volumul conferintei (isbn 978-606-521-045-5)

509

Click here to load reader

Transcript of volumul conferintei (isbn 978-606-521-045-5)

  • Universitatea Politehnica din BucuretiCATEDRA DE ELECTROTEHNIC

    AASSOOCCIIAAIIAA IINNGGIINNEERRIILLOORR EELLEECCTTRRIICCIIEENNII II EELLEECCTTRROONNII

    S

    TTII DDIINN RROOMMNNIIAA

    Simpozionul Naional de Electrotehnic Teoretic National Symposium of Theoretical Electrical Engineering

    NET08 Dedicat Profesorilor Constantin Bl, Alexandru Fransua, Florin

    Manea, Augustin Moraru, Constantin Nemoianu i Andrei ugulea cu ocazia mplinirii frumoasei vrste de 80 de ani

    VOLUMUL CONFERINEI

    5-7 iunie 2008, Bucureti HTTP://SNET.ELTH.PUB.RO

    OFFICIAL SPONSORS:

    Ministerul Educaiei

    i Cercetrii HP

    Romnia

    ISBN 978-606-521-045-5

    http://www.pub.ro/http://www.elth.pub.ro/http://snet.elth.pub.ro/

  • Preedinte

    Prof.dr.ing. Andrei UGULEA, membru titular al Academiei Romne

    Preedini de onoare: Prof.dr.ing. Ecaterina ANDRONESCU

    Prof.dr.ing. Augustin MORARU

    Comitetul tiinific internaional: Prof. dr. ing. Horia ANDREI, U. Trgovite

    Prof. dr. ing. Oszkr BR, T.U. Graz Prof. dr. ing. Constantin BALA, U.P.B. Prof. dr. ing. Costin CEPIC, 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 Romne

    Prof. dr. ing. Toma DORDEA, membru titular al Academiei Romne Prof. dr. ing. Radu ENACHE, H.P.-Romnia

    Prof. dr. ing. Cezar FLUERAU, U.P.B. Prof. dr. ing. Alexandru FRANSUA, U.P.B.

    Prof. dr. ing. Horia GAVRIL, U.P.B. Prof. dr. ing. Constantin GHI, U.P.B.

    Prof. dr. ing. Vasile IANCU, U.T.Cluj-Napoca Prof. dr. ing. Valentin IONI, 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 MNDRU, U.T.Cluj-Napoca Prof. dr. ing. Marlene MARINESCU, U.Wiesbaden

    Prof. dr. ing. Adelaida MATEESCU, U.P.B. 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. Miruna NIESCU, U.P.B.

    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 RDOI, U.P.B.

    Prof. dr. ing. Alecsandru SIMION, U.T.Iai Prof. dr. ing. Emil SIMION, U.T.Cluj-Napoca

    Prof. dr. ing. Fnic SPINEI, U.P.B. Prof. dr. ing. Florin Teodor TNSESCU, C.E.R. Prof. dr. ing. Dumitru TOADER, U.P.Timioara Prof. dr. ing. Vasile OPA, U.T.Cluj-Napoca Prof. dr. ing. Nicolae VASILE, I.C.P.E.-S.A.

    Comitetul de organizare:

    .l. ing. Mihai MARICARU, [email protected] - Preedinte Prof.dr.ing. Florin CONSTANTINESCU, [email protected]

    Prof.dr.ing. Florea I. HNIL, [email protected] Conf.dr.ing. Viorel Constantin MARIN, [email protected]

    .l.dr.ing. Oana DROSU, [email protected] .l.dr.ing. Ruxandra COSTEA, [email protected]

    .l.dr.ing. Emil CAZACU, [email protected] Drd.ing. Marius A. MOICEANU, [email protected] Drd.ing. Mioara PREDA, [email protected]

    mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]

  • Universitatea Politehnica din Bucureti CATEDRA DE ELECTROTEHNIC

    AASSOOCCIIAAIIAA IINNGGIINNEERRIILLOORR EELLEECCTTRRIICCIIEENNII II EELLEECCTTRROONNIITTII DDIINN RROOMMNNIIAA

    Simpozionul Naional de Electrotehnic Teoretic

    5-7 iunie 2008, Bucureti

    Dedicat Profesorilor Constantin Bl, Alexandru Fransua, Florin Manea, Augustin

    Moraru, Constantin Nemoianu i Andrei ugulea cu ocazia mplinirii frumoasei vrste

    de 80 de ani sponsori:

    Ministerul Educaiei

    i Cercetrii HP

    Romnia

    CUPRINS

    ANALIZA CMPULUI ELECTROMAGNETIC I ELECTROTERMIE

    1. The Electromagnetic Circuit Element - the Key of Modelling EM Coupled Integrated Components, Gabriela Ciuprina, Daniel Ioan, Diana Mihalache, Alexandra Stefanescu.........7-12

    2. Energy Consideration in Magnetic Coils Design, Radu Ciupa, Laura Darabant, Mihaela Plesa, Octavian Cret, Dan D. Micu....................................................................................................12-18

    3. Optimizarea bazat pe algoritmi genetici a unei instalaii de nclzire dielectric n cmp electric de nalt frecven, Camelia-Mihaela Petrescu, Lavinia Ferariu............................................19-24

    4. Complex interpolation methods applied in electromagnetic compatibility problems, Dan D. Micu, I. Lingvay, C. Lingvay, E. Simion, A. Ceclan..........................................................................25-30

    5. 2D analysis of electrical transformer's leakage magnetic field generated by the magnetizing magnetomotive force, Constantin Ghi, Ioan Drago Deaconu, Aurel Ionu Chiril, Valentin Nvrpescu, Ion Daniel Ilina...................................................................................................31-36

    6. Eddy Current Controlling of the Liquid-Solid Transition Surface in Moving Solidifying Ferromagnetic Bodies, Mihai Maricaru, Florea Ioan Hnil, Stelian Marinescu, Cezar Fluerau..................................................................................................................................37-42

    SNET 08 5-7 iunie 2008, UPB, Catedra de Electrotehnic, Facultatea de Inginerie Electric

    Spl. Independenei 313, TEL/FAX: (0040-21) 4029144, E-mail: [email protected], http://snet.elth.pub.ro

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    1/507

  • 7. Study of the dynamic behaviour during start-up and reversal at the two-phase induction machine, Alecsandru Simion, Leonard Livadaru, Dorin Lucache...........................................43-48

    8. A Highly Simplified Mark and Cell (HSMAC) Scheme for the Study of Convection Heat Transfer in Electroconductive Fluids, H. Kawahara, A.M. Morega, M. Morega....................................49-54

    9. Modelarea numeric a proceselor de nclzire prin inducie utiliznd Flux 2D, Mihaela Novac, Teodor Leuca, Ovidiu Novac, Gabriel Chereg........................................................................55-60

    10. nclzirea cu microunde n aplicatorul cu concentrator ceramic, Teodor Leuca, Radu Sebean.................................................................................................................................61-66

    11. Some Aspects Regarding the Optimisation of Electrothermal Induction Systems using Informational Techniques, Teodor Leuca, Claudiu Mich-Vancea...........................................67-72

    12. About the simultaneous induction hardening method of pinions with rectangular coil using dual frequencies, G. R. Cheregi, T. Leuca, M. N. Arion.................................................................73-78

    13. Numerical analysis of the coupled electromagnetic and thermal field question within industrial induction heating systems, M. N. Arion, T. Leuca, G. R. Cheregi, V.D. Soproni, F.I. Hathazi...................................................................................................................................79-84

    14. Magnetic Material Characterization by Open Sample Measurements, Valentin Ioni, Lucian Petrescu.................................................................................................................................85-90

    15. Numerical modelling of the coupled electromagnetic and thermal fields in the solidification structure's formation control processes, tefan Nagy, Teodor Leuca, Claudiu Mich-Vancea, Ioan Florea Hanil.........................................................................................................................91-96

    16. Aspects Regarding the Numerical Modelling of the Induction Heating Devices, C. Mich-Vancea, St. Nagy, T. Leuca, M. Gordan.............................................................................................97-102

    17. Time-harmonic Electromagnetic Field Diffusion into an Exponentially Decreasing Conductivity Half-space, Andrei ugulea, Iosif Vasile Nemoianu...........................................................103-108

    18. Observaie experimental asupra unui curent indus rezidual, Nicolaie N.Vlad..................109-111 19. Densitatea de curent n sigurane cu structur multiplu conex, Valer Giurgiu, Florea Ioan

    Hnil, Lucian Ochean, Mihai Maricaru, Mircea Arion....................................................112-114 20. Curenii turbionari n ecrane subiri, Florea Ioan Hnil, Augustin Moraru, Mihai Maricaru, Mihai

    Vasiliu, Mihai Octavian Popescu........................................................................................115-118 21. Using of Static Magnetic Field for Testing of Flaws in Ferromagnetic Bodies, Florea Ioan

    Hnil, Mihai Maricaru, Stelian Marinescu, Fnic Spinei................................................119-123 22. O aplicaie a ecranrii electromagnetice n instalaiile metalurgice care conin cuptoare electrice

    cu arc, Andrei ugulea, Cornelia Ionescu, Ion Ionescu......................................................124-133 23. The use of Matlab in Electrical Engineering, Marilena Stnculescu, Emil Cazacu, Florin-Daniel

    Ruiu....................................................................................................................................134-137

    ANALIZA CIRCUITELOR ELECTRICE

    24. Network Function Generation in Symbolic Matrix Form, Mihai Iordache, Lucia Dumitriu...138-146 25. Aplicaii ale teoriei operatorilor liniari compleci, n rezolvarea circuitelor electrice liniare n regim

    periodic nesinusoidal, Gheorghe Mihai..............................................................................147-152 26. Aplicaii ale teoriei operatorilor liniari compleci n rezolvarea circuitelor electrice liniare,

    trifazate, n regim permanent nesinusoidal, Gheorghe Mihai.............................................153-158 27. Simularea n domeniul timpului a regimurilor normale i de avarie ale transformatoarelor de

    putere, L. Mandache, D. Topan, P.M. Nicolae, I.G. Sirbu, D. Stanescu, F. Alexandru......159-164

