7 ZAKLJU»AKU radu je opisan model transformatora primjenjivu prijelaznim pojavama relativno niskih frekvencija.Za energetske transformatore velikihsnaga pokazano je da se krivulja magnetiziranjakvalitativno moæe predstaviti preko dva pravca.Pokazane su granice upotrebe analitiËkih metodaproraËuna prijelaznih pojava u transformatorima.Za numeriËko rjeπavanje sustava krutih diferencijalnihjednadæbi iskoriπteno je implicitno trapeznopravilo. Razvijeni algoritam je moguÊe apliciratiu niskofrekvencijskim prijelaznim pojavama kaoπto su: uklapanje transformatora, ferorezonancija,ispad tereta, kvarovi transformatora itd. Na krajuje pokazan primjer upotrebe realiziranog algoritmana proraËun prijelazne pojave uklapanja trofaznogtrostupnog transformatora. Kompariranjemmjerenih i simuliranih struja uklapanja trofaznogtransformatora ustanovljeno je da se pogreπke nalazeu zadovoljavajuÊim granicama (maksimalno3,56 %).7 CONCLUSIONA transformer model applicable to relatively lowfrequency transient phenomena is described in thearticle. For power transformers with high power ratings,it was demonstrated that the magnetizing curvecan be adequately presented with two straight lines.The limits for the use of analytical methods for thecalculation of transient phenomena in transformersare presented. The implicit trapezoidal rule wasused for the numerical solution of a system of stiffdifferential equations. The developed algorithm canbe applied to low frequency transient phenomenasuch as transformer energization, ferroresonance,load switch-off, transformer faults etc. An exampleof the application of the developed algorithmwas presented for the calculation of the transientsthat occur during the energization of a three-phase,three-legged transformer. Through comparison ofthe measured and simulated inrush currents of thethree-phase transformer, it was established that theerrors were within acceptable limits (a maximum of3,56 %).TokiÊ, A., UglešiÊ, I., NumeriËki proraËun niskofrekvencijskih..., Energija, god. 56(2007), br. 5., str. 584-607TokiÊ, A., UglešiÊ, I.,The Numerical Calculation of..., Energija, vol. 56(2007), No. 5, pp. 584-607606
LITERATURA / REFERENCES[1] CIPCIGAN, L., XU, W., DINAVAHI, V., A New Technique to Mitigate Inrush Current Caused by TransformerEnergization, IEEE PES, Summer Meeting, July 2002, Vol. 1[2] LIN, C. E., CHENG, C. L., HUANG, C. L., YEH, J. C., Investigation of Magnetizing Inrush Current inTransformers: Part II ∑ Harmonic Analysis, IEEE Transaction on Power Delivery, Vol. 8, No. 1, January1993[3] YABE, K., Power Differential Method for Discrimination Between Fault and Magnetizing Inrush Currentin Transformers, IEEE Transaction on Power Delivery, Vol. 12, No. 3, July 1997[4] KITAYAMA, M., NAKABAYASHI, M., A New Approach to Fast Inrush Current Discrimination Based onTransformer Magnetizing Characteristics, 14 th PSCC Conference, Sevilla, June 2003[5] MAO, P. L., AGGARWAL, R. K., A Novel Approach to the Classification of the Transient Phenomenain Power Transformers Using Combined Wavelet Transform and Neural Network, IEEE Transaction onPower Delivery, Vol. 16, No. 4, October 2001[6] LIN, X., LIU, P., MALIK, O. P., Studies for Identification of the Inrush Based on Improved CorrelationAlgorithm, IEEE Transaction on Power Delivery, Vol. 17, No. 4, October 2002[7] RIOUAL, M., SICRE, C., DRISS, K. B., Special Methods for the Calculation of Temporary OvervoltagesDue to Transformer Saturation, IEEE PES, Winter Meeting, January 2001, Vol. 2[8] SCHEI, A., EKSTROM, A., Stresses on Metal Oxide Surge Arresters in HVAC Systems by Temporaryand Transient Overvoltages and Related Tests, International Conference on Large HV Electrical Systems,Paris, 1986[9] BAR, R. A., PLATT, D., Modelling and Mapping Ferroresonant States in Series Compensated Distributionand Subtransmission Lines, IEEE Transactions on Power Delivery, Vol. 11, No. 2, April 1996[10] EMIN, Z., AL ZAHAWI, B. A. T., TONG, Y. K., Voltage Transformer Ferroresonance in 275 kV Substation,International Symposium on High Voltage Engineering, Vol. 1, August 1999[11] Working Group, Modeling and Analysis Guidelines for Slow Transients ∑ Part III: The Study of Ferroresonance,IEEE Transaction on Power Delivery, Vol. 15, No. 1, January 2000[12] ONG, C. M., Dynamic Simulation of Electric Machinery using MATLAB ® /SIMULINK, Prentice HallPTR, New Jersey, 1998[13] GREENWOOD, A., Electrical Transients in Power Systems, John Wiley & Sons, New York, 1991[14] MIRI, A. M., MÜLLER, C., SIHLER, C., Modelling of Inrush Currents in Power Transformers by aDetalied Magnetic Equivalent Circuit, International Conference on Power Systems Transients IPST,Rio de Janeiro, August 2001[15] BRUNKE, J. H., FRÖHLICH, K. J., Elimination of Transformer Inrush Currents by Controlled Switching∑ Part I: Theoretical Considerations, IEEE Transaction on Power Delivery, Vol. 16, No. 2, April2001[16] SEMLYEN, A., DE LEON, F., A Simple Represetation of Dynamic Hysteresis Losses in Power Transformers,IEEE Transactions on Power Delivery, 1, 1995[17] PRESSS, W. H., VETTERLING, W. T., TEUKOLSKY, S. A., FLANNERY, B. P., Numerical Recipes in C,The Art of Scientific Computing, Cambridge University Press, New York, 1994[18] SHAMPINE, L. F., REICHELT, M. W., The MATLAB ODE site, Matlab/ toolbox/ ode, 1999[19] Power System Blockset, User’s Gude, The MathWorks, Hydro-Quebec, TEQSIM International, 1999[20] TOKIΔ, A., NumeriËki proraËun niskofrekvencijskih elektromagnetskih prelaznih pojava u transformatorima,Doktorska disertacija, Fakultet Elektrotehnike i RaËunarstva SveuËiliπta u Zagrebu, Zagreb,listopad, 2004.Uredniπtvo primilo rukopis:2007-07-10PrihvaÊeno:2007-07-29Manuscript received on:2007-07-10Accepted on:2007-07-29607TokiÊ,A., UglešiÊ, I., NumeriËki proraËun niskofrekvencijskih..., Energija, god. 56(2007), br. 5., str. 584-607TokiÊ, A., UglešiÊ, I.,The Numerical Calculation of..., Energija, vol. 56(2007), No. 5, pp. 584-607
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05/07ENERGIJAIZDAVA»Hrvatska elekt
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UVODINTRODUCTIONDragi Ëitatelji,u
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ULOGA REGULATORNOG TIJELA UDONO©EN
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U radu Okruglog stola po pozivu su
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azdvajanja energetskih djelatnosti,
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3 RESTRUKTURIRANJEELEKTROENERGETSKO
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nizma, ukljuËujuÊi i sadræaje i
