8. СОВЕТУВАЊЕ. Охрид, септември ANALYSIS OF NO LOAD APPARENT POWER AND FREQUENCY SPECTRUM OF MAGNETIZING CURRENT FOR DIFFERENT CORE TYPES

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1 8. СОВЕТУВАЊЕ Охрид, септември Leoardo Štrac Frajo Keleme Kočar Power Trasformers Ltd. ANALYSS OF NO LOAD APPARENT POWER AND FREQENCY SPECTRM OF MAGNETZNG CRRENT FOR DFFERENT CORE TYPES ABSTRACT This paper presets aalyses of o load apparet power ad magetizig currets for various core types of power trasformers. A overview is preseted of apparet power calculatio ad priciples of step-lap cores. Measuremets of apparet power for differet core types are compared to calculatio results. Also, the compariso of apparet power betwee differet core types is show. the secod part of the article a mathematical model of the core with the oe-dimesioal etwork of the equivalet magetic reluctaces is preseted. A frequecy spectrum of magetizig curret is calculated usig the model with implemeted fast Fourier trasform algorithm. Calculatio results are compared with the measuremet o series of trasformers, icludig the frequecy spectrum. Keywords: power trasformer, apparet power, magetizig curret, frequecy spectrum of magetizig curret, reluctace etwork NTRODCTON No load apparet power ad magetizatio curret ad their values represeted a challege durig trasformer desig process ot so log ago. Magetizatio curret irush used to be quite high ad trasformer cosumed relatively high apparet power. Situatio chaged substatially with the itroductio of step-lap cores. This approach to core cuttig ad stackig allowed the magetic flux to cross betwee sheets more gradually i the corers ad T-joits (Figure ) resultig i lower losses, apparet power ad oise. This paper represets the overview of o load apparet power i moder power trasformers. Figure Magetic flux trasitio from sheet to sheet i step lap cores. The secod part of the article gives a overview of typical frequecy spectra of magetizig currets for differet core types. Higher harmoics of magetizatio curret develop due to strog oliearity of magetic material. However, there are differet iflueces o the harmoic curret cotets chage with respect to differet magetic paths of usual core types, as well as various differet widig coectios. The behavior of some of them are explaied i [], [2]. All aalysis ad measuremet i this paper are provided for the same set of uits. There are two basic group of materials, covetioal ad HiB. Covetioal material is divided i two grades, 30-30C ad 7-30C, while HiB group has oly oe grade 05-30H. There are three types of core: A2-00R /6

2 MAKO CGRE 203 A2-00R 2/6 three-limb sigle-phase cores (/2), three-limb three-phase cores (3/0), five-limb three -phase cores (3/2). The total umber of aalyzed uits is 62 (Table ). Table Core types ad grades aalyzed ad the umber of uits core\grade /2 3/0 3/ C - 5 uits 2 uits 7-30C - 2 uits 4 uits 05-30H 2 uits 9 uits 8 uits 2 NO LOAD APPARENT POWER 2. Method of calculatig o load apparet power The geeral equatio for calculatig o load apparet power is: S 0 = s 0 K F KC m, () where S 0 [VA] is total apparet power of the core, s 0 [VA/kg] is specific apparet power, K F is frequecy factor, K C is core type factor, m [kg] is core mass. f we wat to compare cores of differet mass ad type, we have to compare specific apparet power s 0. order to calculate that value several additioal equatios are eeded: % 0% S0 = S, (2) m % = 00, (3) 0m 0% = 00, (4) f K F =, (5) 50 where S 0 [VA] is total omial power of the trasformer, % [%] is measured voltage, m [V] is measured voltage, [V] is omial voltage, 0% [%] is measured curret, 0m [V] is measured curret, [V] is omial curret, f [Hz] is measured frequecy. Fially, equatio for specific apparet power s 0 is: 0 m S s0 =. (6) f Kc m 50