    SNET 08 5-7 iunie 2008, UPB, Catedra de Electrotehnic, Facultatea de Inginerie Electric

    Spl. Independenei 313, TEL/FAX: (0040-21) 4029144, E-mail: [email protected], http://snet.elth.pub.ro

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    2/507

  • 28. Calculul i importana senzitivitii n analiza i proiectarea circuitelor electrice, Mihai Iordache, Drago Niculae, Iulia Dumitrescu, Gheorghe Despina.......................................................165-170

    29. Metoda hibrid de analiz a circuitelor neliniare n regim dinamic, Gabriela Popescu, Rodica Voiculescu, Adrian Guinea.................................................................................................171-176

    30. Synthesis of a new RC model for body cell mass prediction, A. G. Gheorghe, C. V. Marin, F. Constantinescu, M. Niescu................................................................................................177-181

    31. Analysis of the Absorbed Power in D.C. Networks with Modifiable Parameters, Horia Andrei, Ion Caciula, Fanica Spinei, Paul Cristian Andrei......................................................................182-187

    32. Analiza circuitelor electrice prin nregistrri numerice ale mrimilor instantanee, Petre-Marian Nicolae, Dan-Gabriel Stanescu, Marius Voinea.................................................................188-193

    33. Asupra modelrii regimurilor dinamice ale mainii sincrone, Mihai Iordache, Mihai Dogaru, Drago Niculae...................................................................................................................194-199

    34. Performane ale circuitelor ru condiionate, D.Micu, A.Micu, L.Chira, D.D. Micu.............200-205 35. Almost Periodical Slow Oscillations in Nonlinear Electric Circuits with Resonance by Jump,

    Mircea V. Nemescu, Dorin D. Lucache..............................................................................206-211 36. Consideraiuni asupra unor caracteristici utile ale unui program de simulare a circuitelor

    electrice, Corina Fluerau, Cezar Fluerau.......................................................................212-217 37. Iterative Procedure for Real Single-Tone Frequency Estimation, Liviu Toma, Aldo De Sabata,

    Robert Pazsitka..................................................................................................................218-222 38. Un algoritm nou pentru analiza circuitelor neliniare n domeniul frecvenei, F.Hanil,

    F.Constantinescu, A. G. Gheorghe, M.Niescu..................................................................223-229 39. Inregistrari si prelucrari numerice ale regimului deformant datorat unui consumator trifazat

    nesinusoidal, Petre-Marian Nicolae, Ileana Diana Nicolae, Dan Gabriel Stanescu...........230-235

    MAINI ELECTRICE, MATERIALE ELECTROTEHNICE I ELECTROENERGETIC

    40. Microwave Field Reticulation of the Epoxy Resin Used for Single Layer Electrical Insulations, Vasile Darie oproni, Francisc Ioan Hathazi, Carmen Otilia Molnar, Mircea Arion............236-241

    41. Wavelet Analysis used in the Detection of Broken Rotor Bars in AC Motors, Eleonora Darie, Costin Cepic, Emanuel Darie..........................................................................................242-247

    42. About Condition Monitoring of Squirrel Cage AC Motors Fed by PWM, Eleonora Darie, Costin Cepic, Emanuel Darie.....................................................................................................248-251

    43. Analytical flux-linkage model of switched reluctance motor, Ioan-Adrian Viorel, Larisa Strete, Ioan Felician Soran.............................................................................................................252-258

    44. Analysis of some current decomposition methods: comparison and case studies, Alexandru Bitoleanu, Mihaela Popescu, Felicia Nastasoiu, Vlad Suru................................................259-264

    45. A proper mathematical model for the study of the two-phase induction machine, Alecsandru Simion.................................................................................................................................265-270

    46. Mid Term Forecasting using ANN, Petrua Mihai, Claudia L. Popescu, Mihai O. Popescu..............................................................................................................................271-274

    47. Systems for generalized models development for electrical machinery, Marcel Ionel, Dorin Le, Traian Ivanovici..................................................................................................................275-280

    SNET 08 5-7 iunie 2008, UPB, Catedra de Electrotehnic, Facultatea de Inginerie Electric

    Spl. Independenei 313, TEL/FAX: (0040-21) 4029144, E-mail: [email protected], http://snet.elth.pub.ro

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    3/507

  • 48. Synchronized phasor measurements for state estimation, Mihai Gavrila, Ionu Rusu, Gilda Gavrila, Ovidiu Ivanov.......................................................................................................281-286

    49. Analiza golurilor de tensiune din reeaua de alimentare cu energie electric, Mircea Horgos, Liviu Petrean, Zoltan Erdei, Drago Nicolae.......................................................................287-292

    50. Parametri schemei echivalente si performantele de exploatare ale motorului asincron trifazat, Marin Mihalache................................................................................................................293-298

    51. Caracteristica unghiulara a motorului asincron sincronizat, Marin Mihalache...................299-304 52. Assessment of Two Single-end Fault Location Algorithms in an ATP Approach, Marcel Istrate,

    Mircea Gu.......................................................................................................................305-310 53. Fenomene tranzitorii specifice cuplarii directe la retea si la aparitia unui scurtcircuit intr-un

    sistem eolian cu SCIG, Nicolae Badea, Ion Voncila, Sergiu Ivas, Ciprian Vlad, Marcel Oanca, Ion Paraschiv......................................................................................................................311-319

    54. Strip Method for evaluating a.c. Losses in Slot Portion of Roebel Bars - Errors Analysis, Toma Dordea, Aurel Cmpeanu, Gheorghe Madescu, Ileana Torac, Marian Mo, Lucian Ocolian..............................................................................................................................320-325

    55. Increasing of effective resistence with the frequency of the courrent in the conductive foil of low voltage coil of power transformers, Codrut Chivulescu, Gelu Ionescu...............................326-334

    ELECTRONIC INDUSTRIAL, APARATE ELECTRICE, TEHNOLOGIA INFORMAIEI

    56. Analiza wavelet pentru detecia fenomenului de explozie la motoarele cu ardere intern,

    Anamaria Rdoi, Vasile Lzrescu, Adriana Florescu.......................................................335-340 57. O metod de evaluare a duratei de via a uleiului electroizolant, Helerea Elena, Munteanu

    Adrian.................................................................................................................................341-346 58. Metod statistic pentru stabilirea duratei de via a izolaiei nfurrii transformatoarelor de

    putere, A. Munteanu, L. Iulian............................................................................................347-352 59. Loss Distribution in Three-Level Active NPC Converter for a STATCOM Application, Dan

    Floricu, Dan Olaru, Elena Floricu, Ioan Popa.................................................................353-358 60. Theoretical Background of Intelligent Switching of The High Voltage Circuit-Breakers, Florin

    Munteanu, Ciprian Nemes..................................................................................................359-364 61. Data Flow Encryption between Terminals using Hash Functions, Tomoiaga Radu, Stratulat

    Mircea.................................................................................................................................365-369 62. Data Encryption using Hash Functions,Tomoiaga Radu, Stratulat Mircea.........................370-376 63. Implementarea codurilor SEC-DED la nivelul Cache a unei ierarhii de Memorii, Ovidiu Novac,

    Mircea Vlduiu, Mihaela Novac, Gabriel Cheregi..............................................................377-382 64. Numerical Modeling of High Currents Dismountable Contacts, Ioan Popa, Ioan Cauil, Dan

    Floricu...............................................................................................................................383-388 65. Evaluating the size of intrinsic safety barriers of the electric equipment intended for use in

    atmospheres with explosion hazard, Dragos Pasculescu, Sebastian Ilie Stepanescu, Vlad Pasculescu.........................................................................................................................389-393

    66. Fuzzy Algorithms for Improvement PID Control in PLC Systems, Ovidiu Neamu.............394-399 67. About Modulation Strategies in Single-Phase Flying Capacitor Multilevel PWM Inverter, Adrian

    Schiop.................................................................................................................................400-407 68. Three-phase on-line ups system with reduced number of switches, Daniel Albu..............408-413

    SNET 08 5-7 iunie 2008, UPB, Catedra de Electrotehnic, Facultatea de Inginerie Electric

    Spl. Independenei 313, TEL/FAX: (0040-21) 4029144, E-mail: [email protected], http://snet.elth.pub.ro

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    4/507

  • 69. Single-phase uninterruptible power supply with reduced number of switches, Daniel Albu....................................................................................................................................414-419

    70. Steganography applications in communication security, Florin-Daniel Ruiu, Marilena Stnculescu........................................................................................................................420-423

    BIOINGINERIE I MAGNETISM TEHNIC

    71. New method for parameter identification in bioimpedance spectroscopy, C. V. Marin, D. Marin...................................................................................................................................424-432

    72. Diamagnetic material usage in micro and nano levitation devices, Emil Cazacu, Iosif Vasile Nemoianu...........................................................................................................................433-437

    73. Scanned-Forward-Looking Method for Automatic Centerline Extraction in Virtual Endoscopy, Gabriel Preda, Radu Cristian Popa, Ctlin Ciubotaru, Radu Marian, Alexandru Popiel...438-443

    74. Numerical Characterization Method for Magnetic Materials with Vector Hysteresis, Mihai Rebican, Radu C. Popa, Gabriel Preda, Valentin Ioni, Lucian Petrescu.........................444-449

    75. Medical Imaging Solution for Mesh Generation in Bioengineering Applications, Gabriel Preda, Radu Cristian Popa, Mihai Rebican, Radu Marian, Alexandru Popiel, Iolanda Costache..450-454

    76. Analiza comparativ a influenei temperaturii asupra forelor transmise prin intermediul cuplajelor frontale i coaxiale cu magnei permaneni, Ion Voncil, Nicolae Badea...........455-460

    77. Localizarea tumorilor de sn prin metode termografice, I.F.Hnil, M.Maricaru, O.Drosu, Cl. Popescu, G.Preda..............................................................................................................461-466