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Tarifni sustav /Tariff systemSlika
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Stopa povrata koja omoguÊuje nakna
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Troškovi poslovanja /Operational c
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znati polugodiπnji ukupni troπkov
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dræava i njihovih odgovarajuÊih e
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ili naroËito u sluËajevima kada s
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metode regulacije i metodologije ta
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Na spomenuti kontekst ulaganja u od
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greater cooperation and the transfe
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Hrvatska je na poËetku uvoappleenj
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∑ treba li regulatorno tijelo bit
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izraappleuje temeljem Strategije en
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P max (t - 1) ∑ gornja granica do
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azina investicija ukljuËiti u regu
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je porast potroπnje te zamjena pos
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Tablica 3 ∑ Pojednostavljen primj
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eguliranih cijena. Stabilna razina
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4.2.1 Iskustva VijeÊa za regulacij
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4.2.2 Iskustva Hrvatske energetske
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zakonskih akata, provede sve nuæne
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latornog tijela tijekom procesa utv
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LITERATURA / REFERENCES[1] Zakon o
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1 UVODU niskofrekvencijske prijelaz
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Slika 1Krivulja magnetiziranjatrans
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2 MATEMATI»KI MODELPRI UKLAPANJUNE
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Slika 5Uklapanjetransformatora ∑p
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4 NUMERI»KI PRISTUPSada Êe se ana
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Tada je opÊe rjeπenje jednadæbe
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gdje su:where:(31a)(31b)Implicitno
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5 TEST PRIMJERProgrami dobiveni pre
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(36)(37)gdje su:j = 1, 2, 3 oznake
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1 UVODSustavi relejne zaπtite u el
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∑ Ëesti problem sliËnih baza po
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slike (npr. jednopolne sheme), dija
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Pojedinim korisnicima u ovoj grupi
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· opis svih relacija u bazi podata
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Slika 4IzvjeπÊe o udeπenjuzaπti
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UPUTSTVO ZA RUKOPISUPUTEAUTORIMA1.
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DIJAGNOSTI»KI PREGLEDRASPADA ELEKT
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Slika 1Jednopolna shemasustava na p
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1 UVODU niskofrekvencijske prijelaz
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Slika 1Krivulja magnetiziranjatrans
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2 MATEMATI»KI MODELPRI UKLAPANJUNE
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REGULATORNA POLITIKA I NJENUTJECAJ
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Hrvatska je na poËetku uvoappleenj
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∑ treba li regulatorno tijelo bit
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U Bugarskoj se financijski nadzor p
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ZakljuËak koji se moæe izvuÊi iz
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no tijelo na osnovi troπka kapital
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nih razdoblja. Ukoliko je energetsk
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zakonskih akata, provede sve nuæne
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koji se primjenjuju na davanje odob
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integralnog tarifnog sustava koji j
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zatim s vremenom, kako su svi sudio
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knjigovodstvenog praÊenja po izdvo
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ma, kod svih regulatornih tijela i
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træiπta, odnosno razvoja i uspost
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tuacijama regulatorna tijela postup
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UVODINTRODUCTIONDragi Ëitatelji,u
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ULOGA REGULATORNOG TIJELA UDONO©EN
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U radu Okruglog stola po pozivu su
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azdvajanja energetskih djelatnosti,
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3 RESTRUKTURIRANJEELEKTROENERGETSKO
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nizma, ukljuËujuÊi i sadræaje i
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Tarifni sustav /Tariff systemSlika
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Stopa povrata koja omoguÊuje nakna
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Troškovi poslovanja /Operational c
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znati polugodiπnji ukupni troπkov
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dræava i njihovih odgovarajuÊih e
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ili naroËito u sluËajevima kada s
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metode regulacije i metodologije ta
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Na spomenuti kontekst ulaganja u od
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greater cooperation and the transfe
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