimensiunea topologică Dimensiunea topologică este identică, în cazurile simple – adică acolo unde mulţimile sunt „regulate” – cu dimensiunea analitică (obişnuită). Aceasta din urmă reprezintă numărul minim de parametri independenţi necesari pentru a determina, fără echivoc, poziţia fiecărui punct al mulţimii. Principalul interes al dimensiunii topologice este acela că are o aplicabilitate foarte largă. Ea este, prin definiţie, mereu întreagă. Dimensiunile fractale Există mai multe definiţii pentru dimensiunea fractală. În cele ce urmează sunt prezentate trei dintre acestea: dimensiunea Hausdorff-Bezicovici, dimensiunea Minkowski-Bouligand şi dimensiunea de omotetie. Dimensiunea Hausdorff-Bezicovici Dimensiunea Hausdorff-Bezicovici nu are semnificaţie decât în spaţiile zise „metrice”, dotate cu propia lor topologie naturală. Pentru a o defini, se consideră o submulţime oarecare X a unui spaţiu metric E. Se construieşte pe X o funcţie reală care depinde de doi parametri: ( ) (∑= p

isp AdXm inf, ) , unde sunt submulţimi ale lui E al căror diametru este mai mic sau egal cu s şi a căror

reuniune reprezintă o acoperire numărabilă a lui X. Prin construcţie, funcţia creşte atunci când s descreşte şi tinde spre o limită atunci când s tinde spre 0.

iAAA ,..., 21

( )Xm sp,

Aceasta limită, care poate lua valoarea 0 (şi, în general, chiar o ia) sau infinit, este, prin definiţie, măsura p-dimensională Hausdorff a lui X, notată cu ( )Xmp . Pentru o mulţime X determinată se poate studia variaţia lui ( )Xm p în funcţie de p. Valoarea critică a lui p - pentru care măsura ( )Xm p „sare” brusc de la infinit la zero - este, prin definiţie, dimensiunea Hausdorff-Bezicovici a lui X sau, mai simplu, dimensiunea Hausdorff, notată cu

. ( )XHdim

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Pentru mulţimile fractale, dimensiunea Hausdorff este diferită de dimensiunea topologică (în sensul că este superioară ei). Lucrul acesta este, bineînţeles, valabil atunci cand dimensiunea Hausdorff are o valoare fracţionară. Dimensiunea Minkowski-Bouligand Dimensiunea Minkowski-Bouligand, numită şi dimensiune de entropie, dimensiune capacitară, densitate logaritmică, dimensiune de informaţie, dimensiune de numărare a cutiilor (box-counting dimension) etc., datează din anul 1930. Ca şi dimensiunea Hausdorff, ea nu are sens decât în spaţiile metrice. Fie F o submulţime mărginită a unui spaţiu metric E oarecare, de exemplu Rn. Se notează cu cel mai mic număr de sfere cu diametrul d necesare pentru a acoperi pe F. Prin definiţie, dimensiunea Minkowski este egală cu limita, atunci când d tinde la zero, a raportului dintre logaritmul lui şi logaritmul lui 1/d. Dacă se notează cu dimensiunea Minkowski a lui F, avem:

( )FNd

( )FNd ( )FMdim

( ) ( )( ) ( )dFNF dM /1log/loglimdim = . (1) Dimensiunea de omotetie Dimensiunea de omotetie, numită şi dimensiune de similitudine, nu este definită decât pentru un tip special de mulţimi: mulţimile autosimilare, adică cele în care părţile reprezintă o imagine redusă a întregului. Fie F o mulţime ce poate fi descompusă în N părţi, fiecare parte aflându-se într-un raport r cu întregul. Dimensiunea de omotetie a lui F este, prin definiţie, raportul dintre logaritmul lui N şi logaritmul lui 1/r. Dacă se notează cu ( )FSdim dimensiunea de omotetie a lui F, rezultă: ( ) ( )rNFS /1log/logdim = . (2) Aceasta dimensiune nu este nici ea neapărat întreagă.

2 Metode de determinare a dimensiunii fractale

Există mai multe metode de determinare a dimensiunii fractale dar cea care se pretează cel mai bine în practică este metoda „numărării cutiilor” („box counting”). Iată, pe scurt, în ce constă această metodă, utilizată în cazul lucrării. Se consideră o curbă dată, desenată într-un plan. Se alege dimensiunea maximă a obiectului (curbei) şi se construieşte un pătrat care conţine obiectul de analizat. Lungimea laturii acestui pătrat poate fi considerată unitatea de măsură. Se împarte această unitate în 2

părţi egale; se obţin, la scara 21 , 4 domenii din care doar ( )1n sunt ocupate de structura

analizată. Se împarte, din nou, fiecare pătrat în patru părţi egale (scara 41 ) şi se obţin 16

domenii, din care ( sunt ocupate de părţi ale obiectului de analizat. Se procedează asemănător, până la limita rezoluţiei de care se dispune. Se obţin, deci, două şiruri:

)2n

• unul pentru scări: 21 ,

41 ,

81 ,

161 ,...;

• unul pentru numărul de domenii ocupate raportat la numărul total de domenii, dependent de

scară: 41n

,16

2n,64

3n,256

4n,...

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Se consideră un punct M care are coordonatele (x,y), respectiv, (scara, numărul caracteristic

determinat la acea scară). De exemplu: ⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛

21

11 ,

21

nn

M , ⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛

41

22 ,

41

nn

M , etc.; aceste puncte se

reprezintă într-un sistem ortogonal, de coordonate logaritmice. Dimensiunea fractală a obiectului va fi numeric egală cu panta dreptei descrisă de punctele , ,..., . Odată găsită valoarea lui , se poate identifica obiectul, ca fiind fractal sau nu. Dacă este foarte aproape de 1 sau 2, atunci obiectul analizat este de tip euclidian. Dacă are valoare intermediară, fracţionară, atunci acel obiect este fractal, caracterizat de valoarea determinată.

1M 2M nMDf Df

Df

Această metodă este uşor de aplicat cu ajutorul calculatorului, care face ca precizia să crească foarte mult. Un exemplu de măsurare a lui cu această metodă este prezentat mai jos (fig. 1). Df

Fig. 1: Metoda „box counting” Fig. 2: Graficul log-log care permite determinarea dimensiunii aplicată la curba la curba Koch fractale prin calcularea pantei dreptei obţinute Fractalii pot fi înţeleşi ca fiind mulţimi speciale de puncte (din anumite spaţii metrice), care se diferenţiază de alte mulţimi de puncte prin faptul că dimensiunea lor este fracţionară, adică au dimensiunea neîntreagă. Determinarea dimensiunii fractale - ca pantă a dreptei obţinute în maniera descrisă mai sus – este prezentată în figura 2. Dimensiunea fractală este un număr care cuantifică gradul de neregularitate şi de fragmentare a unei structuri geometrice sau a unui obiect din natură.

3 Determinarea dimensiunii fractale a curbelor de regim cvasistaţionar ale acţionărilor cu motoare de inducţie clasice şi cu motoare speciale

Acţionările electrice moderne reclamă reglarea continuă a vitezei (fie la cuplu constant, fie la putere constantă). Pentru a reuşi acest lucru, este necesară alimentarea şi comanda motorului de antrenare prin intermediul unui convertor static. Datorită particularităţilor constructive şi funcţionale ale acestor convertoare, în lanţul de alimentare cu energie electrică apare un conţinut ridicat de armonici, armonici care generează, apoi, multe efecte negative: creşterea valorii efective a curentului şi, implicit, a pierderilor Joule, creşterea pierderilor în miezurile feromagnetice, înrăutăţirea randamentului (ca urmare a creşterii pierderilor), instabilităţi funcţionale, reducerea duratei de viaţă (ca urmare a scăderii randamentului) etc.. Deşi, evaluarea conţinutului de armonici se face, la ora actuală, cu ajutorul analizei spectrale (transformata Fourier), oscilografierea curbelor de tensiune/curent – din cadrul acţionărilor electrice, de curent alternativ, în primul rând – reliefează un grad mare de neregularitate – atât în regim dinamic cât şi în regim cvasistaţionar – motiv pentru care, în această lucrare se propune o analiză duală, pentru evaluarea performanţelor acestor categorii moderne de acţionări electrice, respectiv, analiza fractală. Această analiză se poate face numai pe baza determinării dimensiunii fractale a curbelor de regim cvasistaţionar din cadrul acţionărilor electrice moderne.

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Plecând de la aserţiunea că efectele negative se amplifică la creşterea conţinutului de armonici, s-a realizat o analiză comparativă între motoarele asincrone clasice (de inducţie) – alimentate direct de la reţeaua electrică trifazată (considerată sinusoidală) - şi motoare electrice speciale (inclusiv cel de inducţie) ce necesită, neapărat, alimentarea prin intermediul unui convertor static (un invertor). Motorul asincron (de inducţie) – alimentat de la o sursă trifazată sinusoidală – constituie referinţa în cadrul analizei. Întreaga analiză a fost efectuată cu ajutorul mediului de progamare PSIM [2]. În figura 3 este prezentată schema de principiu utilizată pentru alimentarea motorului asincron ales ca referinţă.

Fig. 3: Schema de principiu utilizată pentru alimentarea de la o sursă pur sinusoidală a unui

motor asincron trifazat (de inducţie)

a) b)

Fig. 4: Variaţia curenţilor şi spectrul de armonici la motorul asincron ales ca referinţă: a) variaţia curentului printr-o fază statorică; b) spectrul de armonici din curba curentului statoric

Figura 4 prezintă variaţia – în timp – a curentului printr-o fază statorică, respectiv, spectrul de armonici din curba curentului statoric al motorului (obţinut prin aplicarea transformatei Fourier rapide – FFT), în cazul alimentării acestuia de la o sursă pur sinusoidală. Merită menţionat faptul că motorul asincron analizat a fost considerat - în cele de mai sus – ca fiind la gol, interesând mai puţin amplitudinea curenţilor, cât forma de variaţie a acestora. În cazul alimentării aceluiaşi motor asincron prin intermediul unui invertor – realizat cu tranzistoare bipolare de putere (IGBT) (fig.5) – s-a obţinut variaţia curenţilor şi spectrul de armonici de forma celor prezentate în figura 6.

Fig. 5: Schema de principiu utilizată pentru alimentarea prin intermediul unui invertor cu IGBT-uri a

unui motor asincron trifazat (de inducţie) De data aceasta – pentru a obţine amplitudini mai ridicate ale curenţilor absorbiţi – s-a considerat că motorul asincron antrenează o sarcină având cuplul rezistent constant.

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a) b)

Fig. 6: Variaţia curenţilor şi spectrul de armonici la motorul asincron alimentat prin invertor: a) variaţia curentului printr-o fază statorică; b) spectrul de armonici din curba curentului statoric

Se constată că, în acest caz, în curba curentului statoric apar multe armonici de ordin superior armonicii fundamentale, spre deosebire de cazul alimentării aceluiaşi motor de la o sursă pur sinusoidală (când, desigur, exista numai armonica fundamentală (fig.4)). Situaţia se agravează în cazul unor motoare de construcţie specială şi, desigur, cu destinaţii speciale. Iată, în fig. 7 schema de principiu utilizată pentru alimentarea unui motor sincron autopilotat.

Fig. 7: Schema de principiu utilizată pentru alimentarea prin intermediul unui invertor cu IGBT –uri a

unui motor sincron autopilotat (cu senzori Hall)

Variaţia curentului printr-o fază a unui astfel de motor cât şi spectrul de armonici sunt prezentate în figura 8.

a) b) Fig. 8: Variaţia curenţilor şi spectrul de armonici la motorul sincron autopilotat alimentat prin invertor:

a) variaţia curentului printr-o fază statorică; b) spectrul de armonici din curba curentului statoric

Spectrul de armonici – înregistrat în acest caz – este mult mai larg decât în cazul unui motor asincron clasic alimentat prin intermediul unui invertor. Dacă în cazul motorului asincron (de inducţie) se întâlnesc supraarmonici până la frecvenţe de ordinul 5 kHz, la motorul sincron autopilotat – alimentat tot prin intermediul unui invertor cu IGBT –uri – frecvenţele supraarmonicilor ajung până la 15 kHz.

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4 Analiză comparativă între informaţiile oferite de analiza spectrală şi analiza fractală a curbelor din regimurile cvasistaţionare ale acţionărilor electrice

Deşi, analiza spectrală oferă suficiente informaţii în ceea ce priveşte conţinutul de armonici din curbele curenţilor, ea nu reflectă gradul de iregularitate a curbelor de tensiune/curent pentru convertoarele electromecanice alimentate prin intermediul unor convertoare statice. Iată, de ce, în cadrul lucrării s-a realizat – prin metoda „numărării cutiilor” („box counting”) determinarea dimensiunii fractale a curbelor de regim cvasistaţionar, pentru cazurile precizate mai sus, la care s-a utilizat, deja, analiza spectrală. În figura 9 sunt prezentate rezultatele obţinute în MATLAB [5] – utilizând metoda „numărării cutiilor” – pentru cele trei curbe ale curenţilor statorici de la motoarele analizate; totodată, este calculată şi dimensiunea fractală a curbelor analizate.

100 101 102 1030.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

r, box size

- d ln

n /

d ln

r, lo

cal d

imen

sion

2D box-count

100 101 102 103

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

r, box size

- d ln

n /

d ln

r, lo

cal d

imen

sion

2D box-count

100 101 102 1030.8

0.9

1

1.1

1.2

1.3

1.4

1.5

r, box size

- d ln

n /

d ln

r, lo

cal d

imen

sion

2D box-count

Df = 1.6138 Df = 1.3132 Df = 1.1536 a) b) c)

Fig. 9: Determinarea dimensiunii fractale a curbelor de regim cvasistaţionar ale curenţilor statorici la: a) motor asicron alimentat de la o sursă sinusoidală; b) motor asincron alimentat prin invertor; c) motor

sincron autopilotat alimentat prin invertor Din analiza comparativă a informaţiilor oferite de cele două metode de analiză (spectrală, respectiv, fractală) se constată că la creşterea conţinutului de armonici din curba curenţilor se obţine o reducere a dimensiunii fractale a curbei.

5 Concluzii

În urma întregii analize efectuate în cadrul lucrării, pot fi formulate următoarele concluzii: • Cuplarea celor două metode de analiză (spectrală, respectiv, fractală) oferă posibilitatea

unei cunoaşteri aprofundate a performanţelor acţionărilor electrice moderne • Dimensiunea fractală se poate determina atât pentru regimurile cvasistaţionare cât şi

pentru regimurile dinamice din cadrul acţionărilor electrice • La motoarele alimentate prin intermediul unui invertor (conţinut ridicat de armonici în

curba curenţilor), dimensiunea fractală este mai mică decât la cele alimentate de la surse sinusoidale

• Valorile fracţionare pentru dimensiunile fractale ale curbele cureţilor statorici indică caracterul fractal al tuturor acţionărilor moderne de curent alternativ.

Referinţe [1] K. Falconer. Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons,

Ltd, 2003. [2] ***PSIM. Simulation software, POWERSYS-France-licence, 2007. [3] D. Olivier. Fractali, Editura Teora, Bucureşti, 1994. [4] B. B. Mandelbrot. The Fractal Geometry of Nature, New York: W. H. Freeman, 1983. [5] ***MATLAB 7.0. Simulation software, MathWorks-licence, 2004.

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Linear Circuit Synthesis Using Matlab

Alexandru Bujor “Politehnica” University. Bucharest, Romania; bujor.alexandru89@gmail.com

Mihai Iordache “Politehnica” University. Bucharest, Romania; mihai.iordache.44@gmail.com

Abstract. The purpose of this paper is to show how to use Matlab in order to determine the circuit

parameters of the linear circuit from experimental data. Given a specific dataset and the structure of

the circuit we can reproduce the original circuit using the Matlab product.

1. Method description

Fig.1. Description of the synthesis procedure.

The method is based on the system identification theory. The general structure of a time invariant

system is given below:

ttt

ttt

DuCxy

BuAxx

(1)

We intend to create a grey state space model described by specific equations. From these

equations we deduce the state space matrices and we use Matlab to estimate the parameters of the

circuit. The experimental datasets are pre-processed and then used in the parameter identification

process.

If necessary we can use the Shannon-Nyquist theorem to simplify datasets.

“If a function x(t) contains no frequencies higher than B Hz, it is completely determined by

giving its ordinates at a series of points spaced 1/(2B) seconds apart”, [1].

Shannon-Nyquist theorem can be used to reduce the size of the dataset in order to improve

the speed of the parameter estimation process.

2. Using System Identification toolbox from Matlab

The System Identification toolbox from Matlab is a powerful tool that can be used to estimate

the parameters of a system described by specific state space matrices from an experimental dataset.

In order to use the parameter estimator (pem) we need a .m file to describe the system model.

The function should have the following prototype:

function [A,B,C,D,K,X0]=model_function_name(pars,Tsm,Auxarg) (2)

where A,B,C,D,K,X0 are system matrices and the pars is a vector of the parameters to be estimated

(the initial circuit parameters). We consider K is a null matrix.

After describing the model in a .m file it is necessary to create an idgrey object.

Moreover, we need to create an iddata object to store the experimental dataset. The iddata object

can be resampled in accordance with the Shannon-Nyquist theorem. In order to estimate the

parameters of the model we can use pem command. After estimation the parameter we can access the

Topology of

the circuit Experimental

Dataset

Matlab

Processing Equivalent

Circuit

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parameter vector or we can compare the estimated model with the initial dataset using the compare

command.

3. The synthesis of a RLC circuit from experimental data using Matlab System Identification

Toolbox

We intend to show how to use the method on a concrete case. We consider that an experimental

dataset is supplied and the parameters of the initial RLC circuit should be discovered using the

System Toolbox from Matlab.

The Dataset

The Dataset should contain the values of state variables and input variables at specific time

moments. We consider that the electric current through the inductor (iL) and the voltage over the

capacitor (un c) are the state variables and the voltage of the voltage source is the input variable.

Additional processing for initial time moment and time sample might be required.

We assume that a Matlab function with the following prototype exists:

function [u,y,tStart,ts]=si_read_file(file_name) (3)

The si_read_file function extracts from the file_name file the initial time moment (tStart) and the

time sample (ts) measured in seconds. It creates a vector u that contains the values of source voltage at

moments separated by ts seconds starting from tStart moment. In the same way the function

constructs a matrix of two columns for the state variables values.

The Model

A simple analysis starting from the equations of the circuit unveils the state space matrices transfer

functions of iL and uC. The state equations of the RLC series circuit have the following form:

tiCt

uL

C 1

d

d

teL

tiL

Rtu

Lt

iLC

L 11

d

d .

(4)

The state – space matrices have the structure:

. ,0

0 ,

10

01 ,1

0 ,

1

10

L

C

i

u

LL

R

L

C x DCBA

(5)

The voltage gain is

1

12

RCsLCssE

sUsA C . (6)

The driven point admittance has the following expression:

12

RCsLCs

sCsY (7)

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Hence, the model of the circuit is a linear one. In Matlab, a linear model should be described in a

.m file by a function with the following prototype:

function [A,B,C,D,K,X0]=rlc_lin(pars,Tsm,Auxarg) (8)

The prototype of the function is fixed and cannot be changed. In our example we will use only the

pars vector from the input variables list. In fact, pars would be a 3 component vector with the

structure [r, l, c] (r- the resistance of the resistor, l-the inductance of the inductor, c-the capacity of the

capacitor). The purpose of the method is to deduce these parameters.

The function should construct matrices A,B,C,D,K and X0 from parameters in the par vector:

r=pars(1);

l=pars(2);

c=pars(3);

A=[0 1/c; -1/l -r/l];

B=[0; 1/l];

C=[1 0;0 1];

D=zeros(2,1);

X0=zeros(2,1);

K=zeros(2,2);

Identifying the parameters

Considering the model description is ready leads us to the next step: the parameters estimation.

First of all, we need to construct an iddata object from our experimental dataset. This task is simple in

Matlab and can be done as in the example below:

[u,y,tStart,ts]=si_read_file(file_name);

z=iddata(y,u,ts);

z.Tstart=tStart;

In this example, z is the name of the iddata instance object, constructed from the data extracted by the

si_read_file function.

After creating the dataset, we have to create a idgrey object. Idgrey type describes a grey linear system

model in the System Identification Toolbox.

m=idgrey('rlc_lin',initial_vector,'c',[],'DisturbanceModel','None'); (9)

The first parameter is the name of the file that describes the model. initial_vector is a 3 component

vector of initial guesses for the parameters to be estimated. Due the fact that Matlab uses an iterative

algorithm to estimate the parameters this vector is necessary. The third parameter ('c') describes the

model as a continuous model. The next parameter in the list is a vector used in the rlc_lin model as

Auxarg. In our example is a void vector. Setting the disturbance model to none is optional (can be

forced through the state-space matrices structure).

Finally, invoking the pem method will estimate the parameters of the model using an iddata model.

pem(z,m);

A simple Matlab function for estimating the parameters of a RLC circuit is listed below:

function [rlc,m]=si_rlc_lin(file_name,initial_vector)

[u,y,tStart,ts]=si_read_file(file_name);

z=iddata(y,u,ts);

z.Tstart=tStart;

% additional processing of the iddata object could be inserted here

m=idgrey('rlc_lin',initial_vector,'c',[],'DisturbanceModel','None');

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% configuring the estimating algorithm

m.Algorithm.MaxIter=300;

m.Algorithm.Tolerance=0.0001;

m=pem(z,m);

% configuring the simulation algorithm

m.Algorithm.SimulationOptions.AbsTol = 1e-8;

m.Algorithm.SimulationOptions.RelTol = 1e-7;

rlc=m.ParameterVector;

end

The function above returns the vector containing the estimated values of the parameters (rlc) and

the idgrey model (m). A very useful function for comparing the estimated model with the initial

dataset is compare:

compare(z,m)

The function plots the simulated output and the measured output on separated graphics for each

output.

Compare could be used also as below:

[yh,fit,x0] = compare(z,m)

compare computes the output yh that results when the model m is simulated with the input u. The

result is plotted together with the corresponding measured output y. The percentage of the output

variation that is explained by the model

fit = 100*(1 - norm(yh - y)/norm(y-mean(y)))

is also computed and displayed. For multiple-output systems, this is done separately for each

output.[2]

4. Method analysis

The method described in this paper provides a fast way to reproduce a circuit from an

experimental dataset. However, it has some weaknesses.

Numerical stability

Take as example the estimation of the RLC circuit. In practice, the difference between the

resistance of the resistor and the capacity of the capacitor is huge. Therefore, the state space

matrices are ill-conditioned. For example, let r be 1000 ohms, l be 0.01H and c be 1.0e-9 F.

The A matrix has the structure:

L

R

L

C1

10

A .

(10)

The condition number of the A matrix is 1.0000e+07, a huge one.

This explains why the estimated parameters are not very accurate (in some cases far from the real

values). Sometimes, even the simulation of the model with real instead of estimated parameters

unveils unexpected differences compared to the experimental data.

For example, consider r is 50 ohms, l 0.1 H is, c 0.01 F is . The Matlab function provides the

following estimation: r - 59.76 ohms, l - 0.0655 H, c- 0.0097 F .

In Figure 1 is shown the estimated model output data.

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Fig. 2. Output data from a RLC circuit.

Fixing the parameter vector to the real values does not provide a better simulation:

Fig. 3. Output data from a RLC circuit for the real values of the circuit parameters.

In order to solve this problem it is recommended to implement your own parameter estimation

algorithm for specific ill-conditioned matrices.

Theoretical Method

There is always a difference between the theoretical behaviour and the real behaviour of a circuit.

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Therefore additional processing of the experimental dataset might be required in order to get the best

results.

Moreover, the values measured might not be accurate because the method used for gathering

experimental data could be improper.

5. Conclusions

Matlab System Identification Toolbox is a powerful tool that can provide a fast way to synthesis a

circuit from an experimental dataset, considering the structure of the circuit to be known. However,

due to numerical calculus problems, the method may fail to provide the best answer. The fact that

Matlab uses an iterative algorithm to estimate the parameters of the system transforms the procedure

into a fast one at the expense of numerical stability.

References

[1] - www.wikipedia.org.

[2] - Matlab product Help.

[3] - M. Iordache, Lucia Dumitriu, L. Mandache, “Time-Domain Modified Nodal Analysis for

Large-Scale Analog Circuits”, Revue Roum. Sci. Techn.- Électrotechn. et Énerg., Bucarest,

Tome 48, No. 2-3, Bucarest , 2003, pp. 257-268, RM-ISSN 0035-4066.

[4] - M. Iordache, Lucia Dumitriu, “Efficient Decomposition Techniques for Symbolic Analysis of

Large – Scale Analog Circuits by State Variable Method”, Analog Circuits and Signal

Processing, Kluwer, Vol. 40, No. 3, September 2004, Kluwer Academic Publishers, pp.235-

253, Springer Netherlands ISSN: 0925-1030 (Paper) 1573-1979 (Online).

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Rezolvarea numerică a circuitelor rezistive care conţin modele companion

Alexandru Gabriel GHEORGHE, Florin CONSTANTINESCU

Universitatea “Politehnica” din Bucureşti, Spl. Independenţei 313, 060042, Bucureşti; florin.constantinescu@lce.pub.ro

Abstract. Se propune rezolvarea în precizie long double a circuitului liniar care conţine modele companion. Acest algoritm, care da rezultate mai bune decât iteraţiile GMRES, a fost implementat într-un program de analiză tranzitorie care alege pasul de timp pe baza unor erori de bilanţ energetic. Sunt prezentate două exemple în care acest program dă rezultate mai bune decât SPICE.

1 Introducere

Răspunsul tranzitoriu al unui circuit neliniar este calculat folosind metode numerice ca Euler implicit, metoda trapezelor, sau metode de tip Gear. Aceste metode au fost dezvoltate pentru a calcula soluţia ecuaţiei de stare în forma normală ),( txfx =& , unde x este vectorul de stare. Cu toate acestea, nici un program comercial pentru analiza circuitelor nu foloseşte ecuaţiile de stare datorita calculelor laborioase necesare pentru a ajunge la forma lor normală. Toate simulatoarele de circuite cunoscute, care lucrează în domeniul timp utilizează modelele companion [1], care sunt circuite rezistive. Valoarea unor rezistenţe din aceste modele creşte odată cu creşterea pasului de timp h în timp ce valoarea altor rezistenţe scade odată cu creşterea lui h. Utilizarea altor metode numerice conduce la dependenţe similare ale valorilor rezistenţelor funcţie de h [1]. Din acest motiv, circuitul rezistiv care conţine modele companion conţine rezistenţe ale căror valori diferă cu câteva ordine de mărime. În cazul circuitelor RF, care conţin atât semnale purtătoare de frecvenţă înaltă şi semnale modulatoare de frecvenţă joasă, h trebuie să ia valori foarte mici, în scopul de a calcula detaliul de înaltă frecvenţă al răspunsului circuitului. De exemplu, în cazul în care h=10-10s poate fi obţinută o gamă largă de valori ale rezistenţelor (între 10-6Ω şi 107Ω). În acest caz trebuie să fie rezolvat un sistem de ecuaţii algebrice liniare care poate avea o matrice slab condiţionată. Contribuţia principală a acestui articol este legată de rezolvarea acestui sistem.

Parcurgerea unui pas de timp în analiza tranzitorie a unui circuit implică rezolvarea unui circuit rezistiv ai cărei parametri sunt calculaţi în funcţie de o anumită valoare a lui h, urmată de calcularea unei erori şi o decizie de a accepta sau respinge valoarea presupusă pentru h. Trei tipuri de erori sunt cunoscute pentru a estima corectitudinea valorii lui h; aceste erori sunt prezentate în secţiunea 2. Secţiunea 3 se referă la rezolvarea sistemelor liniare cu matrice slab condiţionate şi include abordarea noastră. Două exemple sunt prezentate în secţiunea 4, în timp ce secţiunea 5 conţine concluziile.

2 Erori utilizate în analiza tranzitorie

Valoarea pasului de timp în analiza tranzitorie a circuitelor electrice este aleasă în funcţie de anumite erori. Trei tipuri de erori sunt utilizate în analiza tranzitorie a circuitelor. Prima dintre ele este eroarea locala de trunchiere (LTE), care este utilizată în simulatoarele de circuite de tip SPICE (SPICE, PSPICE, HSPICE, SPECTRE, SPECTRE RF). Atât LTE a fiecărei variabile de stare cât şi LTE a derivatei sale sunt utilizate. LTE este estimata în cel mai rău caz corespunzător unei erori relative şi unei erori absolute. De exemplu, eroarea derivatei în raport cu timpul al unei variabile de stare este:

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annrx

xx εεε +⎟⎠

⎞⎜⎝

⎛⋅=•

+

•

• ,max 1 (1)

în care 1+

•

nx este curentul printr-un condensator sau tensiunea pe o bobină. O eroare similară este definită pentru 1+nx . Acest algoritm pentru calculul pasului de timp include o procedură de tipul “cut and try” [1].

Un alt algoritm pentru alegerea pasului de timp, bazat pe o eroare de tip energetic, este propusă în [3]. Energia acumulată de către un condensator neliniar controlat în sarcină cu ecuaţia constitutivă )(ˆ qvv = în pasul de timp [tj, tj+1] poate fi calculată exact astfel:

dqqvvdtdtdqEE

j

j

j

j

q

q

t

tjj )(ˆ

11

1 ∫∫++

==−+ (2)

unde q este sarcina condensatorului, qj este sarcina condensatorului la tj şi qj+1 este sarcina condensatorului la tj+1. Pentru acest condensator, bilanţul energetic la acest pas de timp este diferenţa dintre energia acumulată şi energia furnizată de circuit condensatorului:

( ) ( )∫+

−−=Δ +

1

1

j

j

t

tjj dviEEE τττ (3)

unde i este curentul prin condensator. Dacă 0≠ΔE , algoritmul de integrare oferă o estimare eronată a soluţiei. În timp ce energia

acumulată depinde numai de qj şi de qj+1, energia transferată de circuit condensatorului depinde şi de funcţiile ( )τi şi ( )τv .

Un algoritm pentru calculul pasului de timp bazat de controlul lui EΔ este dezvoltat în [3]. Valoarea maximă permisă pentru 1+Δ jE în intervalul de timp [tj, tj+1] este calculată într-un mod similar cu (1).

Bilanţul energetic pentru un pas de timp poate fi calculat luând în considerare energiile acumulate de către toate elementele dinamice şi energiile absorbite de rezistenţe şi surse:

( ) ( )∫ ⋅=h

SR dttituE0

, (4)

Eroarea absolută de bilanţ energetic este definită ca: ∑=

=Δn

kka EE

1

(5)

şi eroarea relativă de bilanţ energetic este definită ca:

∑=

Δ=Δ

n

kk

ar

E

EE

1

2

(6)

unde n este numărul elementelor de circuit incluzând sursele. Pasul de timp este ales calculând rEΔ şi presupusul pas de timp este acceptat dacă

EEREr ≤Δ , unde EER este limita impusă a erorii relative de bilanţ energetic. Algoritmul pentru alegerea pasului de timp poate fi prezentat după cum urmează [4]:

nnn htt +=+1 rezolvă pentru 1+nt

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calculează rEΔ dacă 10EEREr <Δ

acceptă 1+nt

nn hh ⋅=+ 5.11 ( )TMAXhh nn ,min 11 ++ =

continuă altfel dacă EEREEER r <Δ<10

acceptă 1+nt nn hh =+1

continuă altfel dacă EEREr >Δ

respingă 1+nt 5.11 nn hh =+

dacă min1 Hhn <+ afişează TIME STEP TOO SMALL; analiza este întreruptă Acest algoritm permite un calcul simplu al estimării globale a corectitudinii analizei tranzitorii

pentru tot circuitul şi pentru întreg intervalul de timp (de la tstart la tstop). Este calculată eroarea globală ∑Δ=Δ atotal EE , unde aEΔ este dată de (5), iar suma este luată în considerare pentru toţi paşii acceptaţi.

3 Rezolvarea sistemelor liniare care au matricea slab condiţionată

Se consideră sistemul liniar Ax=b corespunzător circuitului rezistiv care conţine modele companion. Acest sistem poate fi rezolvat, de exemplu, folosind descompunerea LU. În cazul în care pasul de timp utilizat pentru integrarea ecuaţiilor circuitului este foarte mic, valorile numerice din această matrice diferă cu câteva ordine de mărime iar matricea sistemului poate deveni slab condiţionată. Acest lucru introduce erori în calculul soluţiei sistemului. Din acest motiv s-au dezvoltat metode iterative pentru îmbunătăţirea soluţiei, cea mai cunoscută şi utilizată fiind GMRES [10]. Pe scurt algoritmul acestei metode este următorul:

calculează reziduul xAbr ⋅−= rezolvă rdA =⋅ actualizează soluţia dxx +=

până când “r” este suficient de mic sau s-a atins numărul maxim de iteraţii. Acest algoritm funcţionează bine până la un punct. Dacă numărul de condiţie este foarte mare,

reziduul nu este înrăutăţit în schimb soluţia x, deşi este de aşteptat să fie îmbunătăţită prin acest procedeu, frecvent este înrăutăţită [8].

Pentru a estima corectitudinea soluţie acestui sistem liniar, următoarele erori ale bilanţului de puteri, sunt utilizate:

- eroarea absolută a bilanţului de puteri: ∑=

=Δn

kkabs PP

1 (7)

- eroarea relativă a bilanţului de puteri:( )∑

=

=Δn

kk

absrel

P

PP

1

2

(8)

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Se pare că folosind o precizie mai mare în calcul se obţine o soluţie mai bună chiar şi fără iteraţii GMRES, într-un timp mai scurt. Abordarea noastră este de a folosi precizie long double în calcul pentru rezolvarea circuitelor rezistive care conţin modele companion. Două exemple prezentate mai jos arată că abordarea noastră dă rezultate mai bune decât SPICE, care utilizează o pivotare parţială, combinată cu criteriul Markowitz pentru număr minim de umpleri.

4 Exemple

Descompunerea LU pentru rezolvarea sistemului liniar care apare în analiza tranzitorie a fost implementată într-un program folosind algoritmul de alegere a pasului de timp din [4].

Primul exemplu conţine un element neliniar şi o latură rezonantă (Fig. 1 a). Sursa este un semnal sinusoidal de 1 MHz, frecvenţa de rezonanţă a laturei RLC fiind 100 MHz. Elementul neliniar este o diodă modelată cu o rezistenţă PWL în serie cu o sursă de tensiune (Fig. 1 b).

Fig. 1 a. Circuitul nelinear Fig. 1 b. Rezistenta neliniara

Detaliul tensiunii pe bobină dat în fig. 2 arată diferenţa dintre soluţia obţinută cu precizie

double şi soluţia obţinută cu precizie long double

Fig. 2. Tensiunea pe bobina Utilizând precizia double, cu sau fără GMRES, eroarea relativă a bilanţului de puteri este

aproape aceeaşi. Acelaşi lucru poate fi observat şi pentru eroarea absolută a bilanţului de puteri. Tabel 1

precizia GMRES maxrelPΔ maxabsPΔ CPU time double da 5.5E-5 2E-9 0.54s

long double nu 1.7E-8 1.05E-12 0.43s Dacă în loc de precizie double folosim precizia long double pentru rezolvarea sistemului, atât

eroarea absolută a bilanţului de puteri cât şi eroarea relativă a bilanţului de puteri, sunt semnificativ îmbunătăţite chiar şi fără GMRES. Rezultatele sunt prezentate pe scurt în Tabelul 1.Se poate

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observa că folosind precizia double nu se pot atinge erorile de la long double indiferent cat de multe iteraţii GMRES se fac (chiar şi 100). Folosind precizia long double soluţia corectă se obţine într-un timp mai scurt decât folosind precizia double şi iteraţii GMRES.

Al doilea exemplu este un filtru trece bandă construit cu două rezonatoare BAW şi a fost analizat cu SPICE şi cu algoritmul propus. Un model de circuit neliniar având elemente cu neliniarităţi polinomiale în latura de mişcare [7] este folosit pentru fiecare rezonator (Fig. 3). Acest circuit este alimentat cu un semnal sinusoidal de 2.025 GHz (frecvenţa de rezonanţă serie a primului rezonator).

