Reetima Mary Sah, Jyoti Srivastava / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.984-987984 | P a g eModelling And Simulation Of Distribution Transformer ForAnalysing The Transformer Losses Using Analytical AndSimulation Method1Reetima Mary Sah, 2Jyoti SrivastavaSam Higginbottom Institute Of Agriculture,Technology & Sciences Allahabad, IndiaAbstractIn this paper, losses due to linear loadhas been calculated using analytical andsimulation method and also losses due toharmonic load current has been calculated byanalytical method .Transformer is basiccomponent of power system and it is usuallyconstructed and basically designed to work atrated frequency and perfect sinusoidal loadcurrent .Now days use of non linear load hasincreased a lot ,so losses due to harmoniccurrent has increased .This in turn detoriatesthe insulation of the winding and life oftransformer due to heating .In this paper a 200KVA 3 phase distribution transformer is takenand losses has been calculated under linear load,using two methods . i.e computational methodand simulation method .Also losses due toharmonic current has been calculatedanalytically and has been compared with lossesof linear load. For simulation method ,aSIMULINK model of transformer is designedand finally both the method has been compared.Keywords: Transformer losses ,non linear loads,harmonic current, KVA rating ,Eddy currentINTRODUCTIONTransformer is most important electricalmachine of power system and it is interfacesbetween consumer and supplies. With increasingdemand of electrical energy, number of distributiontransformer to be installed is increasing .Efficiencyof transformer is usually 97% to 99% as we allknow but because of increase in total number oftransformer in power system network ,losses hasincreased. Now days use power electronics devicehas increased .Because of use of non linear device,has detoriated and reduced the life of transformer.There are many reason that detoriates theinsulation of transformer. Harmonic also effectoverall performance of a transformer ,which in turnreduces the life of a transformer ,which may alsocalled aging of transformer .The major effects ofharmonic distortion is to increase both load and noload losses. Most important losses due to eddycurrent losses occurring in winding. Increase ofeddy current loss because of harmonics increasesthe temperature of transformer and as mentionedabove reduces life of transformer.In this paper we have used MATLAB software anddesigned a SIMULINK model and calculatedlosses due to linear load by simulation method andfinally we have compared this simulation methodwith our analytical method. Also we havecalculated losses and rated output under harmoniccurrent analytically and has compared withanalytical method used for calculating losses due tolinear load.LOSSES IN TRANSFORMERTwo types of losses occur in transformer (1) noload losses or core losses (2) load lossesTotal loss =no load loss +load lossPTOTALLOSS=PNOLOADLOSS+PLOADLOSS(1)Load losses = copper losses +eddy current losses inwinding+ other stray lossesPLOADLOSSES=PDC+PEDDYCURRENT+POTHERSTRAYLOSSES(2)NO LOAD LOSSES:The No load losses or core losses arises intransformer because of the voltage which isinduced in core. As we know that the number ofdistribution transformer is high in power systemnetwork and they are always in service. So no loadlosses is high but it is merely constant. These lossesoccur because of eddy current and hysteresisphenomenon in the core. Load losses which consistof (a) I2R LOSSES (b) EDDY CURRENTLOSSES (c) OTHER STRAY LOSSES.PDC is calculated by knowing the value ofresistance and square of load currentPDC=I2RIII .EDDY CURRENT LOSSES INWINDINGTwo effect is responsible for eddy current losses inwinding(1) SKIN EFFECT (2) PROXIMITY EFFECTThe eddy current losses occurring inwinding in power frequency spectrum is directlyproportional to f2and I2,where f and I arefrequency and load current. The effect of low orderharmonics on skin effect is usually taken negligiblein windings of transformer.