    78. Microwave Continuous Flow Heating of Food Liquids, Ioan Florea Hnil, Mihai Vasiliu, Valer Turcin, Paul Pencioiu..........................................................................................................467-470

    SESIUNE DE COMUNICRI STUDENETI

    79. Utilizarea FEMM pentru soluionarea problemei de cureni turbionari, Jelea Alexandru

    Tudor..................................................................................................................................471-478 80. Metode de analiz a toleranelor aplicate filtrelor, Andrei Marascu, Mihai Iordache..........479-484 81. Utilizarea ecuaiei integrale a curenilor turbionari la soluionarea problemelor de cmp

    electromagnetic n regim cvasistaionar, Andrei Linc.......................................................485-490 82. Difuzoare cu magnei permaneni, Bogdan Vrticeanu....................................................491-495 83. Calculul parametrilor lineici transversali pentru linii de transmisie multiconductor, Nicolae Ivan,

    Alexei Rus, Catalin Puiu.....................................................................................................496-501 84. Tolerance analysis of analog circuits, Andrei Marascu, Dragos Niculae, Mihai Iordache..502-507

    SNET 08 5-7 iunie 2008, UPB, Catedra de Electrotehnic, Facultatea de Inginerie Electric

    Spl. Independenei 313, TEL/FAX: (0040-21) 4029144, E-mail: [email protected], http://snet.elth.pub.ro

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    5/507

  • SNET 08 5-7 iunie 2008, UPB, Catedra de Electrotehnic, Facultatea de Inginerie Electric

    Spl. Independenei 313, TEL/FAX: (0040-21) 4029144, E-mail: [email protected], http://snet.elth.pub.ro

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    6/507

  • 1

    The Electromagnetic Circuit Element the Key of Modelling EM Coupled Integrated Components

    Gabriela CIUPRINA, Daniel IOAN, Diana MIHALACHE, Alexandra STEFANESCU

    Politehnica University of Bucharest, Spl. Independentei 313, 060042m Romania, [email protected],ro

    Abstract. This paper shows how the electromagnetic circuit element can be used to model parasitic inductive couplings in integrated circuits. The advantages of this approach are the reduction of computational complexity for the model extraction process, the inherent parallelism and the possibility of using different, independent models in several sub-domains, adapted to the analysed structure.

    1 Introduction

    In the transition to the nanoscale era, the RF designers need improved IC automation tools to model and simulate full blocks, taking into account the electromagnetic (EM) coupling among the down-scaled individual devices integrated on one chip. At the high frequencies that are now envisaged, the couplings and loss mechanisms, including EM field coupling and substrate noise are becoming too strong and too relevant to be neglected, whereas more traditional coupling and loss mechanisms are more difficult to describe given the wide frequency range involved and the greater variety of structures to be modelled [1]. All this will cause extra design iterations, over-dimensioning or complete failures, unless appropriate solutions are found to resolve these design issues. These problems were addressed in the FP6/Chameleon-RF project (www.chameleon-rf.org) whose general objective is that of developing methodology and prototype tools that take a layout description of typical RF functional blocks that will operate at RF frequencies up to 60 GHz and transform them into sufficiently accurate, reliable electrical simulation models taking EM coupling and variability into account. The RF block is partitioned in basic devices (active and passive) and their compact models are augmented with connectors (hooks) that allow EM interaction with and representation of their environment. The hooks that were searched for, turned out to be the boundary conditions proposed in 1971 by Al. Timotin [2] who introduced the concept of passive electromagnetic circuit element, a generalization of the multipolar circuit element proposed in 1966 by the Academician Remus Radulet, Alexandru Timotin and Andrei Tugulea [3]. The missing link was internationally promoted again in [4] and the first very promising results in the frame of the Chameleon-RF project were obtained by using this concept for the simulation of EM coupling [5]. This paper shows how the electromagnetic circuit element can be integrated in a new methodology to model parasitic inductive couplings in integrated circuits. Benchmark tests from the Chameleon project are used, the final check being the comparison between simulation results and measurements.

    2 The Electromagnetic Circuit Element

    One of the main theoretical problems encountered in the modelling of RF components is the difficulty to define a unique terminal voltage, independent of the integration path. This independence is compulsory, since it is the only one that allows the connection of the component to an electric circuit, where the voltage does not depend of the path shape). Apparently, Kirchhoff voltage law is not valid in the case of RF structures. The solution found in our approach is to adopt appropriate boundary conditions for the field problem associated to the analysed components, in order to allow the consistency with the electrical circuit which contains this component. The only restriction is to consider only simple connected domains as

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    7/507

  • 2

    components; with voltage integration paths included in the domain boundary (not going inside component). Moreover, Kirchhoff current law is valid in case of RF structures if it is written for the total current (conduction + displacement). The correct definition of the component terminals (used for intentional interconnections) and connectors ("hooks" which represent parasitic couplings), an important challenge of the research, is based on the correct formulation of the EM field fundamental problem, particularly

    on the appropriate boundary conditions which ensure the uniqueness of the problem solution. Fortunately, the theoretical basis was set almost forty years ago by Al. Timotin [2] who rigorously introduced the concept of passive electromagnetic circuit element (EMCE), a generalization of the multipolar circuit element proposed by the Remus Radulet, Alexandru Timotin and Andrei Tugulea [3]. The concept of Electro-Magnetic Circuit Element is briefly recalled here.

    Figure 1. The Electromagnetic Circuit Element

    By definition, an EMCE (Error! Reference source not found.) is a simply connected domain D bounded by a fixed closed surface on which there are ne disjoint parts ''2

    '1 ,..., neSSS , called

    electric terminals and nm disjoint parts ''''2''

    1 ,..., nmSSS called magnetic terminals (hooks) on which the following conditions hold: a) ( ) 0,curl = tPEn , ''kSP U ,; b)

    ( ) 0,curl = tPHn , 'kSP U ; c) ( ) 0En = tP, , 'kSP U ;d) ( ) 0Hn = tP, , ''

    kSP U ,where n is the unitary vector, orthogonal to the boundary , in the point P. These conditions are less restrictive than usual approximations of the electric and magnetic circuit theory, because they are related only to the boundary and not to the internal structure or field in the defined circuit element. Condition a) interdicts the inductive couplings through the domain boundary, excepting for the magnetic terminals. This condition can be complied by enlarging the boundary, so that the magnetic field has a negligible normal component or it may be considered perpendicular to the magnetic terminals. Condition b) interdicts the conductive and capacitive couplings through the boundary, excepting for the electric terminals. Condition c) interdicts the variation of the electric potential over every electric terminal, allowing its connection to a node of an external electric circuit. Consequently, the current lines are orthogonal to the electric terminal surfaces. It is automatically satisfied, if these terminals are perfect conductors. Finally, condition d) interdicts the variation of the magnetic potential over every magnetic terminal, allowing its connection to a node of an external magnetic circuit. Consequently, the magnetic field lines are orthogonal to the magnetic terminal surfaces. It is automatically satisfied, if these terminals are made by perfect magnetic materials. Consequently the magnetic lines are orthogonal on the magnetic terminal surfaces. With these boundary conditions, the interaction between the EMCE and its environment is completely described by two scalar variables for each terminal (for an electric terminal, its current and voltage, and for a magnetic terminal, its magnetic flux and magnetic voltage). From the point of view of boundary conditions, we will use the terminology of terminals either

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    8/507

  • 3

    electric or magnetic. The term of hooks appeared from the necessity of showing that these boundary conditions will allow the parasitic coupling of this element with electric or magnetic circuits, or with other compatible compact models. The term hooks will not be used for intentional electric terminals.

    For each electric terminal k, its current is defined as the magnetic field loop-integral ( )

    =k

    dtik rH , where 'kk S= is a closed curve, the boundary of the

    'kS surface (representing

    the total current) and its voltage is defined as the line integral ( ) =kC

    rEdtvk along an arbitrary

    curve Ck, included in ""

    kk TS UU which is a link between a point on Sk and a point on Sn. Here Tk is a path belonging to which links a point on Sk with a point on Sk+1.

    For each magnetic terminal k, its flux is defined so that its time derivative is

    =k

    rEd)t(k& , where ''

    kk S= is the contour - boundary of Sk surface and its magnetic

    voltage is defined as the line integral ( ) =kC

    k dtu rH along an arbitrary path Ck, included in

    ''kk TS UU which is a link between a point on Sk and a point on Sn. Here Tk is a path in

    , which links a point on Sk with a point on Sk+1. An uniqueness theorem has also been formulated. It is important to note that according to the EMCE definition, the electric and magnetic hooks can not be overlapped.

    Details on the implementation of this concept in the Finite Integration Technique [6] are given in [7].

    3 Domain Partitioning in Integrated structures

    Integrated components and systems with complex structures generate complex EM field problems that are difficult to solve. An efficient approach to manage this complexity is to decompose (partition) the computational domain in sub-domains, generate simpler field problems for each sub-domain and couple the resulting models to obtain a simpler model of the initial complex structure.

    The numerical approach we propose is based in the domain decomposition of the RF block in its active and passive components as well in the environmental components, for instance the substrate and the upper air. Each of these simple connected sub-domains are assumed to satisfy EMCE boundary conditions; they being interconnected by means of several hooks. In our approach, each of these components are analysed independently and a compact or a reduced order model is extracted. The equivalent circuits of these models are re-connected together to generate the model of the entire RF block. The electric environment can be represented by an electric circuit, and the magnetic environment by a magnetic circuit. These two circuits can be coupled together by means of controlled sources, representing e.g. induced voltages. The electric terminals allow the modelling of the electric interaction whereas the magnetic terminals allow the modelling of the inductive interaction. Thus, the EMCE boundary conditions allow the coupling of the component model with its EM environment. The component model can be a field model generated by any numerical method (finite or boundary elements, finite differences etc). From the coupling point of view, the models can be interchanged if they were derived from the EMCE boundary conditions.