Pentru latura de mişcare a primului rezonator s-au folosit următoarele elemente neliniare: ( ) ( )3

12

1111 65.055.056.4 RmRmRmRmRm ieieiiu ⋅−+⋅−+⋅= ( ) ( )3

12

1111 5135991.69 LmLmLmLmLm ieieiei ⋅−+⋅−+⋅−=ϕ ( ) ( )3

12

1111 106861529.88 CmCmCmCmCm ueueueuq ⋅−+⋅−+⋅−= iar pentru latura de mişcare a celui de al doilea rezonator:

( ) ( )32

22222 65.055.056.4 RmRmRmRmRm ieieiiu ⋅−+⋅−+⋅=

( ) ( )32

22222 5135970 LmLmLmLmLm ieieiei ⋅−+⋅−+⋅−=ϕ

( ) ( )32

22222 1068615166.93 CmCmCmCmCm ueueueuq ⋅−+⋅−+⋅−=

Fig. 3. Filtru trece bandă

Fig. 4. Tensiunea de ieşire a filtrului trece bandă

După parcurgerea a 100 de perioade ale sursei de alimentare, tensiunea de ieşire V(2) calculată cu algoritmul propus este identică cu soluţia SPICE (Fig. 4).

Erorile impuse în cei doi algoritmi au fost alese astfel încât numărul de paşi acceptaţi să fie similar. Folosind aceeaşi metodă numerică pentru integrarea ecuaţiilor circuitului (metoda trapezelor), s-au obţinut forme de undă similare aşa cum era de aşteptat. Rezultatele V(2) obţinute cu cei doi algoritmi au proprietăţile din Tabelul 2.

Tabel 2 erorile impuse paşi acceptaţi paşi respinşi totalEΔ CPU time propus EER=9E-5 7863 448 3.906E-15 0.25s SPICE reltol=5.5E-6 7816 3031 1.04E-14 0.32s

Rezultă că, pentru valori similare ale erorii globale totalEΔ , algoritmul propus este mai bun din

punctul de vedere al numarului paşilor respinşi şi al timpului de calcul Este interesant de observat evoluţia erorii relative de bilanţ energetic pentru soluţia SPICE şi de comparat cu eroarea relativă de bilanţ energetic calculată pentru algoritmul propus (Fig. 5). Evoluţia pasului de timp pentru SPICE şi pentru algoritmul propus este dată în Fig. 6.

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Fig. 5. Eroarea relativă de bilanţ energetic pentru

soluţia SPICE şi soluţia algoritmului propus

Fig. 6. Evoluţia pasului de timp pentru SPICE şi

pentru algoritmul propus

5 Concluzii

S-a arătat că analiza tranzitorie a circuitelor de RF poate duce la sistemele de ecuaţii liniare slab condiţionate. Soluţiile acestora sunt calculate cu erori, chiar dacă sunt utilizate iteraţii GMRES. Calculul acestor soluţii fără iteraţii GMRES folosind precizie long double conduce la soluţii mai precise decât cele corespunzătoare iteraţiilor GMRES folosind precizie double. Mai mult decât atât, în primul caz este necesar un timp de calcul mai scurt.

Acest algoritm a fost implementat într-un program de analiză tranzitorie care alege pasul de timp pe baza unor erori de bilanţ energetic. Au fost prezentate două exemple pentru care acest program oferă rezultate mai bune decât SPICE.

Autorii doresc să mulţumească prof. univ. Angelo Brambilla de la Politecnico di Milano şi prof. univ. Mihai Iordache de la Universitatea Politehnica Bucureşti, pentru discuţiile utile.

Referinţe [1] L. W. Nagel, SPICE2: A computer program to simulate semiconductor circuits, Memorandum No.

UCB/ERL M520, 1975. [2] L. O. Chua, P. M.Lin, Computer aided analysis of electronic circuits, Prentice Hall, 1975. [3] A. Brambilla, D. A’Amore, Energy-Based Control of Numerical Errors in Time-Domain Simulation

of Dynamic Circuits, IEEE Transactions on Circuits And Systems – I: Fundamental Theory And Applications, Vol. 48, No.5, May 2001.

[4] F. Constantinescu, A. G. Gheorghe, M. Nitescu, A time step choice algorithm for transient analysis of circuits, Proceedings of AFRICON 2009, September 23-26 2009, Nairobi, Kenya.

[5] A. Brambilla, Private communication, March 2007. [6] F. Constantinescu, A. G. Gheorghe, M. Nitescu, Large signal analysis of RF circuits – an overview,

Proceedings of ATEE 2006. [7] F. Constantinescu, A. G. Gheorghe, M. Nitescu, “New Circuit Models of Power BAW Resonators”,

Revue Roumaine des Sciences Technique – Electrotechnique et Energetique, no.1, 2008 [8] Y. Saad and M. H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Non-

symmetric Linear Systems, SIAM J. Sci. Stat. Comput., Vol. 7, No. 3, July 1986 [9] X. S. Li, J. W. Demmel, D. H. Bailey, Greg Henry, et.al, Design, Implementation and Testing of

Extended and Mixed Precision BLAS, October 20, 2000, http://repositories.cdlib.org/lbnl/LBNL-45991

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Test Frequency Selection in Fault Dictionary Appoach

Marin Constantin Viorel, Gheorghe Alexandru University Politehnica Bucharest

Abstract. The paper proposes an efficient method for selecting the frequencies of sinusoidal test signals based on the analysis of linear analog circuit sensitivitaties in fault dictionary approach Key words: analog fault diagnosis, fault dictionary, frequency selection

1 Introduction

Modern analog circuit tehnologies developed new circuits of high complexity. The cast resin tehnologies, makes the embedded elements of circuits inaccessible for direct measurement. Consequently, a great interest present diagnostic techniques and isolation of faults of analog circuits that do not need direct access to individual elements of the circuit. Some of these techniques are based on the concept of simulation of faults, called simulation before test (SBT), which leads to the generation of faults dictionaries [1-9]. In this approach, the values of the various components are changed so as to simulate the failure of components and nodes voltages are calculated. Simulation results are then used to achieve fault dictionaries used for diagnosing circuit faults. The main disadvantage of this approach is the large number of circuit simulations required to consider all possible failures of components. An important advantage of the method is that it can be used in any field (time, frequency or parametric) and for any circuit, linear or nonlinear. Recent works [1-3] deal with STB techniques in diagnosing faults in analog circuits. Papers [2-3] propose new methods based on analysis of linear analog circuits for selecting the frequencies of sinusoidal test signals. Another approach in analog fault diagnosis is the simulation of circuits, called simulation after test (SAT). The results of measurements, together with circuit topology and nominal values of components, considered known, are used in a computer program to determine the actual values of circuit elements. The components whose values overpass the tolerance limits imposed by design are considered faulty. So, the faulty components are then identified and located by comparison with their nominal values. The papers [4, 5, 6] propose methods to improve the selection of the set of test points for hard single faults diagnosis in fault dictionary approach. In [4, 5] is proposed the entropy index method to select the test points used to build the fault dictionary. The paper [7] use a global sensitivity approach carried out by randomised algorithms. The papers [8, 9] proposes methods for test frequency selection in hard single fault diagnosis. The paper [8] proposes an evolutionary method that uses entropy index to define a fitness function and employs genetic programming. The paper [9] proposes a metod based on simulated annealing with fuzzy objective function. The paper [10] proposes an exclusive method whose basic idea is to delete the frequency that correspond to the ambiguity set that contains the largest number of faults. Analog fault diagnosis is an important method for improving manufacturing technologies of integrated circuits. The present paper proposes a new method for selecting the frequencies of sinusoidal test signals based on the analysis of linear analog circuit sensitivities in fault dictionary techniques and entropy criterion.

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2 Fault dictionary for parametric faults (soft faults)

Soft or parametric faults are defined as a variation of parameter values of components that lead to abnormal functioning of the circuit. In paper [5], soft faults are considered as components whose parameter values are greater or less than their nominal values with an order of magnitude. In paper [7], soft faults are defined as components whose parameter values varition produce inacceptable loss of performance characteristics of the circuit under test (CUT). For example, in the case of a filter, the criterion for soft faults is considered as the varition of components values that produces a variation of the cutt-off frequency, from the nominal value, by more than 20 %. Soft or parametric faults have a continuous nature and a complete fault dictionary containing all possible faults obviously can not be generated. Fault analog diagnosis in the SBT approach [7] containes the following steps: 1. identification of the test nodes with the highest level of observability of the CUT; 2. selection of the most suitable test stimuli able to excite CUT so that the effect of fault can spread to a noticeable test node; 3. selection of a set of CUT specific characteristics, which may be revealed from measured signals at test nodes, so that faults can be identified (eg amplitudes and phases of voltages at the test nodes, the amplitudes and phases of currents at the test nodes), 4. the realization of fault dictionary, that stores the circuit behavior patterns corresponding to a list of faults, including the no fault case; 5. the realization of the classifier that uses the information contained in the fault dictionary in purpose to identify and locate faults. Identifying the most efficient test nodes and the input test stimuli selection, are two important steps to achieve a fault dictionary, able to solve the problem of analog fault diagnosis in a reasonable time. In order to optimize the fault dictionary, the following criteria has to be considered: - reducing the number of test nodes, because each of them requires measurements; - selection of characteristics to be extracted taking into account the impact on the volume of calculation determined by extraction algorithms; - selection of input stimuli considering the cost for each entry.

3 The sensitivity analysis

The sensitivity analysis can be used to assess the ability of a stimulus to highlight a fault, by the spread of its effect to the test node. This capacity depends on type of stimulus, the location and typology of the fault, the circuit topology and selected test nodes. The sensitivity analysis could be used for the selection of test set of sinusoidal stimuli of different frequencies with the highest efficiency. Information obtained through sensitivity analysis can be used to identify test stimuli and test nodes. The algorithm determines the following elements: - the fault list, that containes the set of potential faulty components, which may alter CUT characteristics; - the variations of CUT parameter for every item in the fault list; - sensitivity functions to be evaluated for each output considered parameter; - the curves of sensitivity versus frequency, corresponding to a specific fault. For the optimum test frequency range determination, two heuristic rules could be employed [1, 3]: 1. the larger the sensitivity , the higher the detectability; 2. the more different the sensitivity, the higher the detectability. The detectability is defined as the measure of capacity to identify and locate the fault. The two rules are the intuitive concept that gives the possibility

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to distinguish faults, if the sensitivities present a different behavior from other. The sensitivity analysis can determine the optimum frequency ranges, but can not indicate the optimum frequencies. The present paper proposes a new method for the selection of optimum test frequencies based on Shannon information theory [9]. The entropy is determined with the formula:

)1(log)( 21

i

N

ii pppH ∑

=

= (1)

Where the probability p is the vector ),...,,( 11 Nppp and the entropy )( pH is measured in bits. Another name for the entropy H of a discrete random variable X is the uncertainty of X because the entropy is a measure of the amount of uncertainty associated with the value of X. The paper deals with the selection of the frequencies that could identify univoquely the faults. The minimization of the entropy is used as a criterion to select the measurements that contain the least amount of uncertainty. In the ideal case, the measurements at a single frequency are different for every fault, so all the faults are univoquely identified, the probabilities for every fault are 1 and as a consequence the entropy is null. This event is rarely achieved. Usually, several frequencies have to be employed. If an inclusive algorithm is used, the frequency that corresponds to the minimum entropy is added. The stop test is null entropy value or two equal consecutive entropy values. If an exclusive algorithm is used, the frequency that corresponds to the maximum entropy is excluded.

4 Example

The circuit presented in figure 1 is used in the paper order to exemplify the method. The circuit represents a Biquad filter which was described and analyzed with different methods in reference papers [1, 3]. The faults [5] are considered as components whose parameter values are greater or less than their nominal values with one order of magnitude.

Figure 1: The circuit under test

The problem is to determine the fault dictionary of this circuit.

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The nominal values are: Ω===== kRRRRR 1054321 , Ω== kRR 10076 , nFCC 121 == and the tolerances are 2% for resistences and 5% for capacitors. For the CUT

there are identified seven fault classes including three ambiguity groups [7]: class1: R6, R7 faulty; class2: R3, C1 faulty; class3: R4, C2 faulty; class4: R5 faulty; class5: R2 faulty; class6 R1 faulty; class7 no faulty component (fault-free condition). CUT is simulated with the program SAPWIN and result the circuit network function )(sH . Potentially faulty components are given in symbolic form. The network function coefficients are introduced in program MAPLE and the module or phase of the network function are determined. Starting from the network function )(sH , and replaceing the complex frequencies wjs ⋅= , the frequency dependent network function is:

)()()( wjBwAjwH += (2) the module (3) and phase (4) functions are:

)()()( 22 wBwAjwH += (3) )()(()( wAwBarctgw =ϕ (4)

The senzitivity vs. frequency is determined for each component from the fault list. The sensitivity functions used in the paper are the derivatives of network function module in symbolic form, for each parameter potential faulty. The optimum frequency range is chosen employing the two heuristic rules presented in the third part (senzitivity magnitude criterion).

Figure 2: a. The sensitivities 1CMS and 2C

MS vs. frequency; b. 1CMS - 2C

MS vs. frequency;

For example, there are presented in figure 2a the sensitivities of 11 dCdMS C

M = and

22 dCdMS C

M = vs. frequency and in figure 2b 1CMS - 2C

MS vs. frequency. Employing the senzitivity magnitude criterion, it results that the optimum frequency range is approximately

kHzfopt )355( ÷∈ .

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5 Results

The CUT was excited with the input stimulus sinusoidal of 4 V [6] voltage and the test frequencies were chosen heuristically liniarely spatiated in the predetermined optimum range

7,,2,1,5* L== kkHzkfk . The faults in fault list were simulated with program Spice and the corresponding values of voltiges were determined for the exit node N8. The blind range due to tolerances from nominal values of the circuit elements can be determined by Monte-Carlo simulation [5, 6, 7]. In the paper the blind ranges were determined for the worst case with program Spice and result the maximum deviation DY for every preselected frequency (Tabel 1).

Tabel 1 NODE N8 Frequency

[kHz] DY [V] Ymax [%]

5

.2289

105.82

10

.3498

109.8

15

.3517

112.47

20

.3081

115.19

25

.2523

117.51

30

.1961

118.68

35

.1525

119.29

Faults/AS AS1,i AS2,i AS3,i AS4,i AS5,i AS6,i AS7,i F0 S1,1 S2,1 S3,1 S4,1 S5,1 S6,1 S7,1

F1(R1*10) S1,2 S2,2 S3,2 S4,2 S5,2 S6,2 S7,2 F2(R1/10) S1,3 S2,3 S3,3 S4,3 S5,3 S6,3 S7,3 F3(R2*10) S1,1 S2,1 S3,1 S4,4 S5,4 S6,4 S7,4 F4(R2/10) S1.4 S2,4 S3,2 S4,2 S5,2 S6,2 S7,2 F5(R3*10) S1,5 S2,5 S3,2 S4,2 S5,2 S6,2 S7,2 F6(R3/10) S1,1 S2,6 S3,4 S4,1 S5,1 S6,5 S7,5 F7(R4*10) S1,6 S2,2 S3,2 S4,2 S5,2 S6,2 S7,2 F8(R4/10) S1,10 S2,7 S3,5 S4,5 S5,5 S6,6 S7,6 F9(C1*10) S1,5 S2,5 S3,2 S4,2 S5,2 S6,2 S7,2 F10(C1/10) S1,1 S2,6 S3,4 S4,1 S5,1 S6,5 S7,5 F11(C2*10) S1,6 S2,2 S3,2 S4,2 S5,2 S6,2 S7,2 F12(C2/10) S1,10 S2,7 S3,5 S4,5 S5,5 S6,6 S7,6 F13(R5*10) S1,7 S2,8 S3,1 S4,1 S5,1 S6,1 S7,1 F14 (R5/10) S1,2 S2,2 S3,2 S4,2 S5,2 S6,2 S7,7 F15(R6*10 ) S1,8 S2,9 S3,6 S4,6 S5,6 S6,5 S7,8 F16(R6/10 ) S1,9 S2,10 S3,7 S4,7 S5,7 S6,7 S7,9 F17(R7*10) S1,9 S2,10 S3,7 S4,7 S5,7 S6,7 S7,9 F18(R7/10) S1,8 S2,9 S3,6 S4,6 S5,6 S6,5 S7,8

H

6.569 6.933 4.985 -------

5.995 --------- --------- ---------

7.711 6.933 5.974 5.559

7.659 6.792 5.974 5.559

7.659 6.792 5.974 5.559

7.134 6.183 5.974 5.559

6.569 5.621 -------- --------

The calculus presents a bigger sensitivity if applied to every frequency. If the difference between two values measured at the same frequency is smaller than the maximum deviation DY, the corresponding faults are contained in the same ambiguity set (AS). If the difference between several consecutive values, measured at the same frequency is smaller than DY, the corresponding faults form a chain of faults and are contained in the same ambiguity set (AS), despite the fact that the difference between nonconsecutive links of the chain could be larger than DY. If a medium fault of the chain is eliminated, the remained ones could cease to belong to the same ambiguity set. This is why the ambiguity sets and the fault codes have to be refreshed after every step of the algorithm. As a consequence, the redundant measurements are avoided.

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Considering the hypothesis of equiprobability, for the events contained in an ambiguity set, the probability ip is equal with the ratio between the number of of the events contained in the ambiguity set and the number of faults. The single events that can univoquily identify a fault, have the value of certitude, the probability ip is equal with 1 and the entropy is null. Analyzing quickly the values in the table of faults, it can be observed that the values of the following pairs are the same F5, F9, F6, F10, F7, F11, F8, F12, F15, F18, F16, F17. As o conclusion, those faults form groups of ambiguity and is very probable that they can not be uniquovably identified. The frequency 10 kHz present the lowest entropy and is chosen first. Three faults F2 S2,3, F4 S2,4 and F13 S2,8 are uniqly identified. The remained 16 faults are gathered in seven ambiguity sets: S2,1=F0, F3, S2,2=F1, F7, F11, F14, S2,5=F5, F9, S2,6=F6, F10, S2,7=F8, F12, S2,9=F15, F18, S2,10=F16, F17. The identified faults, F2, F4 and F13 are erased from the coded table, the new number of faults is 16 and the result is presented in Table 1. The second chosen frequency is 35 kHz. There are uniquely identified the faults: F0 S2,1; S7,1, F3 S2,1; S7,4 and F14 S2,2; S7,7. For measurements at frequencies 10 kHz and 35 kHz , the remained 13 faults form the following six ambiguity sets: (S2,2; S7,2) = F1, F7, F11, (S2,5; S7,2)=F5, F9, (S2,6; S7,5) =F6, F10, (S2,7; S7,6)=F8, F12, (S2,9; S7,8)=F15, F18, (S2,10; S7,9)=F16, F17. The identified faults F0, F3 and F14 are erased from the coded table, for f =5 kHz the remained ambiguity set S1,1 splits in two S1,1 =F6, F10 and S1,10= F8, F12, the new number of faults is 14 and the result is presented in Table 1. The third chosen frequency is 5 kHz. The fault F1 (S2,2; S7,2; S1,2) is uniquely identified. For measurements at frequencies 10 kHz , 35 kHz and 5 kHz, the remained 12 faults are grouped in the following six ambiguity sets: (S2,2; S7,2; S1.6) = F7, F11, (S2,5; S7,2;S1,5)=F5, F9, (S2,6; S7,5;S1,1) =F6, F10, (S2,7; S7,6;S1,10)=F8, F12, (S2,9; S7,8; S1,8)=F15, F18, (S2,10; S7,9; S1,9)=F16, F17. Because no further fault is eliminated from the coded table, the values of entropy remain unchanged for the frequencies 15, 20, 25 and 30 kHz. The stop test of the algorithm is achieved. Twelve faults, grouped into six sets of ambiguity that represents canonical ambiguity groups can not be identified unequivocally. There is possible to identify only the ambiguity groups they belong to. In the presented example, faults are unequivocally identified through simulations at three frequencies that are determined in four iterrations. In reference paper [1], that uses a global sensitivity approach and randomised algorithms to solve the same problem, there are selected seven test frequencies from the neighborhood of cut-off frequency ( kHzf offcut 9,15=− ). In reference paper [7], that uses fuzzy fitness function to solve the same problem, there are employed three frequencies too, but a number of 460 iterrations are performed. 5. conclusions 1. The paper proposes an efficient method for selecting the optimal frequencies of sinusoidal test signals based on the sensitivity analysis and entropy criterion for linear analog circuits 2. In the presented example, faults are unequivocally identified employing less test frequencies and less number of iterrations than the reference methods. 3. The method identifies quickly, in a simple manner, the groups of ambiguity, if the algorithm stop test is achieved but the value of entropy is not null.

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References [1] M. Catelani, A. Fort, Soft Fault Detection and Isolation in Analog Circuits: Some results and a comparison between a fuzzy approach and radial basis function networks, IEEE Transaction on Instrumentation and Measurement, vol. 51, no. 2, pp. 196-202, April 2002. [2] C. Alippi, M. Catelani, A. Fort, M. Mugmaini, Automatic Selection of Test Frequencies for the diagnosis of Soft Faults in Analog Circuits, Proc. IEEE Transaction on Instrumentation and Measurement Technol. Conf., vol. 2, pp. 1503-1508, 2002. [3] C. Alippi, M. Catelani, A. Fort, M. Mugnaini, Automated Selection of Test Frequencies for Fault Diagnosis in Analog Electronic Circuits, IEEE Transaction on Instrumentation and Measurement, vol. 54, no. 3, pp. 1033-1044 June 2005. [4] V. C. Prasad, N. S. C. Babu, Selection of test nodes for analog fault diagnosis in dictionary approach, IEEE Transactions on Instrumentation and Measurement, vol. 49, pp. 1289–1297, Dec. 2000. [5] Liu, Zhi-Hong, Mixed-signal testing of integrated analog circuits and modules, A Dissertation Presented to The Faculty of the College of Engineering and Technology, Ohio University, In Partial Fulfillment of the Requirement for the Degree Doctor of Philosophy, March, 1999, http://www.ohiolink.edu/etd/send-pdf.cgi/Liu%20ZhiHong.pdf?ohiou1181174339 [6] J. A. Starzyk, D. Liu, Z.-H. Liu, D. E. Nelson, J. O. Rutkowski, Entropy-Based Optimum Test Pointss Selection for Analog Fault Dictionary Techniqes, IEEE Transactions on Instrumentation and Measurement, Vol. 53, No. 3, pp. 754–761, June 2004. [7] C. Alippi, M. Catelani, A. Fort, M. Mugnaini, SBT Soft Fault Diagnosis in Analog Electronic Circuits: A Sensitivity-Based Approach by Randomised Algorithms, IEEE Transactions on Instrumentaton and Measurement, Vol. 51, No. 5, pp. 1116–1125, October 2002. [8] Golonek T., Grzechca D., Rutkowski J., Evolutionary Method for Test Frequencies Selection Based on Entropy Index and Ambiguity Sets, ICSES 2006, International Conference on Signals and Electronic System, Łódź, Poland 2006. [9] Grzechca D., Golonek T., Rutkowski J., The Use of Simulated Annealing with Fuzzy Objective Function to Optimal Frequency Selection for Analog Circuit Diagnosis, 14th IEEE International Conference on Electronics, Circuits and Systems (ICECS2007), 11-14 December 2007, Marrakech, Morocco , pp. 899–902, 1-4244-1378-8/07/2007 IEEE. [10] David J. C. MacKay. Information Theory, Inference, and Learning Algorithms Cambridge: Cambridge University Press, 2003. ISBN 0-521-64298-1. Acknowledgments - This paper was supported by grant New Methods In Analog Fault Diagnosis, code project ID_1698, contract nr. 683/2009 with addendum nr. 1/2009, from the National Council for Scientific Research of Higher Education (CNCSIS) - UEFISCSU.

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Estimation of the Measurement Uncertainties in the Control

Loop of Active Filters. Part I.

Ana-Maria DUMITRESCU, Melania NAUMOF, Razvan MAGUREANU, Mihaela ALBU, Universitatea Politehnica din Bucuresti, 313 Splaiul Independentei,Bucuresti, Romania;albu@ieee.org

Abstract. Active filters represent a common solution for improving power quality in

distribution networks. The nowadays philosophy of active distribution grids imposes new

requirements for active filters considering that the grid parameters and energy flow can

dramatically change in time. In the paper recommendations for a more efficient filter design

are presented together with a presentation of the main measurment equipment used for the

proposed solution.

1 Introduction

Distortions of the current waveform are generated by non-linear loads, such as switching power

supplies and motor speed controllers, and are often encountered in today’s power systems.

These harmonics interfere with sensitive electronic equipment and cause unnecessary losses in

electrical equipment. An active power filter uses a switching inverter to produce harmonic

compensating currents. It is only with the recent advances in semiconductor technology that

high-speed, high-power switching devices suitable for designing active power filters have

become available. Applying the appropriate control algorithm and choosing the current and

voltage sensors represent the most important means of achieving optimal solutions. Best

experimental cases show that the Total Harmonic Distortion (THD) of the current waveform,

after compensation, cannot be lower than 3.5%, and many cases are exhibiting THD values

larger than 5%, which is beyond the acceptable values set by IEC recommendations [1].

The paper aims to present sources of uncertainties that occur at designing an active power filter

and also an algorithm for reducing those uncertainties.

A shunt active filter connected to a non-linear load is presented in Fig.1. For signal and data

acquisition a dSpace platform was used [2]. Load and filter currents, voltages on the supply side

and on the DC capacitor are measured and then supplied to the digital control. A Phase Lock

Loop (PLL) module and a PWM unit are used in order to obtain the control signals for the

inverter drives. Using the model of the active filter, the following components have to be

considered: the A/D converters and D/A converter, current and voltage sensors, the PWM unit

and its working frequency and the PLL module.

2 Description of the Shunt Active Filter

An active filter used for power quality improvements can be implemented in various ways. One

possible solution is indicated in Fig. 1. The d-q approach is the most suitable for high performance

results. Presently, the European Norms specify a maximal limit of the THD for currents and

voltages [1].

The active filter used for the purposes of this paper is based on an 50kVA IGBT inverter, working

with a PWM unit at 5 kHz [3]. The nonlinear load in this case is a thyristor rectifier bridge (control

angle close to 90 degrees) with RL load on the DC side. The system control is implemented in

dSpace environment as a standard way for controlling all measured voltages and currents, obtained

at the output of LEM current and voltage transducers. For correcting the current waveforms

LcLbLa iii ,, a quasi-sinusoidal voltage is used through the schematics of Fig. 1. In order to generate

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the reference for the current controllers the first phase of the supply voltage is used as input for the

PLL unit.

a)

b)

Figure 1. Basic current harmonic compensation scheme using an Active Parallel Filter

a) power diagram; b) control diagram

3 Description of the transducers

The LEM transducers are usually small semiconductor chips, with current input and voltage output

electrodes on opposite edges, placed in a magnetic field with the flux normal to the surface, are

based on Hall effect and allow to get insulated information (Fig. 2). The closed-loop transducer,

also called compensation or zero-flux transducer has an integrated compensation circuit in which

the overall performance is improved over that of an uncompensated Hall sensor. The output

current is shunted through a measuring resistance to develop the output voltage. The range in value

of this resistor is constrained by several factors. The value of the measuring resistance must be

within the range shown in the Hall Effect sensor data sheet: between the minRM resistance

(determined by power dissipation), and the maxRM resistance. maxRM is defined to avoid the

electronic saturation of the circuit, taking into account the minimum available supply voltage

which determines the maximum measuring range [4].

In [5-7] a simplified approach of considering LEM transducers as being linear systems is

presented. The non-linearity error of a transducer is generally considered as the maximum

deviation of its output from the output of an ideal linear instrument. The metrological

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characterization of a transducer leads to a properly frequency response from the transducer, also

being a way of compensating its errors, by using the FFT and multiplication in frequency domain

[8]. The systematic effect of uncertainties within the measured output of a LEM transducer is to be

found in frequency variation, temperature and excitation level. If the calibration of the LEM

transducers is made over a range of different voltages and currents, a curve of error against

excitation level will be obtained, and the slope of that curve represents a component of the overall

uncertainty. The change in uncertainty due to the change of frequency is the same for a voltage

transducer as a change of same percentage in voltage level. For current transducer, the change in

frequency is the same for the same percentage change in total burden, which represents the

impedance equal to externally connected burden plus the internal resistance and leakage reactance

of the secondary winding [9].

Concerning the current transducers, their accuracy is expressed as maximal uncertainty at rated

current; their output is affected by a linearity error, usually smaller than 0.2% [7].

Fig 2. LEM transducers: a) voltage; b) current

Accuracy for current transducers also depends on the electrical parameters that are of interest and

on the environment conditions. For example, at ambient temperature, the factors that determine the

accuracy are the DC offset current and the nonlinearity error and for different values of the

operating temperature the important accuracy factor is the offset drift [8].

In our case, for current measurements we used a LEM sensor LA100 P with the input ranges 100A

and 10A. The maximal uncertainty at 250C is 0.45% (from the rated rms current). The offset drift

with temperature is of 10± mA, meaning for a maximum measured value of 50A and with a ratio

of 1:100 the output current will be of 500mA, and the offset drift will represent 2% from the

measured value of the current. Therefore, the maximum deviation due to the above factors can be

expressed as a percentage of the nominal value of the current as being the most 2.45%, for the

rated current of 100A [10]. The linearity error for the LEM LA100-P transducer is less than 0.15%

from the measured value [5, 6]. For voltage measurements we used LEM transducers LV25P, with

a linearity error lower than 0.2%.

4 Proposed Method

The case of the implementation of the active filter in Fig. 1 was practically realized in the

laboratory of Electrical Engineering Faculty, Electrical Machines and Drives Department. Fig. 4

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presents the experimental results [3], when the control algorithm is based on PI regulators. The

obtained THD of the current waveform is 9.69%.

The control used in this is article is based on resonant regulators tuned using the Naslin polynomial

theory (Fig. 5) in the d-q synchronous referential frame [11] and provides better results than other

choices like using classical PI controllers in stationary or synchronous frame, predictive control,

etc. but uses a more complex algorithm. The controller is based on a P-term and a resonant

regulator at fundamental frequency on ( )βα , referential, together with a set of resonant regulators

on frequencies multiple (6, 12 and 18) of the fundamental. The choice of these harmonics derives

from the d-q decomposition of the three-phase odd harmonics [12] in the synchronous frame.

Fig. 4. Waveform for AC absorbed current and its corresponding voltage:

a) without compensation; b) with compensation [3]

pk

2

1

2

1

ω+s

ski

*

,αβFi

αβ,Fi

*

,αβFvΣ

+−

2

6

2

6

ω+s

ski

2

12

2

12

ω+s

ski

θje

− θjeΣ

θ

Fig. 5. Control structure using resonant regulators

With this control algorithm was possible to achieve an improvement of the current waveform level

as low as 3.3% THD. Possible reasons for the differences that appear between classical approaches

and this method are detailed in [13].

Conclusions

As presented in this paper, in order to improve the overall efficiency of the active filter

implemented in the laboratory is necessary to study the equipment from different points of view

like the control algorithm, the reference generation and the transferable uncertainties. If the first

two are part of the common area of research the later is a novel approach to the problem and

implies the necessity of developing and specific sets of equations and algorithm. In order to do so

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the voltage and current transducers, the A/D and D/A converters, the PLL module should be

considered from the propagation of uncertainty point of view in the measure chain of the active

filter and consequently an implemented in the steps of future studies.

Acknowledgment - This work was supported by the CNCSIS contract Advanced measurement

solutions and parameter estimation techniques for active distribution networks- TAMPERE

(2009-2011), and the FP6 European Project CRISTAL (2008-2009). The measurements

performed for the LEM current and voltage transducers were the result of the cooperation

between the Electrical Engineering Faculty and the National Institute of Metrology. We are

deeply grateful to dr. Ioana Odor and Mr. Doru Flamanzeanu for their constant support.

References

[1] IEC61000-4-7 Testing and measurement techniques- General guide on harmonics and

interharmonics measurements and instrumentation, for power supply systems and equipment

connected thereto Gunnar Fernqvist- “High Precision Measurements”, CAS 2004

[2] http://www.dspaceinc.com/ww/en/inc/home.cfm (last opening:10.02.2009)

[3] R. Magureanu, D. Creangă, S. Ambrosii, V. Bostan: “Particular Aspects of Shunt Power Active

Filter Control”, OPTIM 2004, Brasov, 20-21 Mai, Romania

[4] Niclas Bjorsell –“ADc and DAC characterization”, IMU school 2009

[5] LEM LTS25NP-data sheet, last opening-10.02.2009;

[6] LEM LV25-P-data sheet, last opening 10.02.2009;

[7] LEM LA100-P- data sheet, last opening 10.02.2009;

[8] Antonio Delle Femine, Carmine Landi, Mario Luiso-“A Fully Automated Measuring Station for

the Calibration of VoltageTransducers”

[9] Stephen A. Dyer- “Survey of Instrumentation and Measurement”, Wiley-IEEE Press, 2001

[10] Melania Naumof, Ana-Maria Dumitrescu, Mihaela Albu, R. Magureanu, D.

Flamanzeanu, Ioana Odor – “A study of the measurement chain in the power active filters.

Uncertainty and control performances”, AMUEM 2009

[11] Dumitrescu A.M., Bostan V, Griva G, Bojoi R, Magureanu R, “Design of Current

Controllers for Active Power Filters using Naslin Polynomial Technique” 12th European

Conference on Power Electronics and Applications, EPE’07, 2 - 5 September 2007, Aalborg,

Denmark

[12] R.Bojoi, G.Griva, V.Bostan, M.Guerriero, F.Farina, F.Profumo, “Current Control

Strategy for Power Conditioners Using Sinusoidal Signal Integrators in Synchronous Reference

Frame”, IEEE Transactions on Power Electronics, Vol.20, November 2005, pp.1402-1412.

[13] Aurelian Doka, Ana-Maria Dumitrescu, Daniel Roiu, Radu Bojoi, Razvan Magureanu,

Serial Hybrid Active Filters for Medium Voltage Distribution Grids, ATEE 2008, Bucharest,

Romania

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Estimation of the Measurement Uncertainties in the Control

Loop of Active Filters. Part II.

Melania NAUMOF, Ana-Maria DUMITRESCU, Mihaela ALBU, Razvan MAGUREANU, Universitatea Politehnica din Bucuresti, 313 Splaiul Independentei,Bucuresti, Romania;albu@ieee.org

Abstract. Active filters represent a common solution for improving power quality in

distribution networks. The nowadays philosophy of active distribution grids imposes new

requirements for active filters considering that the grid parameters and energy flow can

dramatically change in time. In the paper a thoroughly approach of the measurement chain and

associated uncertainties is presented taking into account one of the most efficient desgin

solutions.

1 Introduction

For the purposes of this article a shunt active filter connected to a non-linear load is used. The

block diagram for this set-up is presented in Fig.1. For signal and data acquisition a dSpace

platform was used [1]. Load and filter currents, voltages on the supply side and on the DC

capacitor are measured and then supplied to the digital control. A Phase Lock Loop (PLL)

module and a PWM unit are used in order to obtain the control signals for the inverter drives.

Using the model of the active filter, the following components have to be considered: the A/D

converters and D/A converter, current and voltage sensors, the PWM unit and its working

frequency and the PLL module.

2 Filter Control Equations for Transferable Uncertainty

The algorithm described below will use the expression of the uncertainties, involved in the

estimation of the control quantities [2], [3]. The following represents part of the procedure,

explained in [3].

1st step: measurement of the load currents ( mLai , and mLbi , ), line voltage ( mav , and mbv , ), filter

currents ( mfai , and mfbi , ) and DC link voltage ( mDCv , ).

Let 7:1),(][ ,,,,,,, === iixviivviix mDCmfbmfambmamLbmLa , be the vector of measurement values, with

xu the corresponding standard uncertainties derived from the transducers specifications. It was

assumed a uniform distribution of these uncertainties.

⋅⋅=

÷==

100

)(

3

1)(

71)],([][

ixiu

iiuu

i

x

xx

ε (1)

where iε , for 6,5,2,1=i represents the maximal uncertainty of the LEM current transducer

(0,15%) and for 7,4,3=i the maximal uncertainty for the LEM voltage transducer (0,2%).