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5 MAKO CGRE 203 A2-00R 5/6 N + N = Hd + H (2 d + d ) C 2 2C p2, (0) N + N = H d A 2 2A, air air N + N = H d B 2 2B 2, air air N + N = H d C 2 2C 3, air air, (), (2), (3) 0 = μμ H S μμ H S μμ H S μh S 0 r 0 r 0 r , air air 0 = μμ H S + μμ H S μμ H S μh S 0 r r r , air air 0 = μμ H S + μμ H S μμ H S μh S 0 r r r , air air, (4), (5), (6) where N i is the umber of turs of the excited widig, ia the part of magetizig curret of the phase A, H i is the magetic field stregth (module of vector), d i,j is the mea path legth through the core, μ 0 is the magetic permeability of vacuum, μ ri is the relative permeability of the material ad the idices i,j are give accordig to the geometric path otatio i 0. t is assumed that relative permeabilities of the material remai costat across each path leg, but are differet o other flux paths. The relatioship betwee modules of vectors of magetic iductio ad magetic field stregth of Grai Orieted Electrical Steel (GOES) is give usig the oliear B-H curve i Figure Relative permeability of GOES Module of magetic field stregth (A/m) Figure5 Relative permeability vs. module of magetic field stregth of the Grai Orieted Electrical Steel (GOES) The mathematical relatios (7)-(9) betwee applied voltages ad magetic fluxes complete the model. V cos( ωt) = μμ ( H ) H S +Φ 0 r, air ωn, (7) V 2π cos ωt = μ μ ( H ) H S +Φ 0 r , air ωn 3, (8) V = ωn 4π cos ωt μ μ ( H ) H S +Φ 0 r , air 3, (9) V deotes the voltage amplitude ad ω is the circular frequecy, Φ,air to Φ 3,air are magetic fluxes outside the core. The model for the three limb core is derived usig the same priciples.

6 MAKO CGRE 203 A2-00R 6/6 3.2 Measuremet of magetizig curret frequecy spectrum Measuremet of magetizig curret frequecy spectrum was performed at omial iductio ad omial frequecy for middle tap positio. The compariso of calculated ad measured spectra is give i Table 2. The calculatio results fit the measuremets very well, especially whe take ito the accout the complexity of oliear behavior of the trasformer cores. Table 2 Measured ad calculated curret frequecy spectrum 3/ C 3/0 7-30C 3/ H harmoic meas. avg. model meas. avg. model meas. avg. model % 34.3% 6.7% 5.3% 8.% 4.2% 5 4.0% 29.7% 3.% 0.2% 7.7% 5.4% % 5.3% 5.7% 0.3% 9.2% 3.6% 9 4.4% 0.4% 0.9%.2%.5% 2.9% 7.% 5.6%.6% 0.8% 2.3% 0.6% 3 3.7% 3.9% 0.3% 0.7% 0.8%.4% 5 0.7%.6% 0.% 0.4% 0.2% 0.5% 3/ C 3/2 7-30C 3/ H harmoic meas. avg. model meas. avg. model meas. avg. model 3 3.3% 5.6%.% 4.9% 5.7% 5.4% 5 5.% 3.9% 6.4% 3.3% 7.8% 2.9% 7 8.6% 3.5% 3.9% 2.8% 3.9% 2.7% 9 0.8%.2% 0.7%.3% 0.9%.6% 2.3%.9%.6%.2%.0%.5% 3 0.4% 0.7%.4% 0.5% 0.4% 0.7% 5 0.% 0.6% 0.% 0.7% 0.% 0.9% 4 CONCLSON No load apparet power ca be successfully calculated usig oly two groups of material, HiB ad covetioal, istead of separatio of materials to idividual grades. For lower iductio below.6 T the values of specific apparet power are very close for both groups of material. However, for higher iductace, betwee.6 ad.9 T HiB materials offer much lower (up to five times) apparet power tha covetioal materials. HiB materials also provide lower average deviatio betwee measured ad calculated values, as well as lower dissipatio of results. However, with moder step-lap cores o-load apparet power ad magetizatio curret is ot loger a issue with either HiB or covetioal materials. t has to be metioed that the measured data of curret frequecy spectrum represets average values over the phases ad therefore it is reasoable to have some differeces whe compared to the calculatio. The mathematical oliear model, as a tool, ca be used, but is ot limited to, for magetizig curret calculatio ad spectrum predictio. 5 LTERATRE [] Keleme Frajo, Štrac Leoardo, Berberović Sead. fluece of a Delta-Coected Widig o Magetizig Currets of a Five-Limb Core Power Trasformer. CEM 200 The XX teratioal Coferece o Electrical Machies, Proceedigs, Rome, 200. [] Keleme Frajo, Štrac Leoardo, Berberović Sead. mpact of Geomagetically duced Currets o Magetizig Currets der No-Load Coditios. Proceedigs of the teratioal Colloquium Trasformer Research ad Asset Maagemet-CGRE, Cavtat, 2009.