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    9/507

  • 4

    The coupling between sub-models

    can be carried out in various ways, depending on the model representation [6]. For instance, if two EMCEs are finally described by semi-state-space representations,

    .,d

    dkkkkkkk

    kk t

    xLyuBxGxC ==+ wh

    ere 2,1=k then, the global representation can be easily obtained by combining the sub-blocks kjC , where

    3,1=j of the sub-models,e.g.

    .222321

    121311

    =C0C0C00CC00C

    C

    If the systems are described by means of transfer matrices ( ) kkkkk j BCGLH 1( += , that link the complex representations of outputs to the complex representation of inputs, and these transfer matrices are split according to the number of terminals that are connected together a then, the global transfer matrix H defined by can be easily computed, as

    ( ) [ ].)2(22)1(211)2(22)1(22)2(12

    )1(12

    )2(11

    )1(11 HHHH

    HH

    H00H

    H +

    = .

    In brief, terminals act as hooks between sub-domains. They allow independent meshing, and even using independent PDE or different numerical method in each sub-domain. If adjoin sub-domains have conformal aligned meshes, the number of hooks can be increased up to the limit when each node on the interface is an independent terminal. In this degenerate case, the interface does not perturb the field solution, thus being numerically transparent. According to the convergence theorem, in correct discretizations, the numerical solution tends to the exact one, when the norm of the mesh goes to zero. In these conditions, the number of hooks tend to infinity and the interface becomes perfectly transparent [7].

    4 Numerical Examples

    The first validations were carried out on simple benchmark tests, such two U-shaped coupled coils, placed in a Si layer, above a SiO2 substrate. The reference result was obtained by simulating this passive device, the computational domain including the substrate below and the air above. The problem was then partitioned in a top part which includes the coils and the air above, and a bottom part consisting only of the substrate. On the cutting interface EMCE boundary conditions have been imposed.

    Table 1 gives the results obtained for various settings of the hooks. It can be noticed that if node-hooks are used, i.e. if each node on the interface is defined as a distinct terminal, the error due to DP is zero when the union of the grids used for the submodels is exactly the grid used for the full simulation. In this case each electric and magnetic node on the common surface represents a distinct terminal the surface is in fact transparent for the EM field. Since the full

    Figure 2. Domain Partitioning in integrated structures

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    10/507

  • 5

    simulation perfectly overlaps the simulation with DP and with node-by-node interconnection between the models this validates the theory of hooks and its implementation in the framework of the FIT numerical methods. However, in such a case, the number of inputs/outputs increases drastically (more than 200 for this simple example which used a coarse grid). This affects the CPU time needed for the evaluation of each sub-model, and this choice would not be effective for real cases. That is why it is very important to decrease the number of hooks.

    Table 1. Results obtained by using various settings of the hooks

    No of DoFs No of I/O Test ne nm

    Top Bottom Top Bottom Rel er [%]

    All elmag node hooks 120 99 3399 1349 220 218 0 Only el node hooks 120 0 3301 1251 122 120 39 Only mag node hools 0 99 3279 1299 100 98 5.36 Only 15 mag surface-hooks 0 15 3091 1041 16 14 6.13 Only 9 mag surface-hooks 0 9 3087 1037 10 8 6.12

    The second test kept only the electric node-hooks and the third test kept only the magnetic hooks. It can be noticed that the use of magnetic hooks is very important, which was expected for this configuration in which the coils are close and inductive coupling is important. The final two tests used less number of hooks obtained by clustering the magnetic nodes, according to the expected magnetic field pattern. For instance, in the last test, the magnetic hooks are placed as shown in Figure 3. The result has an acceptable global accuracy, of about 6 % (Figure 4).

    Figure 3 Interface between sub models with 9 magnetic hooks (8 surface hooks and 1 node

    hooks)

    Figure 4 Imaginary part of the admittance component. Full simulation vs. simulation with

    hooks This simulation methodology was also applied for real benchmarks, realized and

    characterized at our industrial partners. Figure 5 shows the layout of a coupled pair of coils embedded into a layered structure made and characterized at austriamicrosystems (www.austriamicrosystems.com). In this case three separate EMCE models were computed, two of them corresponding to the environmental components (top part the air; bottom part the substrate), whereas the third one (middle part) included the coils and their neighborhood. On each interface, 14 hooks were used, the models obtained having respectively 17138 (top, MS) 81453 (middle, FW) and 15427 (bottom, MS). Figure 6 shows the comparison between the measurements (scattering parameters) and the results obtained from this simulation.

    5 Conclusions

    The technique we propose for the modelling of ICs is based on domain partitioning and use of the EMCE formulation. Its main advantages are the reduction of computational complexity for the model extraction process and the possibility of using different, independent grids in

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    11/507

  • 6

    several sub-domains, locally refined and adapted to the local modelled structure. In this manner the main drawback of numerical methods based on the rectangular, uniform grids, such as FIT and FDTD is eliminated.

    Figure 5 Real benchmark Figure 6 Measurements vs. simulation The difficulties come from the fact that the use of hooks introduces a new numerical

    error, the interface being no longer transparent. The hooks technique has practical importance only when their number is reduced to 110. With such values, the sub-domains having different shapes can be modeled independently and in parallel. Next, the reduced size models (represented as matrices frequency dependent circuit functions, state equations or reduced order Spice circuits) are interconnected, aiming to obtain a model for the global system. The global modeling effort is then reduced, replaced by the independent model extraction for each sub-domain. In order to identify the hooks, nodes on interface have to be merged in a minimal number of clusters, so that approximation error be kept below an acceptable level. Hence, the pseudo-optimal hooks identification, problem related to so called "terminal reduction" has to be formulated as a discrete optimization problem. In addition to the clustering algorithms, heuristic rules may be also applied for this reduction. For instance, as suggested by the simple example shown, the placement of magnetic hooks in the holes of spiral inductors. Other tests showed that placement of electric hooks near conductors, allow a proper modeling of capacitive couplings, especially at high frequencies. As a general rule, the interface should be as close as possible to a constant potential surface, orthogonal to the field lines. Investigation related to this optimization task will be carried out in our future research. References [1] J Kanapka, J Phillips, J White, Fast Methods for Extraction and Sparsification of Substrate Coupling,

    Proc. ACM IEEE DAC, Los Angeles, California, United States, pp 738-743, 2000. [2] Al. Timotin. Elementul electromagnetic pasiv de circuit. St. cerc. energ. electr. 21(2):347-362, 1971. [3] R. R. Radulet, Al. Timotin si A. Tugulea, Introducerea parametrilor tranzitorii in studiul circuitelor

    electrice liniare avand elemente nefiliforme si pierderi suplimentare. St. cerc. energ. electr. 16(4):857-929, 1966.

    [4] Daniel Ioan, Irina Munteanu, Missing link rediscovered: The electromagnetic circuit element concept, JSAEM Studies in Applied Electromagnetics and Mechanics, vol.8, pp 302-320,1999,IOS Press, Amsterdam.

    [5] D. Ioan, W. Schilders, G. Ciuprina, N. Meijs, W. Schoenmaker, Models for integrated components coupled with their EM environment, COMPEL Journal, vol.27, no.4, pp.820-828,2008.

    [6] Gabriela Ciuprina, Daniel Ioan and Diana Mihalache, Magnetic Hooks in the Finite Integration Technique: A Way Towards Domain Decomposition, IEEE CEFC 2008.

    [7] D. Ioan, G. Ciuprina, L.M. Silveira, Effective Domain Partitioning with Electric and Magnetic Hooks, Proceedings of the CEFC 2008.

    [8] T. Weiland, A discretization method for the solution of Maxwell's equations for 6 component fields, AE, Electronics and Communication, vol. 31, pp. 116-120, 1977.

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    12/507

  • Energy Consideration in Magnetic Coils Design

    Radu CIUPA, Laura DARABANT, Mihaela PLESA, Octavian CRET, Dan D. MICU Technical University of Cluj-Napoca. 15 Ctin Daicoviciu, Cluj-Napoca, Romania;

    [email protected]

    Abstract. The preoccupation for improving the quality of life, for persons with different handicaps, led to extended research in the area of functional stimulation. Due to its advantages compared to electrical stimulation, magnetic stimulation of the human nervous system is now a common technique in modern medicine. A difficulty of this technique is the need for accurate focal stimulation. Another one is the low efficiency of power transfer from the coil to the tissue. To address these difficulties, coils with special geometries must be designed.

    1 Introduction

    The preoccupation for improving the quality of life, for persons with different handicaps, led to extended research in the area of functional stimulation. The human nervous system can be stimulated by strong magnetic field pulses that induce an electric field in the tissue, leading to excitation of neurons [1]. A disadvantage consists, however, in the fact that the need of focal stimulation can not always be fulfilled. This is why the design of magnetic coils can help achieving this goal. The present paper starts by emphasizing the theoretical background of magnetic stimulation, referring to the mathematical model for the computation of the electric field, the electric circuit of the stimulator and the computation of the inductivity of magnetic coils. Then, for coils of optimal shape, that provide an improved focality of the stimulation Slinky coils - we analyze where the turns should be placed, inside the coil, to achieve activation with minimum energy cost.

