International Power, Electronics and Materials Engineering Conference (IPEMEC 2015)

Transcription

1 International Power, Electronics and Materials Engineering Conference (IPEMEC 2015) Calculation of Stray Losses and Temperature Distribution in Power Transformer Using Coupled Electro-Termal Field Analysis Xiuke Yan 1, a, Xiangdong YU 2, b, Min Sen 3, c 1 Scool of Electrical Engineering, Senyang University of Tecnology, Senyang, , Cina 2 Scool of Electrical Engineering, Senyang University of Tecnology, Senyang, , Cina 3 Scool of Electrical and Information Engineering, Jiangsu University, Jiangsu, , Cina b @qq.com Keywords: Electro-Termal Coupling; Stray Losses; Temperature Distribution; Power Transformer Abstract. In order to calculate stray losses and predict temperature distribution as accurately as possible in power transformer tank walls and oter mental constructive parts, an analysis metod of te electro-termal coupling is presented. TEAM Problem 21 (P21-B, P21 a -2, P21 c -M1) are adopted to verify te validation of te stray losses calculation by MagNet FEM software, sowing tat te calculation results are in good agreement wit measured results. Ten, taking te material properties affected by temperature into consideration, te two-way coupling analysis metod is used to te calculation of stray losses and temperature distribution in power transformer. Introduction In te design of large power transformers, it is very important to determine as accurately as possible te amount and space distribution of stray losses due to leakage of flux, occurring in te winding and oter metal parts. Many researcers and transformer manufacturers ave proposed different analysis metods to calculate and reduce te stray losses in flitc plates, frames, and tank walls for eliminating te local overeating and efficiency decreasing [1][2][3][4]. Most transformer manufacturers still use te semi-empirical formulae to calculate stray losses and predict te maximum temperature rise. However, tese metods are too oversimplified so tat te results are inaccurate, or based on empirical tecniques wit questionable validity. Due to te complicated construction of power transformers, te stray losses in structural parts of power transformers, especially for te concentration regions of eddy current wic are induced by leakage field, may cause local overeating. Most of te power transformers are strongly restricted by termal regulation specifying ot-spot temperature inside te transformer tank [5]. Terefore, it is essential to predict tose temperature rises accurately and take some measurements to reduce te eddy current losses and eliminate te ot spots. Based on electro analytical formulation linked wit termal finite element metod, Paper [6] proposed 3-D metodology for te eating azard assessment on transformer covers. Taking account of te temperature dependence of te eat transfer coefficient and of te conductivity, te paper [7] establised a strong coupling between te termal and electro equations to calculate eddy loss and predict temperature distribution of busing adapters in tree-pase generator step up transformer. In tis paper, taking te material properties affected by temperature into consideration, te electro-termal coupling analysis for te temperature rise prediction in power transformer structural parts is adopted. Tis strong coupling analysis metod is able to improve te calculation accuracy and give important guiding suggestions for reducing eddy current losses and avoiding local overeating. Metod Description and Simulation Model To determine stray losses, a full tree-dimensional (3D) finite-element-metod (FEM) analysis Te autors - Publised by Atlantis Press 317

2 of te power transformer is required. Te tree-pase five column transformer simulation model of OSFPS9-360MVA/330GY is sown in Figure1. MagNet FEM software, wic as a time-armonic analysis modular, is used to calculate te stray losses by T Ω metod. Tis coupling analysis as two steps. Firstly, te stray losses of electro model sould be calculated to obtain te eat source. Next, te termal model is solved wit te eat source obtained from electro analysis. Considering te material properties affected by temperature, suc as: eat transfer coefficient, te conductivity and te curve of B-H or B-W, eat sources are recalculated according to flow cart of coupled metod iteratively in Figure2. Start Electro Field Slover Transformer Geometry and Model Material Properties Boundary Condition Mes Power Losses Calculation Material Properties Boundary Condition Temperature Rise Prediction Termal Field Slover Fig.1. One-eigt of te simulation model Update Solutions Properties N Temperature Rise<Ɛ Y Fig.2. Flow cart of Electro-Termal coupling field analysis End Electro Analysis Considering te effect of displacement current, T Ω metod is adopted to calculating te stray losses in metal structural parts of power transformer. 1 E = σ + ε T t (1) Governing equation in eddy domains 1 σ + ε T + µ ( T Ω ) = 0 t t (2) According to B=0, we can get: µ ( T Ω ) = 0 (3) Governing equation in no eddy region include iron core, non-conductive parts and current source region µ ( H s Ω ) = 0 (4) Te stray losses in metal structure parts of power transformer include eddy current loss P e and ysteresis loss P. Te calculation of eddy current loss and ysteresis loss are respectively sown as equation (5) and (6). J J J0rms J0rms Pe = dv = dv s s (5) J represents current density and J 0 is vector, related to J. σ is electrical conductivity of metal parts. Owing to te ysteresis lossw is treated to be as a function of te peak value of te flux density B [9], te ysteresis loss will be calculated by: m 318