Reetima Mary Sah, Jyoti Srivastava / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.984-987985 | P a g ePROXIMITY EFFECT: In the given figurebecause of charging current, the hv windingproduces a flux density. The core and LV windingcuts the flux density and hence eddy current whichis also called circulating current is produced. Wecall this effect proximity effect. This effect iscaused by magnetic field or current carryingconductors that induce currents in other conductorsin close proximity to the other current carrying ormagnetic fields. Power loss Pec will occur due eddycurrents.Fig 1. Forming eddy current by proximity effectThe proximity effect loss is given byPPE= . (3)where n is number of conductor, d is stranddiameter, and I is maximum current. Gr isproximity factor and by consideringOther stray losses in transformerTotal stray losses=sum of eddy current losses+other stray losses(4)With the help of above equation, we can calculateother stray losses. As we have studied earlier,whenever a conductor is linked byelectromagnetic flux. Because of this a voltage isinduced in the conductor. Hence eddy current isproduced. The losses which takes place instructural parts of transformer for example likeclamps, tanks ,walls of enclosure are known asother stray losses. The other stray losses are thepart of eddy current loss which takes place instructural part of transformer. Many experimentshave been done to determine the effect offrequencies on other stray loss value.At low frequency (0-360) HzROSL=1.29 mΩ (5)At high frequency (420-1200) HzROSL=9.29-.59 (6)Hence POSL is proportional to (i) I2i.e square ofload current (ii) f.8Where f is frequencyHARMONIC EFFECT ON NO LOADLOSSESAs we know by Faraday’s law that the voltage atthe terminal determines the transformer flux levelN =v (t) (7)We transfer the above equation in frequencydomainN j (h )=V h (8)So from above equation it is clear that, themagnitude of flux is directly proportional toharmonic voltage and is inversely proportional toharmonic order h. Also in most power systems, thetotal harmonic distortion THD of the systemvoltage is below 5%. The harmonic component ofvoltage is small if compared to fundamentalcomponent. So by neglecting the effect ofharmonic voltage and hence considering that the noload losses which occured by the fundamentalvoltage component will give rise to an insignificanterror. But in case THDV is not negligible then thelosses which occurs under distorted voltagescalculated with following equation based on ANSI-C.27-1920 standard.P=PM [Ph+Pec( )2]. (9)V h r ms and V r ms are the r ms values of distortedand sinusoidal voltages, PM and P are no-loadLosses under distorted and sinusoidal voltages, PHand PEC are hysteresis and eddy current losses.HARMONIC EFFECT ON NO LOADLOSSES EFFECT OF HARMONICCURRENT ON OHMIC LOSSESThe I2R losses occur due to distortedprimary and secondary current flowing throughprimary and secondary winding of transformer. TheI2R loss occurring in winding of transformer undereffect of harmonic condition is given by.PDC=RDC*I2=RDC*( ) watt (10)EFFECT OF HARMONIC CURRENT ONEDDY CURRENT LOSSES IN WINDINGThe eddy current losses varies by thesquare of I2RMS and f2.where f is frequency and IRMSis rm s value of current.Pec=Pec- (11)FHL= = (12)Ih &I1 is harmonic current and fundamental currentand IR is rated load currentSo, it is important to multiply eddy current lossesoccurring in winding by harmonic loss factor FHL.According to IEEEC57.110 standards, amount ofrated eddy current loss of windings is about 33% oftotal stray loss for oil-filled transformers
Reetima Mary Sah, Jyoti Srivastava / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.984-987986 | P a g eEFFECT OF HARMONIC CURRENT ONOTHER STRAY LOSSESWe know that other stray losses is proportional tothe square of IRMS and f.8,where IRMS is rms currentand f is frequency.POSL is given by following formulaPOS=POSL-R (13)The harmonic loss factor for POSL is given byfollowing expressionFHL-STR= = =(14)So , it is very important that POSL should bemultiplied by FHL-STR under harmonic losses factor,where FHL-STR.TRANSFORMER MODEL In above figure.2 isshown that the proximity effect loss is representedas potential difference defined as the secondderivative of load current and other stray losses isrepresented as a resistor in series with leakageinductance and dc resistance.Fig2 PROPOSED EQUIVALENTTRANSFORMER MODEL REFEERED TOPRIMARYSIDECALCULATION AND RESULTLosses is calculated using two methods (1)ANALYTICAL METHOD (2) SIMULATIONMETHOD.ANALYTICAL METHOD A 200 KVAtransformer parameters are given below V1(V) V2(V) I1(A) I2(A) PO(W) PSC(W)11KV 433 10.5 266.7 5003000R1 R2 L1 L2 RC Xm3.27Ω.0041Ω.003H.067mH728KΩ32105HTo calculate PTSL is calculated belowPTSL=PSC-PDC=3000-3(10.52*3.27+266.7*.00413)=1043.57WattPEC=.33*1043.57=3443.7wattPOSL=PTSL –PEC =699.2wattHARMONIC LOAD SPECIFICATION ISGIVEN BELOW1 5 7 11 13 17 19.966 .208 .093 .069 .045 .031 .023EFFECT OF HARMONIC ON THECAPACITY OF TRANSFORMER DUE TONON LINEAR LOADWhen a transformer supplies a non linear loadlosses are increased, as a result the rated powerdecreases. To determine the capacity of atransformer under harmonic load, we use followingequation and per unit basis is used.PLL-R(PU)=1+PEC-R(PU)+POSL-R(PU) (F)Now ,if we have non sinusoidal load currentPLL-R(PU)= [1+FHLPEC-R(PU)+FHL-STRPOSL-R(PU)](15)The maximum permissible load current oftransformer is given by following equationIPU= ]0.5(16)Sh=S* Imax(pu)Where,PLL-R=Rated load loss of transformer, PEC-R=Eddycurrent loss winding at rated load.1 is per unitamount of Pdc loss, S=Transformer rated capacity,Sh=Transformer capacity under non sinusoidalload.Also PEC-R(PU) = , POSL(PU)= .With the help of above formula, we can calculatemaximum permissible load current of a transformerand reduction of transformer capacity under non-sinusoidal current.So, IPU == ].5= (.736).5=.858 puCurrent=.858*266.7=228.8AEquivalent KVA=.858*200 =171.6KVALOSSES UNDER RATED LOAD CURRENTAND HARMONIC LOAD CURRENT BYANALYTICAL METHODTypesoflossesRatedlosses(W)Lossesunderharmonicloadcurrent(W)HarmoniclossesfactorCorrectedlossesunderharmonicload(W)Noload500 500 ------------500Dc1956.431989.72 ------------1989.72
Reetima Mary Sah, Jyoti Srivastava / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.984-987987 | P a g eWindingeddycurrent344.37365.03 3.843 1402.8Otherstraylosses699.2 741.15 1.193 884.19Total 3499.973595.9 4776.71OUTPUT KVA underRATEDCURRENT(KVA)OUTPUT KVAUNDER HARMONICCURRENT(KVA)200 171.6SIMULATION METHOD: With the help ofsimulation method we will calculate losses underlinear load and compare the losses under linearload obtained from analytical method. For this wewill design SIMULINK model for no load test,short circuit test, and load test. Finally we willobtain losses by simulation method.COMPARISON OF LOSSES UNDER RATEDCURRENT BY ANALYTICAL METHODAND SIMULATION METHODRATEDLOSSES(Watt)ANALYTICAL METHODSIMULATION METHODNO LOAD 500 498.6D.C 1956.43 727.36WINDINGEDDYCURRENT344.37 309.02OTHERSTRAYLOSSES699.2 627.42TOTAL 3500 2162.64CONCLUSIONIn this paper transformer losses i.e,I2Rlosses, winding eddy current losses, stray losseshave been calculated by analytical method andsimulation method. These calculation determinesthe transformer equivalent KVA, when it issupplying non linear load. From above calculation,we conclude that losses increase when transformeris supplying non linear load because of harmoniccomponent and hence rated capacity get decreasedunder harmonic current. Also we conclude thatwhenever there is change in harmonic current,there is change in harmonic loss factor anddefinitely change occur in losses and capacity oftransformer. Also we conclude that by simulationmethod, losses are less and hence we conclude thatsimulation method is more accurate than analyticalmethod .So in power system network it is importantto monitor voltage and current, so that to reach theuseful capacity of transformer based on availablestandard and proposed model if harmoniccomponent is existing.REFERENCE IEEE Std C57.110-1998, “IEEERecommended Practice for EstablishingTransformer Capability When SupplyingNon sinusoidal Load Currents” SAFET AYASUN,1 CHIKAO.NWANKPA “Transformer Tests UsingMATLAB/SIMULINK and theirIntegration into Undergratuade ElectricMachnery Courses.IEEETRANSEDU,2005 .. S.B.Sadati, A.Tahani, M.Jafari,M.Dargahi, Derating of transformersunder Nonsinusoidal Loads, Proc. of the11th International Conference onOptimization of Electrical andElectronicEquipment OPTIM 2008, Brasov,Romania.. Sadati, S.B., A. Tahani, B. Darvishi, M.Dargahi and H. Yousefi, 2008.Comparison of Distribution TransformerLosses and Capacity under Linear andHarmonic Loads. In the proceedings ofthe IEEE 2nd International Power andEnergy Conference, 2008, PP: 1265-1269. M.Yazadani-Asrami,M.mirzaie andA.Shayegani Akmal. Calculation oftransformer losses under non sinusoidalcurrents using analytic methods and finiteelement analysis .World appliedjournal.Vol. II, IMECS 2011, March 16-18, 2011, Hong Kong. Amit Gupta,Ranjana Singh. Comparisonof transformer losses under the effect ofnon sinusoidal load currents, AnInternationalJournal,vol.2,No.6,November 2011.. Mohammed k,Edan. Non SinusoidalLoading Effect On Oil Immersed PowerTransformers .Eng & Tech Journal ,Vol29,No 12,2011. A.H. Al-badi, A. Elmoudi, I. Metwally.Losses reduction in distributiontransformers, Proceedings of theInternational Multi Conference ofEngineers and Computer Scientists 2011VOL II IMECS 2011,MARCH 16-18.2011,HONG KONG H.I.Zynal, Ala’a a.Yass.The Effect ofHarmonic Distortion on a Three PhaseTransformer losses. Canadian Journal ofElectrical and Electronics EngineeringVol.3,no .5,May 2012.