2nd

step: variables obtained from the A/D converter:

71),()()( ÷=⋅= iixikixD (2)

We will consider all uncertainties as identical for the analogue-to-digital conversion, as specified

by the dSpace platform, i.e. for the vector describing the conversion [ ])(/ ikk DA = , the

corresponding vector of maximal uncertainties will be [1]

[ ] 71/// ].1...1[)( xDxADxADxA iuu ⋅== ε (3)

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The A/D converter used in this paper is a 12 bits parallel converter, which is part of the dSpace

system (FSR=10V). For this converter we considered the offset error, the span error, the integral

non-linearity, the gain, the differential nonlinearity and the missing code. The DNL (differential

non-linearity) is a measure of how individual steps may be in error, representing the difference

between the ideal step position and its actual position. The INL (integral non-linearity) is defined

as the difference between the actual transition at any level and the ideal transition. It occurs if there

is an accumulation of very small DNL errors over the input signal [4].

The significant uncertainties are due to the offset, span, the differential nonlinearity and the

integral nonlinearity. For the gain and offset uncertainty there is a mathematical connection

between them

ε++= offsetVtTG )( ,

where G is the gain of the converter, )(tT is the input value, ε represents the residual error.

The integral nonlinearity is defined as being:

%1002

)()(

1

1

⋅⋅

=

−+⋅=

QINL

Q

tTVtTG

N

nomoffset

ε

ε

, (4)

where Q represents the ideal code width.

The differential nonlinearity is mathematically expressed by:

[ ]Q

QtTtTGDNL

−−+⋅=

))()1((

In order to eliminate the uncertainties, the ADC characterization is usually performed by

estimating the ADC transition levels from measurement [5].

For this converter we considered the offset error, the span error, the integral non-linearity.

( ) 222

/ INLspanoffsetDxA uuuiu ++= is the total uncertainty of the converter, the offset uncertainty

represents FSRuoffset ⋅±= %003,0 , the uncertainty corresponding to the span error is

FSRu span ⋅±= %1,0 , the uncertainty corresponding to the integral non-linearity error (INL) is

FSRuINL ⋅±= %003,0 .

3rd

step: calculation of the PLL output digital voltage ( PLLv ) and control current of the DC

capacitor ( )1(

0di ) further used as part of the reference for the current regulator on the d axis [19].

Its last component is PLLu (3), calculated below:

( ) ( )

( ) ( )

( ) ( ) ( ) ( )DC

I

DCPDCDC

I

Pd

dPLL

DC

DC

dDC

DC

d

vuk

vkvuv

kkiu

iuu

vuv

ivu

v

iu

2

2

*2

2

*)1(

0

)1(

0

2

2)1(

0*2

2

*

)1(

0

1

3

⋅

−+−+⋅

⋅+=

=

⋅

∂

∂+⋅

∂

∂=

(5)

4th step: transformation from ( )cba ,, digital values to ( )βα , axes and evaluating their

uncertainties [2];

( )( )

=

=

2

1

D

D

bD

aD

Dx

x

i

ii (6)

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[ ]

[ ]

( ) ( )( )

( ) ( )( ) ( )( )

( )

( ) ( )( )

( ) ( )( ) ( )( )

( )2

1

2

1

22

1

2

1

2

1

22

1

33

2

33

1

63

21

3

1

35

33

2

33

1

23

21

3

1

31

3

2

3

101

⋅+

⋅=

⋅+⋅=

==

⋅+

⋅=

⋅+⋅=

==

⋅

=

=

εε

ε

εε

ε

β

β

α

β

β

α

βα

βαβααβ

f

DDf

Df

DD

D

D

T

T

ff

iu

xuxuiu

xuiu

iu

xuxuiu

xuiu

iii

iiiiX

(6’)

The same relation can be applied for the filter currents, in the end resulting the corresponding set

( )αβiu of the maximal uncertainties [19].

( ) [ ]Tff iiiiiu βαβααβ = (7)

5th step: calculation of the ( )qd , components of the load and filter currents [19]:

[ ]TfqfdqPLLdPLLqddq iivviiX ,,= (8)

⋅+⋅⋅+=⋅+

⋅+⋅⋅+=⋅+

))4()3(())4()3(()6()5(

))4()3(())2()1(()2()1(

dqdqdqdq

dqdqdqdq

XjXXjXXjX

XjXXjXXjX

αβαβ

αβαβ

and their corresponding uncertainties:

( ) ( )( ) ( )( ) ( )( ) ( )( )[ ]( )( )[ ]

( )( )( )( ) ( ) ( ) ( )( )

( )( ) ( ) ( ) ( )( )

( )( )( )( ) ( ) ( ) ( )( )

( )( ) ( ) ( ) ( )( )

( )( )( )( ) ( ) ( ) ( )( )

( )( ) ( ) ( ) ( )( )

( )( )( )( ) ( ) ( ) ( )( )

( )( ) ( ) ( ) ( )( )

⋅+⋅+

+⋅+⋅=

⋅+⋅+

+⋅+⋅=

⋅+⋅+

+⋅+⋅=

⋅+⋅+

+⋅+⋅=

==

=

3333

44446

4444

33335

3131

42422

4242

31311

6:1,

6521

22

22

22

22

22

22

22

22

dqdq

dqdq

dqD

dqdq

dqdq

dqD

dqdq

dqdq

dqD

dqdq

dqdq

dqD

DD

T

dqDdqDdqDdqDD

XuXXXu

XuXXXuXu

XuXXXu

XuXXXuXu

XuXXXu

XuXXXuXu

XuXXXu

XuXXXuXu

kkxuu

XuXuXuXuku

αβαβ

αβαβ

αβαβ

αβαβ

αβαβ

αβαβ

αβαβ

αβαβ

(9)

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6th step: extracting the DC component of the previous ),( qd currents which corresponds to the

first harmonic in ( )cba ,, axis using a Low Pass Digital Filter (LPF), by applying the Monte Carlo

method [2].

For the currents the normal distribution is considered and therefore ( )3

maxXiu

∆= , for each current

of the four of dqX array.

7th step: calculation of harmonic components in the ),( qd frame.

( ) ( ) ( ) ( ) ( )[ ]( ) ( ) ( ) ( ) ( )[ ]Th

fq

h

fd

h

q

h

d

h

dq

T

fqfdqddq

iiiiX

iiiiX

=

= 00000

( ) ( )

( ) ( )

( ) ( )

( ) ( )

−=

−=

−=

−=

)4()6()4(

)3()5()3(

)2()2()2(

)1()1()1(

0

0

0

0

dqdq

h

dq

dqdq

h

dq

dqdq

h

dq

dqdq

h

dq

XXX

XXX

XXX

XXX

(11)

The corresponding uncertainty of all the components of the vector containing the harmonics of the

currents is estimated

( ) ( )

( ) ( )

( ) ( )

( ) ( )

−=

−=

−=

−=

)))4(())6((())4((

)))3(())5((())3((

)))2(())2((())2((

)))1(())1((())1((

022

022

022

022

dqDdqD

h

dqD

dqDdqD

h

dqD

dqDdqD

h

dqD

dqDdqD

h

dqD

XuXuXu

XuXuXu

XuXuXu

XuXuXu

(12)

The output of the current regulators is first transformed from ( )qd , frame to stationary ( )βα , one

and then to the ( )cba ,, in order to be used as reference for the PWM inverter of the active filter.

In this way, an overall quality of the active filter algorithm is given by considering all elements in

the measurement and digital signal processes and estimating their standard uncertainty.

Conclusions

In order to study the influence of the transferable uncertainties in the measurement chain of the

active filter the voltage and current transducers, the A/D and D/A converters, the PLL module

were considered from the propagation of uncertainty point of view and consequently an

implemented in the steps of an algorithm. The purpose of finding the proper way of minimizing

the effects of the measurement uncertainties associated to different components of an active filter

can be reached by means of mathematical relations and practical measurements.

Acknowledgment - This work was supported by the CNCSIS contract Advanced measurement

solutions and parameter estimation techniques for active distribution networks- TAMPERE

(2009-2011), and the FP6 European Project CRISTAL (2008-2009). The measurements

performed for the LEM current and voltage transducers were the result of the cooperation

between the Electrical Engineering Faculty and the National Institute of Metrology. We are

deeply grateful to dr. Ioana Odor and Mr. Doru Flamanzeanu for their constant support.

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References [1] http://www.dspaceinc.com/ww/en/inc/home.cfm (last opening:10.02.2009)

[2] Melania Naumof, Ana-Maria Dumitrescu, Mihaela Albu, R. Magureanu, D. Flamanzeanu, Ioana

Odor – “A study of the measurement chain in the power active filters. Uncertainty and control

performances”, AMUEM 2009

[3] Ferrero A, Salicone S, “The random –fuzzy variables: a new approach to the expression of

uncertainty in measurement”, IEEE Transaction on Instrumentation and Measurement, volume

53, issue 5, oct 2004, pages 1370-1377

[4] J.Pickering – “ADCs to DACs (analog-to-digital and digital-to-analog converters)”

[5] Niclas Bjorsell –“ADc and DAC characterization”, IMU school 2009, lecture notes

[6] Evaluation of measurement data — Supplement 1 to the “Guide to the expression of uncertainty

in measurement” —Propagation of distributions using a Monte Carlo method, JCGM 2006

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Stand-Alone Wind Energy System Using a Lead Acid Battery for Energy Storage

Luminiţa BAROTE, Corneliu MARINESCU, Ioan ŞERBAN

Transilvania University of Brasov, 29 Eroilor, Brasov, Romania; luminita.barote@unitbv.ro

Abstract. This paper deals with a wind-based stand-alone generating unit with Permanent Magnet Synchronous Generator (PMSG) and a Lead Acid Battery (LAB) for energy storage, during wind speed variation as well as transient performance under variable load. The main purpose is to supply 230 V/50 Hz domestic appliances through a single-phase inverter. Simulations and experimental results validate the stability of the supply.

1 Introduction

The requirements for clean and Renewable Energy Sources (RES) have resulted in the introduction of rather small power sources, supplying autonomous electrical systems. Among these, wind based generating units are of real interest. For powers under 10 kW, permanent magnet synchronous generators (PMSG) are used to obtain an efficient configuration [1], [2]. For stand-alone systems, energy storage devices are essential to store electricity for use when the wind speed is under a certain level. Wind energy systems have a fluctuating power output due to the wind speed variations, with power output varying by the cube of the wind speed. Integrating an appropriate energy storage system in conjunction with a wind generator removes the fluctuations and maximizes the reliability of loads power supply. In addition, both system voltage and frequency must be controlled. The reason of using Lead Acid Battery (LAB) is the proven reliability of their technology for stand-alone wind energy systems [3], [4].

2 System Configuration

The proposed wind stand-alone system, designed for a residential location, is a 3kW wind turbine system with a permanent magnet synchronous generator (PMSG), diode-rectifier bridge, boost converter, LAB storage device, inverter, transformer and resistive loads. It supplies single-phase consumers, at 230V and 50Hz.

Figure 1: System configuration.

3 Simulation and Experimental Results

The proposed system has been modeled and simulated using the Matlab/Simulink environment. Figure 2 shows the block diagram. Measurement blocks are also included. The boost converter controls the electromagnetic torque by means of wind speed, in order to extract optimum power from the available wind resource.

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Energy storage system is composed of an inverter and storage element, in this case a bank of lead-acid batteries. The storage system is composed of a full bridge single-phase inverter that converts the DC voltage of the battery in AC voltage. Further, this voltage is applied to a single-phase transformer, which boosts-up the voltage to 230 V. The inverter controls the power transfer, changing the amplitude and phase of the voltage on the primary side of the transformer [5].

The battery bank consists of ten 12 V LABs connected in series. The LAB is able to supplement the power provided to the load by the wind turbine when the wind speed is too low.

powergui

Continuous

Wind Turbine

Generator speed (pu)

Wind speed (m/s)Tm (pu)

v+

-

A

B

C

+

-

Vabc

IabcA

B

C

a

b

c

Signal 1

Resistive AC Loads

Tm

mA

B

C

mw

m

1 2

Lead Acid Battery(LAB - 120 V)

+

-

Inverter

g

A

B

+

-

i +-

PWM

9

BoostConverter

In +

In -

Out +

Out -

Figure 2: Simulink block diagram.

The PMSG has a sinusoidal flux distribution and eight pairs of poles. Its parameters are

listed below: - Rated power: P = 2kW; - Rated voltage / frequency: 120 V / 50 Hz; - Rated current: 17 A; - Rated speed: 400 RPM; - Per-phase stator resistance: Rs = 2 Ω; - The d-axis and q-axis stator inductances: Ld = Lq = 0.001 H; - Flux induced by magnets in the stator windings: ψ = 0.46 Wb. The experimental results are obtained on a laboratory test bench, including the described

system with a wind turbine emulator that drives the PMSG. The control system is implemented in a dSPACE DS1103 real-time board. This emulator is able to reproduce the steady and dynamic behavior of a real wind turbine. The hardware scheme is based on a frequency converter, Danfoss VLT - FC302 (5 kW) with vector control and open loop torque control, and real-time control system dSPACE DS1103. The operating principle is based on a control loop, where the input signal is the electromagnetic torque of the asynchronous motor (AM), and the output signal is the motor speed. The wind speed can be modified through one independent input of the emulator [6], [7]. The block diagram of the wind turbine emulator is presented in Figure 3.

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Figure 3: Wind turbine emulator.

In order to investigate the system’s operation, the following simulations and experiments

were carried out: - Variation in the wind speed, while the load is constant; - Load switching, with fixed wind speed.

A. Variation in the wind speed, while the load is constant In the following example, wind speed drops from 9 m/s (at t=3s) to 5 m/s (at t=7s). The output voltage and current for the LAB are shown in Figures 4 and 5. The considered initial battery state of charge (SOC) is 80 %. When the LAB is discharging, the battery SOC decreases in order to ensure the stable supply for the loads.

The results can be seen in Fig. 6. The wind turbine cannot supply the entire energy load demand (0.5 kW) in the transient regime, therefore the battery will supply the difference. Fig. 7 shows that the active power balance of the system is maintained with the LAB, which will pass from charging to discharging mode. It can be observed in the experimental results, small changes are reflected in the waveform of voltage and current through the battery. The explanation for these differences is that the real system is more complex than the model used in simulation and its performance can be affected by many parameters that are not considered in the simulation. As the complexity and number of components used in the experimental scheme increase the system becomes more susceptible to functional changes. However, passing over these small differences, it can be concluded that the developed simulation model is accurate and reliable for further studies.

1 2 3 4 5 6 7 8 9 10118

118.5

119

119.5

120

120.5

121

121.5

122

Time [s]

LAB

Vola

tge

[V]

(a)

(b)

Figure 4: The LAB voltage variation: (a) Simulation results; (b) Experimental results.

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1 2 3 4 5 6 7 8 9 10-10

-5

0

5

10

Time [s]

LAB

Cur

rent

[A]

(a)

(b)

Figure 5: The LAB current variation: (a) Simulation results; (b) Experimental results.

1 2 3 4 5 6 7 8 9 1079.99

79.995

80

80.005

80.01

80.015

80.02

Time [s]

LAB

SOC

[%]

(a) (b)

Figure 6: The LAB state of charge (SOC) variation: (a) Simulation results; (b) Experimental results.

1 2 3 4 5 6 7 8 9 10-2000

-1500

-1000

-500

0

500

1000

1500

2000

P [W

]

Time [s]

LAB

Wind turbine

Resistive AC loads

(a)

Wind turbineRezistive AC loadsLAB

Time [s]10

(b)

Figure 7: The active power balance of the system. (a) Simulation results; (b) Experimental results.

B. Load switching, with fixed wind speed For the following simulation, the wind speed is maintained constant at 9 m/s. The LAB voltage, current, and LAB SOC variation, are provided in Figures 8, 9 and 10, respectively. At t=3 s, a 1 kW load is connected and disconnected at t=7s.

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In Figures 8 and 9, it can be seen that the LAB operating mode changes from charge to discharge during the transient event. Because initially no load is connected, the power difference supplied by the wind turbine is stored in the battery.

The LAB stored energy is released when the 1 kW load is connected, in this way the supply of the load is ensured. The SOC slope changes when the load is switched on and off , as shown in Fig. 10, which means that the battery passes from charging to discharging mode. Consequently, Fig. 11 shows that the active power balance of the system is maintained regardless the load change.

1 2 3 4 5 6 7 8 9 10118

119

120

121

122

123

124

Time [s]

LAB

Volta

ge [V

]

(a)

(b) Figure 8: The LAB voltage variation:

(a) Simulation results; (b) Experimental results.

1 2 3 4 5 6 7 8 9 10-10

-5

0

5

10

15

Time [s]

LAB

Cur

rent

[A]

(a)

(b)

Figure 9: The LAB current variation: (a) Simulation results; (b) Experimental results.

1 2 3 4 5 6 7 8 9 1080

80.005

80.01

80.015

80.02

80.025

80.03

80.035

80.04

80.045

Time [s]

LAB

SOC

[%]

(a)

(b) Figure 10: The LAB state of charge (SOC) variation:

(a) Simulation results; (b) Experimental results.

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1 2 3 4 5 6 7 8 9 10-2000

-1500

-1000

-500

0

500

1000

1500

2000

Time [s]

P [W

] LAB

Resistive AC Loads

Wind Turbine

(a)

(b) Figure 11: The active power balance of the system.

(a) Simulation results; (b) Experimental results.

4 Conclusion

• In this paper, a LAB model and its integration in a typical stand-alone wind energy conversion system is analyzed. Simulation and experimental case studies show that the active power balance of the system proves to be satisfying during transient loads and variable wind speed conditions.

• LAB always ensures the safe supply of the loads (households) regardless of the problems caused by wind speed and loads variations.

• In conclusion, the power system’s stability can be ensured by using the proposed configuration.

References [1] T. Nakamura, Sh. Morimoto, M. Sanada and Y. Takeda, Optimum Control of IPMSG for Wind

Generation System, IEEE Power Conversion Conference, 2002, pp 1435-1440. [2] L. Barote and C. Marinescu, Control of Variable Speed PMSG Wind Stand-Alone System,

OPTIM’06, Brasov, 18-19 May, 2006, vol. II, pp. 243-248. [3] T. Markel, M. Zolot, K. B. Wipke, A. A. Pesaran, Energy Storage System Requirements for Hybrid

Fuel Cell Vehicles, Advanced Automotive Battery Conference Nice, France June 10-13, 2003. [4] A. El-Ali, J. Kouta, D. Al-Samrout, N. Moubayed and R. Outbib, A Note on Wind Turbine

Generator Connected to a Lead Acid Battery, SIELMEN’09, Iasi, Romania, pp. 341- 344. [5] Siegfried Heier, Grid Integration of Wind Energy Conversion Systems – second edition, John

Wiley & Sons Ltd, SUA, 2006. [6] R. Teodorescu, F. Iov and F. Blaabjerg, Flexible Development and Test System for a 11 kW Wind

Turbine, in Proc. of 34th IEEE Power Electronics Specialists Conference (PESC03), June 2003, Vol. 1, pp. 67-72.

[7] H. M. Kojabadi, L. Chang and T. Boutot, Development of a Novel Wind Turbine Simulator for Wind Energy Conversion Systems Using an Inverter-Controlled Induction Motor, IEEE Transactions on Energy Conversion, Vol. 19, No. 3, September 2004, pp. 547-552.

Acknowledgments - This work was supported in part by the Romanian Ministry of Education, Research and Innovation through contract CNCSIS-IDEI – 134/2007 and PN2 – E-FARM no. 22134/2008 projects.

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Simulation software for static rectifiers and static switchcontrollers

Maria Daniela ORBAN, Marius Daniel MARCU, Florin POPESCUUniversity of Petrosani, str. Universitatii nr.20, orban@upet.ro

Abstract: The static converters (CS) have become an important element in supply systems withelectrical energy of every kind of consumers. The static converters are used in adjustable systems tothe static action, in this case the assignment being an electrical engine most frequently. Hereby, by anadequate command given by a controller in to a close circuit, the static converters adjust the outputelectrical energy parameters, to the necessity demand by electrical engine.

1. Introduction

The development of industrial automation leads by default also to the improvement ofelectrical drives systems as more than these systems represent the most spread conversiontype of the electrical energy in the mechanical energy.

The static converters (CS) have become an important element in supply systems withelectrical energy of every kind of consumers. The static converters are used in adjustablesystems to the static action, in this case the assignment being an electrical engine mostfrequently. Hereby, by an adequate command given by a controller in to a close circuit, thestatic converters adjust the output electrical energy parameters, to the necessity demand byelectrical engine.

The rectifiers are static converters with natural switching which realize the electricalenergy changeover from alternative current into continuous current and reverse due to theirpower semiconductor elements components.

There are single-phase rectifiers and three-phase rectifiers taking into account thephase numbers.

In dependence with the operating quadrants the rectifiers are:- the rectifier by one quadrant- where the voltage and the current have one way

( semi commanded rectifiers);- the rectifiers with two quadrant where the output voltage can be positive or

negative (the complete command rectifier);- the four quadrant rectifiers – where the output voltage can be negative or

positive and the current can get about both ways.The two quadrant rectifiers can be with central tap (the rectifier with two pulses), the

single phase bridge and rectifier with the null diode.The rectifier of one quadrant or semi commanded rectifier are realized through the

bridge scheme and are made by thyristors and diodes.The rectifiers with forced switching are for two types: the unitary power factor

rectifier and Pulse Width Modulation (PWM) rectifier.The simulation software for static converter function it is realized like a Windows

independent application helping with Visual Basic’s software package. Once the simulationsoftware is launched one window is opened, allowing choosing the simulation type to be run,using radio buttons. The window also contains two buttons, one for continuing the simulation(Continua), and the other for exit the application (Iesire).

Following the simulation start-up, the simulation window is opened, containing threemain parts: a part which contains the simulation scheme. The simulation scheme isdynamically modifying its side colors which are in conduction at a certain moment; anotherpart it is dedicated to the information zone. This zone is presenting the text type information

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as regards to function mode to the converter analyzed (semiconductor elements which are inconduction, semiconductor elements directly polarized, etc.). Inside of this zone it is also findbuttons for command angle modification, for choosing the function dial; the third part is thezone where is dynamically getting up the wave forms characteristic to the static converteranalyzed.

Beside this zones, one of simulation windows also containing a pull-down menu type,for modification of some parameters or for choosing of different type of loads. The windowalso have two command buttons, one for starting up the simulation (Simulare), which then itis transforming in button for hold up the simulation (Stop) and a button for the exit of thewindow (Iesire).

The main window of simulation of static rectifier’s application is shown in the figure1, from where you can choose the rectifier with two quadrant simulations, the rectifier withone quadrant simulation or the simulation of rectifier with forced changeover.

Fig.1 The rectifier’s simulation

2 The types of rectifiers2.1The rectifier with two quadrants

The figure 2 presents the simulation window for two quadrants rectifier with centraltap single phase (it can choose the rectifier type). During the simulation, the command angleis modified for emphases even the voltage adjusting mode and the load current. The commandangle can be modifying using the up-down arrows, showing this value.

Fig.2 Single phase rectifier with central tapThe figure 3 is presenting a simulation window for a three phase’s rectifier with null

conductor. The thyristor input conduction appears when the voltage on the thyristor is positiveas only the natural commutation dot.

Fig.3 The three phases rectifier with null conductor

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The figure 4 is presenting a simulation window of single phase bridge rectifier. It hasfour tyristors and the load is connected on the continuous current diagonally, and pair ofthyristors T1T4, T2 T3 is simultaneous in conduction.

Fig.4 The single phase bridge rectifier

The figure 5 is presenting the three phase’s bridge rectifier. These are the most usedrectifiers. It should be taken into account divided in two rectifiers with null conductor, madethe positive branch N and the negative branch N. The output straightened voltage of the threephases rectifier full commanded is given by the difference between the straightened voltagesfrom the two branches.

Fig.5 The three phases bridge rectifier

2.2The rectifier with the null diode

The commanded rectifiers in phase have a lot of shortcomings as:- the power factor is decreasing; - the current harmonics amount even in the straightened voltage waveforms.To improve some of these shortcomings it is necessary to put a diode in parallel with

the load. The straightened voltage is polarizing the null diode in opposite way, and start theconduction when the instantaneous value of voltage begin zero. In this way the straightenedvoltage is only made by positive pulses.

The figure 6 is representing the simulation window for a single phase rectifier withnull diode. During the simulation, it has been modified the command angle of the rectifier, inorder to evidence also the way of voltage modification, respectively the load current. Thecommand angle may be modified using up/down arrows, being shown their values.

Fig.6 The single phase rectifier with null diode

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It can notice that the thyristor lead the current on the ap / period of time and on thea period of time the load current is led by the null diode.

Fig.7 The three phases rectifier with null diode

In the figure 7 is represented the simulation window for a three phase rectifier withnull diode. In this case the null diode start to lead only for command angle greater than 3/p .Form waveforms it can notice that each thyristor switched twice into a period, and theswitching period of thyristor is reducing. The null diode leads the load current on

3// pap - . The command angle can’t overtake the value 2 3/p

2.3One quadrant rectifierThe semi commanded rectifiers are only made in bridge scheme. It’s made by

thyristors and diodes. There are two methods of semiconductors elements placement forsymmetrical or asymmetrical way for the single phase rectifier.

It can notice that the straightened voltage has only positive values and the averagevalue of straightened voltage varies between Ua0 and zero for a command angle between 0-180 degree.

In the figure o it is shown the simulation window of single phase rectifier. Onequadrant rectifier has two thyristors T1, T2 and two diodes D1, D2 and the load is connectedon the bridge diagonally of continuous current. The lead way is T1, D2 respectively T2, D1.

Fig.8 The single phase rectifier with one quadrantFigure 9 represents the three phase rectifier with one quadrant. This can be considered

like a semi commanded rectifier in three phase bridge made by positive branch P and negativebranch N. The straightened output voltage is made by the difference between straightenedvoltages from the two branches.

Fig.9 The three phases rectifier with one quadrant

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3. Static switch controller simulationThe static switch controllers are converters were the exit size has the same form with

the entry size, after modifying the command angle a of thyristors obtaining the converter output of voltage variation.

Figure 1 shows the application of main window of static switch controller’s simulationsoftware application, it allows selection for a. c. switch controllers, single-phase or three-phase, respectively the simulation for d.c. switch controllers.

Fig.10. The application of main window of static variators simulation software application

3.1. A.c. switch controllersFigure 11 shows the simulation window for a single-phase switch controller with

resistive charge. It can be seen the main menu to choose the type of switch controller (withtwo thyristors, with one thyristor or with a thyristor across a diode bypass), and also thecharging type. The charge may be resistive, inductive or resistive-inductive type.

Fig.11.The simulation window for a single/phase switch controllerwith resistive charge

During the simulation, it has been modified the command angle of the switchcontroller, in order to evidence also the way of voltage modification, respectively of thecurrent through charge. The command angle may be modified using up/down arrows, beingshown their values.

Figure 3 shows the simulation windows for single-phase switch controller withresistive-inductive charge. In case of resistive-inductive charge the software request by anadditional window the input of power factor value.

Fig. 12.The simulation windows for single/phase switch controllerwith resistive-inductive charge.

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For the three-phase a.c. switch controller, the simulation window it is showed in figure4 for a resistive charge. The simulation has been performed by modifying command angle.

Fig.13.The simulation windows for three-phase switch controller with resistive charge.

3.2. D.c. switch controllerThe d.c. switch controller, the chopper, it is the static converter who transform the

entry continue voltage into a orthogonal voltage impulses. The exit voltage medium value itsmay be modified between 0 and entry value of voltage, in function with the rapport betweenthe period when the chopper is controlling and the period when this is blocked. Figure 14shows simulation window for function simulation of one of static variator by a quadrantrealized with thyristor, being represented the wave forms characteristic to the charge, the mainthyristor and the switch off circuit. Entering command in the main thyristor conductivity is tobe done by pushing the related command button and to switch off the main thyristor, itsrelated push button is pressed. Figure 15 shows the simulation window related with the d.c.switch controller, in four quadrants from the same window, it is possible to be modified theoperation quadrant (using the four radio buttons) and also the period for the switch controlleror conductivity period.

Fig. 14. Simulation window for d.c. switch controller by a quadrant realized with thyristors.

Fig.15.The simulation window related with the d.c. switch controller, in 4 quadrants. 4. CONCLUSIONSThis documentation describes a Windows application, useful for understanding the

functioning of the static variators, converters, typing to cover all the needed aspects. Thisapplication has a teaching purpose, being useful for the students studying static converters.

5.REFERENCES[1]. Marcu, M., Borca,.D. Convertoare statice în acţionări electrice. Editura TOPOEXIM, Bucureşti,1999.[2]. M. D, Marcu, M.D. Orban A.C. switch controllers, cycloconverters and inverters,Ed.Libris Hoffnung, Stei, ISBN:973-98855-6-x. 2001

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STUDIUL INFLUENŢEI INSTALAŢIILOR DE RĂCIRE

ASUPRA EFICIENŢEI ENERGETICE TOTALE A

SISTEMELOR CCHP REZIDENŢIALE CU PILE DE

COMBUSTIE

Nicolae BADEA , Ion VONCILĂ, Nelu CAZACU Universitatea “Dunărea de Jos” din Galaţi , Str. Domnească 47, 800008, Galaţi;

nicolae.badea@ugal.ro ion.voncila@ugal.ro, nelu.cazacu@ugal.ro

Abstract. Lucrarea are drept scop principal evidenţierea influenţei instalaţiilor de răcire –

utilizate în cadrul lanţurilor de trigenerare – asupra eficienţei energetice globale a acestor

sisteme (CCHP). Analiza a fost efectuată pentru sisteme de microtrigenerare, având drept

obiectiv secundar găsirea diferenţelor semnificative dintre sistemele de mică putere – utilizate

pentru clădirile rezidenţiale – şi sistemele de medie şi mare putere – utilizate la nivel

industrial.

1 Introducere

Un concept important în domeniul energiei la nivelul UE introdus prin Directiva 8/2004,

este acela de promovare a cogenerării (CHP), prin descentralizarea producerii de energie

electrică şi termică. În cadrul cogenerării – ca o particularitate nouă - pentru satisfacerea

criteriilor de calitate şi confort în clădirile rezidenţiale se remarcă apariţia trigenerării.

Trigenerarea presupune utilizarea căldurii pentru încălzirea locuinţei în perioada de iarnă şi

posibilitatea răcirii spaţiului în perioada de vară. Sistemele de cogenerare/trigenerare

(CHP/CCHP) folosite în sectorul rezidenţial trebuie elaborate şi proiectate pentru a avea

capacitatea de a produce simultan căldura sau frig şi electricitate dintr-o singură sursă de

energie. Cogenerarea/trigenerarea aplicată în domeniul locuinţelor trebuie să acopere uzual

cerinţele de putere pe partea electrică P<5 kWe iar pe partea termică Pth<25 kWth. Indicatorii de

performanţă ai sistemelor de producere în trigenerare - faţă de producerea separată a energiilor -

sunt: raportul energie electrică / energia termică (indicele de cogenerare); eficienţa electrică a

producerii în trigenerare; economia de combustibil; eficienţa termică; eficienţa producerii

frigului; eficienţa energetică totală. Relaţia matematică de calcul a eficienţei energetice anuale

totale este [1]:

i

gengen

chpmH

QE 6,3 (1)

unde: genE - producţia de energie electrică anuală [kWh/an], genQ - producţia de energie termică

anuală [kWh/an], m - consumul de combustibil anual [kg/an], iH – puterea calorifică inferioară

a combustibilului.

Procentul de combustibil salvat (PFS) al sistemului CCHP faţă de producerea separată de

energie SHP, poate fi determinat cu relaţia:

mPFSQ

Q

e

e )1(

(2)

unde: e - randamentul electric al sistemului CCHP, Q - randamentul termic al sistemului

CCHP, e - randamentul electric al sistemului SHP, Q - randamentul termic al sistemului SHP.

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2 Sistem rezidenţial CCHP cu pile de combustie

Dezvoltarea sistemelor CHP/CCHP în UE este caracterizată de o mare diversitate, atât în

ceea ce priveşte scara cât şi natura dezvoltării. În conformitate cu Directiva CE nr. 8/2004 a

Parlamentului Consiliului European, privitoare la promovarea cogenerării, unităţile de

producere combinată, cu puteri electrice unitare de la câţiva kW până la 50 kW sunt micro-

CHP, între 50 şi 1000 kW sunt de medie putere şi între 1000 kW şi maxim 10 MW sunt de

mare putere. Din multitudinea de mCHP-uri de obţinere a energiei termice şi electrice, pe plan

european se prognozează o creştere accentuată a cercetărilor pentru sistemele cu motoare

Stirling şi celule de combustie. Primul indicator de performanţă al sistemului de producere în

trigenerare este indicele de cogenerare al sistemului CHP/CCHP. În baza raportulului dintre

energia electrică şi energia termică utilă P/Pth din locuinţă, raport determinat pe baza cererii

consumatorului rezidenţial se poate alege, rezultat al comparării cu indicele de cogenerare

structura de sistem CCHP ce se poate realiza cu raport apropiat. Variabilitatea ridicata orară,

lunară şi sezonieră a acestui factor implică introducerea de sisteme de încălzire sau stocare a

energiei pentru asigurarea cerinţelor consumatorilor casnici. Sistemul CCHP propus se

compune, în aceste condiţii, dintr-o pilă de combustie ce poate urmări şi asigura cererea de

energie electrică şi un sistem de generare de căldură ce trebuie să acopere necesarul termic, în

condiţii de vârf. Instalaţia de generare a frigului poate fi cu compresie mecanică, caz în care

energia de intrare în instalaţia frigorifică este electrică sau instalaţie cu compresie termică, caz

în energia de intrare în instalaţia frigorifică este termică. Indiferent de tipul de refrigerare,

agentul frigorific este apa răcită la 3-5 oC care este pompată în ventiloconvectoare. Acestea din

urmă realizează transferul final de frig în spaţiul de locuit. Ventiloconvectoarele oferă

posibilitatea unei funcţionări duale, apă rece/apă caldă astfel încât - în perioada de iarnă - pot fi

folosite la încălzire schimbând calea de circulaţie a agentului termic, în speţă de la acumulatorul

de apă caldă şi unitatea de încălzire la vârf. Schema funcţională a sistemului CCHP este redată

în figura 1.

cc

apa

caldura

incalzire retur

incalzire turtanc de acumulare apa calda

incalzire la varf

pila de combustie

gaz metan

apa rece

apa calda menajera

incalzire / / racire

rezidenta

convertor cc-ca electricitate

aer

reformer

gaz metan

Convector

hid

rog

en

frig prin absorbtie

frig prin compresie

Convector

Fig. 1: Schema funcţională a sistemului mCCHP propus

3 Elemente componente ale sistemului CCHP

3.1 Pila de combustie

Pilele sau celulele de combustie transformă energia electrochimică prin coversia

hidrogenului şi oxigenului în electricitate şi căldură în prezenţa unui catalizator [2]. Hidrogenul

necesar pilei se poate obţine din reformarea gazului metan. Reformarea reprezintă o

descompunere termică având la bază reacţia endotermă: 24 2HCCH , şi se poate realiza în

exteriorul sau în interiorul celulei, în funcţie de temperatura de lucru a celulei de combustie.

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Performanţele şi caracteristicile pilelor de combustie sunt prezentate în tabelul 1. Tabelul 1

Tip pilă Putere Tip de

electrolit

Catalizator Oxidant Combustibil Temperatura de

operare

Randament

PEMFC (1-250) kW Membrană

polimerică

Platină Aer sau

oxigen

Hidrocarburi sau

metanol

(50-70) oC (30-50) %

Pentru sistemul mCCHP analizat s-a ales o pilă de combustie de tip PEMFC cu un

randament electric de 40 % şi termic de 30 %.