3 i ( ) N() i () i () = = m i= 1 P W W B ρvi () (i) W denotes te dc ysteresis loss (W/kg), density of te steel plate, (i) elements. P= P + P e (i) Bm (6) is te peak value of te flux density, ρ is te V is te volume of an element, and N( i) A. Verified wit TEAM Problem 21 (P21-B, P21 a -2, P21 c -M1) is te total number of (7) (a) Te Front view (b) Te Left view (c) Te curve graps of B x Fig.3. Compare te value of measured B x wit te calculated in specific locations in P21-B model And oter results of Team Problem 21 models are listed in Table I: TABLE I COMPARISON OF COMPUTATION RESULT OF STRAY LOSS IN TEAM PROBLEM 21 (UNIT: W) Measured Calculated Eddy Loss Hysteresis Relative Model results [8] Total Losses Loss Error (%) P21-B % P21 a % P21 c -M % B. Te Results and Analysis of Simulation Model In Figure 4 we know tat sielding on tank walls may absorb te leakage flux, and cange te route of leakage flux. Compared wit tank walls witout sielding in Figure4(a), te maximum flux density decrease 0.05T in Figure4(b). Eddy current density distribution in tank walls is more uniform in Figure5 (b) tan in (a), but, te sielding may cause oter ot spots in mental parts. (a) Tank walls witout sielding (b) Tank walls wit sielding Fig.4.Te flux density distribution of te tank walls (a) Tank walls witout sielding (b) Tank walls wit sielding Fig.5.Te arrow plot of eddy current density distribution of te tank walls In order to block te concentration of eddy current and eliminate ot spots in tie-plate, slotting is adopted in Figure 6. Te concrete results are listed in Table II. 319

4 Fig.6.Te arrow plot eddy current density distribution of te tie-plate and yoke clamping TABLE II COMPARISON OF COMPUTATION RESULT IN SIMULATION MODEL Mental structure parts Tank walls Yoke Clamp Tie-plate Witout sielding Wit sielding Witout sielding Wit sielding No slot Two slots Loss density/(w/m 3 ) Eddy current loss/(kw) Hysteresis loss/(kw) Stray losses /(KW) Termal Analysis According to te teories of eat transfer, eat transfer process are carried out by eat conduction(referred to as termal conductivity), convection eat transfer and radiation eat transfer eat excanger tree basic forms of complex formed [10]. Te eat source can be obtained from electro analysis by MagNet FEM software, wic would be coupled wit TermNet FEM analysis as follows. A. Governing equation: T k T = Q+ρc t (8) Were k is te termal conductivity, Q is te eat flux density(w/m 3 ), ρ is te density (kg/m 3 ), c is eat capacity(w/m ), T is te specific temperature( ) for boundary condition. ( k T) n= q+ qc + qr (9) And q is te eat flux flow out of te system, q c and q r are te eat flux produced by convection eat transfer and radiation eat transfer, respectively. qc = c( T)( T Te) (10) 4 4 qr = r( T)( T Te ) (11) Were c (T) is te convection eat excange coefficient; r (T) is te radiation eat excange coefficient; T e is te ambient temperature. B. Heat Transfer Coefficient k = Nu δ (12) 2 1/ Ra Nuv = /16 8/ Pr (13) 1/4 Nu = 0.27Ra (14) 320

