Prediction Of Core Losses Of Three-Phase Distribution .

DJournal of Energy and Power Engineering 7 (2013) 2347-2353DAVIDPUBLISHINGPrediction of Core Losses of Three-Phase DistributionTransformerMihail Digalovski, Krste Najdenkoski and Goran RafajlovskiFaculty of Electrical Engineering and Information Technologies, Karpos II, bb, Skopje 1000, Republic of MacedoniaReceived: February 08, 2013 / Accepted: June 13, 2013 / Published: December 31, 2013.Abstract: Transformers are normally designed and built for use at rated frequency and sinusoidal load current. A non-linear load on atransformer leads to harmonic power losses which cause increased operational costs and additional heating in transformer parts. It leadsto higher losses, early fatigue of insulation, premature failure and reduction of the useful life of the transformer. To prevent theseproblems, the rated capacity of transformer which supplies harmonic loads must be reduced. In this work, a typical 50 kVA three-phasedistribution transformer with real practical parameters is taken under non-linear loads generated due to domestic loads. The core lossesis evaluated using the three dimensional model of the transformer developed in FEM (finite element method) program based on validmodel of transformer under high harmonic conditions. And finally a relation associated with core losses and amplitude of highharmonic order are reviewed & analyzed and then a comparison is being carried out on the results obtained by different excitationcurrent in transformer windings.Key words: Core losses, three-phase transformer, harmonic, 3D model, finite element method, magnetic flux distribution.1. IntroductionThe power transformer is one of the most importantand expensive equipment of electric power systems.Cost-effective operation of electric power generation,transmission and distribution systems is related toreliability and availability of their power transformers.However, most investigations have been performed forthe three-phase three-limb core, generally since thevast majority of all built transformers have cores of thistype. As an example, Valkovic [1, 2] has investigatedthe effect of core geometry, core material, joint designand induction on core losses, primarily for three-phasethree-limb cores, and to some degree for single-phasetransformers. Valkovic and Rezic [3, 4] alsoinvestigated the effect of the step lap koint design oncore losses.The present day situation dictates fewer very largetransformers where the transportation heightCorresponding author: Krste Najdenkoski, Ph.D., associateprofessor, research fields: power transformer, wind energy andpower quality. E-mail: krste@feit.ukim.edu.mk.limitations would force the design to be a three-phasefive-limb core or have the transformer bank split upinto three single-phase transformers. However, thereare not abundant analytical works dealing withtransformer core losses which have been focused uponthis type of cores. From rare research works in this field,Chen and Neudorfer [5] had a motivation fordeveloping a transient model for the five-limbtransformer with an interest in transformerferroresonance, a problem which has been vexing thepower industry for over 60 years. Mairs et al. [6] alsostudied this type of transformers from overvoltagespoint of view. Due to calculation of transformer losses,teNyenhuis et al. [7] employed 2-D FDM (finitedifference method) to predict flux distribution andmagnetic loss in cores with this structure. In spite ofhigh precision, such calculation needs considerabledegrees of processing ability [8].In the past years, there has been an increased concernfor the effects of nonlinear loads on the electric powersystem. Nonlinear loads draw current which is not

2348Prediction of Core Losses of Three-Phase Distribution Transformersinusoidal and include such equipment as fluorescentlamp, gas discharge lighting, electronic motor drives,electrical energy converters, static converters, rectifiers,arc furnaces, electronic phase control, switch modepower supplies, pulse width modulated drives and t et type (I order) and are set onthe outer surfaces of the domain. Also that tangentialcomponent Ht of the magnetic field vector is acontinuous function, while the normal component Hn isFig. 4 3D simulation model of three-phase transformer.zero. This means that magnetic field lines will beparallel to the border area. Figs. 5 and 6 presented B-Hand P-B curves.In order to provide correct numerical computationalresults for core losses, the mesh in the region of interestshould be with high density. Meshed model oftransformer is presented in Fig. 7.The transient models are defined three cases ofcurrent load and shown in Table 1.For those three cases of loading, in programpostprocessor are reading core losses and they arecompared with the approximate analytical values. Hence,reflected the impact and change core losses by changingof harmonic components in excitation currents.Currents wave form for the three typical cases aregiven in Figs. 8a-8c.