3.2 Sistemul de generare a căldurii de vârf

Pila de combustie de tip PEMFC produce o cantitate de căldură proporţională cu cererea

de energie electrică întrucât are un indice de cogenerare cuprins între 0,8-1,1. Parametrii

termodinamici scăzuţi ai pilei în generarea de căldură face ca apa caldă din acumulatorul de

căldură AC să nu poată fi utilizată în încălzirea rezidenţei decât dacă se introduce un sistem

intermediar de încălzire de tip centrală cu condensare. Energia termică degajată este refolosită

în instalaţia termică (figura 2,a). Bilanţul energetic al unui astfel de cazan încălzitor este redat

în figura 2, b.

a) Principiul condensaţiei b) Bilanţul energetic

Fig. 2: Sistem intermediar de încălzire

3.3 Sistemul de răcire

Procesele de răcire se desfăşoară între două nivele de presiune: de vaporizare şi de

condensare. Pentru determinarea celor două nivele de presiune trebuie cunoscute temperaturile

de vaporizare şi de condensare ale fluidului de răcire. Procedeele actuale de producere a frigului

pot fi cu:

• cu compresor sau comprimare mecanică de vapori;

• cu activare termică ce poate fi cu absorbţie sau adsorbţie.

Procedeul de obţinere al frigului prin absorbţie este similar compresiei de vapori dar are

câteva diferenţe semnificative [3].

Procedeul de adsorbţie utilizează căldura pentru a vaporiza fluidul de răcire la presiuni

înalte, motiv pentru care se mai numeşte compresor termic a cărui caracteristică esenţială este

că nu are elemente în mişcare.

a) Compresie mecanică b) Compresie termică

Fig. 3: Sistem de răcire

Răcitoarele cu absorbţie, practic, au nevoie de o cantitate de căldură - pe partea de

compresor termic şi un mediu absorbant-refrigerant. Două combinaţii de medii refrigerant-

aborbante s-au impus şi anume apa-bromura de litiu (LiBr), în care apa este refrigerantul iar

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bromura de litiu absorbantul şi amoniac-apa (apă/NH3, apă amoniacală) unde amoniacul este

refrigerantul iar apa este absorbantul.

În cazul sistemelor frigorifice se defineşte coeficientul de performanţă al producerii

frigului, COP, ca raport dintre energia necesară producerii frigului şi energia consumată.

Performanţele sistemelor de răcire sunt descrise de COP care are valori cuprinse între 2-5 pentru

sistemele cu compresie mecanică şi între 0,5-0,8 pentru cele cu activare termică.

3.4 Diagrama conversiei energiilor în sistemul CCHP

Schemei funcţionale a sistemului CCHP redată în figura 1 îi corespunde diagrama

energetică din figura 4. În baza performanţelor individuale ale elementelor componente se

analizează eficienţa energetică totală a sistemului CCHP. Celor două variante de răcire le

corespund - conform figurii - următoarele relaţii între energii:

a) Varianta cu compresie mecanică

c

cccg

COP

FEEEE , cgcg EQ , AMcgD QQQ , ICVD QQQ (4)

b) Varianta cu compresie termică

EEcg , cgcg EQ , AMcgD QQQ , a

aICVD

COP

FQQQ (5)

Relaţiile sunt completate cu

cg

cg

eW

E ,

V

CVQ

W

Q , Vcg WWW ,

W

QQFE AMICCHP

(6)

unde este indicele de cogenerare al pilei de combustie.

Ecg Ed E

Eb

Fc

EF F

QA

Qcg

F a

QD QI

W Wcg

QAM

Wv

PC

AC

FC

DC /AC

R

C V

FA

Fig. 4: Diagrama distribuţiei energiilor în mCCHP-ul propus

4 Studiu de caz al simularii sistemului CCHP

Mărimile de intrare în acest sistem sunt energiile cerute de consumatorul rezidenţial.

Datele despre consumurile standardizate de energie au fost preluate din informatiile publicate

de ANRE [4]. Conform Ordinului preşedintelui ANRE nr.117/14.08.2008, pe partea electrică

sunt definiţi cinci consumatori casnici standard iar din punct de vedere al consumului de gaze

naturale sunt trei categorii de consumatori finali casnici. Fiecare categorie este caracterizată de

consumul anual la energie electrică şi gaze naturale. Tabelul 2 Consumul de energie electrică – Sursa ANRE

Utilizatori finali casnici Consum de energie electrică anuală [kWh]

minim maxim

Tranşa - DA 1000

Tranşa – DB 1000 2500

Tranşa – DC 2500 5000

Tranşa – DD 5000 15000

Tranşa - DE 15000

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Tabelul 3 Consumul de gaze naturale – Sursa ANRE * Putere calorică superioară Utilizatori finali casnici Consumul anual de gaze [GJ] – PCS*

minim maxim

Tranşa – D1 20

Tranşa – D2 20 200

Tranşa – D3 200

Pentru fiecare tip de utilizator final casnic, consumul lunar de energie electrică s-a

considerat constant. Pentru a determina consumul de energie termică necesar încălzirii spaţiului

rezidenţial s-a considerat consumatorul de tip D3 cu un consum anual al gazului natural de

400[m3] în care consumul lunar a fost repartizat proporţional cu indicele termic, degree-day, din

zona Galaţi. Tabelul 4 Cantităţile lunare de energie vehiculate de mCCHP

Rezultatele simulării numerice, pentru un COP egal cu 3 al sistemului de răcire cu

compresie mecanică şi un COP egal cu 0,8 al celui cu compresie termică, evidenţiază - la consum

redus de energie electrică - un randament superior al instalaţiei cu compresie mecanică (figura 5,

a). La consumuri ridicate ale energiei electrice, randamentul instalaţiei cu activare termică se

apropie de cel al sistemului de răcire cu compresie mecanică (figura 5, b).

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

1 2 3 4 5 6 7 8 9 10 11 12

EET-FC

EET-FA

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1 2 3 4 5 6 7 8 9 10 11 12

EET-FC

EET-FA

a) Cerere de energie electrică 100 kWh/lună b) Cerere de energie electrică 200 kWh/lună

Fig. 5: Randamente ale sistemului mCCHP analizat

Energia gazului metan este consumată, în perioada de iarnă, atât de pilă cât şi de sistemul

de încălzire suplimentară (figura 6, a). Diferenţa între cele două moduri de realizare a

sistemului de răcire îşi pune amprenta asupra consumului de combustibil, în perioada de vară

(figura 6, a,b), în care sesizăm o cantitate mai mare de combustibil consumat de sistemul de

încălzire, în special, la cerere redusă de energie electrică.

Luna

Căldură

degree-days

Frig

degree-days Q(kWh) F(kWh) E(kWh) QAM(kWh)

Ianuarie 611 0 586 0 100 50

Februarie 521 0 500 0 100 50

Martie 403 0 387 0 100 50

Aprilie 207 33 199 0 100 50

Mai 40 208 0 199 100 50

Iunie 0 300 0 288 100 50

Iulie 0 363 0 348 100 50

August 0 363 0 348 100 50

Septembrie 6 234 0 225 100 50

Octombrie 195 53 187 0 100 50

Noiembrie 390 0 374 0 100 50

Decembrie 539 0 518 0 100 50

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0,00

0,50

1,00

1,50

2,00

2,50

3,00

1 2 3 4 5 6 7 8 9 10 11 12

Wv/Wcg-FCWv/Wcg-FA

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1 2 3 4 5 6 7 8 9 10 11 12

Wv/Wcg-FCWv/Wcg-FA

a) Cerere de energie electrică 100kWh/lună b) Cerere de energie electrică 200kWh/lună

Fig. 6: Raportul energilor sursă intermediară/pilă combustie

Economia de energie realizată prin utilizarea sistemului de răcire cu compresie mecanică

poate fi dedusă din figura 7 unde a fost prezentată energia combustibilului consumat pentru

cele două cereri de energie electrică. Pentru o cerere lunară de energie electrică de 100 kWh,

economia de combustibil este de 80 [m3].

0100200300400500600700800900

1000

1 2 3 4 5 6 7 8 9 10 11 12

W-FCW-FA

0

200

400

600

800

1000

1200

1 2 3 4 5 6 7 8 9 10 11 12

W-FCW-FA

a) Cerere de energie electrică 100kWh/lună b) Cerere de energie electrică 200kWh/lună

Fig. 7: Energia combustibilului

6 Concluzii

În urma analizei întreprinse, pot fi formulate următoarele concluzii:

Prin particularităţile lor constructive şi functionale (prin intermediul

coeficientului de performanţă al producerii frigului, COP), instalaţiile de răcire

influenţează, în mod radical, comportarea globală a sistemelor de trigenerare

(CCHP)

Sistemele de mCCHP au comportări diferite faţă de sistemele CCHP de medie şi

mare putere

În sistemele mCCHP răcirea prin compresie mecanică este superioară celei prin

compresie termică (eficienţă energetică mai ridicată)

La sistemele mCCHP – datorită eficienţei energetice ridicate a compresiei

mecanice – economia de combustibil este substanţială, în cazul utilizării acestei

metode în raport cu cea a compresiei termice.

Referinţe [1] I. Zamora, J.I. San Martín, A.J. Mazón, J.J. San Martín, V. Aperribay, J.M Arrieta, “Cogeneration in

Electrical Microgrids”, International Conference on Renewable Energy and Power Quality, Spain,

2006.

[2] I. Pilatowsky, R. J. Romero, C. A. Isaza, S. A. Gamboa,W. Rivera, P. J. Sebastian, J. Moreira,

“Simulation of an Air Conditioning Absorption Refrigeration System in a Cogeneration Process

Combining a Proton Exchange Membrane Fuel Cell”, International Journal of Hydrogen Energy,

2007

[3] V. Dorer, R. Weber and A. Weber, Performance assessment of fuel cell micro-cogeneration systems

for residential buildings, Energ Buildings 37 (11) (2005), pp. 1132–1146.

[4] *** ANRE nr.117/2008

Precizări – Prezentul studiu este susţinut financiar din PNCD II, proiectul nr.21063/2007.

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A specific study of art gallery lighting

TEOFIL OVIDIU GAL , DIANA POPOVICI,

University of Oradea, Armatei Române 1, 410087, Oradea ,Email, tgal@uoradea.ro

,dianap@uoradea.ro,

OVIDIU POPOVICI , LUCIAN MARIUS VELEA , LUMINITA CAMELIA PORUMB University of Oradea, Armatei Române 1, 410087, Oradea

Abstract -The present paper deals with the lighting system specific to an exhibition room

presenting art works (paintings, showcases and 3D exhibited items). The gallery is to be

designed so as to host more types of exhibitions. The main goal is to equip the art gallery with

a lighting system consisting of a certain number of different types of lighting aparates that

can be set on rails. These aparates can shed light on different exhibitions displaying 2D and

3D items different as far as their value, sensibility, material, age, colouring and ornament is

concerned. The dimension of the lighting is set both for an exhibition containing paintings

placed on the walls, easels and 3D items set in showcases and also for the future exhibitions.

1. Introductions

As contrasted with the museums that mainly exhibit objects, the galleries that temporarily

show paintings and sculptures require a project that will lighten the exhibits. The lighting of the

devised project will be important for keeping the architectural balance of the art.

A lighting system meant for art galleries has to take into consideration the setting of the

proper light for the exhibits, their protection,[3] the flexibility and performances of the special

lighting systems so as to adjust them to other types of exhibits.

The main goal of the special lighting systems is to prevent the artificial light from

damaging the exhibits; the light should be guiding, it should create the atmosphere, define the

spaces so as the viewers could enjoy each exhibit to the fullest without being disturbed by a too

intense or too dim light. Too intense or too dim light can simply diminish the experience when

visualizing the art works or other exhibits.

Light is an electromagnetic radiation that is only partly perceived by the typical human

eye. We distinguish only visible radiations including all rainbow colors (the spectrum) and the

wavelengths are measured by means of manometers.

1 nanometer = ( 1 millionth of millimetre )

A light source, whose illumination generates power radiation equaling all spectral colors,

produces a white light. Depending on the size of one glittering color or another, white varies

towards warm or cold. Visible radiations range between 400 nm and 750 nm, from violet to red.

Regardless the light color variations, our main focus here regarding the art works lighting

are the visible radiations, given the unfortunate effects thereof. Ultraviolet light ( over 400 nm )

and infrared light ( over 750 nm ).

The ultraviolet radiations are the most harmful for the exhibited works, and particularly

radiations below 360 nm. The rest ranging between 400 and 500 [4] nm correspond to violet

and blue while infrared radiations are to be found over the 700 nm limit and the heating effects

thereof are quite frightening. They share the effects with the entire visible spectrum and this heat

level increase may trigger harmful chemical effects.

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2. Light Sources

Besides the visible ones, light sources of either artificial or natural origin, generate ultraviolet

and infrared waves. Since the human eye does not distinguish them, they have, therefore, no

contribution to the increase of the brightness the objects receive (except for fluorescent pigments) [2]

3. Exhibit Lighting

Exhibition halls - related specific lighting must be designed so as to comply with the

following requirements:

a) Maximum exhibit protection against light harmful radiations:

UV waves elimination

Minimization of I.R. waves effects (heat)

Limitation of lighting level and of light exposure time, depending on exhibit value

and sensitivity level, as per the C.I.E. (Commission Internationale de Eclirage) classification.

b) Visitors must be provided with a perfect exhibit visibility and observation

Assurance of an adequate lighting level

Assurance of the exhibit lighting level uniformity

Avoidance of the direct or reflection glare effects

Accurate color and detail rendering

c) Assurance of light effects in order to create a specific atmosphere, direct the visitors

flow or draw the attention on certain focus-objects [5].

d) Flexibility and adaptability of the lighting system, for the exhibition re-arrangement or

change situations, as well as for the lighting of both two-dimensional and three-dimensional

objects that are placed in the same location

e) Possibility of control and command

f) Facilitation of subsequent development

g) Simple and low-cost maintenance

4. Ligting System Design

In order to comply with the requirements as stated[1] under section II, the devices are

selected so as to provide the following:

Light spectral stability

Adequate color temperature

Adequate power

Heating and mechanical stability of the lighting devices

Possibility to provide the lighting devices with certain accessories (UV and IV

filters, “sculpture” type lenses, etc)

Electric and mechanical stability of the auxiliary gear (rails, stands, etc)

Power efficiency

Limitation of the devices noise level

.

5. Lighting System Sizing

Throughout the system design process, we had the following at our disposal:

Location map of the space in question

Hall decoration blueprint, with the position of all exhibits

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3

A list of exhibits, with data regarding: size, materials and classifications under the

4 light sensitivity categories, as per the C.I.E. specifications

The exhibition special lighting project was designed in close cooperation with all

factors involved: exhibit restoration and preservation specialists, exhibition design specialists,

electrical design engineers, lighting design engineers

The light is meant to put the art works under the spotlight, without causing any damage.

Regarding the oil paintings conservation aspect, the annual lighting dose is set for 600.000

lxh/year, which means that we calibrated the exhibit lighting level around 150 lx. In what the

aquarelle and chalk paintings are concerned, the annual lighting dose is set for 150.000 lxh/year,

the recommended lighting level is 50 lx, but at this light level the visitor can hardly take any

delight in the paintings, we therefore calibrated the level at 100 lx according to the international

custom, yet under the specification that the exposure time must be limited.

In order to put under the spotlight both the paintings (chalk and oil) and the glass

window exhibits, I used the “panorama technique”, i.e. the visitors watch the well-lighted

painting from a poorly lighted spot. The ceiling and the walls color also leads us to using the

technique. Within this given context, we shall use mixed emphasis techniques (such as windows,

part of the paintings on the wall and the oil painting on the easel) and wall washing (wall light

wash for another part of the paintings on a wall). By emphasizing the exhibits, the light also

becomes the adequate guide for visitors by leading them through the various exhibition

themes/stages.[6]

Fig.1 Lighting accent

Fig.2. Wallwashing ( wall wash )

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4

Fig.3. Light Wallwashing

The lighting system sizing implies the selection of the adequate gear and devices,

depending on:

Lighting maximum level (lx)

Exhibits features and number

Exhibition hall sizes

The following stand for the technical content:

Accessories rails (power supply and electric connection couplings, mechanical

support devices)[6].

Various lighting devices (of the spot, flood or wall washer type)*

Various accessories: filters, flow control blades, lenses

Light sources, adjusted in terms of power, color temperature, type, U.V.

protection.

Fig.4.*Spot = a narrow distribution lighting device

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Fig. 5. * Flood = a wide distribution lighting device

Fig.6. Wall washer – wide, asymmetric distribution

lighting device for wall uniform lighting

5. Conclusions

The quality of the lighting is very important.

The lighting system of the art galleries is designed by means of stripes or bright lines set

on the contour and directed towards the display walls.

The lighting system must be designed so as to quickly adjust to new situations without

changing the draught. The lighting level of the art galleries must be decreased due to the

degradation effects caused to the exhibits.

References

[1] Bianchi, C. “L’effect de la distribution des luminances” Bul. Ştiinţific I.C.B., nr.1,

1972.

[2] CIE. “Guide on Interior Lighting”, nr.29/2-1986.

[3] Feller, R.L 1967. “ Control of deteriorating effects of light on museum

[4] IESNA.1996 “ Museum and art gallery lighting: A recommended practice”. New

York: Illuminating Engineering Society of North America.

[5] Michalski, S. 1987. “Damage to museum objects by visible radiation and ultraviolet

radiation” Proceedings of the Conference on Lighting Museums, Galleries and Historic Houses.

London: Museums Association. 1-16.

[6] Porumb, Camelia: “Studies and research regarding museums and art galleries related

lighting techniques”, PhD Thesis, 2007

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Aspects Regarding the Processing of Boxthorn Fruits in a

Microwave Electromagnetic Field

Teodor LEUCA*, Livia BANDICI* and Paula PALADE* University of Oradea, Faculty of Electrical Engineering and Information Technology,

nr. 1 Univeristii Str. 410087, Oradea, Romania

Abstract. This paper presents aspects regarding the role of the high frequency electromagnetic

field on the processing of boxthorn fruits. For the analysis of the electromagnetic field we used

a 3D model and the Method of the Finite Elements. We solved problems regarding the

coupling of the electromagnetic field with the thermal field and the mass.

1 Introduction

The continuous development of the branches of the food industry imposes both the

modernization and the development of some existing technological processes, and the

elaboration and implementation of some new methods of processing, using technological lines

of maximum efficiency.

The drying of wet products is a very difficult thermal and diffusion process. For complex

systems, like the boxthorn, the drying process has two components: the thermo-physical

component and the thermo-technological component, respectively [1].

The thermo-physical component of the drying process determines only the transfer of heat and

moisture through the thickness of the product layer, the thermo-technological component

presents the combination of the processes of heat and moisture transfer, associated with

chemical, biochemical and structural-mechanical transformations.

The choice of the drying procedure, of the optimum regime and of the construction of the drying

installation must be closely connected with the characteristics of the material and the drying

technology of one product or the other, based on the scientific theories of the drying technology

[2].

Nowadays, the technology of the drying process is connected with the basic laws of the heat and

moisture transfer in different products including the food products. The intensification of the

drying process of food products, including horticultural products must be directly connected

with the characteristics of the product and must develop with the securing of the quality of the

finite product.

Dried boxthorn represents a valuable product due to the wide range of nourishing substances

that it possesses. The most useful for drying are considered the boxthorn fruits with dense,

succulent pulp (the mass of a fruit is 0,7 gram/piece).

2 The Influence of the Characteristics of the Material on the Drying Process of Boxthorn

Using the High Frequency Electromagnetic Field

One of the main components that characterize boxthorn as a dielectric material is the oil

contained in the pulp of the fruits. The pulp of the fruits contains almost 8 % fat oil, and in the

kernel up to 12 %. Boxthorn in fresh state has a moisture of 83 % [2].

In the presence of the high frequency electromagnetic field, boxthorn heats depending on the

dielectric losses, determined by the values of the relative dielectric permeability ε’’ and the

tangent of the dielectric loss angle tgδ.

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The frequency of the electromagnetic field, the intensity and the electrophysical characteristics

of stone fruits influence the heating power and speed. The elaboration of the technological

regime for the drying of fruits is possible when the electrophysical properties and the

dependences of these properties on the electric field, temperature and moisture of the fruits are

known [3].

The dielectric constant (ε') represents the capacity of the material to store electromagnetic

energy. The dielectric loss factor (ε'') represents the capacity of the material to convert

electromagnetic energy into thermal energy. The calculation relation for permittivity is the

following:

ε = ε’- jε’’ (1)

The tangent of the loss angle is the relation between the dielectric loss factor and the dielectric

constant:

'tan

''

ε

ε=δ

(2)

The values of the dielectric constant and of the dielectric loss factor are used to estimate the

penetration depth in the case of the processing of a material in a microwave field. The

penetration depth is calculated with the relation:

[ ]1tan1'2f2

c

2

0

p

−δ+επ

=δ (3)

where: c0=3⋅108 [m/s]; f = 2,45 [GHz].

3 The Analysis of the Dissipation of the Electromagnetic Field in a Dielectric Situated in the

Interior of the Microwave Applicator

The power dissipated in the heating systems with microwaves is proportional with the

frequency, the dielectric properties and the distribution of the electric field [5]: 2

0

2 E"f2Ep ⋅ε⋅ε⋅⋅π=⋅σ= (4)

The electric field oscillating at the frequency of 2,45 [GHz] is calculated with the relation: z

0 eEE α−⋅= (5)

where:

1'

''1

2

''f2

25,0

00 −

ε

ε+

ε⋅ε⋅µ⋅µ⋅π=α (6)

Subdomain settings - Electromagnetic Waves:

00

j'20

kxr

1x =

ε⋅ω

σ−ε−

∇

µ∇ (7)

where: ε’- dielectric constant;

σ - electric conductivity;

µr - relative permeability.

Boundary Settings – Electromagnetic Waves:

n⋅E=0 (8)

The theoretical models for the distribution of the temperature and moisture during the drying

process with microwaves of the dielectric materials, including the food products has been

studied in detail by [6], [7], [8].

The mathematical model

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The fundamental theory of the heating and mass transfer in the interior of a microwave oven

was adopted taking into account a continuous distribution process of the electric field along the

wave guide.

The attenuation constant in this case must be adjusted taking into account the presence of the

dielectrics in the centre of the applicator according to the relation:

2'

0

g

a

w''37,17

λ⋅

λ⋅πε=α [dB/m] (9)

Subdomain Settings - General heat transfer:

( ) pTkt

TC

pts=⋅∇⋅−⋅∇+

∂

∂⋅ρ⋅δ

(10)

where: T- temperature (K);

δts - time scaling coefficient;

ρ - density (kg/m3);

Cp - heat capacity at constant pressure (J/(kg.K));

k – thermal conductivity (W/(m.K)).

Subdomain settings - General heat transfer:

( ) pTk =⋅∇⋅−⋅∇ (11)

The thermal transfer equation, neglecting the losses through convection and radiation during the

process of drying with microwaves is given by the relation:

p

1

h

p

v2

T

C

p

t

ML

CT

t

T

⋅ρ+

∂

∂ε+∇α=

∂

∂ (12)

The solving of the coupled problems regarding the phenomena of thermal and mass transfer is

extremely difficult, that is why we will consider some simplifying hypotheses, we will divide

the process into three regions: in the first we will consider the losses through convection and

radiation, in the second we will consider the process of drying with microwaves and in the third

the heating without drying, this will not be taken into account.

4 Numerical results In this paper it is shown an application of 3D numerical modelling, of a multimode applicator and in its interior we considered four boxes in which there are placed boxthorn fruits using the Method of the Finite Elements [9], [10]. The results we obtained allow the evaluation of the uniformity grade of the electric field both in the interior of the dielectrics and on their surface. The boxthorn fruits are static and have the same humidity (M= 50 %). The boxthorn fruits are considered uniform and homogenous, with constant dielectric and thermal properties. In fact, it is non homogenous, and the dielectric constants vary with the temperature. In fig.1, we present the geometry of the microwave applicators.

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Fig.1. Application geometry

In fig. 2, 3, we present the distribution of the electric field in a perpendicular plane on the port and in the boxthorn fruits.

Fig.2. Electric field distribution in port Fig.3. Electric field distribution in boxthorn fruits

In fig. 4, 5 we present the temperature distribution in the boxthorn fruits and variation of the

temperature from numerical modelling

Fig.4. Temperature distribution in the boxthorn fruits Fig.5. Variation of the temperature

In fig.6 we present the variation of the temperature in the mass of boxthorn fruits determined in

experimental way using a multimode applicator. The duration of the drying process is of 4 min.

at the power of the applicator of 300 W. The initial moisture of the fruits is 50%, and the final

moisture after 4 min. reaches the value of 17%.

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In fig. 7 we present the variation of the temperature using a power of 300 W in the initial phase

of the drying (T1=60s, T2=90s), and in the final phase of the drying, when the temperature is

stabilized, a power of 450 W (T1=120s, T2=90s). In this phase, the final moisture reaches the

value of 9%.

Fig.6. Variation of temperature (P=300 W) Fig.7. Variation of temperature (P=300/450 W)

In the first phase of heating, when the risk of thermal agitation appears, we used a lower power

(300 W), reducing the risk of deterioration of the boxthorn fruits. In the final phase of the

drying process we increase the power to the value of 450 W, thus reducing the drying time from

4 min. to 3 min.

Conclusions

The phenomenon of non uniformity can be removed by modifying the position of the wave

guide, the use of the modes agitators or, in the case of the cavities of large sizes, through the

movement of the load in the interior of the oven.

Taking into account all these problems which appear during the processing in a microwave

field, we can however state that the transfer phenomenon of the electromagnetic field in

microwave structures is performed faster, assuring thus higher efficiency and the absence of the

energy losses through thermal radiations.

At the same time with the increasing of the temperature, the conductivity coefficient of the

moisture increases suddenly; this phenomenon is determined on the one hand by the size of the

coefficient of the diffusion of the water vapour, and on the other hand on the decreasing of the

viscosity of liquid water in capillaries.

In the first phase of the heating, the moisture of the boxthorn fruits does not decreased

significantly, due to the negative gradient of temperature that exists in that moment.

In the period of actual drying, the temperature reaches the highest value, and then it decreases

gradually as the moisture approaches the balance moisture, but without reaching it.

References

[1] A. Gherghi, I. Burzo. Biochimia i fiziologia legumelor i fructelor. Editura Academiei Române,

2001.

[2] T. Funebo, T. Ohlsson. Dielectric properties of fruits and vegetables as a function of temperature

and moisture content. Journal of Microwave Power and Electromagnetic Energy. 34(1): 42-54.

[3] S.O. Nelson. Dielectric properties of agricultural products. IEEE transactions on Electrical

Insulation", 26(5): 845-869, 1991.

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[4] J.Tang. The Microwave Processing of Foods. Woodhead Publishing Limited. Schubert, H., and

Regier, M. (Eds) Cambridge, England 22-42, 2005.

[5] A.C. Metaxas, R.J. Meredith. Industrial microwave heating. Peter Peregrinus Ltd, London, UK,

1983.

[6] A.K. Datta. Mathematical modelling of microwave processing of foods An overview. Food

processing operations modelling: design and analysis, New York, pp. 147-187, 2001.

[7] L. Lu, J.Tang, X.. Ran. Temperature and Moisture Changes During Microwave Drying of Sliced

Food. Drying Tech, 17(3):413-432, 1999.

[8] Livia Bandici, T. Leuca, Paula Alexandra Palade. Some aspects regarding the optimization of the

electromagnetic field propagation in microwave structures. Journal of Electrical and Electronics

Engineering, 27-29 May, Oradea 2009, pp. 7-12, Vol. 2, nr.2

[9] Livia Bandici. The Influence of the High Frequency Electromagnetic Field on the Processing of

Forest Fruits. 13th IGTE Symposium on Numerical Field Calculation in Electrical Engineering,

September 22 – 24, 2008, pp. 375-378.

[10] T. Leuca, Livia Bandici, Paula Alexandra Palade, I. Stoichescu. Numerical analysis of the

electromagnetic field in microwave processing of forest fruits. Journal of Electrical and Electronics

Engineering, 27-29 May, Oradea 2009, pp.64-67, Vol. 2, nr.1.

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Performance Evaluation of a Class F Electrical Insulation System for Three Phase Induction Motors

Sonia DEGERATU, Nicu George BIZDOACA, Anca PETRISOR

University of Craiova, Faculty for Engineering in Electromechanics, Environment and Industrial Informatics, Bvd. Decebal 107, 200440, Craiova, Romania; sdegeratu@em.ucv.ro

Abstract. In order to assess the performances of AIIPGE class-F insulation system the authors present a comparison between the characteristics of this system and those of two similarly class-F insulation systems used by famous companies, ANSALDO-Italy and ELIN-Austria. AIIPGE insulation system has an important contribution to improve the performances of 6kV Romanian induction motors, with a power up to 2500 kW, and to assure a long life and high operation reliability compared to the same kind of motors using the ancient insulation system.

1 Introduction

The candidate insulation system, symbolized by AIIPGE, is the result of the theoretical and experimental studies performed on seven types of class-F insulation systems, conceived by the authors for the stator winding of 6kV induction motors, the AIIPGE being the powerful tested insulation system [1–3]. These studies constitute a response to the needs of Electroputere Romanian Company, which was decided to modify the range of the 6 kV induction motors, in order to provide a power up to 2500 kW, one of the objectives being the use of a powerful insulation system for the stator winding.

The AIIPGE insulation system allows reducing the unilateral thickness of the main insulation of the coils from 2 mm to 1.6 mm, compared to the ancient insulation system. Due to this fact and as well its excellent properties, was created the possibility to reduce both weight and size up to 15 % compared to the same kind of motors using the ancient insulation system [1, 3].

In order to ensure the quality level of AIIPGE, candidate insulation system, the experimental results obtained using this system will be compared with those of two reference systems, tested in the same way [4, 5].

Due to their excellent properties we have chosen the ANSALDO-Italy and ELIN-Austria as reference insulation systems [6, 7]. More else, the long successful experience in on-line service activity proves their outstanding reliability.

2 Test models

In order to establish the characteristics of the three analyzed systems we have used the formettes for the AIIPGE and ANSALDO insulation systems and three motors of HKG 150 K04 type, with 1000 kW, 6 kV, 1500 rpm (labelled M1, M2, M3), for ELIN system.

Electroputere Company manufactured 12 coils (of a real motor with 1000 kW, 6 kV, 1500 rpm), six with AIIPGE and the other with ANSALDO insulation system. The coils were released in groups of two same type coils, inserted (in double-layer) into a slot simulator, in order to obtain a formette [8].

The formettes are test motels, specially used for evaluation of insulation systems for windings [4].

Each coil had a different number punched on its upper part. This number represents the formette in which the coil was placed: 1, 2, 3 for ANSALDO coils, and 4, 5, 6 for AIIPGE coils.

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3 Results and discussion

Several tests were performed, on the manufactured models or motors, in order to evaluate the performances of analyzed systems.

Each value of the presented characteristics, referring to a certain formette, indicates the medium average value calculated for the two coils of the same formette.

The main tests carried out are presented hereafter.

High Voltage Test of the Main Insulation The rated withstand voltage of 13 kV has be applied, for 1 minute, between coil terminals and earth. All the three analyzed insulation systems passed this test.

Voltage Test of the Interturn Insulation The interturn insulation must support a voltage value Uw = 1.3UN/W (where UN represents the nominal voltage and W the number of the wires), applied during 5 minutes.

Uw = 600 V was chosen as test value. All the three analyzed insulation systems passed this test.

Polarization Index and Absorption Coefficient Test If the polarization index, Kp, and the absorption coefficient, Kabs, are small, the conduction is relatively high, generally due to humidity or to a great amount of conductive pollution in the insulation materials. On the other hand, if these index are large (greater than 2 and respectively 1.3) then the insulation is considered to be dry and in good state [1, 9, 10].

The figures 1 and 2 indicate the values of the Kp index and respectively the values of the Kabs coefficient for 4AIIPGE, 5AIIPGE, 6AIIPGE type of coils, and for the three ELIN motors, labelled M1, M2, M3 [1, 10].

The polarization index Kp and the absorption coefficient Kabs don’t give us any information about a particular malfunctioning of the isolation, but an overview on the general state of the insulation system. They don’t allow a prediction of the failure risks.

By analyzing the two figures we have to point out that high and grouped values of Kp and Kabs were obtained for the two insulation systems.

Dielectric Loss Factor Test This is one of the most efficient tests in order to establish the quality of an insulation system.

A good insulation system should have a tanδ-U/UN curve as linear as possible, where U/UN represents the relative values of applied voltage. Its ionization threshold should be greater than its service voltage in order to avoid a premature wear.

Figure 1: Kp values for the AIIPGE type of coils and for the three ELIN motors (M1, M2, M3)

Figure 2: Kabs values for the AIIPGE type of coils and for the three ELIN motors (M1, M2, M3)

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At the same time, the asymptotes attached to both of the curve branches should make a small angle compared to the ionization threshold. A great angle means that a great number of air pockets are present in the insulation.

Figure 3 gives the average values of tanδ, noted by A, corresponding to the relative applied tension U/UN = 0.2, for all AIIPGE type of coils and for the three ELIN motors. A good insulation system corresponds to values lower than 0.04, limit given by international norms [11].

Figures 4 and 5 indicate the average values of B and C, calculated for all AIIPGE type of coils and for the three ELIN motors. B and C have the following significance [1, 9, 11]: ( )2.06.0 tantan

21B δ−δ= (1)

( )60802

1.. tantanC δδ −= (2)

where: tanδ0.2; tanδ0.6; tanδ0.8 represent the average values of tanδ for all AIIPGE type of coils and for the three ELIN motors, at a relative tension applied (U/UN) of 0.2; 0.6 and respectively 0.8.

To avoid ionization threshold before reaching the rated voltage, the insulation systems must encounter the following relations: 31052 −⋅≤ .B and 3105 −⋅≤C .

By analysing the figures 3, 4 and 5 we notice very low values, either for A, or for B and C, in the case of AIIPGE and ELIN systems. So, the two tested insulation systems are efficient. Figure 6 indicates the tanδ-U/UN variation for all the AIIPGE or ANSALDO coils and for the three ELIN motors [1, 6, and 7]. In this figure tanδ represent the medium average values for all similar types of coils or motors at different relative applied voltages. Figure 6 shows that the three analyzed insulation systems present very little dielectric loss factor and very flat characteristics.

Figure 6: Curves tanδ-U/UN for the following insulation systems: 1-ANSALDO; 2-AIIPGE;

3-ELIN Figure 5: C values for the insulation systems

marked on the figure

Figure 3: A values for the insulation systems marked on the figure

Figure 4: B values for the insulation systems marked on the figure

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Insulation Time Factor Test The insulation time factor, T10, is not dependent on the motor’s size.

Values of T10 more than 25000 seconds correspond to a good insulation system resistance [1, 6, and 9]. Figure 7, gives us the values of T10 insulation time factor for the AIIPGE coils and for the three ELIN motors. By analyzing the figure, we notice that high and grouped T10 values were obtained for the AIIPGE and ELIN sistems.

Impulse Voltage Test The tests were carried out on the coils grouped in the following formettes: 5, 6 for AIIPGE system and 2, 3 for ANSALDO system.

The level of 29 kV is based on a standard lightning impulse having a front time of 1.2 μs and a time tohalf-value of 50 μs [10, 12, 13]. The level of 29 kV is obtained by application of the formula: 5kV4UU

NP+= (3)

where: UP = the rated lightning impulse withstand voltage (peak), given in [kV]; UN = the rated voltage, given in [kV].

This step includes the impulse voltage test of the interturn insulation and of the main insulation. This test was passed by all tested coils.

Breakdown Voltage Test The test includes the following steps [2, 12–15]: • the selection of the tested coils: we chose all the coils of type AIIPGE and ANSALDO; • their thermal ageing: exposure to a temperature of 170o C for 28 days; • their mechanical stress: endurance of an oscillation movement of 50 Hz with 0.3 mm amplitude; • their moisture stress: exposure to a 95% humid environment during 48 hours at 25o C; • the determination of the breakdown voltage of the main insulation.

The obtained results are presented in Figure 8. In this figure, the values of the breakdown voltage for the coils also tested with the impulse

voltage are presented with green bars and for the other coils, with white bars. The analysis of Figure 8 shows that the impulse voltage test did not affect in a significant way

the values of the breakdown voltage for the tested insulation systems. These tested systems were presented higher and approaching values for the breakdown voltage.