5 Were is eat transfer coefficient andδis caracteristic lengt(m). Respectively, Nu v and Nu are Nusselt number of vertical plane and Nusselt number of orizontal plane, and Ra and Pr represent Rayleig number and Pandtl number, respectively [5]. C. Temperature distribution in te structural parts Te predicted temperature distribution on te surface of mental parts in te power transformer by te coupled analysis metod is sown in Figure7, wic sows tat ot-spot temperature rising up to 116.3, Te specific ambient temperature is 25, and te temperature rise is near 91K. Terefore, it is essential to take some measurements to lower te maximum temperature rise. As seen in Figure 8, slotting on te tie-plate enable te igest temperature below 100 in te yoke clamp and tie-plates. Fig.7. Temperature distribution in te mental structural parts of transformer Fig.8.Temperature distribution in te yoke clamp and tie-plate wit two slotting Te temperature distribution of te outside surface of tank walls reaced 98,it may cause overeating azard during te operation, sown in Figure 9(a). From te Figure 9(b), we can see te igest temperature rise lower to 59.8,wen te sielding is adopted. (a)tank walls witout sielding (b) Tank walls wit sielding Fig.9. Temperature distribution in te outside surface of transformer 321

6 Conclusion Based on te two-way electro-termal coupling analysis metod, te total stray losses in structural parts of power transformer are calculated as eat source. Considering te conductivity and eat transfer coefficient affected by temperature, te calculation of stray losses and temperature rise distribution in power transformer mental parts are more accurate. Tank walls wit sielding and slotting on te tie plate can reduce stray losses significantly and eliminate ot spots. Terefore, te proposed metod is considered to be available and could be adopted in te termal design of power transformers. Acknowledgement Tis work was supported by Senyang Power Transformers of TBEA CO., LTD. References [1] Lenart Kralj, Damijan Miljavec, Stray losses in power transformer tank walls and construction parts, XIX International Conference on Electrical Macines - ICEM 2010, Rome. [2] Livio Susnjic, Zijad Haznadar, Zvonimir Valkovic, 3D finite-element determination of stray losses in power transformer [J], Electric Power Systems Researc.2008:78, [3] Maxym V. Ostrenko, Olexandr L. Tarcutkin, Bogdan Y. Andriienko, Power Transformers and Reactors Stray Losses and Temperatures Calculation Using Coupled IEM and FEM Tecnique, IEEE Region 8 SIBIRCON Irkutsk Listvyanka, Russia, 2010: [4] S.V. Kulkarni, J.C. Olivares, R. Escarela-Perez, V.K. Lakiani and J. Turowski. Evaluation of eddy current losses in te cover plates of distribution transformers [J]. IEE Proc.-Sci. Meas.Tecnol. 2004: 151(5). [5] Hyun-Mo An, Byuk-Jin Lee, and Sung-Cin Han, An Efficient Investigation of Coupled Electro-Termal-Fluid Numerical Model for Temperature Rise Prediction of Power Transformer, International Conference on Electrical Macines and Systems(ICEMS),Beijing, 2011,1-4. [6] Xose M. López-Fernández, Patricia Penabad-Durán and Janusz Turowski. 3-D Metodology for te Heating Hazard Assessment on Transformer Covers. XIX International Conference on Electrical Macines - ICEM 2010, Rome. [7] Kurt Preis, Oszkár Bíró, Gerard Bucgraber, and Igor Ticar. Termal-Electro Coupling in te Finite-Element Simulation of Power Transformers [J]. IEEE TRANSACTIONS ON MAGNETICS. 2006:42(4). [8] Z. Ceng, R.Hao, Norio Takaasi. Engineering-Oriented Bencmarking of Problem 21 Family and Experimental Verificationp [J]. IEEE Trans. on Magn. 2004:40( 2): [9] Ziguang Ceng, Norio Takaasi, Sumei Yang. Loss Spectrum and Electro Beavior of Problem 21 Family [J]. IEEE TRANSACTIONS ON MAGNETICS. 2006:42(4). [10] Ceng Ziguang, Norio Takaasi, Bezad Forgani. Electro and Termal Field Modeling and Application in Electrical Engineering [M]. Beijing: Science Press,