    2 Theoretical Background

    The current required to induce the electric field (high field strength are required in magnetic stimulation) is delivered by a magnetic stimulator (RLC circuit). The current waveform through the discharging of a capacitor, with an initial voltage , to the coil is [2]: 0U

    ( ) ( )ttLUI = expsin0 (1) where )2/( LR= , 2/1 = LC , C is the capacitance, and R and L are the resistance and inductance of the coil, respectively. According to the electromagnetic field theory, the electric field E can be computed as a function of the electric potential V and the magnetic vector potential [2]:

    gradVtAE

    = (2)

    The first term of equation (2), called primary electric field - AE , is determined by means of the magnetic vector potential. For coils of non-traditional shapes, one can compute A using an approximation method in which the contour of the coil is first divided into a variable number of equal segments, and the magnetic vector potential in the calculus point is obtained by adding the contribution of each segment to the final value [2, 3]. Considering the notations in fig. 1 and the fact that the current I(t) flows through the conductor, the magnetic vector potential created by the segment into point P can be written, using the vectors defined above, as:

    1

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    13/507

  • lrlr

    lrllrl

    lltIA

    +

    = ln4

    )(0

    (3)

    0

    z

    dz

    h

    -z1

    l

    r

    r l

    z2

    P

    Figure 1: Notation for the computation of the magnetic vector potential produced by a conductor

    segment

    The second term of (4) represents the secondary electric field - VE . It depends on the geometry of the tissue-air

    boundary. A common application of magnetic stimulation is to excite peripheral nerves [3]. The tissue-air interface is considered a flat surface. This term is computed knowing that on the surface, the boundary condition to be fulfilled is: VA EnEn = (continuity of the normal component of the current density vector, valid considering the fact that the regime of the electromagnetic field is quasistatic (f < 1000Hz) and therefore the time variation of the charge accumulated on the tissue-air boundary is zero). The electric field created by a flat surface charged with a certain charge density is 02 = rSE , and the charge accumulation occurs until the normal component of the primary electric field equals the normal component of the secondary electric field; therefore one can compute S as

    ArS En = 02 . One of the major problems that appear in the design phase is the computation of the

    inductivity of the stimulating coil. For simple shapes of the coils (circular), one can determine analytical computation formulas. When, however, the shape and the spatial distribution of the coils turns do not belong to one of the known structures, a numerical method needs to be used for determining the inductivity. The inductance is evaluated by taking the line integral of the vector potential around the coil, for unit current [4]: dlAL = . This formula permits the computation of inductances of the special coils, designed to improve focality.

    The idea is to divide the coils in small portions. Starting from this method, two computation systems were developed by the authors of this paper: The first one is classical and it just consists of a software implementation (Matlab); The second one consists of realizing a hardware architecture that exploits the intrinsic

    parallelism of the problem. The physical support of this architecture is an FPGA device. The problem with the software implementation is its running time. Coils are designed by trial-and-error, and this approach is impractical if each trial requires half a day of computation. Besides, as this time grows with the complexity of the coil, it prevents designing complex coils. The FPGA-based hardware acceleration is able to solve this bottleneck [5]. The self-inductance of the circuit, divided in n parts, can be computed with formula (4). This mainly adds up the self-inductivities of the separate segments with the mutual inductivities of all the involved segments [6]:

    (4) ( kiforMLLn

    k

    n

    iki

    n

    kk +=

    = ==

    ,1 11

    )

    The self inductivity of a short straight conductor, with round cross-section, for low frequencies, is [6]:

    2

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    14/507

  • +

    = 22

    0

    445128

    432

    2 lr

    lr

    rllnlL (5)

    with l the length of the conductor, and r the radius of its cross-section. The mutual inductivity between two straight conductors converging into a point is evaluated as [6]:

    +++

    ++++

    =abccbalnb

    baccbalnacosM

    40 (6)

    The given quantities are represented in Fig. 2, with a and b representing the length of the conductors and the angle between them. For the general case, we consider two conductor segments in space. The first segment is between points of coordinates (xa, ya, za) and (xb, yb, zb), while the second segment is between points (xc, yc, zc) and (xd, yd, zd), see fig. 3. On the second segment, we consider a point of coordinates (x, y, z). The parametric equation of the second segment is:

    ( ) ( )( ) (( ) ( )

    +=+=+=

    szzzszsyyysysxxxsx

    cdc

    cdc

    cdc ) (7)

    a

    bc

    1

    (xa,ya,za)

    rl 1 1l

    (xb,yb,zb)

    (x,y,z)

    (xd,yd,zd)

    (xc,yc,zc)

    r 2 2l

    Figure 2: Computing the mutual inductivity between two converging conductors

    Figure 3: Two segments in space

    With the above geometrical coordinates, we can find the mutual inductivity between these segments (using Neumann formula). For two circuits, 1 and 2, in a homogenous media with permeability , the mutual magnetic flux 21 is:

    ==

    2 2

    2212121S

    dlAdSB (8)

    Since circuits 1 and 2 are shaped like two straight segments, the mutual flux can be evaluated by integrating the magnetic vector potential created by the first segment along the second one. Considering the magnetic vector potential generated by a conductor segment (see (3)), the mutual inductivity can be computed using the following equation:

    +

    =2

    2

    1

    1

    1

    1

    1

    1

    11

    021

    ln4

    dll

    l

    lrlr

    lrllrl

    L

    (9)

    The limits of the integral in equation (9) are given by [ ]1,0s . In order to asses the efficiency of energy transfer from the stimulator to the target biological tissue, we focus on stimulators with a fixed rise time of the current I(t) from 0 to peak, which is sufficient for comparing relative figures of merit of the stimulators. The value of the coils inductance, L, can be evaluated with the algorithm described above. The coils resistance is:

    3

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    15/507

  • (10) =

    =N

    ii

    rAR1

    12

    where A is the cross-sectional area, the resistivity of the wire and ri the radius of the i-th loop. Given the values of L and R, the capacitance C is obtained requiring that the rise time of the current is fixed (=70sec). Because of the same requirement, we may substitute dI/dt (from (3)) with . Assuming that the activation of the nerve fiber occurs for a preset value of the electric field E, we obtain U0, the necessary initial voltage on the capacitor that would lead to activation.

    LUdtdI t // 00 ==

    The energy dissipated in the circuit during one pulse of duration t is [1]:

    (11)

    =t

    J dttIRW0

    2 )(

    The peak magnetic energy in the coil WB required to induce a given electric field is [1]:

    221

    peakB LIW = (12)

    The temperature rise in the coil after one pulse of duration t is (assuming there is no cooling):

    =t

    dttIAc

    T0

    22 )(

    (13)

    where is the resistivity, the density, c the specific heat and A the cross-sectional area of the copper wire of the coil. These three quantities are evaluated to establish the parameters of energy transfer from the coil to the target tissue.

    3 Results and Discussions

    Considering a coil with N turns, the Slinky-k coils are generated by spatially locating these turns at successive angles of degrees, were i = 0, 1,, k-1 [3]. If the current passing through this coil is I, then the central leg carries the total current N x I. With this definition, the circular coil is considered a Slinky-1 coil, and the figure of eight is a Slinky-2 coil.

    ( 1/180x ki )

    For a circular coil, and then for our specially designed Slinky-4 coils, we tried to establish how the dimensions and position of the turns (the coil profile) influence its energetic parameters.

    Figure 4: Slinky_4 coil and the target point. The distance from the coil to the tissue-air interface is 5mm

    in all cases

    d

    air

    tissue

    First, we estimated the strength of the induced electric field at the target due to a single filamentary loop. The loops radius is r, and its distance from the target point is d see fig. 4. The target is at radial distance R from the loops axis. The rate of change of current is assumed to be 100A/s, and the plot is given in fig. 5. From fig. 5 one can conclude that the largest loop nearest the target induces the larger electric field. Therefore, for simple circular coils, the coil profile should mimic the behavior of fig. 5 (i.e. the number of turns should decrease with the level distance from the target).

    4

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    16/507

  • 0

    5

    10

    15

    20

    25

    30

    0 20 40 60 80 100 120

    Turn radius of a Slinky_4 coil (mm)

    Ener

    gy (J

    )

    W_magW_Joule

    Figure 5: Strength of the induced electric field at the target point due to a single filamentary loop

    Figure 6: Variation of energy consumed by a Slinky_4 coil as a function of leaf radius

    Considering the previous conclusion, we tried to establish how the coil profile of a Slinky-4 influences its energetic parameters. For a Slinky-4 coil, 3-1-1-3 turns/leaf, the computations were performed considering that activation occurs when the value of the electric field induced in the target point reaches the value of 100V/m. We computed the total electric field 5mm below the tissue-air interface (the total distance from the coil to the target point is 10mm), and we evaluated the variation of the Joulean and magnetic energy, as a function of the radius of the leaf. Results are depicted in figure 6, and one can see that the optimal value of this radius the one that leads to the lowest energy consumption is about 30mm. For this value, the magnetic energy consumed is minimum, and although the Joulean energy still decreases as the radius increases, this decrease is no longer significant. Then, we considered 25 different configurations of a larger Slinky_4 coil. All these configurations respect the structure of the previous Slinky-4 coil (established to produce a more focal induced electric field [4]), having more turns on the horizontal leafs (leafs 1 and 4) than on the bended ones (leafs 2 and 3). In all cases, there are 25 turns on each of the two horizontal directions and 10 turns on each of the two bended ones (a total number of 70 turns). These larger coils are necessary since most stimulators require that the coils inductivity is above 50H. Such a coil will have several turns, and therefore computing the inductivity is a very long process using the software implementation of our algorithm. But the hardware one is able to solve this problem. The geometrical parameters of the coil are: outer radius 30mm, wire radius 1mm and insulation gap between turns 0,2mm. Considering now that the activation threshold is set to 60V/m in the target point positioned 10mm under the center of the coil, table I presents the energetic parameters evaluated for these coils. The configuration section of table I gives only the number of turns and levels for the first and second leafs of the Sliky-4 coil. Leaf 3 is symmetrical with leaf 2 and leaf 4 is symmetrical with leaf 1. For example, the optimal coil, highlighted, has, on the first leaf: 11 turns on the first level, 8 turns on the second one and 6 turns on the third level; on the second leaf, we have: 4 turns on the first level, and 3 on the second and the third one; fig. 7 gives a better understanding of the position of the turns inside the coil.