Figure 7: T10 values for the AIIPGE type of coils and for the three ELIN motors (M1, M2, M3)

Figure 8: Values of breakdown voltage for AIIPGE and ANSALDO type of coils

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Evaluation of the thermal endurance For this test, effectuated in our laboratories on the AIIPGE insulation system, were used parts of a real motor’s stator called motorettes. The motorette contained 10 coils. Three motorettes, corresponding to a different exposure-temperature (170oC, 190oC, 210oC), were manufactured for the AIIPGE tested system [1, 14].

The AIIPGE system was evaluated using the aging method by repeated cycles of heat, vibration, moisture and electrical stress [14, 16]. After each exposure to moisture, the voltage is applied in succession to ground, and between conductors for ten minutes, when the specimens are still in the humidity chamber exposed at approximately room temperature. Experience has shown that applying voltage during an extended time, in humidity conditions is necessary to detect failures.

The ageing cycles repeat until the end point of insulation system life is established. The thermal endurance graph for the AIIPGE tested insulation system is presented in

Figure 9. The abscissa contains the values of the time to failure (in hours) for each ageing temperature while the ordinate gives us the reciprocal thermodynamic temperatures.

This thermal endurance graph was acquired by means of statistical computing of the results [2], [8], [9], using a home developed Visual C++ 6.0 program [1].

From Figure 9 we can observe a long life (around 28 years) at the optimal motor‘s temperature, a thermal index of 167oC, and an active energy E = 1.025 eV, for the AIIPGE system.

After the thermal endurance test the AIIPGE system was approved in the class-F temperature. Figure 10 indicates the life-curve of the MICASYSTEM-ANSALDO insulation system

(obtained after similar tests), with a thermal index 166oC [7]. If we choose an ageing temperature of 180oC, the average life time for the systems AIIPGE, and MICASYSTEM-ANSALDO are 9146 h and respectively 9890 h.

4 Conclusion

In this paper, comparative parameters are presented for the AIIPGE, ANSALDO and ELIN electrical insulation systems. The analysis of the results allows us to conclude that: • AIIPGE candidate system provides performances virtually identical with those of reference

systems, ANSALDO and ELIN. • AIIPGE insulation system was approved in the class-F temperature, after the thermal endurance

test. AIIPGE system being used in class-F and having an index temperature of 167oC, it follows

Figure 9: Thermal endurance graph for the AIIPGE system

Figure 10: Thermal endurance graph for the MICASYSTEM – ANSALDO system

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that it has a large thermal reserve, so a thermal stability that ensures superior reliability of the motor to normal operating temperature of 155oC, while concurrently allowing it to withstand exposure to higher temperatures, short duration, on overload, without risk.

• The tests achieved in our laboratories show that AIIPGE insulation system presents the following excellent properties: high breakdown voltage of the main insulation; very high insulation time factor (more than 25000 seconds that means very high insulation resistance); non-susceptibility to ingress of humidity, due to very high Kp and Kabs; very little dielectric loss factor, tanδ, with very flat characteristic tanδ-U/UN; long life and high operation reliability. That is why the AIIPGE system is used at all the windings of 6kV induction motors made by

Electroputere Romanian Company. References [1] S. Degeratu, Contribuţii în realizarea şi atestarea schemelor de izolaţie ale maşinilor asincrone de

înaltă tensiune. Teză de Doctorat, Universitatea din Craiova, 2002. [2] M. Spanu., S. Degeratu, s.a., Scheme noi de izolaţie pentru maşinile electrice de joasă şi înaltă

tensiune. Contract 146C/1994, M.I.S., Departamentul Ştiinţei, Bucureşti. [3] S. Degeratu, V. Degeratu, D. Alexandru, Analyse des données expérimentales des systèmes d’isolation

AIIPGE et AIIP pour les moteurs asynchrones de 6kV – Partie I: Evaluation des performances. Annals of the University of Craiova, 26 (2002), 110-118.

[4] Publication CEI 34-18-1/1992, Evaluation fonctionnelle des systèmes d’isolation des machines électriques tournantes.

[5] IEEE Std. 275/1981, Test Procedure for Evaluation of Systems of Insulating Materials for A-C Electric Machinery Employing Form – Wound Preinsulated Stator Coils.

[6] ELIN. Technical Catalogue MA 23, PRO-MOTOR. .A New Series of Threephase Asynchronous Motors with Squirrel-Cage Rotor for High Voltage “surface cooled”, No. 8/1993.

[7] MICASYSTEM C-1695 Insulation System for A.C. Rotating Machines. Group ANSALDO, Siag-Genova, No 4, 1984.

[8] T. Hillmer, H. Brandes and Nancy Frost. New Generation of a Class 180 (H) Electrical Insulation System for High Voltage Machines, Iris Rotating Machine Conference, June 2007, San Antonio. [9] D. Phillipe, Etude de la dégradation des isolations solides sous moyenne tension alternative en

régime de décharges partielles. Doc. Thèses, Université Paris 6, 1991. [10] R. Goffaux, Sur les conditions de développement de la défaillance de l’isolation entre spires de

bobinages statoriques de machines C. A. Revue Générale Electrique, No.1, 6-12, 1993. [11] VDE 0530 Teil 1/11.1992. Bestimmungen fur umlaufeude elektrische maschinen, 74-75, 1992. [12] R. Brütsch and P. Weyl. A New Winding Wire for Inverter Driven Motors, 9th INSUCON

International Electrical Insulation Conference, Berlin, 2002. [13] R. Brütsch, T. Hillmer and R. Scollay. A New Insulation System for Inverter Driven Motors, Coil Winding, Insulation and Electrical Manufacturing Conference, Berlin, 2000. [14]Publication CEI 610/1978. Principaux aspects de l’évaluation fonctionnelle des systèmes

d’isolation électrique: Mécanismes de vieillissement et procédures de diagnostic. [15] A. Sh. Azizov, A. M. Andreev, A. M. Kostel’ov and Yu. A. Polonskii. The Improvement of the

Electrical Insulation of High Voltage Electrical Machines, Russian Electrical Engineering, 78 (2007), 109–112.

[16] IEEE Std. 101/1992, Guide for the Statistical Analysis of Thermal Life Test Data. Acknowledgments - This work was carried out in cooperation with the Department of Electrical Machines from Electroputere Romanian Company. We are deeply grateful to Eng. Marin Teodorescu, Head of this Department, who provided excellent conditions, candid support and encouragement during this work.

This research was financially supported by the Electroputere Romanian Company.

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Thermal Characterization and Design of an Actuator based on a Shape Memory Alloy Wire working against a steel spring

Sonia DEGERATU, Rotaru PETRE, Nicu George BIZDOACA, Horia Octavian MANOLEA University of Craiova, Faculty for Engineering in Electromechanics, Environment and Industrial

Informatics, Bvd. Decebal 107, 200440, Craiova, Romania; sdegeratu@em.ucv.ro

Abstract. The paper presents the thermal characteristics and the design strategy for a shape memory actuator structure of intelligent systems, using as active element Ni-Ti SMA wire working against a conventional steel spring. For design optimization a comprehensive graphical interface, which runs under Visual Basic environment, has been developed for this actuator structure.

1 Introduction

Shape Memory Alloys (SMAs) are smart materials which exhibit some unique properties i.e. shape memory effect and pseudo-elasticity [1, 2]. The cause is a martensitic phase transformation between a high temperature parent phase, austenite (A), and a low temperature phase, martensite (M). In absence of stress, the start and finish transformation temperatures are typically denoted Ms, Mf (martensite start and finish) and As, Af (austenite start and finish) [2, 3].

Due to their unique properties and behavior, SMAs play an increasingly important role in the intelligent systems performance. Recent applications in structural actuation and sensing demand increased material capabilities, and SMAs possess a great potential for use in these applications [3, 4].

The paper presents the thermal characteristics and the design strategy of an actuator structure of intelligent systems, using as active element a Ni-Ti SMA wire working against a conventional steel spring (referred to in this case as the “biasing” spring).

Ni-Ti, known commercially as Nitinol, is the material used for the studied SMA wire, due to its several advantages: very large recoverable motion, great ductility, excellent corrosion resistance, stable transformation temperatures, high biocompatibility and the ability to be electrically heated for shape recovery [2, 3, 5–7].

The Ni-Ti SMA wire, with a 0.35 diameter, was purchased from the Mondo-Tronics. The attention of the authors was focused on thermal analysis experiments, in order to

determine the transformation temperatures for the studied Ni-Ti SMA wire. For design optimization a comprehensive graphical interface (based on the thermal analysis

results), which runs under Visual Basic environment, has been developed for the Ni-Ti SMA actuator structure.

2 Experimental

SMAs exhibit a large temperature dependence on the material shear modulus, which increases from low to high temperature. Therefore, as the temperature is increased the force exerted by a shape memory element increases dramatically [1, 2, and 7]. Consequently, the determination of the transformation temperatures is necessary to establish the real shear modulus values at these functional temperatures for a high-quality design of intelligent systems [2, 3, 7–9].

Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC) methods were used to determine the required transformation temperatures of SMA wire, and Thermogravimetric Analysis (TG) was used to prove the stability of the alloy [10–12].

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During the tests, both isothermal and non-isothermal regimes combined with heating–cooling experiments, were used in order to characterize Ni-Ti SMA samples.

The measurements were carried out on a horizontal Diamond Differential/Thermogravimetric Analyzer from Perkin-Elmer Instruments in dynamic air atmosphere (150 mL/min), in aluminum crucible, using as reference similar amounts of inert α-A2O3 powder.

Initial, the phase transitions of the test sample were identified by analyzing his behavior at programmed heating up to 100oC and cooling to ambient temperature, using a linear non-isothermal regime. It was noticed that the mass of the sample does not undergo any changes at heating and cooling. In consequence, the TG curve is ignored in further measurements and in the present paper.

3 Results and discussion

Several Thermal Analysis measurements (DTA and DSC) of Ni–Ti SMA wire material (0.35 diameter) were carried out in dynamic air atmosphere.

The thermo analytical curves, DSC and DTA, during heating regime by 10 K/min, in dynamic air atmosphere, for 5.092 mg Ni–Ti SMA wire material, are presented in the figures 1 and 2.

The thermo analytical curves, DSC and DTA, during cooling regime by 1K/min, in dynamic air atmosphere, for 5.067 mg Ni–Ti SMA wire material, are presented in the figures 3 and 4.

The cooling regime of speed was slower than it was the heating one and that was in order to distinguish all the transformations that took place during that testing process.

By analyzing the figures 1, 2, 3, and 4 we can observe two phase transitions. The first occurs during the heating process, while the second one appears during the cooling process. The transitions, as can be seen from DSC curves in these figures, correspond to typical first order phase transitions.

Figure 1: The DSC curve for 5.092 mg SMA wire during heating regime, by 10 K/min.

Figure 2: The DTA curve for 5.092 mg SMA wire during heating regime, by 10 K/min.

Figure 3: The DSC curve for 5.067 mg SMA wire during cooling regime, by 1 K/min.

Figure 4: The DTA curve for 5.067 mg SMA wire during cooling regime, by 1 K/min.

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The details of these thermal effects are presented in figures 5 and 6 (reported from the DSC curves).

DSC parameters for the thermal analysis of Ni–Ti SMA wire material, in dynamic air atmosphere, are presented in Table 1.

Table 1 - DSC Parameters for Ni-Ti SMA Wire Material Phase

transition Thermal effect Endo/Exo

Transformation temperatures

°C

Transferred heat

ΔH/J·g-1

Temp. of the max. transformation rate

oC

Peak height mW

Martensite to austenite

(at heating) endothermic As=62.30

Af=70.60 3.7937 65.77 -0.6613

Austenite to martensite (at cooling)

exothermic Ms=33.90 Mf=31.40 -1.3200 32.90 0.0571

4 Design strategy

This article also includes the design strategy for an actuator based on the SMA wire with biasing spring. The first step an engineer should take when undertaking a design involving shape memory material is to clearly define the design requirements. These usually fall into one of the following interrelated areas: operating mode, design assumptions, actuation mode, operational temperatures, computation algorithm (with force, motion and cyclic requirements) [2, 3, 8, 12, and 13].

SMA’s operating modes The most used operating modes of SMAs are: free recovery, constrained recovery and work production [2, 3 and 6]. The application presented in this paper uses a work production operating mode; the SMA wire works against a varying force to perform work.

Design assumptions In the design of SMA actuator structure the friction effect is neglected and a linear stress-strain behavior is assumed, in order to simplify the analysis [2, 3 and 12].

Actuation mode The Ni-Ti SMA wire is actuated via direct current (change in temperature is internally generated by resistance heating), because of the high resistivity of Ni-Ti. It is possible to apply direct D.C. or A.C. currents to a Ni-Ti wire, but care must be taken so that the maximum temperature reached is at or below 250 oC, in order to avoid thermal instability [2, 14].

Figure 6: Detail of DSC curve for computation transition at cooling of Ni-Ti SMA wire material

Figure 5: Detail of DSC curve for computation transition at heating of Ni-Ti SMA wire material

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Operational temperatures The operational temperatures of SMA wire, at heating and cooling, are identical with the transformation temperatures, Af=70.60°C and respectively Mf=31.40°C, presented in the Table 1.

Computation algorithm In the analyzed actuator system (SMA wire with biasing spring) the varying force is produced by a steel spring (middle part of Fig. 7). The force which the SMA wire must now work against varies with deflection. At low temperature the steel spring is able to deflect the SMA wire to its elongate length. When the temperature of the SMA wire is raised, it compressed, expanding the steel spring and moving, for example, a push-rod.

It is assumed that there is no friction present in the system, in order to simplify the analysis. The basic problem here is to design a SMA actuator wire of the smallest total force output possible which will generate the required net output force Fn. This means that the spring rate of the biasing spring, Kb, must be as low as possible in order to minimize the force which the SMA wire must provide to deflect the biasing spring at high temperature.

The most important relations involved for the actuator structure design are presented hereafter. • SMA wire diameter [2, 3]

hπσ

4Pd = [mm] (1)

with: P = total force required from the SMA wire at high temperature (P = Fn + Fh), in [N]; Fn = required net output force of SMA wire; Fh = force exerted by the biasing spring; σh = maximum design stress at high temperature, in [MPa]. • Required (free) SMA wire length [2, 3]

hl

f εεsrokeL−

= [mm] (2)

where εl and εh are the low and high temperature strain. • High temperature SMA wire length fhfh LLL ⋅+= ε [mm] (3)

• SMA wire reset force [2, 3]

4

2dR l

⋅⋅=π

σ [N] (4)

where σl is the low temperature tensile stress. • Bias rate [2, 3]

stroke

FFK lh

b−

= [N/mm] (5)

where Fl is the low temperature force which the biasing spring must exert, equal to the SMA wire reset force, R. • Bias wire diameter [2, 3]

3 552T

DF.d bh

b××

= [mm] (6)

where: Db = average bias spring diameter; T = maximum bias shear stress; • Number of bias active turns [2, 3]

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bb

b

KD

Gdn

3

4

8= (7)

where G is the bias spring shear modulus, in [MPa]; • Bias spring length at high temperature hbh LthicknessplugsystemoflengthtotalL −−⋅⋅= [mm] (8)

Numerical example A Visual Basic project for the analyzed actuator system, made of SMA wire and biasing spring, was implemented. The list of the most important relations involved in the background application computations was already presented.

Below, a numerical example is given illustrating the abilities of the Visual Basic application.

For the present design example, assume the following requirements: • a Ni-Ti wire - biasing spring combination is required providing a net force Fn=10.04N with

an 2.2mm stroke; • the total length and the width of system are 146.5mm and 4.7mm respectively.

Assume that the force exerted by the biasing spring Fh=6.5N, the maximum SMA wire design stress at high temperature σh = 172MPa, and the low temperature shear strain γl = 0.02 (in order to ensure a good cyclic life).

The transformation temperatures, at heating and cooling, are those presented in Table1, that are Af=70.60°C and Mf=31.40°C respectively. For these temperatures the experimental determined values of Young’s modulus are Eh = 66000MPa and respectively El = 3200MPa.

Also assume that the wire and spring are separated by a plug of thickness 2.5mm. Using standard steel spring design procedure, assume that the maximum shear stress for the steel material is T = 895MPa. The bias spring shear modulus is G = 79300MPa.

When the Visual Basic project is run, a user interface is displayed, figure 7.

Figure 7: Dialog interface for the SMA wire with biasing spring.

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After providing the initial parameters in the dialogue boxes of this user interface, by pressing the compute button the designed parameters are being displayed in the upper part of the window.

The middle of the window displays the SMA actuator structure as well as all design parameters.

5 Conclusion

The paper presents the design strategy for an actuator based on a SMA wire working against a conventional steel spring. For this strategy the authors defined: operating mode, design assumptions, actuation mode, operational temperatures, and computation algorithm.

Using Thermal Analysis Methods the authors determined the experimental transformation temperatures for the studied SMA wire. These temperatures were necessary to precisely establish the shear modulus values for a high-quality design.

For design optimization a Visual Basic application was developed, providing: • adequate dialogue boxes for fast and easy initial parameters configuration; • fast computation and display of all required information for a SMA actuator design; • remarkable facilities to analyze results and choose an optimal solution.

This Visual Basic application is already used by ICMET Craiova for engineering purposes and by the Faculty of Electromechanical Engineering of Craiova for didactical ones.

The actuator based on SMA wire with biasing spring is used in connecting part of modular robotic structures, in locking-unlocking mechanisms. References [1] G. Ramanathan et al. Experimental and Computational Methods for SMAs, Proceedings of 15th ASCE

Engineeering Mechanics Conference, June 2-5, Columbia University, 2002, pp. SA 40. [2] T. C. Waram. Actuator Design Using Shape Memory Alloys, Ontario Press, Canada, 1993. [3] S. Degeratu and N. G. Bizdoaca. Shape Memory Alloys: Fundamentals, Design and Applications,

Universitaria Press, Craiova, Romania, 2003. [4] N. Vincenzo, R. Cesare and S. Savino. Perspective Transform in Robotic Applications, WSEAS

Transactions on Systems, 5 (2006) 678-685. [5] J. Rena and K.M. Liewa. Meshfree modelling and characterisation of thermomechanical behaviour of NiTi alloys, Engineering Analysis with Boundary Elements 29 (2005) 29–40. [6] Kiyohide Wada and Yong Liu. Shape recovery of NiTi shape memory alloy under various

pre-strain and constraint conditions, Smart Mater, 14 (2005) 273–286. [7] Antonio Vitiello, Giuseppe Giorleo and Renata Erica Morace. Analysis of thermomechanical behaviour of Nitinol wires with high strain rates, Smart Mater, 14 (2005) 215–221. [8] T. W. Duerig et al. Engineering Aspects of SMAs, Butterworth- Heinemann, London, 1990. [9] Tan Wee Choon, Abdul Saad Salleh, Saifulnizan Jamian, and Mohd. Imran Ghazali. Phase Transformation Temperatures for Shape Memory Alloy Wire, World Academy of Science, Engineering and Technology, 25 (2007) 304-308. [10] J. Cao. Numerical simulation of DSC and TMDSC curves as well as reversing and non-reversing

curve separation, Journal of Applied Polymer Science, 106 (2007) 3063-3069. [11] C. Auguet, A. Isalgue, F.C. Lovey, J.L. Pelegrina, S. Ruiz and V. Torra. Metastable effects on

martensitic transformation in SMA, Journal of Therm Anal Calorim, 89 (2007) pp. 537–42. [12] Hyo Jik Lee and Jung Ju Lee. Evaluation of the characteristics of a shape memory alloy spring

actuator, Smart Mater. Struct., 2000. [13] S. Degeratu et al. Visual Basic applications for shape memory elements design used in intelligent

systems, Proceedings of 5th International Conference on Informatics in Control, Automation and Robotics, 2008, Madeira, Portugal, 2008, pp. 207–10.

[14] Z.G. Wang, X.T. Zu, X.D. Feng, S. Zhu, J.W. Bao and, L.M. Wang. Characteristics of two-way shape memory TiNi springs driven by electrical current, Materials and Design 25 (2004) 699–703.

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Acknowledgments - This work was supported by the National University Research Council (CNCSIS) of the Romanian Minister of National Education. It is part of a project covering theoretical and applicative researches on SMA actuators used in the robotic field.

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Single-phase operation of a three-phase induction generator

Catalin Petrea ION, Corneliu MARINESCU Transilvania University of Brasov, 29 Eroilor Bvd, 500036 Brasov, Romania; catalin.ion@unitbv.ro

Abstract. This paper presents an efficient method to supply single-phase loads with a three-phase induction generator (IG). A combination between a properly controlled voltage source inverter (VSI) and dump load (DL) ensures, besides the phase balancing of the IG, the voltage and frequency regulation. Simulations and experiments are carried out in order to highlight the reliability of such a configuration.

1 Introduction

The penetration of renewable energy sources in energy production is a consequence of the rapid depletion of conventional fuels and is also due to environmental concerns. In Romania, energy production from renewable sources is based mainly on hydro power; the relief configuration offers a large potential for small and micro hydro plants.

For stand-alone generating units based on micro-hydro, the IG is the most suitable, due to the following advantages over the synchronous one: price, robustness, simpler starting and control. On the other hand, this mode of operation is dependable on the prime – mover speed, capacitor and load. Thus, proper regulators for both voltage and frequency must be employed. In rural and isolated places with installed powers bellow 10 kW, the single-phase consumers are predominant. Thus, the use of a single-phase induction generator appears as the most appropriate solution. Although all single-phase induction motors can operate as generators, they do not give the best performance since they have been designed for optimal motor operation. To overcome this problem, a specially designed two winding single-phase SEIG has been studied [1]. Another inconvenient is that the power of these machines is limited by their constructive characteristics, being used at powers up to 3-4 kW.

With some adaptations, a three-phase induction machine can be used to supply single-phase grids. Over the years, several topologies have been developed [3-7]. In [3], with the use of only one capacitor for self-excitation, several types of the Steinmetz connection resulted. The IG behavior when connected to a single-phase power grid is studied in [4, 5], where the authors analyze the Smith connection and the use of a transformer to inject current into the “free” terminal of the stator winding. For ∆ connected machines, the C-2C connection is employed, and a control topology is given by the authors [6]. In [7], for a star connected machine, three capacitors connected in parallel and series with the single-phase load ensure the phase balancing. Power electronics is also used to obtain balanced operation of a three-phase IG when delivering power to a single-phase grid [2]. A more expensive solution for the same situation with the one presented above proposes the use of two back-to-back converters [8].

The proposed control topology is a combination between a voltage source inverter (VSI) and dump load (DL); it ensures the balanced operation and voltage and frequency regulation for an autonomous three-phase IG that supplies single-phase loads.

2 System configuration

Figure 1 shows the system configuration of the autonomous IG, with the capacitor bank, the VSI and DL circuits and the single-phase consumer loads. The capacitor bank supplies the reactive power for the IG self-excitation process and sustains the rated voltage in steady-state

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regime. The additional reactive power requirements from the loads will be met by the voltage source inverter (VSI).

The voltage source inverter (VSI) operates at constant synchronous frequency (fn=50Hz), maintaining the IG frequency constant. As the single–phase loads are connected between two phases (the IG is ∆ connected), the IG currents become unbalanced. The VSI will perform also the phase balancing, by redistributing its currents in order to obtain balanced currents at the IG leads. An unbalances compensation algorithm is added to VSI control circuit.

The dump load (DL) circuit is connected to the VSI DC side. It is controlled so that the voltage across the CDC capacitor remains at a constant level, maintaining the system voltage in a standard variation range, like in [10]. The amount of power delivered to the DL is varied by modifying the PWM duty cycle that drives the TD transistor.

Figure 1: Circuit diagram of the studied topology.

3 Control structure

The VSI is a three-phase inverter with PWM control, connected to the IG leads through filtering inductances (one for each phase). Its control requires six PWM pulses, one for each of the bridge transistors. By operating at constant 50Hz frequency (excepting the start-up interval), it keeps the IG voltage frequency also constant.

Figure 2: The VSI control strategy.

By connecting the IG in Δ, the phase voltage is 230V. The single-phase loads, as can be seen in figure 1, are connected between two of the three phases. Thus, the IG currents become unbalanced, as well as the currents through the VSI. The control topology aims to balance back the IG currents by modifying the current circulation through the VSI. In order to do that, the VSI will act as an unbalances compensator, according to the load. As the loads are varying randomly, the VSI control must quickly adapt to maintain the IG balance currents.

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In the unbalance compensation control scheme, depicted in figure 2, the A phase current is considered as reference and the B and C current references are obtained by lagging the A current with 120 and 240 degrees. The unbalances compensation control scheme contains two stationary-frame regulators called Proportional-Resonant (PR) controllers, which are based on stationary-frame generalized integrators. These regulators report very good performances, actually achieving the same transient and steady-state performance as a classical synchronous-frame PI regulator [12]. The obtained reference currents are compared with the measured one, and the resulting error serves as input for the two PI regulators.

Figure 3: The unbalances compensation scheme.

To maintain the system voltage in a standard variation range, the control system acts on the

DC capacitor voltage in order to maintain it at a constant level. The difference between the power delivered by the IG and the loads demand will circulate through the VSI towards the CDC capacitor, and will be consumed by the DL circuit resistor.

Two PI controllers are used to regulate the system voltage, as shown in Fig. 4. The first PI controller is the leading voltage regulator. It compensates the voltage drops across the inverter arms and filter, IG leakage impedances, and other circuit elements, which usually led to a decrease of the IG voltage. The IG root-mean-square (RMS) voltage (VAB) is the feedback signal, it is compared with the 230 V reference signal (VREF), and the error feeds the PI controller, giving the reference signal (VDCref) for the second controller. The second PI is used to maintain constant the CDC voltage. The allowed voltage variation (ripple) across CDC capacitor (ΔVDC) will give the frequency and the width of the pulses that drive the DL transistor.

Figure 4: The DL control scheme.

4 Simulations and experimental results

The reliability of the proposed control topology is tested through a series of simulations and experiments. The simulations were made under the Matlab/Simulink environment. The

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configuration includes a 2.2kW IG, a block that models the prime mover (hydraulic turbine), the VSI and DL, an adequate capacitor bank, loads and measurement blocks.

The experimental setup consists in a 2.2 kW three phase induction generator, driven by a 3kW induction motor which emulates a hydraulic turbine (with the use of a DS1102 system from dSPACE). The VSI is actually an industrial converter, connected to the IG leads through a filter with R=0.1Ω and L=6,5mH. On the converter DC side there are two 4700μF capacitors connected in series. The DL circuit consists in an IGBT transistor and a 155Ω dumping resistance. Data acquisition and system command is ensured by a dSPACE 1103 control board. 3.1. Simulation results The IG is connected in Δ, thus its line voltage will be 230V. Initially, the generator produces around 1300W; this power flows through the VSI towards the DL. Then, a 600W single-phase load is connected between two phases. When this thing occurs, at t=2.5s, the unbalances compensator is disabled. At t=3.5s the unbalances compensator is enabled. In approximately 1 second, the IG currents become balanced (around 6.5A each). The RMS IG currents variation is depicted in figure 5 (left).

The unbalances compensation consists in redistributing the currents through the VSI. Before the single phase load connection, the power produced by the generator flows through the VSI towards the DL circuit. After the load is connected, the VSI currents also become unbalanced. The unbalances compensator will redistribute the currents through the VSI in order to obtain balanced currents at the IG leads, as results from figure 5 (right).

2 2.5 3 3.5 4 4.5 5 5.54

4.5

5

5.5

6

6.5

7

7.5

8

Time [s]

IG R

MS

Cur

rent

s [A

]

2 2.5 3 3.5 4 4.5 5 5.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Timp [s]

Cur

enti

IT [A

]

Figure 5: The IG (left) and VSI (right) RMS currents.

3.2. Experimental results The same operating conditions as in the previous paragraph are applied to the experimental setup. After the load connection, the IG currents will become unbalanced, as can be seen in figure 6. The A phase current will settle at 6.5A, the B phase current at 5.8A and the C phase one at 6A. The unbalances compensator activation leads to phase balancing, bringing all three currents to 6.25A. The unbalanced VSI currents modify also, in order to ensure balanced currents at the IG leads, as results from figure 6. In figure 7, the IG currents waveforms before and after the unbalances compensator activation are depicted.

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Figure 6: The IG (left) and VSI (right) RMS currents.

Figure 7: The currents through the IG without (left) and with (right) the unbalances compensator.

After the R load connection, at t=2s, the IG voltage has a little sag, in consequence, the VSI DC capacitor voltage decreases as well, the regulators command an increase of the DC voltage in order to compensate this phenomena. The voltage drop is small (around 6V), and the voltage regulator brings the voltage to its rated value in approximately 1 second. The frequency variation is insignificant, as can be seen in Fig. 8 (right).

Figure 8: The IG RMS Voltage (left) and frequency (right) variation at the load connection.

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5 Conclusion

• This paper investigates the operation of an autonomous three-phase induction generator when supplying single-phase loads.

• The proposed control strategy employs a combination between a VSI and DL. • An unbalances compensation algorithm is developed in order to deal with the asymmetric

currents flowing through the generator. • Both simulations and experimental results have shown that the unbalances compensation

algorithm of the VSI is effective, ensuring a balanced operation for the IG. References [1] K. Tiwari , S.S. Murthy , B. Singh , L. Shridhar, Design-based performance evaluation of two-

winding capacitor self-excited single-phase induction generator. Electric Power Systems Research 67 (2003) 89-97

[2] Machado, R.Q.; Buso, S.; Pomilio, J.A.; Marafao, F.P., "Three-phase to single-phase direct connection rural cogeneration systems " Nineteenth Annual IEEE Applied Power Electronics Conference and Exposition, 2004. APEC '04. Volume 3, 2004 Page(s):1547 - 1553 Vol.3

[3] Li Wang; Ruey-Yong Deng; "A novel analysis of an autonomous three-phase delta-connected induction generator with one capacitor" IEEE Power Engineering Society General Meeting, 2006, 18-22 June 2006, Page(s):6 pp.

[4] Chan, T.F.; Loi Lei Lai; "Single-phase operation of a three-phase induction generator with the Smith connection" IEEE Transactions on Energy Conversion, Volume 17, Issue 1, March 2002 Page(s):47 - 54

[5] Chan, T.F.; Lai, L.L.; "Single-phase operation of a three-phase induction generator using a novel line current injection method" IEEE Transactions on Energy Conversion, Volume 20, Issue 2, June 2005 Page(s):308 - 315

[6] Singh, B.; Murthy, S.S.; Gupta, S., "Analysis and design of electronic load controller for self-excited induction Generators" IEEE Transactions on Energy Conversion, Volume 21, Issue 1, March 2006 Page(s):285 - 293

[7] S.N. Mahato, M.P. Sharma and S.P. Singh, "Transient performance of a single-phase self-regulated self-excited induction generator using a three-phase machine" Electric Power Systems Research, Volume 77, Issue 7, May 2007, Pages 839-850

[8] Ricardao Quadros Machado, Enes Goncalves Marra, “Electronically Controlled Bi-Directional Connection of Induction Generator with a Single-Phase Grid”, IECON’01 The 27th Annual Conference of the IEEE Industrial Electronic

[9] E.G. Marra and J.A. Pomilio, “Induction-generator-based system providing regulated voltage with constant frequency”, IEEE Trans. Ind. Electronics, vol. 47, no. 4, Aug. 2000.

[10] Ion Catalin Petrea, Serban Ioan, Marinescu Daniela, Operation of an Induction Generator Controlled by a VSI Circuit, ISIE 2007 IEEE International Symposium on Industrial Electronics June 4-7, 2007 Vigo, Spain, page(s):2661-2666

[11] Teodorescu, R.; Blaabjerg, F.; Liserre, M.; Loh, P.C., “Proportional-resonant controllers and filters for grid-connected voltage-source converters”, Proceeding of the IEEE Electric Power Applications, vol. 153, Iss. 5, Sept. 2006, pp. 750 – 762.

[12] D. N. Zmood, D. G. Holmes, “Stationary Frame Current Regulation of PWM Inverters with Zero Steady-State Error” IEEE Trans. on Power Electr., vol. 18, no. 3, May 2003, pp. 814 – 822.

[13] R. Teodorescu, F. Blaabjerg, U. Borup, and M. Liserre, “A new control structure for grid-connected LCL PV inverters with zero steady-state error and selective harmonic compensation,” in Proc. IEEE App. Power Electron. Conf. and Exp. (APEC’04), 2004, vol.1, pp. 580-586.

Acknowledgments - This paper was supported in part by the Romanian Ministry of Education, Research and Innovation, through contract PN II Parteneriate no. 11004/2007.

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Active Power Factor Correction

Dorin Cismasiu University”Lucian Blaga”, Emil Cioran 4, 550025 Sibiu, Romania; dorin.cismasiu@ulbsibiu.ro

Abstract. Power factor correction shapes the input current of off line power supplies to maximize the real power available from the mains. Ideally, the appliance should present a load that emulate a pure resistor, in which case the reactive power drawn by the device is zero. The current is a perfect replica of the input voltage and is in phase with it. In this case the current drawn from the main is a minimum for the real power required to perform the needed work, and this minimizes losses and costs. The freedom from harmonics also minimizes interference with other devices powered from the same source.

1 Introduction Power factor is defined as ratio of real power to apparent power:

powerApparentpoweral

PFRe

= (1)

where the real power is the average, over a cycle, of the instantaneous product of current and voltage, and the apparent power is the product of the rms value of current times the rms value of voltage. If both current and voltage are sinusoidal and in phase, the power factor is 1.0. If both are sinusoidal but not in phase, the power factor is the cosine of the phase angle. This occurs when load is composed of linear elements. Switched mode power supplies present a non linear impedance to the mains, because of the input circuit. The input circuit usually consist of a rectifier followed by a storage capacitor.

Figure 1: SMPS input without PFC.

Figure 2: Voltage and current waveforms in simple rectifier circuit

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Current is drawn from the input only at the peaks of the input waveform, and this pulse of current must contain enough energy to sustain the load until the next peak. It does his by dumping a large charge into the capacitor during a short time, after which the capacitor slowly discharge the energy into the load until the cycle repeats. The current and voltage can be perfectly in phase, in spite of severe distortion of the current waveform. Applying the “cosine of the phase angle” definition would lead to the erroneous conclusion that this power supply has a power factor of 1.0. When the current is not sinusoidal and the voltage is sinusoidal, the power factor consists of two factors:

• the displacement factor related to phase angle • the distortion factor related to wave shape

Equation (2) represent the relationship of the displacement and distortion factor as it pertains to power factor.

( )θθ KK

II

PF drms

rms ⋅== cos1 (2)

Irms(1) is the current’s fundamental component and Irms is the current’s RMS value. Therefore, the purpose of the power factor correction is to minimize the input current distortion and make the current in phase with the voltage. When the power factor is not equal to 1, the current wave form does not follow the voltage waveform. This results not only in power losses, but may also cause harmonics that travel down the neutral line and disrupt other devices connected to the line. The closer the power factor is to 1, the closer the current harmonics will be to zero since all the power is contained in the fundamental frequency.

2 Boost converters in power factor correction

Boost converter topology is used to accomplish active power factor correction in many discontinuous / continuous modes. The boost converter is used because it is easy to implement and works well.

Figure 3: PFC Boost preregulator

The input to the converter is the full-rectified AC line voltage. No bulk filtering is applied following the bridge rectifier, so the input voltage to the boost converter ranges, at twice line frequency, from zero to the peak value of the AC input and back to zero. The boost converter must meet two simultaneous conditions:

• the output voltage of the boost converter must be set higher than the peak value of the line voltage

• the current drawn from the line at any given instant must be proportional to the line voltage

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3 Modes of operation

There are two modes of operation; discontinuous and continuous mode. Discontinuous mode is when the boost converter’s MOSFET is turned on when the inductor current reaches zero, and turned off when the inductor current meets the desired input reference voltage as shown in figure (4). In this way, the input current waveform follows that of the input voltage, therefore attaining a power factor of close to 1.

Figure 4: Discontinuous mode of operation

Discontinuous mode can be used for SMPS that have power levels of 300W or less. In comparison with continuous mode devices, discontinuous ones use larger cores and have higher I2R and skin effect losses due to the larger inductor current swings. With the increased swing a larger input filter is also required. On the positive side , since discontinuous mode devices switch the boost MOSFET on when the inductor current is at zero, there is no reverse recovery current on the boost diode. This mean that less expensive diodes can be used.