Prediction of Core Losses of Three-Phase Distribution Transformer2351Current Curve2.00100806040B (tesla)Percentage1.501.0020Sinusoidal Current0-20 0306090 120 150 180 210 240 270 300 330 360-40-60-800.50-100Degrees0.000.00E 0005.00E 0041.00E 005H (A per meter)(a) Current curve (I case)1.50E 005Fig. 5 B-H curve.Current Curve2.50604020Percentage3.00100802.00P1.500-20 0-40-60x30 60 90 120 150 180 210 240 270 300 330 ary Current-80-1001.00Degrees0.50(b) Current curve (II case)0.000.000.250.500.751.00B (Tesla)1.251.501.75Current Curve2.00100Fig. 6 P-B curve.8060Percentage40200-20 0306090 120 150 180 210 240 270 300 330 Sumary Current-60-80-100Degrees(c) Current curve (III case)Fig. 8 (a) Current curve (I case); (b) current curve (II case);(c) current curve (III case).finite elements. Distribution of the magnetic field isFig. 7 Meshed model of the three-phase transformer.Table 1Three cases of current load for transient models.Order case123Harmonic KB1(%)100100100KB3(%)02.55KB5(%)036KB7(%)02.555. Results and Comparison of ResultsAfter completion of preprocessor phase andtransformer discretisation with finite elements, themodel is ready for processing. At this phase, Maxwell’sequation system to solve numerically and its solution isobtained magnetic field intensity H for each individualobtained by association of all the values in the domain.The magnetic field intensity H can be expressedmagnetic flux density B and its distribution (as a rangeof colors) is presented in Fig. 9. Obtained magneticflux density distribution is for rated load of thetransformer (I case, only with first harmonic). Fig. 10 isgiven volumetric density of core losses.Figs. 11 and 12 presented magnetic flux densitydistribution and core losses volumetric density (II case).Figs. 13 and 14 presented magnetic flux densitydistribution and core losses volumetric density (III case).After calculation of distributions of magnetic fluxdensity and volumetric density of core losses for allthree cases, in the postprocessor are reading summary

2352Prediction of Core Losses of Three-Phase Distribution TransformerFig. 9 Distribution of magnetic flux density (I case).Fig. 12 Volumetric density of core losses (II case).Fig. 10 Volumetric density of core losses (I case).Fig. 13 Distribution of magnetic flux density (III case).Fig. 11 Distribution of magnetic flux density (II case).Table 2Fig. 14 Volumetric density of core losses (III case).The analytical calculated losses for all three cases.MethodCore lossesPcore1 (W)Pcore2 (W)Pcore3 (W)SimulationAnalyticalMeasuredRelative deviation (%)Increasing of core losses /2.1715.52losses in the transformer core and they are shown inTable 2, together with the analytical calculated losses.6. ConclusionsThe wide spread utilization of electronic devices hassignificantly increased the numbers of harmonicgenerating apparatus in the power systems. Thisharmonics cause distortions of voltage and currentwaveforms that have negative effects on transformersas increased total losses.This paper has described distribution transformerno-load losses, as well as the harmonic impact onno-load losses, and has introduced a methodologybased on FEM model to predict satisfactory theharmonic impact on core distribution transformer. Themethodology introduced in this paper, if implemented

Prediction of Core Losses of Three-Phase Distribution Transformerat the design stage of distribution transformers, mayprovide great services in reducing the no-load losses.References[1][2][3][4][5][6]Z. Valkovic, Recent problems of transformer core design,Physica Scripta T24 (3) 1988 71-74.Z. Valkovic, Flux and loss distribution in three-limb corewith staggered T-joint, IEEE Transaction Magnetics MAG18 (2) (1982) 801-804.Z. Valkovic, A. Rezic, Flux and loss distribution inthree-limb core with staggered T-joint, in: Symposium onElectromagnetic Fields in Electrical Engineering, Lodz,Poljska, Sept. 1988, pp. 85-88.Z. Valkovic, A. Rezic, Improvement of transformer coremagnetic properties using the step-lap design, Journal ofMagnetism and Magnetic Materials 112 (1992) 413-415.X.S. Chen, P. Neudorfer, Digital model for transientstudies of a three-phase five-legged transformer, IEEEProceedings-C 139 (4) (1992) 351-358.D.D. Mairs, D.L. Stuehm, B.A. Mork, Overvoltages on2353five-legged core transformers on rural electric systems,IEEE Transaction Industry Applications 25 (2) (1989)366-370.[7] E.G. teNyenhuis, G.F. Mechler, R.S. Girgis, Fluxdistribution and core loss calculation for single phase andfive limb three phase transformer core design, IEEETransaction Power Delivery 15 (1) (2000) 204-209.[8] E. Hajipour, P. Rezaei, M. Vakilian, M. Ghafouri, Powertransformer no-load loss prediction with FEM modeling andbuilding factor optimization, Journal of ElectromagneticAnalysis and Applications 3 (10) (2011) 430-438.[9] A.M.A. Haidar, S. Taib, I. Daut, S. Uthman, Evaluation oftransformer magnetizing core loss, Journal of AppliedSciences 6 (2006) 2579-2585.[10] A. Gupta, R. Singh, Computation of transformer lossesunder the effects of non-sinusoidal currents, AdvancedComputing: An International Journal (ACIJ) 2 (6) (2011)91-104.[11] S.T. Lundmark, Y. Serdyuk, S. Gubanski, ComputerModel of Electromagnetic Phenomena in Hexaformer,Chalmers University of Technology, Goteborg, 2007.

voltage increase losses in its magnetic core while harmonic currents increased losses in its winding and structure. In general, harmonics losses occur from increased heat dissipation in the windings and skin effect both are a function of the square of the rms current, as well as from eddy currents and core losses.