    Table 1. Energetic Parameters of a Set of Slinky 4 Coils, on 25 Geometrical Configurations Configuration L (H) C (F) Ipeak (A) WJ (J) WB (J) T (C) 5,5,5,5,5 5,5 100,3 20.258 369.5642 1.4882 6.8494 0.0094

    5,5,5,5,5 4,3,3 103,7 19.586 362.4022 1.4527 6.8097 0.0090 7,6,6,6 5,5 93.3 21.8 357.7678 1.3524 5.9711 0.0088

    7,6,6,6 4,3,3 98.7 20.587 350.1528 1.3165 6.0507 0.0084 8,7,5,5 5,5 90.8 22.412 360.2231 1.3624 5.8911 0.0089

    8,7,5,5 4,3,3 96.2 21.132 352.5096 1.3261 5.9770 0.0085 8,7,6,4 5,5 90.3 22.538 361.0413 1.3659 5.8853 0.0089

    8,7,6,4 4,3,3 93.8 21.685 353.2233 1.3280 5.8516 0.0086

    5

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    17/507

  • 8,7,7,3 5,5 89.5 22.741 363.7414 1.3784 5.9208 0.0091 8,7,7,3 4,3,3 91.7 22.191 355.7584 1.339 5.803 0.0087 9,7,5,4 5,5 89.1 22.846 364.6786 1.3853 5.9247 0.0091

    9,7,5,4 4,3,3 93.3 21.801 356.7318 1.347 5.9366 0.0087 10,5,5,5 5,5 86.3 23.604 368.3421 1.4067 5.8544 0.0093

    10,5,5,5 4,3,3 91.7 22.186 360.3239 1.3611 5.9529 0.0089 10,6,6,3 5,5 84.6 24.087 370.9473 1.4179 5.8206 0.0094

    10,6,6,3 4,3,3 88 23.142 362.6989 1.3773 5.7882 0.0090 11,8,6 5,5 76.7 26.61 364.9574 1.3175 5.108 0.0091

    11,8,6 4,3,3 80.3 25.403 355.7643 1.2859 5.0817 0.0087 10,8,7 5,5 79.1 25.786 365.0187 1.3294 5.2696 0.0091 10,8,7 6,4 78.5 25.987 365.891 1.3329 5.2546 0.0092

    10,8,7 4,3,3 82.8 24.621 355.8257 1.2973 5.2417 0.0087 9,8,8 5,5 80.4 25.361 363.0393 1.3207 5.2983 0.0090

    9,8,8 4,3,3 84.1 24.233 353.9403 1.289 5.2678 0.0086 10,9,6 5,5 77.8 26.226 367.5051 1.3417 5.2538 0.0092

    10,9,6 4,3,3 83.4 24.43 358.3462 1.2981 5.3548 0.0088

    One can see that the space distribution of the turns can play a very important role on improving the energy transfer from the coil to the tissue. One can observe that the energy dissipated in the circuit is 15% lower for the most efficient configuration than for the less efficient one, and the coil heating per pulse is also 8% smaller. These results emphasize only the improvements brought to already optimized structures, because compared to a 70 turns Slinky-4 coil, positioned on the configuration 25-10-10-25 (all turns in one level), the improvement is even more significant (energy dissipated in the circuit is 25% higher and coil heating per pulse is 35% higher for this coil).

    4 Conclusions

    This paper analysis the energetic efficiency of Slinky-4 coils used in magnetic stimulation. From the point of view of energy transfer from the coil to the target tissue, the circular coil and even the figure of 8 coil, also called Slinky-2 coil, are much more efficient than the other Slinky coils [4]. But since focality is also an important criterion to be considered when choosing a magnetic coil for a specific application, this paper analyses the optimal inner structure of a Slinky-4 coil, previously proved to be the one that produces an optimal focality of the induced electric field inside the tissue. We establish that the radius of the coils leafs should be about 30mm, and analyze the role played by the space distribution of the turns on improving the energy transfer from the coil to the tissue. The conclusion is that optimization gains a reduction of over 15% in power consumption and of 8% in coil heating per pulse, which can be an important step forward in designing coils for repetitive magnetic stimulation. Therefore, one can conclude that the application is the one that sets the best design for the magnetic coil, and there is no universal solution, suitable for all cases. References [1] J. Ruohonen, J. Virtanen, Coil Optimisation for Magnetic Brain Stimulation, Annals of Biomedical

    Engineering, vol. 25, 1997. [2] B.J. Roth, P.J Basser, A Model of the Stimulation of a Nerve Fiber by Electromagnetic Induction,

    IEEE Transactions on Biomedical Engineering; vol 37, 1990. [3] L Cret. R. Ciupa, Remarks on the Optimal Design of Coils for Magnetic Stimulation, ISEM. Proc,

    Bad Gastein, Austria., 2003, pp 352-354. [4] L Cret, M. Plesa, Magnetic Coils for Localized Stimulation of the Central Nervous System, Acta

    Electrotehnica, Cluj Napoca, Romania., 2006, pp 114-117. [5] I. Trestian, O. Cre, L. Cre and R. Tudoran, FPGA-based computation of the inductance of coils

    used for the magnetic stimulation of the nervous system, Biodevices 2008, 28-31 January 2008, Funchal, Madeira, Portugal, pg.151-154.

    [6] P.L Kalantarov, L.A. Teitlin, Calculul inductivitatilor, Editura Tehnica, Bucuresti, 1958.

    6

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    18/507

  • OPTIMIZAREA BAZAT PE ALGORITMI GENETICI A UNEI INSTALAII DE NCLZIRE DIELECTRIC N

    CMP ELECTRIC DE NALT FRECVEN

    Camelia-Mihaela PETRESCU, Lavinia FERARIU Universitatea Tehnic Gh. Asachi din Iai, Bd. Dimitrie Mangeron 53, 700050, Iai;

    [email protected]

    Abstract. n lucrare se studiaz o problem de optimizare multicriterial, cu ajutorul algoritmilor genetici, a unei instalaii de nclzire dielectric n cmp electric de nalt frecven. Sunt utilizate dou criterii de performan: uniformitatea cmpului de temperatur i nivelul puterii active absorbite, convertite ntr-o singur funcie obiectiv. Cmpul electric i cel termic se determin cu ajutorul MEF. Variabilele de proiectare sunt ase parametri geometrici i unul electric.

    1 Introducere

    Posibilitatea utilizrii cmpului electromagnetic de nalt frecven la nclzirea unor substane dielectrice este cunoscut de mai mult timp, iar aplicaiile industriale ale acestui fenomen dateaz de la jumtatea secolului trecut, consacrate fiind cele din industria alimentar, industria lemnului, industria chimic, i realiznd, n principal, uscarea sau decongelarea unor produse sub form de pulbere, granule sau blocuri masive, sudarea sau nclzirea unor materiale termo-plastice, lipirea unor plci cu adezivi. Dintre componentele sistemului de nclzire n cmp electric de nalt frecven cea care pune probleme deosebite este instalaia propriu-zis (aplicatorul sau condensatorul de lucru) n care este plasat materialul dielectric cu pierderi. n funcie de procesul tehnologic se urmrete ca aceasta s realizeze un anumit cmp de temperatur n sarcin, cel mai adesea fiind vorba de o nclzire ct mai uniform a acesteia. Exist ns i alte criterii de evaluare a performanei instalaiei de inclzire, cel mai important fiind viteza sau timpul de nclzire, aceasta fiind determinat de puterea activ totala absorbit de sarcina dielectric. n literatur s-au propus diverse tehnici de uniformizare a cmpului de temperatur cum ar fi: deplasarea dielectricului (translaie sau rotaie n funcie de tipul de simetrie a aplicatorului, dispunerea unor straturi dielectrice fr pierderi n jurul sarcinii, avnd dimensiuni i permitiviti convenabil alese, alternarea intervalelor de nclzire cu cele de rcire (oprirea alimentrii) [1-3].

    Dintre tehnicile de optimizare a configuraiei instalaiei de nclzire dielectric n vederea ndeplinirii unor criterii de performan prestabilite, s-au impus cele bazate pe calculul evolutiv, n spe pe algoritmii genetici (AG) i pe strategiile evolutive (SE).

    n lucrri anterioare s-a abordat studiul cmpului electric i a evoluiei temperaturii n sarcina dielectric supus nclzirii [4-5], precum i posibiliti de uniformizare a cmpului termic prin deplasarea sarcinii ntre electrozi i prin alternarea intervalelor de nclzire cu cele de rcire. n [6] s-a utilizat o metod de cutare direct a poziiei optime a electrozilor, de tip hill-climbing.

    n lucrarea de fa se prezint rezultatele optimizrii cu ajutorul AG a configuraiei unei instalaii de ncalzire dielectric pentru sarcini sub form de band. Calculul funciei de performan a instalaiei se bazeaz pe o analiz prealabil a cmpului electric cu ajutorul MEF.

    1

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    19/507

  • 2 Modelul fizic al instalaiei i funciile de performan asociate

    nclzirea dielectricilor cu pierderi, sub form de band, se realizeaz n instalaii avnd o succesiune de perechi de electrozi situai de aceeai parte (instalaie de tip strayfield , Fig.1.a) sau de o parte i de alta a benzii dielectrice (instalaie de tip staggered-through-field , Fig.1.b). n cel de al doilea caz, cei doi electrozi care formeaz perechea pot s aib plane mediane diferite sau un plan median comun. n acest ultim caz cmpul electric este mai intens in zona dintre cei doi electrozi i mai slab la mijlocul distanei dintre ei, instalaia numindu-se din acest motiv cu cmp electric n impulsuri (Fig.1.c).