Continuous mode typically suits SMPS power levels greater than 300W. This is where the boost converter’s MOSFET does not switch on when the boost inductor current is zero, instead the current in the energy transfer inductor never reaches zero during the switching cycle.

Figure 5: Continuous mode of operation

The current swing is less then in discontinuous mode resulting in lower I2R losses and lower core losses. Since the MOSFET is not being turned on when the boost inductor’s current is zero, a very fast recovery diode is required to keep losses at minimum.. The heart of the PFC controller is the gain modulator. The gain modulator has two inputs and one output. As shown in fig.6, the left input to the gain modulator block is called the reference current (ISINE).

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Figure 6: Example of active PFC control using Boost converter

The reference current is the input current that is proportional to the input rectified voltage. The other input, located at the bottom of the gain modulator, is from the voltage error amplifier. The error amplifier takes in the output voltage, using a voltage divider, after the boost diode and compares it to a reference voltage of 5V.The error amplifier will have a small bandwidth so as not let any abrupt changes in the output or ripple affect the output of the error amplifier. The purpose of the current loop is to force the current waveform to follow the shape of the voltage waveform. In order for the current to follow the voltage, the internal current amplifier has to be designed with enough bandwidth to capture enough of harmonics of the output voltage. The gain modulator and the voltage control loop work together to sample the input current and output voltage. These two measurements are taken and than compared against each other to determine if a gain should be applied to the input of the current control. This decision is than compared against a sample of the output current to determine the duty cycle of the PWM.

4 Conclusion Power factor correction minimizes losses and costs associated not only with the distribution of the power, but also with the generation of the power and capital equipment involved in the process. The freedom of harmonics also minimizes interference with other devices being powered from the same source References [1] Erickson, R. W., Maksimovic, D., Fundamental of power electronics, Second Edition, Kluwer Academic publisher Group, Massachusetts, 2001 [2] ON SEMICONDUCTOR, Power Factor Correction Handbook HBD853/D/2007 [3] FAIRCHILD SEMICONDUCTOR, AN 42047

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Modeling of an electromagnetic device with hysteretic materials

Lucian Gabriel PETRESCU, Aurel CHIRILÃ University POLITEHNICA of Bucharest,

Electrical Engineering Faculty, 313, 06042 Bucharest, Romania; lucigabipetrescu@yahoo.com

Abstract. Single sheet tester is a device used in measurement of the magnetic characteristics of the electrical sheets. The principle of it is a close magnetic circuit made in a shape of soft magnetic material yoke. The aim of this paper is to model this device with two specialized software, using a real magnetic material as a measure sample. Also, the numerical models results will be compare with an analytical calculus of the magnetic circuit.

1 Introduction

Investigation of magnetic materials cannot be made without using measurement devices which can provide quantitative and qualitative information about the magnetic characteristics [1]. Measure the magnetic field intensity involves a large and multiple methods, each of them proper for a specific application. These applications are varying from a simple detection of the magnetic field to precise determination of the scalar and vectorial properties of the magnetic field.

Close magnetic circuits are preferred to the open ones for measurement of the magnetization curve and hysteresis loops, offering information about the material, the sample geometry, magnetization value and the field magnetic value. The sample should have the proper shape for closing the magnetic flux density or can be part of a special yoke made of high permeability material [2].

2 Single Sheet Tester

The Single Sheet Tester (SST) is made according to the IEC 60404-3 standard, shown in figure 1. The sample has the dimensions 280 mm (long) x 30 mm (width) x 1 mm (thick). The magnetic joke is a double C shape made of grain oriented iron-silicon alloys or laminated sheets of nickel-iron. The faces of the poles are very plane surface to reduce the air gap and the upper part of the yoke is mobile to allow the entrance of the sample. The excitation coil is made of 723 copper turns.

Fig.1. SST circuit

id4502093 pdfMachine by Broadgun Software - a great PDF writer! - a great PDF creator! - http://www.pdfmachine.com http://www.broadgun.com

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SST can be modeled for the analytical calculus with a magnetic circuit shown in figure 2. The following magnetic reluctance are presented: Ry magnetic yoke reluctance; R - air gap reluctance for modeling the ruggedness and covered polish ( ≈ 50 m); Rsh part of the sheet between the poles faces; Rsp sample reluctance (outside the poles); NpIp excitation coil.

Fig.2. Magnetic circuit for analytical calculus of the SST

Sample and yoke are made both of nonlinear materials characterized of a magnetization curve. For the analytical calculus these curves can be approximated with two straight lines with different slopes: for low magnetic fields the slope (permeability) is very high, for the region closed to the saturation the slope decreases very much. There were used an example for each of these cases for the analytical and numerical analysis.

3 Analytical and numerical modeling of the SST in the low magnetic field area

Equivalent reluctance to the source is:

1shyspech H325.770

2

22

kRRR

RR

Wb1067.1770.325

00754,0723 5

ech

pp

R

IN

T566.0

1030

1067,16

5

sp

SB

Fig.3. Magnetization curve for the FeSi sheet used in numerical modeling

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The characteristic of the GO FeSi sheet with density = 7.65 g/cm3 and mass m = 32 g, is shown in figure 3.

The two software used for numerical 2D modeling are quite different: an open sources one (FEMM) and a commercial one (COMSOL Multiphysics). FEMM is a suite of programs for solving low frequency electromagnetic problems on two-dimensional planar and axisymmetric domains. The program currently addresses linear/nonlinear magnetostatic problems, linear/nonlinear time harmonic magnetic problems, linear electrostatic problems, and steady-state heat flow problems [3]. COMSOL Multiphysics (ex FEMLAB) is a software package for finite element analysis and solver for application in the area of physics and engineering sciences, oriented to couple phenomena [4].

For the numerical analysis there were used Dirichlet boundaries conditions (A = 0), and the current density of the modeled coils is bobinãpp / SINJ . For the linear case J = 0.0041

MA/m2 with Ip = 7.54 mA (fig. 4).

Fig.4. Numerical results for modeling the low magnetic field area with FEMM

The magnetic flux density in the sheet is constant (0.545 T), much closed to the analytical value (0.566 T). The geometry for COMSOL is alike in FEMM and the result can be observed in figure 5. The magnetic flux density value in the sheet for this case is 0.54 T.

Fig.5. Numerical results for modeling the low magnetic field area with COMSOL

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4 Analytical and numerical modeling of the SST in the saturation area

In this case, the relative permeability of the yoke and the sample are very low, so the reluctance for these parts of the magnetic circuit is very high. It can be omitted the air gap reluctance, but, for a more occurred analytic approach, it has to take into account the air region between the coils and the sheet, Rair.

Equivalent reluctance to the source is:

1shy

airairsp

ech MH468.142

2

1111

RR

RRR

R

Wb10997.410467,14

1723 56

ech

pp

R

IN

T6658.1

1030

10997,46

5

es

SB

In this case the current density is J = 0.5435 MA/m2 with Ip = 1 A.

Fig.6. Numerical results for modeling the saturation area with FEMM

In the sheet, the value of the magnetic flux density is constant (1.68 T), value much close to the analytic one (1.6658 T). The result obtained with COMSOL for the saturation area is shown in figure 7 and it can be observed that the magnetic flux density is 1.6657 T.

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Fig.7. Numerical results for modeling the saturation area with COMSOL

5 Conclusion

In this paper it was made a comparison between analytical calculus and numerical modeling of an electromagnetic device used in measurement of the electrical sheets Single Sheet Tester (SST). Two cases were approached (low magnetic field area and region closed to saturation) because of the nonlinear character of the sample and the magnetic yoke. There were used two specialized software, FEMM and COMSOL.

In both cases the analytic and numerical results are very close. The relative errors in the first case are 1 - 4% between the numerical values and the analytical calculus, and in the second case the same errors are 8.5%. It is difficult to make an analytic calculus of magnetic circuit involving nonlinear material because the identification of the permeability has to be done from interpolation of the magnetic curve. Also, the small differences between the numerical modeling shown that both software can be used in such identification.

The future work in this domain is to compare numerical results obtained with two software for a 3D analysis of the magnetic circuit of the SST. References [1] H. Gavrilã, V. Ioniþã, Metode Experimentale în Magnetism, Ed. C. Davila, Bucureºti, 2003. [2] F. Fiorillo, Measurement and Characterization of the Magnetic Materials, Elsevier Academic

Press, 2004. [3] David Meeker, Finite Element Method Magnetics, Version 4.2, Users Manual, 2009. [4] *** COMSOL Multiphysics User Guide

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Measurement of nonlinear effects in power BAW resonators

Aurelian FLOREA*, Olivier LLOPIS**, Miruna NIŢESCU*, Florin CONSTANTINESCU*

*Politehnica University of Bucharest, Romania, aurelian.florea@lce.pub.ro **Laboratoire d’Analyse et Architecture des Systémes, Toulouse, France, llopis@laas.fr

Abstract. In this paper we present measurement results on nonlinear effects of the AlN power BAW resonators. The long time purpose is to elaborate both a nonlinear electromechanical field model and nonlinear circuit models reproducing the large signal behaviour of these resonators.

1 Introduction

This paper presents some results which have been obtained in the Laboratory of System Analysis and Architecture (LAAS), Toulouse, France, as a continuation of the research reported in [1]. The measurement bench is described in Section 2. The second and third Sections present the measurement results for the two nonlinear phenomena: the amplitude-frequency effect and the intermodulation effect. Section 5 contains conclusions and plans for future work. Fig 1.a shows the small signal admittance module vs. frequency exhibiting a series resonance fs at about 2.02 GHz and a parallel resonance fp at about 2.05 GHz. The small signal behaviour of a BAW resonator can be modelled by the linear circuit in Fig. 1. b. The intermodulation effect, consisting in the presence of the 2f and 3f harmonic components in the reflected wave of a resonator driven by a sinusoidal wave of frequency f, can be measured starting with power levels of about 22dbm (160mW). The amplitude-frequency effect, consisting in the shift of fs and fp to lower values as the incident power level increases, can be observed above 27dbm (500mW).

-3

-2.5

-2

-1.5

-1

-0.5

1.80E+09 1.85E+09 1.90E+09 1.95E+09 2.00E+09 2.05E+09 2.10E+09 2.15E+09 2.20E+09 2.25E+09 2.30E

Frequency [Hz]

a) b) Fig. 1: a) Small signal characteristic for BAW resonators, b) Butterworth Van-Dyke model

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2 The measurement bench

Figure 2: The measurement bench A picture of the measurement bench is given in Fig. 2. Bottom left we have a vector network analyzer (6) used to measure the S-parameters of the BAW resonator (5) at various power levels. On top we have a spectrum analyzer (7), which measures the 2nd and 3rd harmonic components. The harmonic signal is generated by the source of the vector network analyzer (VNA) (2), which is connected at the port 1 of the measurement circuit. A set of signals having the same power and 800 frequencies has been used for the amplitude-frequency effect measurements. The source signal is amplified by (8); the amplifier is in its linear operating domain as its maximum output power is 30W and the maximum output used in the measurements was 6.4W. Moreover, a low pass filter has been added just to be sure that no 2nd or 3rd harmonic generated by the amplifier will be added to the incident wave reaching the resonator. Before reaching the resonator, the amplified signal passes through a bidirectional coupler. The BAW resonator is a one-port connected with the coupler. The coupler returns the reflected wave to the input of VNA (port 2 of the measurement circuit). VNA measures the real and imaginary parts of the S21 parameter of the measurement circuit. The S11_DUT parameter of the device under test (DUT), that is the BAW resonator in this case, is computed using a “thru” calibration software. To this end two measurements are performed whose results are S21_open (DUT is replaced by an “open”) and S21_DUT (DUT is connected in the measurement

circuit). A soft provided by the VNA producer computes S11_DUT as openS

DUTS

DUTS_21

_21_11 −= .

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a b Fig. 3: Resonator connection a) using RF probe b) wire bonding

The resonator has a GSG input .Firstly we have tried to insert it into the circuit using a RF probe (Fig. 3. a). This led to the destruction of the resonator contacts. Then we have tried wire bonding which proved to be a workable solution (Fig. 3. b). Six AlN resonators, having the same layers configuration but various surfaces and electrode forms, have been measured. The ST2, ST5, and ST7 resonators have square electrodes, while ST9, ST12 and ST14 are apodized resonators (with irregular quadrilateral electrodes), “forced” to have the same area with a corresponding square resonator. Their areas are 25000μm2, 90000μm2, and 160000μm2 - one square resonator and one apodized resonator with the same area.

3. Measurement of the amplitude-frequency effect

For each incident power level 800 frequencies were used to draw the frequency characteristic |Y(jω)|. An example is given in Fig. 4.

Figure 4: ST2 frequency characteristics |Y(jω)| for various incident power levels

The shift of the series and parallel resonance frequencies vs. incident power are given in Fig. 5 for two resonators having the same area.

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a)

b)

Fig. 5: Series and parallel resonance frequency shift a) ST5, b) ST 12. We can observe the decrease of both resonance frequencies as the incident power increases. The apodized resonator characteristic is smoother. It seems that reflections of the mechanical waves in the plane orthogonal on layers, which are less significant for the apodized resonators, are responsible for this lack of smoothness of the characteristic in Fig. 5 a. The reason behind this behaviour will be found solving the electromechanical field problem taking into account the nonlinearity of AlN.

3 Measurement of the intermodulation effect

For the intermodulation measurements at constant power, 20 frequencies were manually selected. The third harmonic can be measured only for the smallest surface resonators (Fig. 6 c.). Even in this case, its level is under the noise floor of the system until close to the parallel resonance frequency. The second harmonic is significantly greater than the third one. The second harmonic of the apodized resonators has a maximum value near the parallel resonance. The square resonators curve (Fig 6.a) is less smoother than that of the apodized resonator (Fig. 6. b) probably due to lateral reflections of the mechanical waves.

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a)

b)

c)

Figure 6: Second harmonic (a- ST2, b- ST9) and third harmonic ( c- ST2) vs. frequency

This aspect will be clarified by solving the electromechanical field problem taking into account the nonlinearity of AlN. The influence of some measurement errors must be taken into account, also.

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5. Conclusions

Six BAW resonators, being built using the same layers, have been measured in order to obtain data on the amplitude-frequency effect and on the interdmodulation effect of AlN resonators. Taking into account that the incident power range is the same for all resonators, the measurement results lead to the following conclusions: • fp shifts in the same range for all rectangular and apodized resonators, • fs shifts in slightly different ranges for various resonators, • the second harmonic has a maximum close to fp, • only the small area resonators have a third harmonic which can be measured, the third

harmonic of other resonators being under the noise floor, • a non-monotonic frequency shift vs. incident power level has been measured, this feature

being emphasized for square resonators, • some local maxima and minima have been observed in the frequency dependence of the

second harmonic amplitude, this feature being emphasized for small area squareresonators • the previous two aspects can be explained by lateral reflections of the mechanical waves

combined with measurement errors. Future work will be devoted to: • estimation of errors in the measurement of S11_DUT_ using an ADS model of the measurement

bench, • development of a family of nonlinear circuit models for these resonators built using the same

layers; these models are similar to those proposed in [3], having parameters depending only on the resonator area and on an aspect ratio which makes the difference between apodized and rectangular resonators,

• finding the constitutive equation of the electromechanical field model which produces the measured nonlinear effects in power BAW resonators and computation of the electromechanical field using this nonlinear model.

References [1] S. Gribaldo, , Modélisation nonlinéare et de bruit pour composants micro-ondes pour application a

faible bruit de phase, These de doctorat, Université Paul Sabatier, Toulouse, 2008. [2] A. Reindhardt, C. Billard, E. Defaÿ, M. Aïd, SMR BAW for high power application, MOBILIS

Report, 2006. [3] F. Constantinescu, A. G. Gheorghe, M. Nitescu, New circuit models of power BAW resonators,

Rev. Roum. Sci. Techn., Ser. Electrotechnique et Energ. No. 1, 2008, pp. 59-66. [4] M. Maricaru, F. Constantinescu, A. Reinhardt, M. Nitescu, A. Florea, Field models of power BAW

resonators, Rev. Roum. Sci. Techn., Ser. Electrotechnique et Energ., No. 1, 2010 (to appear).

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Au-Fe Nanospheres – Assisted Delivery in Breast Tumour IR Thermography

Oana Mihaela DROSU, Florea Ioan HANTILA, Mihai MARICARU

Politehnica University of Bucharest, 313 Splaiul Independentei, Bucharest, Romania; againme_30@yahoo.com

Evangelos HRISTOFOROU National TechnicalUniversity of Athens, 9 Iroon Politehniou, Athens,Greece

Abstract. Nowadays the priorities for breast cancer research include screening and early diagnose methods. The thermography was proved to have great for breast tumor incipient detection, with non-invasive interaction with human tissue [1]. The paper refers to a minimally invasive, low-cost infrared thermography that would improve upon current methods using nano-structured metal-based imaging for early detection of breast malignancies. The 10–20 nm size Fe nano-spheres covered by biocompatible 2-3 nm thin layer of Au can be heated through RF induction. They carry one or many bio-dilutable atomic organic chains, connected also with an antigen. They are inserted in saline solution and then injected into the artery. The thermal radiation of the heated nanoparticles propagates along the tissue by thermal conduction reaching the breast tissue surface. The surface temperature distribution is acquired by a thermal camera and can be analyzed to retrieve and reconstruct nanoparticles temperature and location within the tissue. The technique may function as a diagnostic tool thanks to the ability of specific capacity of these nanoparticles to get attached to the tumor's markers. Hence, by applying a magnetic field, we could cause a controlled elevation of temperature of the targeted nanoparticles which increase the already elevated temperature of the tumor and allows its quicker detection.

1 Introduction

Classical imaging is not so sensitive to the very early presence of a malignant tumor, often failing to yield the data needed for accurate diagnosis and staging. For example, small primary breast tumors go oftenly undetected. Especially the internal, aggressive, non-calcified tumor under 2mm diameter (hence, containing less than 400000 cells) is likely to pass undetected through most breast scans, including CT, MRI, ultrasound etc. At this size, a tumor will undergo continued and uninterrupted growth if not treated . While cancer may be suspected for a variety of reasons, the definitive diagnosis of most malignancies must be confirmed by histological examination of the cancerous cells by a pathologist, that means an invasize detection method. Hence, the majority of diagnosis and therapy modalities is not capable to distinguish between malignant cells and healthy tissue (especially in early stages) and does not provide the physician with adequate precision and specificity.

2 Methods

The method involves the insertion of Au-Fe nanoparticles into a patient's body (either locally to a suspected tissue or systematically to the blood stream by injection into the artery), the nanoparticles arrive in the vicinity of the tumor and a process of bioattachement occurs in compliance with the antigens PH profile. Thus, the tumor's outer surface is bound with nanoparticles with strong chemical bonds configured as antigen-antibody chain.

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Since the biocompatible Au-Fe nanoparticles are able to produce heat under RF induction, the region of interest is placed under a suitable field. Radio-frequency induction or RF induction is the use of a radio frequency magnetic field to transfer energy by means of electromagnetic induction in the near field. A radio-frequency alternating current is passed through a coil of wire that acts as the transmitter that is placed in the vicinity of the human body, and a conducting object, in our case the Au-Fe nanoparticles, acts as the receiver. This emitted thermal radiation propagates along the tissue by thermal conduction reaching tissue surface. The surface temperature distribution is acquired by a thermal camera and could be analyzed to retrieve and reconstruct nanoparticles' temperature and location within the tissue.

3 Disscussions

An important task on the basis of this method is the fact that the Au-Fe nanoparticles are localized specifically and function as mediators situated on the periphery of the tumor. In order to target the tumor and deliver the nanoparticles reliably and specifically, the suggested transportation leans on human's immune system. The malignant tumor tends to present specific antigens on its outer surface. These antigens are able to communicate with corresponding agents of the immune system (e.g., antibodies) to establish antigen-antibody connections. There are numerous parameters affecting the heat generation, which is produced by nanoparticles excited by RF induction. There are some important parameters that should be taken into consideration when heating using the above mentioned nanoparticles, like the characteristics of the applied field, the materials used for the nanoparticles, their dimensions and concentration within the saline delivery solution. The field strength and frequency are controllable parameters that directly affect the power produced by the nanoparticles when alternative electromagnetic field is applied. The field parameters are very complex, and depend on additional parameters such as the nanoparticles' material properties. The nanoshells are comprised of an iron core with diameter of 10–20 nm coated with a layer of biocompatible gold. The gold coatings are made in order to prevent oxidation, hence demagnetization; the metal coatings of Au (2-3 nm) provide long-term stability and biocompatibility for the Fe core. The size of the nanoparticles is a fundamental characteristic in this field. Another parameter is the concentration of the nanoparticle inserted into the body [3]. The concentration should be large enough to produce heat, but small enough not to induce toxicity in the human body. The coating of nanoparticles and suspending medium also affect the heat generation. Upon the heating of the bioattached nanoparticles, we generate a heat source within the body. The heat source, namely the tumor, and in particular the tumor's surface, is actively heated by external and controlled magnetic fields. Based on a two dimensional thermal image acquired from the tissue surface, we consider two main characteristics: the depth of the tumor and the temperature of the tumor and its surroundings The two principle parameters of the externally applied magnetic field, that is, the frequency and strength, are limited by physiological responses to high-frequency magnetic fields [4]. Most of research works in this field are using a single RF coil with a few turns, for example, 3-4 turns. A possible problem of this coil configuration is that the accessibility of the IR camera. . The thermal imaging is carried out by an IR camera (FLUKE), which detect the infrared emission which is emitted from the examined object’s surface. The IR camera is positioned perpendicularly above the object, which is situated within the magnetic field induced between the two coils. When the magnetic field is applied, the nanoparticles generate heat which can be detected by the IR camera.

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4 Conclusions

The method is dedicated to the improvement of the detection of malignant tumors through thermography, based on the physical principle of heat generation for diagnosis. The heat generation and its amplification above the body’s normal temperature level are achieved by nanoparticles which are bio-attached to the tumor and then stimulated by a suitable external electromagnetic field. This procedure is specifically targeted to the tumor since it relies on the capability of the immune system to locate the malignant cells. Hence, the bio-attachement of the nanoparticles to the antigen-antibody chain is probably the most accurate method to reach the real malignancies. The preferable configuration for the generation of the heating is the RF induction. In conclusion, this research work may serve as a modern concept for having diagnosis through a minimally invasive method that is selective and has the potential of being very accurate, reliable, and applicable. This multidisciplinary research comprises various aspects: • production of the AU-Fe nanoparticles; • production of dilutable oorganic chains with antigen connections; • inserting the saline solution containing nanoparticles into the body; • heat generation; heat monitoring; • thermal imaging; • thermal analysis etc. Producing the required external electromagnetic field should be designed to generate a higher magnetic field, preferably with adjusted parameters, for example, magnitude, frequency, distance between the coils. The thermal analysis is based on the acquired raw thermal image and includes the processing for improving the data quality and derivation of desired parameters through various methods implementing different mathematical models, computational algorithms, etc. The current model is a basic model that relies on ideal assumptions (e.g., homogeneous tissue, steady state). Furthermore, the inverse model assumes a point source which an ideal approximation for much more complicated scenarios that involve undefined tumor boundaries, physiological, anatomical abnormalities, etc. Another important problem can be the evacuation of those particles once they achieved their purpose. In this case a magnetic micropump can be used. References [1] F. Hantila, O. Drosu, M. Maricaru, Breast Tumor Detection using the Numerical Analysis of the

Thermal Inverse Problem, JAPMED 07, 16-19 sept. 2007, Larnaca, Cyprus, pp.107-108; [2] C. Tiu, F. I. Hantila, O. DROSU, M. Maricaru, A.S. Nica, “Localizing a Breast Tumor with

Thermographical Methods”, SMIT 28-30 August 2008, Viena, [3] V. S. Kalambur, B. Han, B. E. Hammer, T. W. Shield, and J. C. Bischof, “In vitro characterization

of movement, heating and visualization of magnetic nanoparticles for biomedical applications,” Nanotechnology, vol. 16, no. 8, pp. 1221–1233, 2005.

[4] Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” Journal of Physics D, vol. 36, no. 13, pp. R167–R181, 2003.

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Calculation on a static horizontal diamagnetic levitation

setting for permanent magnets

Emil Cazacu* and Iosif Vasile Nemoianu “Politehnica” University of Bucharest, Electrical Engineering Department

313 Splaiul Independentei, 060042, Bucharest, Romania

Abstract. The paper presents a novel horizontal configuration of a permanent magnet static levitation stabilized by the presence of diamagnetic materials. The magnetomechanical interaction between the levitated magnet and the diamagnetic pieces was evaluated in order to investigate the restoring forces exerted on the floater when shifted from its equilibrium state. Thus, the equilibrium point coordinates of the suspended permanent magnet, and their stability areas are accurately established using both analytical and numerical procedures.

1. Introduction

Despite the well established Earnshaw’s theorem [1], that avoids the stable levitation of magnetic charges in the presence of static magnetic and gravitational fields, one shows that there are at least two situations where the existence of diamagnetic materials may provide a stable levitation configuration [2, 3].

These cases exploit the incidence of very large magnetic fields (up to 10 T) on diamagnetic objects, and also the incidence of conventional intensity magnetic fields (a few mT) on small magnetic dipoles in association to diamagnetic stabilizing sheets.

This phenomenon of stabilizing the intrinsically unstable equilibrium of the levitated permanent magnet (PM) by pieces of diamagnetic materials has awoken a great interest over the latest years due to the innumerous possibilities of technological applications in systems where it is extremely desirable to eliminate any kind of mechanic contact, friction or dissipation [4 - 8].

Previous works regarding the diamagnetic levitation of a permanent magnet concern mainly vertical configurations [9, 10]. This paper proposes a novel levitation setting, in which stabilization is done along the horizontal direction, allowing to the suspended magnet to freely move in the vertical plane. 2. Horizontal configuration

The simple model of the proposed levitation array – Fig.1, consists in a magnetic field source – the two cylindrical coils, the levitated permanent magnet (PM) and two pieces of pyrolytic graphite (PG) as stabilizing diamagnetic material.

* Corresponding author: E-mail: cazacu_emil@yahoo.com Fax: +4021-410 43 55

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)(Δ

Fig. 1 Horizontal configuration for levitation a PM.

Contrary to our intuition, for certain values of the current carried by the two coils

(I0), due to the high absolute value of the magnetic field gradient backwards on z–axis, the developed magnetic force can balance the gravity of the PM, and levitation may occur. The two pieces of diamagnetic material placed normal to the common axis of the coils act like a tiny servo-system providing the restoring forces needed for keeping the floater at the equilibrium point in a stability state.

Due to the cylindrical symmetry of the configuration, the coordinate of the equilibrium point (z0) lies on the axis (Δ) where the magnetic flux density exhibits only a horizontal x- component (Fig. 1):

B(z) = Bx(z)i (1) where i is the unit vector of the x-axis.

Stable static levitation of the permanent magnet requires a minimum of the total energy along with the equilibrium condition fulfilment [9]. Denoting M the magnetic moment of the suspended PM of mass m, the total potential energy U of the floater becomes:

U = – M·B + mgz = – MBx(z) + mgz. (2)

The magnetic torque will align the levitated permanent magnet parallel to the local field direction; therefore, in the magnetic energy expression (2), only the x-component Bx(z) of the magnetic flux density is variable. Then the condition that point (0, 0, z0) is an equilibrium one requires a null value of the resulting force F on the floater, which can be expressed in terms of energy gradient:

,)(

0)(

000 0

0000

0

Mmg

zzBmg

zzBMU

zzyx

x

zzyx

x

zzyx −=

∂∂

⇒=+∂

∂=∇−=

===

===

=== kkF (3)

where k is the unit vector of the z-axis, which is downward oriented. The equilibrium condition is not self-sufficient, stability having to be achieved. That goal requires a positive concavity of the energy surface around the equilibrium point for all possible directions. Therefore, the stability condition read:

.00;0

000

002

2

002

2

002

2

>∂∂

=>∂∂

=>∂∂

=

===

===

===

zzyxz

zzyxy

zzyxx z

UDyUD

xUD (4)

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The left-hand side quantities of the inequalities (4), denoted by Dx, Dy and Dz are called discriminants of stability. For a stable static levitation of the floating permanent magnet, all three stability discriminants at the equilibrium point must be positive simultaneously.

As we already explained in the previous section, two pieces of diamagnetic material placed in the proximity of the levitated magnet along the x-axis, stabilize the intrinsically unstable equilibrium of the floater for this direction. Consequently, a new term Cx2 is added to the right-hand side of (2), which represents the diamagnetic material contribution to the potential energy U.

The expression for the term C (called the diamagnetic influence factor) can be calculated using the dipole approximation of the floater and the corresponding mirror images within the two diamagnetic stabilizing pieces. An analytical expression for C is given in [10]:

5

20

)2(6

hcM

C+π

μχ= , (5)

where: µ0 = 4π×10-7 H/m is the magnetic permeability of vacuum, χ is the magnetic susceptibility of the diamagnetic plates, c is the separating distance between the floater and each diamagnetic sheet, and w and h are the dimensions of the cylindrical floater, as depicted in Fig. 2

Fig. 2 –Suspended permanent magnet between diamagnetic pieces. Due to the geometry of this configuration, without diamagnetic materials, setting

C = 0, the curvature of floater potential energy along the x- axis, at the equilibrium point, becomes negative and thus, the system is unable to provide horizontal stability: Dx < 0. 3. Magnetic flux density computation

According to (3) and (4) the problem of determining the coordinates of the equilibrium point and its stability area for the suspended permanent magnet leads to the evaluation of the magnetic flux density, produced by the two coils at different points located in the vicinity of the equilibrium point. This goal is achieved by using the analytical expression for the off-axis magnetic flux density of a single circular current loop [11] and then by summing up the contribution of all the turns of the two solenoids. Then first and second order spatial derivatives of the flux density may be also determinated.

Due to the cylindrical x-axis symmetry of the magnetic field sources this setting practically allows two levitation points symmetrically place under and above the x-axis.

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Fig. 3 The radial symmetry of the magnetic field sources.

Using the spherical polar coordinates due to the symmetry of the problem Bφ is null.

The other two components are [11] - Fig.3:

( )[ ] ( )

( )[ ] ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−

+++−

++πμ

=ρ kEzra

zrakKzra

zIB 2/122

222

2/122

0

2

and

( )[ ] ( )

( )[ ] ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−

−−+

++πμ

= kEzra

zrakKzra

IBz 2/122

222

2/122

0 12

,

where K and E are complete elliptic integrals of the first and second kind. The argument of both elliptic integrals is given by:

( )[ ]222

1

zaark

+ρ+=

Using these components the modulus B of the flux density is obtained. 5. Numerical example

In order to achieve a quantitative analyze for the above proposed configuration – Fig. 1, specific geometrical data and material properties to the model were set up. Thus, for the cylindrical symmetric coils we assume the distances 2d = 2a = 50 mm and a carring direct current I0 = 550 A, The floater was chosen flat as a tiny NdFeB cylinder (diameter 2w = 4 mm and h = 4 mm height) with magnetic momentum M = 0,051 Am2 and mass m = 0,39 g. The two pieces of pyrolitic graphite (magnetic susceptibility χ = 45010–6), placed initially at c = 1 mm, symmetrically to the levitated magnet, stabilize the equilibrium.

Assuming the above numerical data this levitation configuration asures an stable equilibrium point located at x0 = 0 mm, y0 = 0 mm z0 = 31,95 mm and a value of C = 0.375 for the influence factor.

B

0r

z

z

x

I

φ

y

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Fig. 4 – Equilibrium point and the magnetic flux density variation on symmetry axis Δ .

Fig. 4 presents the coordinate of the equilibrium point determination and the magnetic flux density variation Bx(z) - scaled by a factor of 10 for a better graphical representation - on the equal distant axis Δ from both solenoids.

Fig. 5 – Discriminat of stability vaiation on y-axis Fig. 6 – Discriminat of stability vaiation on z-axis. The discriminant of stability variation along y- and z- axes, denoted with Dx and Dz are shown in Fig. 5 and Fig. 6, respectively. One can notice that their positive value around the equilibrium point asures stability in these directions.

Fig. 7 – Horizontal stability discriminant variation with and without diamagnetic material presence.

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Fig. 7 shows the horizontal stability discriminants variation at the equilibrium point

along x-axis with and without the presence of diamagnetic stabilizing materials denoted with Dx(C) and Dx respectively. In the absence of diamagnetic pieces the value of discriminant Dx is negative and the system becomes unable to keep stability along x-axis.

The maximum value of the gap (stability area) is cmax = 1,30 mm. That corresponds to C = 0.233 which still ensures a positive value for the horizontal discriminant of stability Dx(C) at the levitation point. Thus, the stability area is restricted by c = 0..1.30 mm.

5. Conclusions

The issue of stabilizing the static levitation of a permanent magnet by the usage of diamagnetic materials is treated. The study examines a novel geometrical levitation configuration, in which the diamagnetic materials pieces are horizontally placed in the proximity of the suspended permanent magnet. This configuration, properly adjusted, allows several equilibrium and stability points of the PM in the vertical plane.

The potential energy of the suspended magnet, which provides the static equilibrium equations and stability restrictions, was stated in terms of diamagnetic and magnetomechanical interactions. That enabled one to accurately predict the location and quantify the stability of levitation.

For specific geometrical and material data the analytical and numerical computations results were in a very good match, validating the assumed theoretical predictions.

This kind of static stable levitation could provide simple and inexpensive solutions for a wide area of applications, where frictionless or non-contact is imperiously needed (high-sensitive gravity sensors, magnetic bearings or different geo-physical devices).

In microsystems, the scale reduction favors the diamagnetic effect by enhancing the volume forces and it is therefore desirable to apply diamagnetic levitation mechanisms to ensure accuracy and robustness of microdevices which contains moving components.

References [1] M. F. Reusch, A problem related to Earnshaw’s theorem, IEEE Transactions on Magnetics, 30,

3, pp. 1324–1326, May 1994. [2] G. Küstler, Diamagnetic levitation – historical milestones, Rev. Roum. Sci. Techn.–

Électrotechn. et Énerg., 52, 3 , p. 265-282 , Bucarest, 2007. [3] R. E. Pelrine, Diamagnetic levitation, American Scientist, 92, 5, p. 428, Sep./Oct. 2004. [4] A. Cansiz, Static and dynamic analysis of diamagnetic bearing system, Journal of Applied

Physics, 103, 3, 034510-5, Feb. 2008. [5] C. Pigot, H. Chetouani, G. Poulin, G. Reyne, Diamagnetic levitation of solid at microscale,

IEEE Trans. Magn. , 44, 11, 4521–4524, Nov. 2008. [6] H. Chetouani, B. Delinchant, G. Reyne, Efficient modelling approach for optimization of a

system based on passive diamagnetic levitation for bio-medical applications, COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 26 no. 2, pp. 345 - 355, 2007..

[7] J. Nhut, W.C. Wang, Electric generator using a triangular diamagnetic levitating rotor system, Review of Scientific Instruments, 80, 2, 024702-8, Feb. 2009.

[8] J. Y. Chen, J. B. Zhou, G. Meng, W.M. Zhang, Evaluation of eddy-eurrent effects on diamagnetic bearings for microsystems, IEEE Trans. Ind. Electron., 56, 4, 964–972, Apr. 2009.

[9] M. D. Simon, A. K. Geim, Diamagnetic levitation: Flying frogs and floating magnets, Journal of Applied Physics, 87, 9, 6200–6204, May 2000.

[10] M. D. Simon, L. O. Heflinger, A. K. Geim, Diamagnetically stabilized magnet levitation, American Journal of Physics, 69, 6, 702-713, June 2001.

[11] W. R. Smythe, Static and Dynamic Electricity, 3rd ed., New York Hemisphere, 1989, p. 306.

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MEASUREMENT AND CONTROL SYSTEMS WITH PROGRAMMABLE SMC- PLC AUTOMATION SYSTEMS

Lucian Marius VELEA

Industrial Engineering and Technology VTC-Srl, 24 Burla Vasile, 060207, Bucureşti; lmvelea@yahoo.com

Diana POPOVICI University of Oradea, Faculty of Environmental Protection, 26 Gen. Magheru St., 410048 Oradea,

pdiana@uoradea.ro

Ovidiu POPOVICI University of Oradea, Faculty of Electrical Engineering and Information Technology, 1 Universitatii St.,

410087 Oradea, popovici@uoradea.ro

Zahei PODEA Baia Mare City Council, 37 Gheorghe Sincai St., 430311 Baia Mare, zacheip@yahoo.com

Abstract. The paper presents an infrastructure solution for measurement and adjustment of parameters from the technological processes focused in general on the SCADA systems, but also with the possibility of individual operation, though the creation of a modular system with programmable logics with the possibility of configuration for each process to be monitored. The equipments were executed within the company Engineering and Industrial Technology VTC.

Introduction The paper presents various measurement systems for the monitoring and control of electrical and non-electrical parameters within the processes in view of their adjustment or in order to provide information to certain SCADA systems. These systems were modularly created, with the possibility of implementation in any process that has to be monitored. These systems include two main structures: - a component for data acquisitions from the process - a component for the adjustment of parameters from the process. The modular systems are intended for the measurement of electrical, non – electrical parameters, also combined electrical and non – electrical parameters. At the same time, these systems lead and adjust the processes for which they were created [3],[4]. Up to this point, various data acquisition systems were created, to very high speeds, capable to use both classic transducers with analog outputs and state of the art transducers with serial outputs for the transmission of values and parameters with ASCII, Modbus, Arcnet, CANopen, DeviceNet, Profibus, Ethernet, etc., transmission protocols. We underline the fact that these measuring and adjustment systems have a high accuracy, as well as an improved reliability. An advantage of these systems is that they are capable to work with other systems of other companies that produce similar devices and systems, the compatibility being insured by the existence of a transmission protocol that is going to be used by these systems [1],[3]. Another advantage of these systems is that through the adjustment component, we can create various soft mathematical functions for the adjustment of parameters

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within the monitored and adjusted process, we can create software regulators with integrated P1, PI2 or PID3 adjustment functions.

Measurement systems

Various measurement systems were conceived and created for monitoring and control of electrical and non – electrical parameters within the processes in view of their adjustment or in order to provide information to certain SCADA systems [3]. These systems include two main structures: A. a component for data acquisitions from the process B. a component for the adjustment of the process. A. The component of data acquisitions from the process included monitoring systems of parameters within the process. The parameter monitoring systems have 2 categories, for electrical and non-electrical parameters [1]. 1. Modular systems for the measurement and calculation of SME electrical parameters as: phase and line currents, cc (continuous current) and ac (alternating current) consumer currents, phase and line voltages, voltages for the supply of cc and ac consumers, φ chimney , frequency, active power, reactive power, apparent power, energy, distortions, harmonics. Composition: - Module for the measurement of currents and voltages - Module for the measurement of φ chimney - Module for the measurement of frequency - Measuring module with analyzer - Communication module.

fig.1 ANALYSIS OF MODULAR SYSTEMS a. Module for the measurement of currents and voltages

1 Proportional 2 Proportional Integral 3 Proportional Integral Derivative (controller)

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This module can be created in 3 variants: 1. with classic transducer 2. with classic transducers with output in unified system 3. with state of the art transducers with the transmission of measured unit through Profibus, Ethernet or Modbus network, or combined with all types of transducers. The module has the following configuration: 1. Analog signal acquisition module (fig.2.)

• Multichannel interface for measurement and data acquisitions • Unified signal converter : 0-20mA; 4-20mA; 0-10mA; +/- 1V

+/-2,5V; +/- 5V; +/- 10V; 0-1V ; 0-5V; 0-10V • Binary value converter with unified signal • Calibration and signal processing block • Transmission block

The signals are acquired though a multichannel interface for measurement and data acquisitions made of current and voltage transformers. These current transformers generate an output current proportional to the input current of maximum 1A or 5 A. These currents are introduced in some signal converters that generate output currents proportional to input currents, but within the limits of 0 – 10mA; 0 – 20mA or 4 – 20mA.

fig.2 fig.3 For the measurement of voltages, we use voltage transformers which, at their turn, generate output signals proportional to the input signals acquired in the monitored process. They are also introduced in voltage / unified signal converters that generate output signals proportional to the input signals within the voltage range: +/-1V;+/-2,5V; +/-5V; +/-10V;0 – 10V; or within the current range: 0 – 20mA; 4 – 20mA. These signals are introduced in the binary value converter, where the input signals are converted into binary signals. The binary signals are introduced into a calibration and processing software block and then they are submitted to the central unit of the system through a transmission block though various communication protocols.[2] The communication protocols used are the following: - Profibus with a transmission speed of 10Mb/second - Ethernet with a transmission speed of 100Mb/ second - DeviceNet with a transmission speed of 2,5Mb/ second - Arcnet with a transmission speed of 2,5Mb/ second - CanOpen with a transmission speed of 1Mb/ second - Modbus with a transmission speed of 187,5Kb/ second - ASCII with a transmission speed of 187,5Kb/ second.

2. Signal acquisition module through Profibus network ( fig 3) • Signal acquisition block with transducers with network transmission

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• Calibration and signal processing block • Transmission block

In general, state of the art transducers are created so that the value acquired from the process is transmitted through a communication protocol. The advantage of these transducers is that the acquisition and transformation of signals is significantly reduced, thus eliminating the necessity of multichannel interfaces, signal converters, binary signal converter, because the transmission is binary realized. Within the Signal acquisition module through Profibus network, the Signal acquisition block through transducers can receive information from up to 125 transducers at the same time. The acquisition speed is of 10Mb/second.[1] These signals are introduced into a calibration and processing software block, where, after calibration, the signals represent a data area. This data area is transmitted to the central unit of the system or to a PC through a transmission block which has a preset transmission protocol, possible other than the Profibus protocol. If the transmission block has a Profibus protocol, the speed of transmission towards the central unit of the system or PC is 10Mb/ second. 3. Signal acquisition module through Ethernet network ( fig.4 )

• Signal acquisition block with transducers with network transmission • Calibration and signal processing block • Transmission block.

fig.4 fig.5 The transducers associated with this type of module have serial output with transmission through Ethernet protocol. Within the Signal acquisition module through Ethernet network , the Signal acquisition block through transducers can receive information from 110 transducers at the same time. The acquisition speed is of 100 Mb/second. These signals are introduced into a calibration and processing software block, where, after calibration, the signals represent a data area. This data area is transmitted to the central unit of the system or to a PC through a transmission block which has a preset transmission protocol, possible other than the Ethernet protocol. If the transmission block has a Ethernet protocol, the speed of transmission towards the central unit of the system or PC is 100Mb/ second. 4. Signal acquisition module through Modbus network ( fig 5.)

• Signal acquisition block with transducers with network transmission • Calibration and signal processing block • Transmission block

The transducers associated with this type of module have serial output with transmission through Modbus protocol. Within the Signal acquisition module through Modbus network , the Signal acquisition block through transducers can receive information from 32 transducers at the same time. The acquisition speed is of 187.5 Kb/second [4]. These signals are introduced into a calibration and processing software block, where, represent a data area which is transmitted to the central unit of the system or to a PC through a transmission block which has a preset transmission protocol, possible other than the Modbus protocol. If the transmission block has a

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Modbus protocol, the speed of transmission towards the central unit of the system or PC is 1087.5 Kb/ second. 5. Combined signal acquisition module though analog signals and network (fig.6)

• Signal acquisition block with transducers with outputs in unified system • Signal acquisition block with transducers with network transmission • Calibration and signal processing block • Transmission block

This type of module is a combination made of the modules previously presented and its operation is identical with the operation of these modules.

fig.6 fig.7 The unpredictability of this system is that we can use any type of transducers which monitor the parameters from a process, also that we can couple a variety of SCADA compatible systems. The compatibility is insured by the transmission block which has to be chosen according to the communication protocols of SCADA system where we want to couple the modules.[2],[3] 2. Modular systems for the measurement and calculation of SMN non – electrical parameters, as: temperatures, pressures, torques, movements, angles, accelerations, speeds, positions, forces, vibrations, weights, humidity. The composition is illustrated in fig. 8. - Temperature measurement module – it measures the temperatures through thermal resistances and / or thermocouples that are coupled to a converter module - Pressure measurement module – it measures the pressures through some pressure transducers that are coupled to a converter module - Torque measurement module – it measures the torques through some torque transducers that are coupled to a converter module - Movement measuring module – it measures the movements trough some octal electronic transducers type ruler or magneto-electrical. - Angle measurement module – it measures the angles through some angle transducers - Acceleration measurement module – it measures the accelerations through some acceleration meters that are coupled to a converter module - Speed measurement module – it measures the speeds through some tacho-generators or encoders - Position measurement module – it measures the positions through some absolute encoders, wire encoders and relative encoders - Force measurement module – it measures the forces through some force transducers - Vibration measurement module – it measures the vibrations through some vibration transducers that are coupled to a converter module [2]

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fig.8 - Weight measurement module – it measures the vibrations through some mass cells with strain gauge stamps that are coupled to a converter module - Humidity measurement module – it measures the humidity through some humidity transducers Conclusions - a new data acquisition and adjustment system was created with programmable logics devices - we achieved superior performances in terms of measurement accuracy, acquisition speed and system reliability and we created an infrastructure solution for SCADA systems - the system is capable to operate with other similar data acquisition systems if a common communication protocol can be implemented. - the adjustment component of the system allows the performance of some complex mathematical functions and some software regulators for the adjustment of monitored parameters; this modular system conceived can have an expandable structure, from a minimum to a maximum structure, the restriction being given by the capacities of hardware components. This solution represents an innovation, contributing to the development of measurement and control systems. - the execution of these systems is made with state of the art automation elements from the producers of devices with programmable logics, thus achieving superior performances compared to similar systems from previous generations. References

[1] L.M. Velea and L. Vladareanu and M. Drumea. Interactiv automation system for data acquisition for driving technological processes type S.A.I.A.D. - Int AMSE, MS’2000 Int Conference on Modelling and Simulation, Las Palmas de Gran Canaria, Spain, 25- 27 Sept 2000, pag. 463-471.

[2] L.M. Velea and L. Vladareanu and T. Sireteanu. The Inprovement of the Ahievements of the Acquisition Systems for Monitoring through Vibrations, World Scientific and Engineering Academy Society WSEAS, ESPOCO’2005, Rio de Janeiro, Brazil, April 25-27 2005, no.494-151, pg. 54-60, ISBN: 960-8457-16-5

[3] L. Vladareanu and L.M. Velea and A. Vasile and A. Curaj and A. Vasile. Modular Structures in the Open Architecture Systems, ISI Proceedings of the 9th WSEAS International Conference (AMTA ’08), WSEAS Press in 2008, pag. 100-105, ISBN: 978-960-6766-74-9, ISSN 1790-5095,

[4] D. Popovici and Z. Podea and L.M. Velea and A.L.M. Velea, Weighing and dosing automatic systems with PLC for liquid and powdery materials – Conference Proceedings of The annual Symposium of the Institute of Solid Mechanics SISOM'2009, May 28-29, Bucharest Romania.

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Influence of Dimensions and Density of Water Trees on Residual Electric Field in Polymeric Power Cables

Insulations

Cristina STANCU INCDIE ICPE CA, 313 Splaiul Unirii, Bucharest, cstancu@icpe-ca.ro

Petru V. NOTINGHER, Constantin STOICA, Mihai PLOPEANU University Politehnica of Bucharest, 313 Splaiul Independentei, Bucharest

Petru NOTINGHER JR. University Montpellier 2, Place Eugene Bataillon, Montpellier

Abstract. In this paper, the residual electric field computation in a cable insulation in the presence of water trees and space charge is presented. Considering that, in treed areas, the variations of the permittivity and the space charge density are known, the thermal step current Ic(t) is computed and the curves Im (t) and Ic(t) are compared. The results show an important increase of residual electric field for some dimensions and concentrations of the water trees (up to 10 MV/m). Finally, the influence of the residual electric field on electrically aged cable insulations is analyzed.

1. Introduction

In a series of papers it is shown that, in polyethylene insulations, water trees appear (Fig. 1) and their inception and development is due to existence of ions inside water contained by polymers (and/or which comes into contact with them) and a time variable electric field [1-2]. Studies made on low density and crosslinked polyethylene showed positive and negative ions existence, both inside and outside of trees, and constitute ionic space charge [3-4]. The space charge generates an electric field, which overlaps on the existing one, leading to the electric field enhancement outside of treed areas and to the increase of insulation premature breakdown probability [4]. Furthermore, after the voltage switching-off, the space charge remains inside and in vicinity of treed areas, and the insulation presents a residual electric field for a long time after the voltage is removed [4]. Because residual electric field facilitates the processes of the insulation electrical degradation, knowing its values is very important. The space charge can be easily determined in homogeneous insulations by measuring the thermal step current and by using a relative simple relation [4-5]. In the case of inhomogeneous insulations (with water trees), the use of this method becomes more complicated. In previous papers [4-8], some aspects regarding the electric field computation in cable insulations in service (in the presence of water trees) have been presented. In this paper, a computation method of residual electric field in medium voltage cables in the presence of water trees obtained by accelerated electrical ageing on the basis of thermal step current is proposed.

2. Experiments

2.1. Samples

Accelerated ageing tests on crosslinked polyethylene minicables (having the outer radius of inner semiconductor ri = 1.4 mm and the inner radius of outer semiconductor re = 2.9 mm) were made. The maximum applied field was Emax = 6 kV/mm and frequency f = 50 Hz, for τ =

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200…1000 h. After ageing, on each sample, the thermal step current was measured and slices with 200 μm thickness were taken for trees analysis.

2.2. Thermal step current measurement

For thermal step current measurement on the tested samples, a thermal step of ΔT = 30 °C was applied using a thermal diffuser [5]. The measured current Im(t) is related to electric field E(r) by the relation:

( ) ( ) ( ) ( )∫ ∂

∂−=

e

i

r

r

rt

trTrErCtI d,α (1)

where α = αd - αε represents the difference between the thermal expansion coefficient αd and the permittivity variation factor of insulation with temperature αε, C – sample capacity before the thermal step application, E(r) – electric field strength in a coordinate point and T(r,t) – the temperature in the point of coordinate r at the instant t [9]. The temperature values T(r,t) are obtained from the Fourier equation:

( ) ( ) ( ) ( ) ( )( )[ ]trTrt

trTrcr p ,gradλdiv,γ =∂

∂ , (2)

where γ(r) represents the density, cp(r) the specific heat and λ(r) the insulation thermal conductivity in the point of coordinate r. For the computation of electric field E(r) an iterative computation method is used. It is considered that space charge density ρv(r) is known, the thermal step current Ic(t) is calculated, the condition Ic(t) = Im(t) is verified and, finally, E(r) is computed.

2.3. Dimensions and concentrations of water trees determination For each value of ageing time τ, several slices were taken from cables insulation and the

number of trees Nw, length Lk and diameter Dk of each tree were determined (Fig. 1). The average diameter Dm, length Lm and trees concentration cwtm were computed with the equations:

∑=

=wN

kk

wm L

NL

1

1 ; ∑=

=wN

kk

wm D

ND

1

1 ; nr

Nc

i

wwtm π2

= (3)

where n represents the number of taken slices.

Figure 1: Measurement of water trees dimensions 1 – Sample; 2 – Video Camera; 3 – PC; 4 – Monitor.

Figure 2: Computation domain of electric field.

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2. Electric field computation For electric field computation, it is considered that in cylindrical insulation of a cable were developed – from inner surface S1 – continuous trees (under the shape of cylindrical shell of thickness la) and an ionic space charge layer with the same shape and thickness ls > la. As the electric field has a radial symmetry, for the computation it was considered a flat domain D, constituted from 4 sub-domains D1…4 delimited by the surfaces S1…S5 (Fig. 2): - sub-domain D1 (delimited by S1 and S2), corresponding to the water treed region of length la (εr (r, T) = (1+αε(T - T0)⋅ce-dr)) (T0 is the temperature of the insulation before applying the thermal step). This region is supposed to contain a space charge layer of thickness la and of density ρv(r) = ρv0(ar2+br+e); - sub-domain D2 (delimited by S2 and S3), with a space charge layer of thickness ls – la and of density ρv(r) = ρv0(ar2+br+e); - sub-domain D3 (delimited by S3 and S4), without water trees and without space charge (εr (T) = εrPE(1+αε(T - T0))); - sub-domain D4 (delimited by surfaces S4 and S5), corresponding to the region thermal diffuser/sample of thickness y0, where the electric field is null. The computation of the electric field and the temperature is done with the Comsol Multiphysics software, considering that y0, la, ls, a, b, e, αεPE, αεw, c, c1 d, d1 and g as known and the Poisson ΔV = -ρv/ε and Fourier (eq. (2)) equations. The boundary conditions are: V(r) = 0 on S1, S4 and S5, ( ) 021 =− DDn on S2 and S3, T(r, t) = T1 on S1, and T(r, t) = T5 on S5 (Fig. 2), where D is the electric displacement, T1 and T5 – the temperatures on the semiconductor layers surfaces (Fig. 3). The material constants c and d from the expression of permittivity corresponding to D1 (εr(r) = ce-dr) were determined with the expressions:

( ) PEεε rair lr =+ ; ( )∫+

=ai

i

lr

rarmr lrr εdε ; ( ) PEε1εε rwmrmwmrm cc −+= , (4)

where cwm represents the average water concentration in the water trees, εrm and εrPE - the relative permittivity of water and polyethylene and εrm - the average permittivity in D1. The values of αε were deduced on the basis of the permittivity variation curves for water and polyethylene at temperatures between T5 = -5 °C and T1 = 25 °C [10-11]. It was obtained αεPE = 4.4·10-4 K-1 for polyethylene and αεw = - 7.26·10-3 K-1 for water. Because εr decreases exponentially with r, a variation law similar to the permittivity was considered for αε ( ( ) rdcr 1eα 1ε = ). The values of c1 and d1 have been obtained from the expressions:

( ) εPEε αα =+ ai lr ; ( )∫+

=ai

i

lr

ramlrr εε αdα ; ( ) εPEεε α 1αα wmwwmm cc −+= . (5)

The average values of γ, λ, cp, αεm and εrm for different values of cwm are presented in [7].

3.Thermal step current computation Computed thermal step current Ic(t) represents the time variation of charge Q1 on the surface S1 by the ionic space charge (from D1 and D2) by applying thermal step ΔT [5], respectively:

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22

22

11

dd

dd

ddd

dd

ddd

dd

επ2d

d- )(

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎠⎞

⎜⎝⎛

⋅+⋅−==

yV

xV

tyV

yV

txV

xV

lrt

QtI ic , (6)

where A1 = 2πril represents the area of the surface S1, l – the length of the sample (l = 20 cm), ε1 – the permittivity of the treed area and V1(x,y) – the electric potential in the point P(x,y) near S1. For the space charge density ρv a parabolic variation with the r coordinate was considered:

ρv(r) = ρv0(ar2 + br + e), (7) where ρv0 is considered, at the beginning of the computation, to have values between 0.1 and 0.8 C/m3, and a = 4·106 m-2, b = -1.5 m-1 and e = 14.44 [5].

4. Results

In Figure 3 the time variations of the measured thermal current (curves 1 and 3) and computed thermal step current (curve 2) are presented for τ = 500 h and τ =1000 h. It can be observed that the increase of the ageing time leads to an increase in the values of the measured thermal step currents, their maximum values being 7.5 times greater than initial one when τ doubles.

Figure 3: Variation with the time t of the measured (1 and 3) and computed (2) thermal step current I, for τ = 1000 h (1 and 2) and τ = 500 h (3).

Figure 4: Variation of the residual electric potential V on r-coordinate for water trees with Lm = 370 μm, cwtm = 1.27 wt/mm and Dm = 110 μm (1), Dm = 400 μm (2) and Dm = 790 μm (3).

The values for the dimensions (Dm and Lm) and for the average concentration (cwtm) of the water trees in the samples on which the thermal step current was measured are presented in Table 1. The values of the three parameters increase with τ (phenomenon also observed in [8]).

Table 1 Water trees dimensions and concentrations τ [h] Dm [μm] Lm [μm] cwtm [wt/mm]

500 82.72 342.72 0.31

1000 109.77 370 1.27 On the other hand, the increase of the number and dimensions of the water trees causes an increase of the ionic space charge that leads to an increase of the currents (Fig. 3). In order to determine the width of a continuous water tree la used for Ic(t), it was assumed that the water tree’s cross section area is equal to the sum of areas corresponding to the water trees

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from a cross section, with these parameters Lm, Dm and cwtm. The thickness of the layer corresponding to the space charge was considered 35 % higher than those of la (Table 2). In Figures 4 and 5, the electric potential V and residual electric field E variations with r - coordinate are presented for water trees with cwtm = 1.27 wt/mm and Lm = 370 μm. It can be observed that the electric potential has maximum values in the treed areas (in the vicinity of the

Table 2 Values of la and ls for water trees with a variable diameter Dm (Lm = 370 μm, cwtm = 1.27 wt/mm, nwt = 2.7)

Dm [μm] 110 200 300 400 500 600 787 la [μm] 52 111 140 188 235 282 370 ls [μm] 70 150 189 254 317 381 500

Figure 5: Variation of the residual electric field E on r-coordinate for water trees, with Lm = 370 μm, cwtm = 1.27 wt/mm and Dm = 110 μm (1), Dm = 400 μm (2) and Dm = 790 μm (3).

Figure 6: Variation of electric field Emax on trees concentration cwtm for Lm = 370 μm and Dm = 110 μm (1) and Lm = 343 μm and Dm = 83 μm (2).

inner semiconductor), areas where the charge layer ls is situated. The increase of Dm values (thus of la, Table 2) leads to a decrease in the electric potential’s maximum values and the displacement of these values towards the inside of the insulation (Fig. 6). This variation can be explained by an increase in the space charge layer thickness ls and a decrease in the values of ρv0 (the current Ic(t) remaining constant). The electric field dependence on the r-coordinate has the maximum points also situated in the treed areas (Fig. 5). Along with the increase of Dm (respectively, la) the maximum values for E decrease, and the maximum points move towards the inner semiconductor layer. This decrease is due to the reduction of the charge density’s ρv0 maximum values (in the vicinity of the inner semiconductor layer) as a consequence of the increase – with Dm – in the values for ls (Table 2). The increase in the values for water tree concentration cwtm leads to a reduction in the maximum values of E (Fig. 6, curve 1). This result is in agreement with the results obtained in the case of the computation of the electrical field for a cable insulation that only has an individual water tree [6]. The decrease of the stress time of cables in electric field determines a reduction in the dimensions and concentration of water trees (Table 1). This leads to even lower values for the measured thermal step currents (Fig. 3) and, finally, to obtaining smaller values for la (8.8 μm) and ls (12 μm). Thereby, the maximum values of the electric potential and of the residual electric field were considerably reduced (Fig. 6, curve 2). For the same curve Im(t) (dependent on the water trees dimensions and concentrations), the residual electric fields maximum values obtained by computation (with the COMSOL

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Multiphysics software) may vary with over one size order (Fig. 6). If the ageing time τ increases from 500 h to 1000 h, the water tree density increases from 0.31 to 1.27 wt/mm, but their length increase with only 11 % (their growth rate being lower, Table 1).The decrease of the water trees growth velocity shows that in the curve Lm(τ) [1] the area of slow propagation was reached and a breakdown of the sample is soon possible. The growth of water trees in polymer cable insulations also leads to an accumulation of ionic space charge which generates residual electric fields of relatively high intensities (10 MV/m, Fig. 5). These fields facilitate the appearance of partial discharges and electrical trees that may initiate a process of premature breakdown of cables insulations, even after the voltage is turn off.

5. Conclusions The raise of the operation time of power cables leads to the increase in the dimensions and concentrations of water trees, and, consequently, of the ionic space charge in the insulations. The concentration and dimensions of water trees strongly influence the values and repartition of the residual electric field. Thereby, its maximum values increase along with the average length of the water trees, but decrease along with the increase in diameter and concentration. The existence of some water trees with high lengths and small concentrations facilitates the appearance of high value residual electric fields (up to 10 MV/m), when partial discharges and electrical trees are initiated (3 MV/m). These may lead to premature breakdowns of power cable insulations. References [1] L.A.Dissado, J.C.Fothergill Electrical Degradation and Breakdown in Polymers, Peter Peregrinus

Ltd., London, United Kingdom, 1992. [2] R.Ross, Inception and Propagation Mechanisms of Water Treeing IEEE Transactions on Dielectrics

and Electrical Insulation, 5 (1998) 660-680. [3] Oana Visata Influence des Arborescences d’eau sur les propriétés diélectriques des polymères, PhD

Dissertation, UPB-UJF, Bucharest, 2001. [4] P. Notingher jr., A. Toureille, S. Agnel, J. Castellon Determination of Electric Field and Space

Charge in the Insulation of Power Cables With the Thermal Step Method and a New Mathematical Processing, IEEE Trans. on Industry Applications, 45 (2009) 67 – 74.

[5] Cristina Stancu Caractérisation de l’état de vieillissement des isolations polymères par la mesure des arborescences et de charges d’espace, PhD Thesis, UPB-UM2, 2008.

[6] Cristina Stancu, P.V.Notingher, F. Ciuprina, P. Notingher jr, S. Agnel, J. Castellon, A. Toureille Computation of the Electric Field in Cable Insulation in the Presence of Water Trees and Space Charge, IEEE Transactions on Industry Applications, 45 (2009) 30-49.

[7] Cristina Stancu, P. V. Notingher, P. Notingher jr, M.Plopeanu Electric Field Determination in Water Treed Samples Using the Thermal Step Method, Journal of International Scientific Publications, Materials, Methods & Technologies, 3 (2009) 51-62.

[8] Cristina Stancu, P.Notingher jr., P.V.Notingher, J. Castellon, S. Agnel, A. Toureille, U. Nilsson, A. Campus, D. Wald Water-Tree and Space Charge Characterization of Polyethylene Cable Insulation ac-Aged in Aqueous Environment, Journal of Optoelectronics and Advanced Materials – Symposia, 1 (2009) 925 – 931.

[9] A. Cernomorcenco, P. Notingher jr. Application of the thermal step method to space charge measurements in inhomogeneous solid insulating structures: A theoretical approach, Applied Physics Letters, 93 (2008) 192903 - 1 to 3.

[10] T. Meissner, F. Wentz The complex dielectric constant of pure and sea water from microwave satellite observations, IEEE Trans. Geoscience Remote Sensing, 42 (2004) 1836 – 1849.

[11] V. Svorcik, D. Erkt, V. Rybka, J. Liptak, V. Hnatowicz, Permittivity of polyethylene and polyethylene-terephtalate, Journal of Materials Science Letters, 19 (2000) 1843 – 1845.

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INFLUENŢA MATERIALELOR NEMAGNETICE LA ANALIZA TRIDIMENSIONALĂ A CÂMPULUI ELECTROMAGNETIC LA ALTERNATORUL

CU POLI GHEARĂ

Cristian BARZ, Constantin OPREA, Olivian CHIVER Universitatea de Nord Baia Mare, Str.Victor Babeş 62A, Baia Mare; barz@ubm.ro

Abstract. Lucrarea prezintă analiza 3D a câmpului electromagnetic a unui alternator cu poli gheara. Introducerea materialelor nemagnetice în cadrul rotorului, a urmărit stabilirea unor niveluri mai reduse de saturaţie in diferitele portiuni ale circuitului magnetic. Reducerea saturaţiei indusului conduce la micşorarea pierderilor în histerezis, putere ce va putea fi tranferată în puterea utilă a maşinii.

1 Introducere

Datorită înlocuirii treptată a unor organe hidraulice şi mecanice din cadrul autovehiculelor cu dispozitive electrice, cererea de putere în automobile a crescut foarte mult, iar energia electrică joacă un rol hotărâtor, generatorul convenţional al autovehiculului (alternatorul Lundell) tinde rapid spre limitele maxime ce le poate debita.

Utilizarea alternatoarelor cu poli gheară prezintă avantajul simplităţii constructive şi a fiabilităţii ridicate, dar are şi dezavantajul unor randamente scăzute datorită fluxului de dispersie ridicat.

Comportamentul electromagnetice al alternatorului cu poli gheară şi a interacţiunii sale cu puntea redresoare, sarcina şi sistemul de alimentarea al autovehiculului este, în general, analizată ca o caracteristică spatio-temporală. Utilizând modelul termic, variţia temperaturii al alternatorului cu poli gheră poat fi precizată analitic. Modelul termic a fost validate prin compararea calculării distribuţiei temperaturii cu valorile măsurate. [1]

Anumite studii au la bază ideea de a creşte puterea debitată şi randamentul alternatorului, menţinând punctul de funcţionare al alternatorului în zona sa optimă. Preconizările teoretice sunt comparate cu rezultatele experimentale folosind un alternator auto; creşterile puterii de ieşire de până la 200% şi îmbunătăţirea semnificative a randamentului sunt demonstrate la viteze mari. [2]

Metodele folosind simulări numerice bazate pe elemente finite sunt adesea folosite pentru că permit calcularea cu o bună precizie a performanţei dispozitivelor. Utilizarea acestor metode pot depăşi toate expertizele şi ipotezele făcute pentru a stabili un model analitic adesea lung şi greoi de construit.

Modelele analitice permit realizarea studiilor preliminare de proiectare, astfel cum simulările numerice oferă posibilitatea de a valida şi perfecţiona soluţii bazate pe metodele analitice. Autorii care au utilizat metode analitice, se concentrează în primul rând pe viteza de calcul al modelelor.

Lorilla s.a, Gerling s.a. au analizat în amănunţime fenomenele electromagnetice din alternatorul Lundell, ca maşină sincronă cu poli aparenţi, folosind teoria clasică a maşinilor electrice.

Henneberger s.a , Damerdash s.a., Viorel s.a. au investigat fenomenele electromagnetice şi termice din alternatorul Lundell folosind metoda elementelor finite:

Studiile lui Perreault s.a. au investigat mijloace de a extrage o putere mai mare din alternatoarele cu poli gheară existente folosind un redresor în regim de comutaţie. De

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asemenea, au fost propuse alternatoare conduse prin invertor, acesta putând furniza energie la un factor de putere capacitiv şi fiind capabil să extragă cam de două ori mai multă putere din alternator la turaţii mici.

Soluţiile propuse includ şi alte tipuri de maşini electrice: maşini asincrone, maşini cu reluctanţă variabilă, maşini sincrone cu magneţi permanenţi de suprafaţă şi maşini sincrone cu magneţi permanenţi de interior: Boldea s.a. ,Naidu s.a, Liang s.a. , J.M. Miller s.a. Sistemele alternatoarelor propuse sunt scumpe datorită electronicii de putere şi controlului complex. [3]

Schulte descrie două abordări pentru calculul inductivităţii mutuale între rotor şi stator a alternatorului sincron cu ghearelor cu privire la forma ghearelor. Ne existând un mod direct pentru a masura inductivitatea mutuală, e nevoie de o determinare indirectă. Datorită structurii complexe a rotorului, abordările evaluării sunt dificile. În cazul în care prototipuri sunt disponibile, inductivitatea mutuală poate fi calculată pe baza tensiunii măsurată la mers în gol. Descrierea inductivităţii mutuale obţinute poat fi utilizată pentru punerea în aplicare a circuitului pe bază în simulări [4]

2 Analiza numerică a câmpului electromagnetic

Analiza numerică 3D prin metoda elementelor finite, a câmpului electromagnetic produs de maşinile electrice, constituie în momentul de faţă, din punctul de vedere a preciziei rezultatelor obţinute, unul din cele mai puternice mijloace de analiză a câmpului electromagnetic, respectiv de determinare a parametrilor acestor structuri complexe, indiferent de forma câmpului sau de existenţa sau inexistenţa unor simetrii.

Metoda elementului finit este potrivită pentru a lucra cu componentelor neliniare cum ar fi maşinile electrice rotative care manifestă fenomene anizontropice si de saturaţie.

Relaţiile constituite intre inducţia magnetică (B) şi intensitatea câmpului magnetic(H), sunt, in general, neliniare, pe deasupra anumite materiale prezintă histerezis, in “starea” BH pentru un punct particular in spaţiu şi timp, depinzând de valorile magnetice anterioare.

Pentru a extinde procedura elementelor finite pentru a include proprietaţile neliniare ale materialelor, este necesar un model matematic pentru a descrie proprietăţile materialului.

O abordare mai comună este utilizarea uneia dintre metodele Newton Raphson care converg rapid, furnizând suficiente valori de pornire. Astefel dacă u(0) reprezintă o matrice de valori iniţiale ale soluţiei, u(1) se poate scrie:

)0()0()1( uuu δ+= (1) unde δu(0) – matrice a valorilor erorii.

(K(u)-Q)=F(u) =0 (2) unde Q este independent de u, funcţia F definită in ecuaţia (2) poate fi extinsă prin seriile multidimensionale Taylor ca:

....)()(

2

201

1

1)0()0()0( +∂∂

+∂∂

+=+uFu

uFuFuuF δδ

(3) Schema de iteraţie simplă NewtonRaphson, este posibil să nu conveargă dacă presupunerile

iniţiale nu sunt deajuns de apropiate de soluţie. În practică se obişnuieşte să se obţină valorile iniţialele de pornire prin realizarea câtorva paşi de iteraţie, înaintea schimbării cu metoda Newton Raphson.

Tratarea neliniarităţii cu metoda Newton-Raphson şi aplicarea metodei elementului finit la soluţionarea problemei de câmp pentru fiecare iteraţie este, în prezent, cea mai utilizată metodă de analiză a câmpului magnetic din maşinile electrice rotative.

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Calitatea unei analize prin metoda elemntului finit depinde aproape exclusiv de capacitatea retelei de elemente de discretizare, de a aprecia comportarea cmpului electromagnetic. Dezvoltarea impresionantă a tehnicii de calcul a deschis noi perspective în ceea ce priveşte posibilităţile de simulare a regimurilor de funcţionare a maşinilor electrice, pe baza modelelor de câmp electromagnetic.

Metodele actuale de generare adaptiva automata a discretizarilor sunt: • ”metoda -h”ce adaptează dimensiunea elementelor; • ”metoda-p”ce adaptează ordinul polinomului de aproximare; • ”metoda-hp”combinaţie a celor două metode amintite mai sus.

Programele profesionale de analiza numerică dezvoltate de firme ca ˝Vector Fields˝, ˝Infolytica˝, etc. asigura un mediu competitiv de dezvoltare al aplicabilităţii şi eficientizării metodei. Acestea scutesc specialistul de discretizarea domeniului, întocmirea sistemului de ecuaţii minimizat, rezolvarea acestuia, postprocesarea rezultatelor dar doar la nivel de realizare si transpunere de algoritm în limbaj de programare.

3 Modelarea şi analiza tridimensională a alternatorului cu poli gheară

În lucrare se prezintă modul în care s-au realizat modelele numerice şi analizele tridimensionale a unui alternator cu poli gheară (Lundell), având tensiunea nominală Un = 14 V şi curentul nominal In = 30 A, utilizat în general la generarea curentului electric pentru autovehicule.

Realizarea modelului numeric al analizei tridimensionale se construieşte cu programul realizat în Visual Basic Script. Accesând mediul de calcul Magnet, pentru realizarea analizei de câmp se definesc condiţiile de frontieră, curenţii ce străbat înfăşurările atât cele ale satorului cât şi cele ale rotorului.

Mediul de calcul Magnet, permite alegerea mai multor posibilitati de calcul al câmpului, cea mai utilizata fiind metoda Newton Raphson, totodată permiţând alegerea dimensiunii elementelor finite dar şi a ordinului de calcul al polinoamelor de aproximare. (Figura 1.)

Fig. 1. Opţiunile analizorului

Forma constructivă şi dimensiunile optime ale polilor în gheară sunt impuse de rolul acestora de a convertii fluxul axial produs de înfăşurarea de excitaţie în flux radial în întrefier. Forma polilor este complexă fiind nesimetrică faţă de planul median al maşinii, impunând ca analiza câmpului magnetic sa poată fi realizată doar tridimensional.

Existând diverse studii legate de diverse teşiri sau forme ale geometriei dinţilor [4], s-a încercat să se realizeze câteva opţiuni pentru modificarea acestora, pentru a urmării în cadrul analizei ulterioare influenţele asupra câmpului electromagnetic din alternator (Figura 2.).