    V-VV 000

    D D

    V

    -V-V

    V 0

    00

    0

    D

    V

    -V

    V 0

    0

    0 D D

    (a) (b) (c) Fig.1

    Toate instalaiile din Fig.1 realizeaz un nivel ridicat de neuniformitate a densitii de putere i implicit a temperaturii, din acest motiv impunndu-se adesea o deplasare a benzii dielectrice pentru o relativ uniformizare a cmpului termic. n vederea reducerii neuniformitii cmpului electric n cazul aplicatorului de tip staggered throughfield n impulsuri s-a dovedit util introducerea unui electrod suplimentar avnd potenialul V1 plasat la jumtatea distanei dintre dou perechi consecutive de electrozi principali , avnd potenialeleV0, respectiv V0 (Fig.2) [6].

    g ,tg r

    dd d

    VV

    -V-V

    00

    00

    d1 H

    D/2 D/2

    x = 0 x D = V = 0

    V = 0

    d2V1

    Fig.2 Fig.1

    g

    Fig.2

    Instalaia este ecranat din motive de securitate a muncii, dar i pentru creterea absorbiei de putere. Determinarea cmpului electric n aceast problem bidimensional de analiz a unui regim cvasistaionar electric se realizeaz cu ajutorul MEF, condiiile de frontier fiind de tip Dirichlet pe suprafeele electrozilor i respectiv Neumann omogene n planele de simetrie x=0 i x=D, pentru care fluxul electric este nul. Densitatea de putere absorbit n dielectricul cu pierderi are expresia:

    , (1) 2tg2),( Efyxpv =unde f este frecvena tensiunii aplicate, iar i tg permitivitatea i respectiv tangenta unghiului de pierderi dielectrice.

    Determinarea cmpului de temperatur T(x, y, t) presupune rezolvarea cu ajutorul MEF a ecuaiei difereniale de tip parabolic:

    0),()),,(( =++

    yxptyxTtTc vp (2)

    2

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    20/507

  • unde este densitatea, cp cldura specific, conductivitatea termic. Performana instalaiei de nclzire dielectric se apreciaz, n cadrul acestei analize, cu

    ajutorul a dou funcii obiectiv: F1 care msoar uniformitatea cmpului de temperatur la sfritul procesului de nclzire (t=tmax):

    { }{ }

    +=

    2,

    2,],0[,

    ),,(min),,(max

    max

    max1

    gHgHyDxtyxTtyxTF (3)

    i respectiv F2 care msoar puterea activ absorbit de dielectric:

    . (4) ===D g

    vv v dytyxpdxdvpPF0 0

    max2 ),,(

    n procesul de optimizare se caut un minim pentru F1 (ideal F1=1) i un maxim pentru F2.

    3 Strategia de optimizare bazat pe AG

    Algoritmii genetici standard (sau fundamentali) modific dup metode probabiliste indivizii unei populaii de soluii posibile ale problemei de proiectare, prin utilizarea unor operatori de selecie, ncruciare (recombinare) i mutaie. Un individ (cromozom) este un ir obinut prin concatenarea unor reprezentri codificate ale valorilor variabilelor de proiectare (gene). Codificarea poate fi binar, sub form de iruri de bii, sau real, n virgul mobil.

    Etapele algoritmului genetic fundamental sunt [8]: - la t=0 se genereaz aleator o populaie iniial P(t) =P(0), variabilele lund valori n spaiul de cutare admisibil; - se evalueaz adaptarea (fitness) fiecrui individ pe baza valorii funciei obiectiv; - se aplic un mecanism de scalare a performanei indivizilor i de selecie a unei subpopulaii creia i se aplic recombinarea i mutaia, rezultnd o populaie modificat P(t); - se formeaz populaia urmtoarei generaii utiliznd de exemplu regula

    (5) )("))(')(()1( tPtPtPtP U=+

    unde P(t) conine indivizii cei mai slab adaptai din populaia P(t). - algoritmul continu pn cnd se realizeaz o condiie de oprire.

    n studiul de fa variabilele de proiectare folosite n procesul de optimizare sunt (Fig.2): - H distana dintre ecrane, m; ]5.0,2.0[H- D distana dintre dou perechi succesive de electrozi, m; ]1.0,03.0[D- d1 distana pe vertical ntre electrozii principali, d1[ ]1.0,015.0 m; - d2 distana dintre electrodul de gard i banda dielectric, d2 ]05.0,002.0[ m; - d limea electrodului activ, d m; ]01.0,001.0[- dg limea electrodului de gard, dg ]01.0,001.0[ m; - V1, potenialul electrodului de gard, V1 ]0,[ 0V V. Determinarea cmpului electric i a celui de temperatur se realizeaz cu ajutorul MEF,

    cuplat cu MDF n cazul rezolvrii ecuaiei difuziei temperaturii. Calculul numeric al celor dou criterii de performan se bazeaz pe utilizarea relaiilor (3) i (4).

    n analiza de fa s-a optat pentru o optimizare multicriterial (vectorial) deoarece studii anterioare [6] au artat tendina ca soluiile care minimizeaz neuniformitatea temperaturii s scad nivelul de putere activ absorbit.

    Modalitile principale de abordare a unei probleme de optimizare vectorial sunt: - convertirea problemei multicriteriale n una monocriterial prin definirea unei noi funcii obiectiv n care componentele vectorului criteriu intervin cu ponderi diferite;

    3

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    21/507

  • - abordarea Schaffer, n care populaia de Nind indivizi este mprit n subpopulaii, cte una corespunztoare fiecrui criteriu de optimizare, operaiile de ncruciare i mutaie neinnd seama de frontiera dintre populaii; - optimizarea Pareto utilizeaz o partiionare a populaiei de Nind indivizi bazat pe relaia de dominare dintre acetia; subpopulaiilor li se atribuie un rang egal cu numrul de indivizi care le domin +1, n funcie de acesta calculndu-se probabilitatea de selecie pentru reproducere si supravieuire.. Se spune c o soluie este optimal n sens Pareto (Pareto optimal) dac nu se mai pot aduce, n procesul evolutiv, mbuntiri ale uneia dintre componentele vectorului criteriu, fr a reduce performanele individului n raport cu celelalte componente ale vectorului criteriu.

    n lucrarea de fat s-a utilizat convertirea vectorului criteriu V ntr-o nou funcie

    obiectiv definit de relaia:

    =

    2

    1

    FF

    , (6) 21 FFF +=unde i sunt ponderile celor dou funcii de performan. Dac AG standard este proiectat pentru minimizarea funciei obiectiv, atunci o pondere negativ conduce la maximizare n raport cu criteriul respectiv, iar o pondere pozitiv conduce la o minimizare n raport cu criteriul respectiv. n exemplul analizat n lucrare eate necesar ca >0,

  • c) =1, = 0,0001. Bucla evolutiv s-a reluat pe durata a 10 generaii. Rezultatele considerate a fi optimale, obinute n cele trei cazuri, sunt prezentate n Tabelul 1.

    Tabelul 1 Caz F1 F2 F HR(C/min) Soluia optim: D, H, d1, d2, d, dg, (m),

    V1 (V) a) 1,3085 72,32 0,5853 12,94 0.0680, 0.3320, 0.0260, 0.0030, 0.0090, 0.0040,

    - 1744.6 b) 1,0009 3,65 0,9973 1,65 0.0320, 0.2080 , 0.0720, 0.0320, 0.0050, 0.0050,

    -1330 c) 1,0030 3,71 1,0028 1,12 0.0430, 0.3320, 0.0770, 0.0350, 0.0070, 0.0050,

    -518.3630

    Soluiile obinute evideniaz faptul c orice modificare a unei variabile de proiectare acioneaz n sensuri contrarii asupra celor dou criterii de performan, F1 i F2: creterea puterii, ceea ce implic o scdere a distanei dintre electrozi i a potenialului electrodului de gard, antreneaz o accentuare a neuniformitii cmpului electric n dielectric. Se observ de asemenea c este posibil s se obin o uniformizare foarte bun a temperaturii dup 60 s de nclzire (sub 0,5% n cazurile b)i c)), dar pe seama unei scderi accentuate a puterii totale.

    Viteza de nclzire, apreciat cu relaia:

    , (8) ( max0 /)( tTTmeanHR = )unde mean(T) reprezint valoarea medie a temperaturii n dielectric, arat c totui, din acest punct de vedere, optimizarea n raport cu F2 este mai important dect cea n raport cu F1.

    n Fig.3 este reprezentat temperatura n dielectric corespunztor cazului a) din Tabelul I, pentru tmax=60 s. Fig.4 prezint distribuia temperaturii pentru aceleai valori ale parametrilor geometrici i de material ca n cazul a) , dar corespunztor instalaiei din Fig.1.c, iar Fig.5 i Fig.6 pe cea corespunztoare instalaiilor de tip strayfield i staggered-throughfield din Fig.1.a, repectiv 1.b.

    00.01

    0.020.03

    0.040.05

    0.060.07

    0.1640.165

    0.1660.167

    0.1680.169

    0.1732

    34

    36

    38

    40

    42

    44

    x (m)y (m)

    T (de

    g. C)

    00.01

    0.020.03

    0.040.05

    0.060.07

    0.1640.165

    0.1660.167

    0.1680.169

    0.1724

    26

    28

    30

    32

    34

    36

    38

    40

    x (m)y (m)

    T (de

    g. C)

    Fig.3 Fig.4

    5

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    23/507

  • 00.01

    0.020.03

    0.040.05

    0.060.07

    0.164

    0.165

    0.166

    0.167

    0.168

    0.16924

    24.05

    24.1

    24.15

    24.2

    24.25

    24.3

    24.35

    24.4

    x (m)y (m)

    T (d

    eg.C

    )

    00.01

    0.020.03

    0.040.05

    0.060.07

    0.164

    0.165

    0.166

    0.167

    0.168

    0.16927

    27.5

    28

    28.5

    29

    29.5

    30

    30.5

    31

    31.5

    x (m)y (m)

    T de

    g.C)

    Fig 5 Fig.6

    5 Concluzii

    Studiul de fa pune n eviden, pe de o parte, eficiena AG n gsirea unei configuraii care s ralizeze un cmp de temperatur cu grad nalt de uniformitate n dielectricul supus nclzirii i, pe de alt parte, dificultatea gsirii unei soluii care s realizeze simultan o vitez mare de nclzire (nivel ridicat de putere activ). Principala dificultate legat de utilizarea AG n toate problemele n care calculul funciei de adecvare presupune o analiz numeric a cmpului, este timpul mare de calcul, la fiecare generaie trebuind s se analizeze Nind soluii posibile.

    Cercetrile ulterioare vor viza celelalte modaliti de optimizare vectorial menionate n lucrare, precum i optimizarea altor tipuri de instalaii de nclzire dielectric. Referine [1] A. C. Metaxas, Foundations of Electroheat, John Wiley & Sons, Chicester, UK, 1996. [2] E. Dominguez-Tortajada, J. Monzo-Cabrera, and Al. Diaz-Morcillo. Uniform electric field

    distribution in microwave heating applicators by means of genetic algorithms optimization of dielectric multilayer structures, IEEE Trans. Microwave Theory, 55 (2007) 8591.

    [3] B. Cordes and V. Yakovlev. Computational tools for synthesis of a microwave heating process resulting in the uniform temperature field, Proc. 11th Int.Conf. Microwave and High Frequency Heating, Oradea, Romania, 2007, 7174.

    [4] C. Petrescu. Utilizri ale cmpului de nalt frecven la nclzirea dielectricilor, Tez de doctorat, Universitatea Politehnica Bucureti, 1994.

    [5] C. Petrescu. Temperature evolution in cylindrical dielectric load in radio-frequency applicator, Revue Roumaine des Sciences Techniques, 40 (1995) 453-460.

    [6] C. Petrescu. Numerical study of the temperature field inside dielectric load heated in optimized staggered-through applicator, Proc. 11th Int.Conf. Microwave and High Frequency Heating, Oradea, Romania, 2007, pp. 7578.

    [7] Genetic Algorithm and Direct Search Toolbox, http://www.mathworks.com. [8] Lavinia Ferariu, Algoritmi evolutivi in identificarea si conducerea sistemelor, Editura Politehnium,

    Iai, 2006. [9] ***, Polymer Handbook, J. Brandup, E.H. Immergut, Editors, John Wiley & Sons,N.Y., 1975.

    6

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    24/507

    http://www.mathworks.com/

  • Complex interpolation methods applied in electromagnetic compatibility problems

    Dan Doru MICU

    Technical University of Cluj-Napoca, Cluj-Napoca, Romania; [email protected]

    Iosif LINGVAY, Carmen LINGVAY INCDIE ICPE CA, Bucharest,Romania

    Emil SIMION, Andrei CECLAN Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Abstract. In the paper is presented some practical cases, of subdivision of the zone of influence AC Power Lines / electric traction line / gas pipeline in sections (a circuit model) and is created a special interpolation algorithm based on global interpolation functions for the precise evaluation of the induced voltages values in different points on the pipeline taking into account the measured data.

    1 Introduction

    Pipelines located near power lines, may capture a portion of the energy encompassed by the conductors paths, particularly under unfavourable circumstances such as long parallel exposures and power fault conditions. Interference calculations consist essentially of inductive and conductive interference calculations, which are performed independently; computation results can subsequently be combined together [1], [2], [3].

    2 Interpolation algorithms applied for induced voltage evaluation

    Is made an evaluation of the induced voltages in a pipeline, which runs in the same right of way with a power line and electric traction line (Figure 1). The input data of this problem are: power line and pipelines geometrical configuration; conductor and pipeline physical characteristics (including insulating and coating characteristics); environmental parameters (air characteristics, soil structure and characteristics); power system terminal (or boundary) parameters (power source voltages, equivalent source impedances) [4], [5].

    Figure 1: The right of way electric power line-traction line-gas pipeline

    The results demonstrates that is possible to obtain a precise evaluation of the solicitations if is known the resistance and the adduction current in the pipeline. After the determination in each

    1

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    25/507

  • point the potentials due to the right and left side of the line is applied the superposition method [2], [3]. It was measured the voltages between the pipe and soil, respectively the UAC induced along the medium pressure steel gas pipeline with 300mm diameter and 8 mm width, isolated with polyethylene in 3 layers (total 3mm) according with the EN 10285, and posed in different type of soil and isolated by different organic layers. The pipeline has the same right of way (20 km) with a double traction line and crosses an electric power line 110 kV. The measured results are presented in the Table 1 [4]: Table 1

    Parameter Points of measure 1 2 3 4 5 6 7 8 9 10

    Soil resistivity

    [m] 11 18 16 45 32 93 21 64 17 15

    UAC [Vef.] 8,10 19,1 17,2 29,3* 15,2 26,4** 7,13 1,89 2,11 4,32 E[VCu/CuSO4] - 0,353 -0,398 -0,371 -0,325 -0,394 -0,410 -0,387 -0,324 -0,352 -0,365

    *- maximum value obtained when a train pass from Dej toward Cluj ** - maximum value obtained when a train pass from Cluj toward Dej The calculus and the program made in MathCAD with the predefined functions help us to determine more precisely the values of the induced voltages on the entire influence zone. The values in volt of the induced voltages (y) measured on the common corridor line-pipeline at different distances in meters (x), are introduced in MathCAD program. The predefined functions for the spline and linear interpolation are used for the induced voltage calculus in any point of the right of way [5], [6].

    ( )( )( )

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

    ( ) ( )

    =====

    ===

    =

    =

    7450..801,800:,,linterp:

    ,,,interp:,,,interp:

    ,,,interp:,cspline:,pspline:

    ,lspline:

    32.411.289.113.7

    4.262.153.292.1710.19

    10.8

    :

    745064505450505042503450265024001600800

    :

    ttyxtl

    tyxCtcsptyxPtpsp

    tyxLtlspyxCyxP

    yxL

    yx (1)

    2

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    26/507

  • ( )( )

    ( )

    ( ) ( )[ ] +

    =

    ==

    =

    =

    =

    +

    +

    +

    j

    j

    iij

    jijn

    kjk

    jkjkjk

    jj

    AxtAtN

    A

    A

    Aji

    XXAA

    A

    jnknj

    VAnj

    tXnxvV

    xjxX

    A

    0,0

    1

    0,0

    ,

    1,1,1,

    0,

    :

    0..1for

    ..0for..1for

    ..0for7450..801,800:last

    3lastlast..1:

    :

    (2)

    Figure 2: Induced voltages in the gas pipeline using special interpolation functions

    Is observed that the interpolation spline function with linear end conditions is more precise

    than the linear interpolation polynom but the created algorithm gives us the correct data if the interval of the influence zone is increasing.

    Another example which use numerical interpolation, presents a real case for evaluation the induced voltage in each point of the right of way power electric line (220 kV) metallic gas pipeline [5], [8].

    3

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    27/507

  • Figure 3: Sectorial numerical interpolation with add values and without interpolation functions

    continuity at zone limits

    It was developed a global interpolation function for all corridor sectors. The calculated data for induced voltages is split in four sectors taking into account the configuration of the common corridor. For each zone corresponding at some distance location it was evaluated the induced voltages taking into account the inductive coupling. In the following table is shown the calculated voltages having like origin the beginning of the right of way line-pipeline. By sectorial interpolation without imposed continuity condition on the interpolation function the results is not quite good regarding the estimated voltages.

    Figure 4: Sectorial numerical interpolation without add values and with imposed continuity conditions Sectorial interpolation with imposed continuity conditions at the separation zone limits gives better solutions, (Figure 4). Another version for interpolation starts from choosing a global interpolation function followed by a numerical estimation of a first variation of the induced voltage predictor value, (Figure 5).

    4

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    28/507

  • Figure 5: Global interpolation with spline predictor function

    Based on the obtained data from the sectorial interpolation for each set of data we could estimate by corrector interpolation using a greater number of estimated voltages. This last case of predictor-corrector interpolation verify the real conditions of coexistence in the same right of way the metallic pipelines and electric HV lines, the continuity limits and fits good with the estimated induced voltage values initially calculated, (Figure 6).

    Figure 6: Global interpolation with predictor corrector method

    5

    Volumul SNET'08, 5-7 iunie 2008, Univ. Politehnica din BucuretiISBN 978-606-521-045-5

    29/507

  • 3 Conclusion

    The evaluation of the induced voltage in pipeline is based on the subdivision of the zone of influence in a relatively great number of sections in order to be able to determine voltages at many positions along the pipeline using Thevenin equivalent circuits. The paper presents practical cases of subdivision of the zone of influence in sections (a circuit model) and is made a precise evaluation of the induced voltages using some interpolation functions for the measured data. In the first case is observed that the interpolation spline function with linear end conditions is more precise than the linear interpolation polynom but the algorithm developed in MathCAD gives us the correct data if the interval of the influence zone is increasing. In the second case demonstrates that the predictor-corrector interpolation verify the real conditions of coexistence in the same right of way the metallic pipelines and electric HV lines, the continuity limits and fits very good with the estimated induced voltage values initially calculated. References [1] F. Dawalibi. Analysis of electrical interference from power lines to gas pipelines-PartI Computation

    method, PWRD-4, No3, 1989, pp. 1840-1848. [2] ***, Guide Concerning Influence of High Voltage AC Power Systems on Metallic Pipelines, CIGRE

    Working Group 36.02, Canada, 1995. [3] R. Southey, F. Dawalibi. On the Mechanisms of Electromagnetic Interference between Electrical

    Power Systems and Neighboring Pipelines, NACE 2000 T10B Symposium on DC &AC Interference, Orlando, March 26-31, 2000.

    [4] D.D. Micu, I. Lingvay, E. Simion. Modelarea i predicia fenomenelor de interferen n regim electrocinetic, Ed. ELECTRA, Bucureti, 2006.

    [5] D. D. Micu, E. Simion, D. Micu, A. Ceclan. Numerical Methods for Induced Voltage Evaluation in Electromagnetic Interference Problems, 9th International Conference, Electric Power Quality and Utilisation, Barcelona, 10.1109/EPQU.2007.4424091, October 9-11, 2007.

    [6] J. Epperson. An Introduction to Numerical Methods and Analysis, John Wiley & Sons Inc., New-York, U.S.A, 2001.

    [7] D.D. Micu, E. Simion, D. Micu, A. Ceclan, Laura Cret. Numerical algorithm for the accurate evaluation of the induced voltages in a pipeline, 6th International Conference on Computational Electromagnetics, Aachen, Germany, pp. 230-232, April 4-6, 2006.

    [8] F. Latarullo.