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Fig 2. Modele de poli gheară

În urma analizei câmpului magnetic al alternatoruilui cu poli gheară (Figura 3.), se observă cu uşurinţă că inducţia magnetică la baza polilor gheară este semnificativ mai mare în comparaţie cu alte zone sau componente ale circuitului magnetic.

Fig. 3. Inducţia magnetică în rotorul alternatorului cu poli gheară

Analiza numerică efectuată vizează două variante constructive ale subasamblului rotor. Prima variantă analizată presupune o repartizare a aluminiului intre ghearele rotorului,

înlocuind aerul întrefierului cu aluminiu (Figura 4)

Fig. 4. Repartiţia Aluminiului între polii gheară ai alternatorului

Cea de-a doua constă într-o construcţie de inele în partea periferică a rotorului în vederea scăderii saturaţiei polilor, dar doar în spaţiul liber dintre baza ghearelor (Figura 5).

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Fig. 5. Repartiţia Aluminiului între polii gheară ai alternatorului

Excitarea magnetică puternică a rotorului, combinată cu geometria specifică a polilor gheară, implică scăpări magnetice semnificative, mai ales între gheare. Aceste scăpări devin importante atunci când materialul magnetic este saturat. Saturaţia magnetică scăzută în rotor (figura 6.), permite obţinera unui flux util mai mare.

Fig. 6. Reprezentarea inducţiei magnetice în rotorul alternatorului

Modelul tridimensional fost utilizat în verificarea rezultatelor analitice ale proiectării şi pentru verificarea nivelului de saturaţie a circuitului magnetic al alternatorului standard.

În figura 7. avem reprezentată inducţia magnetică de-a lungul polului gheară pentru cazurile: alternatorului simplu, rezultat în urma proiectării şi construit conform modelului studiat, pentru cazul când între gheare se introduce aluminiu şi cazul când aluminiu este utilizat sub formă de inele pe coroana rotorului, dar doar în spatiul liber dintre baza ghearelor.

Se poate observa o creştere a saturaţia în lungul axei polului gheară în primul caz, cu aluminiul între gheare faţă de cazul alternatorului standard.

În cel de-al doilea caz studiat însă, importantă este scăderea saturaţiei cu până la 15%, când aluminiul este sub formă de inele pe coroana rotorului. Se observă o scădere mai accentuată a saturaţiei magnetice în zona aluminiului, dar scaderea saturaţiei este prezentă semnificativ (până la 5%) şi spre vârful polului gheară, aici saturaţia fiind mai scăzută iniţial.

Rezultatele obţinute din măsurători experimentale nu sunt disponibile momentan, neputând fi comparate cu cele ale analizei tridimensionale ale alternatorului cu poli gheară, în varianta cu inele de aluminiu pe coroana rotorului, neavând disponibilă varianta constructivă a acestuia.

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Inductia în polul gheară

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 5 10 15 20 25 30 35Lungimea polului

Indu

ctia

mag

netic

a [T

]B fara Al

B geara Al

B inel Al

Fig. 7. Inducţia magnetică de-a lungul axei polului gheară

Modificarea circuitului magnetic al alternatorului se bazează pe perspectiva optimizarii rezultatelor ce urmeaza a fi incluse in proiectarea unui prototip al alternatorului cu poli gheară

4 Concluzii

• Programele care realizează analize de câmp pe baza metodei elementelor finite, vin în ajutortul proiectantului prin verificările pe care le pot efectua, în timp util şi cu precizie deosebită, înlăturind astfel eventualele greşeli făcute în timpul proiectării maşinilor electrice, asigurând astfel atigerea scopului propus de proiectant.

• Lucrarea de faţă tratează aspecte specifice privind modelarea şi analiza numerică a unui alternator cu poli gheară, cu anumite porţiuni de materiale nemagnetice (Al), utilizând metoda elementului finit. Investigaţiile numerice efectuate vizează optimizarea constructivă a maşinii prin reducerea saturaţiei magnetice a polilor alternatorului ce apare ca urmare a interacţiunii segmentelor de aluminiu introdu-se în construcţia rotorului.

• Introducerea materialelor nemagnetice în cadrul rotorului, sub formă de inele pe coroanele rotorului, a urmărit stabilirea unor niveluri mai reduse de saturaţie în diferitele porţiuni ale circuitului magnetic (dinti, juguri) şi creşterea puterii utile a alternatorului. Pasul următor fiind confirmarea acestor rezultate obţinute în urma realizării unui model practic.

Referinţe [1] Sai Chun Tang, Member, IEEE, Thomas A. Keim, and David J. Perreault, Member, IEEE, Thermal

Modeling of Lundell Alternators”, IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 20, NO. 1, MARCH 2005, pag 25

[2] Ceuca, E.; Joldes, R.; Olteanu, E Simulation of automotive alternator - solution for increasing electrical power. Automation, Quality and Testing, Robotics, 2006 IEEE International Conference onVolume 1, Issue , 25-28 May 2006 Page(s):292 – 297

[3] V. Comnac, M. Cernat, A. Mailat, J. Vittek, R. Rabinovici, “A New 42 V Automotive Supply System Based on Conventional 14 V Alternator,” in Proccedings OPTIM 2008, Brasov, Romania, 22-24 May 2008, vol. II, pp. 271-276

[4] St. Schulte, K. Hameyer Computation of the Mutual Inductance between Rotor and Stator of Synchronous Claw-Pole Alternators regarding Claw Chamfers, Institute of Electrical Machines, RWTH Aachen University, Schinkelstr. 4 52056 Aachen Germany, 2005

[5] Christian Kaehler and Gerhard Henneberger, Eddy-Current Computation in the Claws of a Synchronous Claw-Pole Alternator in Generator Mode, IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 2, MARCH 2002 1201

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Power mixer for conversion from low to high frequency CMOS

Catalin Adrian BRINZEI, Iulian URSAC

“Politehnica” Bucharest, Electrical Engineering, Romania;catalinbrinzei@gmail.com

Abstract. In this paper a new approach of a wideband transmitter for multi-standard communication systems is presented. The main idea consists in cascoding the output stage and so the power amplifier over the mixer core. In this way the same bias current is shared for main components, mixer and power amplifier. The current signal from the base-band stage is mirrored using a simple current mirror with the multiplicity factor of 11.The power consumption for this power mixer is competitive with which is currently present on the market. A maximum output power of 10.2dBm requires 106.8mA from a 2.5V supply and corresponds to 267mW power consumption.

1 Introduction A wideband transmitter is proposed using two double balanced Gilbert mixers cells for I(in phase) and Q(quadrature phase) summed together to suppress the image ,only one spike remains at high frequency.

2 Quadrature modulation This paper will be focused mainly on those two mixers and the power amplifier unified in a single block named power mixer. In the figure below it is presented a common used method to implement a wideband transmitter.

Figure 1: Transmitter wideband architecture WIMAX standard [7]

Theoretical approach:

The output of the mixer I is denoted A ,the output of mixer Q is denoted B.The output from DAC for both I and Q mixers baseband inputs are ( ) cos BBI t tω= and ( ) cos BBQ t tω= . The high frequency inputs for I and Q mixers are: ( ) cosLO LOI t tω= , sinLO LOQ tω= . It follows:

( )1cos *cos cos( cos( ) )2BB LO BB LO BB LOA t t t tω ω ω ω ω ω= = − + + (1)

( )1sin *sin cos( cos( ) )2BB LO BB LO BB LOB t t t tω ω ω ω ω ω= = − + − − (2)

Making the sum of the outputs of both Gilbert mixers it is obtained:

A+B= ( ) ( )1 1cos( cos( ) ) cos( cos( ) )2 2BB LO BB LO BB LO BB LOt t t tω ω ω ω ω ω ω ω− + + − + − −

= 1 1cos( ) cos( ) cos( )2 2BB LO BB LO LO BBt t tω ω ω ω ω ω− + − = − (3)

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According to (3) the inferior output frequency spike is obtained. If the superior lateral band is desired we will consider the output of the mixer I to be C and the output of the mixer Q to be D.

( )1cos *( cos ) cos( cos( ) )2BB LO BB LO BB LOC t t t tω ω ω ω ω ω= − = − − + + (4)

( )1sin *sin cos( cos( ) )2BB LO BB LO BB LOD t t t tω ω ω ω ω ω= = − + − − (5)

C+D= ( )1 cos(2 BB LO tω ω− + ( )1 cos(

2 BB LO tω ω− + = - ( )cos( BB LO tω ω+ (6)

3 Power mixer proposed solution ,specifications Table 1

Maximum amplitude signal input base band peak differential 400mV

Maximum amplitude signal output RF peak differential 1300mV

Power supply voltage 2.5V

Maximum frequency of the modulation signal >100MHz

Carrier frequency, local oscillator frequency >3500MHz

Output power on the RF output, 100ohms differential load >9dBm

Current consumption from 2.5V supply <110mA

Output 1dB Compression point >9dBm

Voltage gain conversion >10.2dB

Temperature variation -20deg 80deg

Process 0.13um CMOS

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4 Power mixer proposed solution, schematic design, transistor level

Figure 2: Power mixer transistor level

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The output stage is designed in a such a way to establish the maximum output current signal to a known differential load, in our case 100 ohms. The DC bias conditions for each Gilbert mixer must be carefull considered in order to support the big variation of the current. Because an important signal output power (10.2dBm) is requested on a load resistor of 100 ohms, then through the load the signal current is 14.46mA. A such big signal variation could be sustained just if an appropriate current bias is chosen for the output stages.In this case for each switching stage; Ibias on one branch is chosen to be 24.2mA. The following equations describe some design constraints:

[ ] [ ] 30OUT OUTP dBm P dB= + (7)

_ _ 1.446[ ] 10log 10log 10log 19.8062* 2*100

OUT diff OUT efectivOUT

LOAD LOAD

U U VP dB dBR R

= = = = − =10.2dBm (8)

_ _I _ _ 14.46

LOAD

U OUT diffsignal out stage mAR

= = (9)

Because a current mirror with the multiplicity factor of 11 was used to mirror the base band current signal to the bias of the RF part, the value of the current of the base band signal from voltage to current converter can be obtained using the following equation:

14.46I _ _ 1.31411

mAsignal in stage mA= = (10)

Using the signal current value a suitable bias can be chosen and so the current bias will be 2.2mA which is enough to sustain the current variation.Due to the previous calculations we can now show that the total current consumption is 106.8mA, and the specifications are met.

The linearity simulations results are shown next. The 1dB compresson point can be simulated over a large output bandwidth but in this paper we focus on 3.5GHz. The methodology chosen to estimate linearity is the repetitive transient analyses. One transient analysis is run with a small amplitude signal on the IF part (20mV ,100MHz applied differential), keeping on each input a DC value of 1V.In the second transient analysis only the value of the IF signal amplitude is changed to 400mV.The results are shown in Table2: Table 2 Input [mV]

Port IF Output [mV] , 100

ohms load Gain =G Gain [dB] =20logG

20 80.7 4.035 12.116 400 1446 3.615 11.162

Commenting the upper results we can conclude that the one dB compression point in

the output(1dBCP_out) is found to be at 1.446V and one dB compression point in the input(1dBCP_in) is found at 400mV input differential,values which provide a good linearity to this power mixer and also provide the dynamic range of the signal at input and at the output.

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Figure 3: Power mixer output voltage spectrum for 20mV input differential 100MHz

Figure 4: Power mixer output voltage spectrum for 400mV input differential 100MHz

5 Conclusions A power mixer with good performance parameters was presented in this paper. The

performance parameters are very sensitive to the layout parasitics and also to the matching which is realized in the output of the power mixer. Because the output impedance of the power mixer is varying with the bias of the output stage, when the output power is changed the bias is changed and mismatches appear and power losses are present. The simulator used was Spectre RF and the analyses used were: DC, TRAN, AC, PSS and SP. The schematic of this power mixer may be improved in order to provide a better matching between the load and the output of the power mixer and also to decrease the reflections in corners and over supply variations.

The maximum output power of 10.2dBm which is achieved corresponds to 267mW power consumption and with a 0.55dB gain compression. The power mixer will not be used in this region due to its linearity which is dropping if a bigger output power is provided so lower output power will be selected in practice

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6 References [1] Behzad Razavi, RF Microelectronics, Prentice Hall, 1998. [2] Markus Mayer, Smely, Low intermodulation class-F power amplifier, Radio and Wireless

Conference, 2003,pp. 289-292. [3] Mohammed Ismail, RF Power amplifier design, Kluwer Academic Publishers,2002. [4] Derek K. Shaefer , A 1.5 V ,1.5 Ghz CMOS Low Noise Amplifier, IEEE Journal of Solid State

Circuits , Vol.40, No.6, 2005, pp.1397-1398. [5] Behzad Razavi, Design of Analog Cmos Integrated Circuits, McGraw-Hill, 2000. [6] J.P. Carmo, P.M. Mendes, J.H. Correia, A 2.4 Ghz wireless sensor network for smart electronic

shirts, Smart Sensors, Actuators, and MEMS II, Sevilla, Spain ,Vol.5836,579, 2005. [7] Anna-Maria Lann, RF CMOS Power mixer design for short range wireless applications with focus on

polar modulation, Master thesis, Linkoping University, Sweden, 2006. [8] G.Hanington,P.F.Chen, High-efficiency power amplifier using dynamic power-supply voltage for

CDMA applications, IEEE Transactions on Microwave Theory and Techniques, Volume 47 ,Issue 8 August 1999, pp.1471 – 1476,.

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Sintetizator de Frecvenţă cu Oscilator Comandat Digital

Iulian URSAC, Catalin Adrian BRINZEI Universitatea “Politehnica” din Bucureşti, Spl. Independenţei 313, 060042, Bucureşti

ursac.iulian@gmail.com

Abstract. Lucrarea prezinta un circuit sintetizator de frecventa cu bucla cu calare a fazei dezvoltat dupa un concept propriu. In faza de concept, s-a proiectat o topologie si se doreste determinarea performantelor. Pe baza acestui studiu se face o comparatie intre parametrii de functionare ai acestui sintetizator si alte topologii de circuite sintetizoare de frecventa deja implementate si utilizate in practica.

1 Introducere

Sintetizatorul de frecventa este un circuit capabil sa furnizeze un numar mare de frecvente, cu stabilitate ridicata, utilizând o sursa de referinta.

Ca topologie de baza se utilizeaza o bucla cu calare de faza (PLL - Phase Locked Loop). Aceasta tehnica s-a impus, nu atât datorita performantelor legate de numarul frecventelor generate, pasul mic sau calitatea semnalelor - comparabile celor realizabile prin alte tehnici, cât prin marile avantaje oferite în privinta masei, dimensiunilor, consumului de energie.

O bucla o bucla cu calare de faza este practic un sistem automat cu reactie pentru urmarirea fazei. Pentru a evidentia modul de functionate al sintetizatorului de frecventa se va studia modul de lucru in cele doua regimuri de functionare: de achizitie si de urmarire.

2 Schema bloc a sintetizatorului de frecventa

Schema bloc a circuitului sintetizator de frecventa (în forma cea mai simpla) este

prezentata în figura1. Marimile de intrare si de iesire sunt fazele Φi(t) si Φo(t) ale semnalelor de intrare si de iesire vi(t) si vo(t).

Fig 1: Schema bloc a Sintetizatorului de Frecventa

Calitativ, functionarea sintetizatorului de frecventa este :

• Comparatorul de faza (PFD) furnizeaza o tensiune vd(t) proportionala cu diferenta fazelor;

• Circuitul combinational CLC furnizeaza un semnal relativ static ce comanda numaratorul NR (numarare directa sau inversa);

• Numaratorul NR realizeaza incrementarea sau decrementarea decodorului termometric (Th Decoder) in functie de semnalul de comanda;

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• Decodorul termometric furnizeaza semnalul ce comanda oscilatorului comandat in tensiune digitala VCO;

• Oscilatorul controlat în tensiune furnizeaza un semnal ce are frecventa proportionala cu tensiunea de comanda vc. Daca se seteaza bitii de comanda ai oscilatorului intr-o anumita configuratie, oscilatorul va genera o frecventa care, divizata, va fi multiplu a frecventei de referinta de la intrarea detectorului de faza si frecventa.

Sistemul este conceput astfel încât în regimul de lucru normal, numit regim de urmarire (a fazei), faza de iesire sa urmaresca faza de intrare. Acest lucru se poate realiza in doua situatii distincte:

• frecventele de iesire si de intrare sunt egale: ωo = ωi; • între fazele de intrare si iesire se realizeaza o diferenta constanta si mica:

Φo(t)– Φi(t) = constant. Daca faza de iesire se modifica, de exemplu datorita schimbarii frecventei de iesire ωo,

bucla de reactie va actiona pentru a reveni la diferenta de faza constanta Φo(t)– Φi(t) = constant astfel :

• Tensiunea vd(t), furnizata de PFD (comparatorul de faza) se modifica datorita modificarii valorii Φo(t) – Φi(t)

• Circuitul combinational CLC furnizeaza un semnal ce comanda sensul de numarare (direct sau invers) al numaratorului NR

• Numaratorul schimba tensiunea de comanda a oscilatorului • Oscilatorul isi schimba faza semnalului de iesire la valoarea initiala astfel incat

sa satisfaca conditia Φo(t)– Φi(t) = constant Daca faza de intrare se schimba, de exemplu datorita variatiei frecventeide intrare ωi la

ωi1 bucla de reactie ca actiona astfel: • Tensiunea vd(t) furnizata de PFD (comparatorul de faza) se modifica datorita

modificarii valorii Φo(t) – Φi(t) • Circuitul combinational comanda sensul de numarare pentru numaratorul NR • Numaratorul schimba tensiunea de comanda a oscilatorului • Oscilatorul isi schimba faza semnalului de iesire iar diferenta fazelor redevine

constanta, de data aceasta la alta valoare dictata de semnalul de intrare: Φo(t)– Φi(t) = constant1.

In concluzie, în regimul de urmarire faza semnalului de iesire urmareste faza semnalului de intrare la o valoare constanta (care în particular poate fi nula). In acest caz se spune ca bucla este calata.

Reglajul frecventei de oscilatie se face cu pasi ficsi dictati de valoarea capacitatii conectata/deconectata cu ajutorul comutatoarelor. Relatia dintre frecventa de iesire, frecventa semnalului de referinta si factorul de divizare este urmatoarea:

NFF

Intrare

Iesire = (1)

Factorul de divizare trebuie dimensionat corespunzator pentru un zgomot de faza mic. Un aspect ce poate fi imbunatatit la aceasta topologie il constituie zgomotul de faza. Este posibil ca frecventa de calare sa nu coincida cu o frecventa sintetizabila de sintetizator, ci sa se gaseasca intre doua frecvente apropiate F1 si F2 ce pot fi generate cu capacitatile comutate. In acest caz la iesirea sintetizatorului de frecventa vom obtine un semnal de frecventa intre F1 si F2. In aceasta situatie putem afirma ca zgomotul de faza de la iesirea sintetizatorului de frecventa este mare.

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. Fig 2: Factor ce genereaza zgomot de faza

Zgomotul de faza se poate minimiza prin alegerea optima a factorului de divizare al divizorului de frecventa, frecventelor oscilatorului si semnalului de referinta.

3 Oscilatorul comandat digital in tensiune

Oscilatorul comandat in tensiune este componenta functionala cea mai importanta intr-un sintetizator de frecventa. Pasul de frecventa al semnalului din iesirea oscilatorului determina eficienta PLL-ului. Pe langa faptul ca lucreaza la cea mai inalta frecventa, aceasta componenta consuma cea mai multa putere din sintetizatorul de frecventa.

Fig 3: Schema bloc a Oscilatorului comandat in tensiune

Oscilatorul comandat digital in tensiune este de tip L-C-rezistenta negativa. Rezistenta negativa este asigurata de o pereche diferentiala de tranzistori N-MOS.

Ca in orice oscilator de acest tip capacitatea este elementul variabil din circuit. In cazul nostru avem 32 de perechi de condensatori, fiecare pereche fiind activata de 2 comutatoare. Controlul celor 32 de comutatoare se realizeaza cu iesirea pe 32 de biti a decodorului termometric.

Elementul capacitiv folosit in obtinerea frecventei de oscilatie este format din doi condensatori pentru doua moduri de control al frecventei:

• Controlul frecventei de oscilatie cu un pas mic ( Condensator Fine Tune) • Controlul frecventei de oscilatie cu un pas mai mare (Condensator Gross Tune).

Modul de reglaj al frecventei in bucla inchisa:

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Se porneste de la frecventa maxima a oscilatorului (capacitate minima) si se scade frecventa adaugand cate un condensator din aria de condensatoare Fine Tune. In acest fel frecventa va scadea cu pasul minim (rezolutia oscilatorului).

In cazul in care bucla nu s-a calat si am ajuns la capatul benzii de frecventa dictate de condensatoarele din Fine Tune, vom adauga condensatorul Gross Tune si vom reseta numaratorul astfel incat sa se reia aceeasi operatie dar de data aceasta avand adaugat si condensatorul Gross Tune.

Fig 4: a) Schema Oscilatorului comandat in tensiune; b) Domeniul de frecventa in functie de capacitatea din circuitul rezonant; c) Controlul frecventei de oscilatie cu pas mare

(Gross Tune); d) Controlul frecventei de oscilatie cu pas mic (Fine Tune)

In figura 4 punctul a) este prezentata schema de principiu a oscilatorului comandat in tensiune. Acesta este alcatuit dintr-un circuit oscilant de tip L-C-1/gm. La punctul b) al figurii 4 se prezinta castigul discretizat al sintetizatorului de frecventa. La punctele c si d sunt prezentate modurile de conectare ale condensatoarelor “Gross Tune” si “Fine Tune”.

Banda totala de frecventa este: Banda totala Oscilator= (Numar condensatoare Gross Tune) * [Banda (Fine Tune)] (2)

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4 Rezultatele simularilor Timpul de calare al buclei: Viteza de calare a buclei este data de numarul de domenii de frecventa si perioada

ceasului de referinta. In cazul prezentat perioada ceasului de referinta este T=50ns. Timp calare = 2 * 32 Domenii frecventa * T =3200ns In cele ce urmeaza sunt prezentate rezultate simularilor oscilatorului comandat digital

pentru cate doua frecvente de iesire situate la capetele bandei de frecventa. Daca la iesirea decodorului de tensiune toti cei 32 de biti vor avea valoarea 0V (0 logic),

la iesirea oscilatorului semnalul are frecventa de aproximativ 4.4GHz si o amplitudine de 2 volti varf la varf. In tabelul urmator sunt prezentate rezultatele simularilor oscilatorului comandat digital in scopul evidentierii rezolutiei frecventei la capetele celor doua benzi de frecventa.

Iesire Numarator Frecventa din

iesirea OCT

Rezolutia OCT GrossTune FineTune

0 0 0 0 0 4.333 GHz 8MHz 0 0 0 0 1 4.326GHz0 1 1 1 0 3.981GHz 12MHz 0 1 1 1 1 3969GHz

1 0 0 0 0 3. 975 GHz 10MHz 1 0 0 0 1 3.965GHz1 1 1 1 0 3.603GHz 13MHz 1 1 1 1 1 3. 590 GHz

In figura urmatoare sunt prezentate semnalele din iesirea oscilatorului si bufferului.

Astfel putem gasi informatii atat despre spectrul semnalului de iesire cat si forma sa in regim tranzitoriu.

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Fig 5: Semnalele din iesirea oscilatorului comandat digital si buffer Din forma de unda care prezinta spectrul se poate observa ca nu sunt prezente semnale

perturbatoare in jurul semnalului util. Din forma semnalului in timp se observa o amplitudine foarte mare a semnalului din iesirea oscilatorului (2V). Forma semnalului este sinusoidala fara urme vizibile de distorsiuni. Rezulta ca influenta armonicelor (de ordinle 3 si 5), care genereaza de obicei probleme din punct de vedere al zgomotului de faza, este foarte mica.

5 Concluzii 1.Avantaje:

• Majoritatea blocurilor folosite sunt digitale. Astfel timpul de raspuns la un stimul ce comanda schimbarea intre doua stari ale buclei sintetizatorului de frecventa este mai mic. Acest lucru este pozitiv deoarece creste viteza de operare a sintetizatorului de frecventa.

• Arie mai mica decat un PLL clasic (se elimina utilizarea filtrului trece jos si a pompei de sarcina care ocupa destul de multa arie pe circuitul integrat).

• Consumul de putere s-a redus fata de variantele uzuale de sintetizator deoarece nu mai este necesara utilizarea unei pompe de sarcina.

• Timp de calare al buclei mai mic decât în cazul circuitelor convenţionale. 2.Dezavantaje:

• Pasul de variatie al frecventei este mare deoarece rezoluţia frecvenţei este data de condensatoarele fixe.

• Zgomotul de faza este relativ mare. Nu putem folosi condensatoare oricât de mici pentru a avea un pas de frecventa mic deoarece riscăm să ajungem la valori apropiate cu cele ale capacităţilor parazite ale traseelor.

Pentru a imbunatati performantele de zgomot de faza ale acestui circuit trebuie sa imbunatatim topologia actuala de sintetizator de frecventa.

6 Bibliografie [1] M.A. Margarit, J. L. Tham, R. G Meyer, and M. J. Been, A Low-Noise, Low-Power VCO with

Automatic Amplitude Control for Wireless Applications, IEEE Journal of Solid-State Circuits, Volume 34, Issue 6, Jun 1999, pp. 761 - 771

[2] E Herzel, and B. Razavi, A Study of Oscillator Jitter Due to Supply and Substrate Noise, IEEE Trans. Circuits and Systems II (Analog and Digital Signal Processin, Volume 46, Issue 1, Jan 1999, pp.56 – 62.

[3] K. A. Kouznetsov and R. G. Meyer , Phase Noise in LC Oscillators, IEEE Journal of Solid-State Circuits, Volume 35, Issue 8, Aug 2000, pp 1244 – 1248.

[4] J. Craninckx and M. Steyaert , Low-Noise VoltageControlled Oscillators Using Enhanced LC-Tanks, IEEE Transactions on Circuits and Systems II (Analog and Digital Signal Processing), Volume 42, Issue 12, Dec 1995, pp. 794 – 804.

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Energy consumption in Wireless LAN according to different models of encryption

Gheorghe Mülec1, Emil Cazacu2

1Electronics and Telecommunication Faculty Politechnica University of Timisoara

2Electric Engineering Department Politechnica University of Bucharest

Key words: energy, wlan, security, encryption Abstract: As computing devices and wireless connectivity become ubiquitous, the need for efficient secure wireless local area networks becomes a critical concern. Low power consumption is currently one of the major issues for all wireless application. Emerging wireless and mobile appliances are severely constrained in the resources they possess, namely, processor, battery, and memory. Energy consumed by computation and communication intensive wireless security protocols used to provide data privacy, integrity and authenticity is a function of the size of the data transferred and the security level of the session. In this paper we analyze how encryption affects the consumption of battery power with and without data transmission.

1. Introduction

In recent years, wireless connectivity has been gaining increasing attention with devices

like laptops, PDAs, Pocket PCs and handhelds [1]. Features like nomadic access, rapid network

configuration, and lack of wires make wireless networks particularly attractive [2]. Individuals

are using wireless technology for storing private communications, for mobile commerce,

emails and business interactions.

Security is provided through security services [3]. Confidentiality of data ensures that

only the authorized person reads the data and others are prevented from doing so.

Confidentiality in wireless communications is achieved by transmission of encrypted secure

data and maintaining the secrecy of the keys used for encryption[4]. Authentication involves

ensuring that the source of the received message is identified correctly. Integrity enables being

sure that the data has not been modified by an unauthorized entity.[5] Access control restricts

the information availability to allowed parties. Availability requires the system to be available

to the authorized entities whenever needed and non-repudiation ensures that neither the

origination nor the receptor of the information can deny the transaction[6].

Studies indicate that the growth of wireless networks is being restricted by their

perceived insecurity [7]. The amount of security required by the system may depend on the

organization using the wireless network.

In wireless systems, a security protocol should also consider the limited battery power,

small memory and limited processing capabilities of the devices and the available bandwidth.

In addition, the systems need to be able to cater to the requirements of the wide variety of

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wireless devices that could be used for connectivity. Study of the energy consumption of the

encryption schemes in wireless devices is thus essential in design of energy efficient security

protocols tailored to the wireless environment.

2. Energy Efficiency Wireless communication is difficult to achieve compared to wired communication

because of the time varying nature of the RF carrier. In general wireless communication is

dominated by high error rates, varying signal to noise ratio, noise variations, limited bandwidth

and multipath delays. These factors lead to retransmissions and effectively higher power

consumptions.

Recent trends show increased demand for multimedia capable wireless devices.

However, they are limited by the size, battery power and communication bandwidth

constraints. The everincreasing demand of networked services will aggravate the problem even

further. Energy constraint poses restrictions on the functionality that can be implemented on

wireless devices.

Unfortunately, the battery performance improves at a very slow rate in terms of energy

available per unit size or weight.[8][9] An alternative approach of handling the problem is

through energy efficiency at various levels of the system.

Energy efficiency can be achieved at the physical level by improving the

communication protocol to make it more efficient. Quality of service trade offs is another

mechanism to achieve energy efficiency. The requirement for energy efficiency is that the

systems need to adapt so that the communication consumes relatively less energy.

Traditionally, energy efficiency has been achieved through focus on low-powered VLSI design.

Most of the components are currently fabricated using CMOS technology. The power

consumption of CMOS devices is directly proportional to the switching activity due to

computations, capacitance, square of voltage, and frequency of operation. Reducing the

frequency would reduce the power but the energy consumed would remain the same cause the

same operation may be executed over a longer period. Most of the concentration hence is

directed towards reducing voltage and capacitive load.

Dynamic power management schemes that adapt the system are required to achieve

energy efficiency. They concentrate on optimizing the throughput and the performance of the

system by reducing idle time and deactivation units when not required. For example while

communicating the wireless card could be turned off till there is no data to be transmitted since

the energy consumption is significantly different during the transmit/received mode and sleep

mode.

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However, the time to shutdown and wake-up the card should be much less than the data

to be transmitted. The ways of achieving efficiency could be by queuing data and transmitting

it all together or by using an adaptive wake up scheme.

Different devices have different energy utilization patterns. In laptop it has been

observed that energy use of a laptop is dominated by the backlight of the display, the disk and

the processor.

However, generally the network interface consumes the same amount of energy as the

rest of the system. The effective impact of each component on the overall battery life may be

different for different devices due to their difference in operating systems, processor speed,

memory size, battery size and other components.

In secure communication environment factors of concern are communication and

computation efficiency. Computation efficiency depends on the hardware and the software used

for encrypting the data. It would certainly be inefficient to provide customized hardware for

encryption since it would mean lot of additional gates and hence more power consumption.

Programmability of encryption scheme is essential in today’s environment because of

the advancing computational power and increasing key size requirements. Also, for energy

efficiency we should be able to adapt encryption techniques to meet the varying data rates and

quality of service requirement of applications. Another problem of providing customized

encryption hardware is the differential power analysis attack where the electrical activity of the

device is monitored to determine the secret information.

3. Experiment Design

The setup for the experiment is as shown in figure 1. The server used was an HP

compatible PC with AMD Opteron processor.

Fig. 1

The server had Windows XP professional installed on it. The server is connected to the

access point with 100 Mbps Ethernet link.

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The access point used for the experiments is Linksys WRT54GL. The wireless devices

considered in the experiment are two laptops HP 530 with D-link DWL-132 USB wireless

card. The wireless devices are used one at a time and never all at the same time. Transmission

of data is from the wireless devices to the server through the wireless link using TCP/IP

protocol.

3.1 Methodology The battery and computational trade-off of encryption schemes under different

scenarios are considered in various experimental setups but the underlying setup remains the

same. Initialization in case of encryption would be to establish the keys required while in case

of data transmission it would include establishing a connection with the server. For the purpose

of comparing their performance, a big file of size 5MB unless explicitly mentioned is processed

multiple number of times.

Processing in experiment for encryption without data transmission is to read data from

the file encrypt the data and put it in another file. In case of encryption with data transmission

the data is read from the file encrypted and the send to the server through the connected socket.

This is done till the battery drains to 30% of the lifetime left.

The socket connection used is TCP socket for reliable transmission of the data. After a

few runs of processing on the file the battery life left and the system time is recorded. The

average battery life consumed per run and the time taken to do so is the calculated for the

results.

It is expected that the computation time would be closely related to the battery

requirements; however, since the CPU utilization of power depends on parameters like voltage

supply and capacitive load. The capacitive load on the CPU depends on the switching demand,

which again depends on the instructions being executed.

3.2 Comparison of algorithms

The figure 2 below shows the battery consumed for iteration over a 5MB file. The

comparison is done between AES encryption[10][11], CAST encryption and IDEA all with 128

bits key size using Crypto++ library. The ‘No Encryption’ scheme represents the case where

the file was just accessed and the data from this file was put into another file. This was included

to see actually how many extra resources are put into encrypting over accessing the data.

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Fig. 2

Encryption of the plaintext data with AES128 causes increase in battery consumption

by 75% , when compared to the No Encryption scenario. CAST128 consumes 58% and IDEA

consumes 92% more battery than AES128.

3.3 Key size variation We compare ( in figure 3 ) the change in performance by using different key sizes for

AES algorithm. For AES we consider the three different key sizes possible i.e., 128 bit, 192

bits and 256 bit keys.

Fig 3

Increased key size leads to increased security as shown in fig 3. In case of AES it can be

seen that higher key size leads to noticeable change in the battery and time consumption. It can

be seen that going from 128 bits key to 192 bits causes increase in power and time consumption

by about 8% and to 256 bit key causes an increase of 16%. AES128 has 120, AES 192 has 144,

and AES256 has 168 rotate byte operations, which implies 20% and 40% more operations for

AES 192 and AES256 when compared to AES128. Although there seems an increase in power

consumption that is directly proportional to the increased operations, the increase is less

amplified. This can be attributed to the fact that the data access from the file over which the

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operations are performed. However, the increased power consumption of higher key size posses

a compromise that should be considered before choosing the size of the key. For normal

application 128 bits key is considered very secure hence going for higher key sizes would mean

unnecessary wastage of resources for the added security that is actually not required.

4. Conclusion

It is seen that AES is faster and more energy efficient than IDEA and CAST. When

transmission of data is considered there is negligible difference in performance of different

symmetric key schemes as most of the resources are consumed for data transmission rather than

computation.

Even under the scenario of data transfer it would be advisable to use AES scheme

incase the encrypted data is stored at the other end and decrypted multiple number of times.

Increasing the key size by 64 bits of AES leads to increase in energy consumption by about 8%

without any data transfer and with data transfer the difference is not noticeable. Thus real time

applications were data is just transferred between systems and not stored for future retrieval

may prefer to have higher security provided by larger key size. Reducing the number of rounds

leads to power savings but it makes the protocol insecure for AES and should be avoided.

Seven or more rounds can be considered fairly secure and could be used to save energy in some

cases.

5. References [1] WLANS: Wireless Dream, Security Nightmare, Dermot McGrath, Broadband Wireless Business Magazine, Vol. 3, No. 8, January/February 2003 [2] Wireless LANs: Global Market Demand and Opportunity Assessment, InfoTech, PBI Media, Jan 2002 [3] William Stallings, ‘Cryptography and Network Security’, Prentice Hall Publication, 1999 [4] Bruce Schneier, Applied Cryptography, John Wiley & Sons Inc. [5] FIPS Publication 180-1: Secure hash Standard, National Institute of Standards and Technology (NIST), 1994. [6] Wireless Network Security: 802.11, Bluetooth and Handheld Devices, Tom Karyginannis and Les Owens, NIST, U.S. Department of Commerce, November 2002 [7] McMurry Mike, Wireless Security, Jan 22, 2001 [8] David Linden, Handbook of batteries, second edition. McGraw-Hill, Inc. 1994. [9] End User Perspective – Industrial Consumer Electronics Power, Jerry Hallmark, Motorola labs, January 15, 2002 [10] Announcing the Advanced Encryption Standard (AES), Federal Information Processing Standards Publication 197, 26 November 2001 [11] AES Proposal: Rijndael, Joan Daemaen and Vincent Rijmen, March 9, 1999

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