Power Transformer Winding Thermal Analysis Considering Load Conditions and Type of Oil

Transcription

1 International Journal of Material and Mechanical Engeerg Vol. 1 Iss. 6, November 01 Power Transformer Wdg Thermal Analsis Considerg Load Conditions and Tpe of Oil M.A.Taghihani Department of Engeerg, Imam Khomei International Universit, Qazv, Iran taghihani@iiu.ac.ir Abstract Power transformer outages have a considerable economic impact on the operation of an electrical networ. In order to draw maimum power from transformers and, at the same time, avoid thermal mishaps, it is essential to carefull stud its thermal behavior. Furthermore, an acrate computation of the hottest spot temperature (HST helps a realistic estimation of the reliabilit and remag life of the transformer wdg sulation. This paper presents stead state temperature distribution of a power transformer laertpe wdg usg conjugated heat transfer analsis, therefore energ and Navier-Stoes equations are solved usg fite difference method. Meanwhile, the effects of load conditions and tpe of oil on HST are vestigated usg the model. Oil the transformer is assumed nearl compressible and oil parameters such as thermal conductivit, special heat, viscosit, and densit var with temperature. Comparg the results with those obtaed from fite tegral transform checs the validit and acrac of the proposed method. Kewords Power Transformer; Laer-tpe Wdg; Thermal Analsis; Conjugated Heat Transfer; Fite Difference Method Introduction In a power transformer a part of the electrical energ is converted to the heat. Although this part is quite small comparg to total electric power transferred through a transformer, it causes significant temperature rise, which represents the limitg criteria for possible power transfer through a transformer. That is wh the precise callation of temperatures critical pots (top oil and the hottest solid sulation spot is of practical terest. Thermal impact leads not onl to long-term oil/paper-sulation degradation; it is also a limitg factor for the transformer operation [1], []. Therefore, the nowledge of the temperature, especiall the hottest spot temperature, is of high terest. If the temperature rise goes beond the permissible value, the load of transformer must be reduced or an auiliar transformer is used order to preserve the sulation from deterioration. For an oilimmersed transformer, the oil surrounds the transformer bod. Oil is a nearl compressible fluid and densit changes due to temperature rise, therefore oil moves the transformer. The heat transferred b convection is the most important method of heat transfer. Hottest spot temperature must not eceed the prescribed value order to avoid sulation faults. A hottest spot temperature callation is given the International Standards [3]-[5]. The algorithm for callatg the hottest spot temperature of a directl loaded transformer usg data obtaed a short cirit heatg test is given [6]. Heat transfer theor results from wdg to oil are eposed [7], [8]. In this paper, author has proposed a procedure for obtag the temperature distribution the power transformer and the effects of load conditions and tpe of oil are vestigated usg the model. For this reason energ and Navier-Stoes equations are solved usg fite difference method. Therefore, a code has been provided under MATLAB software. The model can be used for temperature callation on the arbitrar change of rrent and outside air temperature. In the paper, thermal model, energ, and Navier-Stoes equations are given section. Results and disssion of the proposed wor have been provided section 3. Thermal Model Energ equation for Newtonian compressible fluid (or nearl compressible fluid such as oil two dimensions is [9] 108

2 International Journal of Material and Mechanical Engeerg Vol. 1 Iss. 6, November 01 ( V ( C p T V T T ( ( ( C p T (1 Contuit Equation: V V 0 (7 Where T is temperature, V is velocit direction, V is velocit direction, is thermal conductivit, is densit and Cp is special heat of the oil the transformer. In equation (1, oil properties var with temperature [1], [10]-[1]. The temperature dependence of oil properties are given as follows: a a1 ep( ( T 73 C p 4 a a T 3 (3 a a T ( a a T 7 (5 a 9 (6 Momentum Equations:.( V V V V ( (.( V V V ( ( V g ( T T 0 ref V P V ( V P V V V ( (8 (9 Where: is viscosit and is volumetric epansion coefficient. The ne constants for transformer oil and silicon oil have been listed Table 1 [3, 4]. It is generall valid for all tpes of transformer oil that the variation of the oil viscosit with temperature is much higher than the variation of other oil properties [11], [1]. Thus, all oil phsical properties ecept the viscosit can be replaced b a constant. However, the variations of all oil properties with temperature have been considered this paper. TABLE 1 OIL CONSTANTS Oil constant Transformer oil Silicon oil a a a a a a a a a In (1 velocit is unnown, and then we must solve Navier-Stoes equations. Navier-Stoes equations two dimensions for Newtonian compressible fluid are [9] Where P is pressure and g is gravitational acceleration.the heat conduction equation for core and wdgs is written [10]-[1] T T Q 0 (10 Where and are thermal conductivit and directions respectivel. The term Q is the volumetric heat source function and has been modified here to tae care of variation of electrical resistance of copper with temperature. The heat source term Q can be of the form Q Q [1 ( T T ] (11 0 c ref Where c is the temperature coefficient of electrical resistance of copper wire. With this representation, the function Q becomes temperature dependent, distributed heat source. Thermal conductivities are unequal different directions. Thermal conductivit has been treated as a vector quantit, havg components both radial and aial direction. Resultant thermal conductivit of the sstem is [10] K (1 109

3 International Journal of Material and Mechanical Engeerg Vol. 1 Iss. 6, November 01 Where r log r ( 1 1 rn log r1 r3 r log log r rn... n n 1 t ( t t t Term K represents resultant thermal conductivit of sulation and conductor sstem. In this paper, the bottom oil temperature rise over ambient temperature has been callated as I R 1 r l n u fl ( (13 Rl 1 Where u is the bottom oil temperature rise over ambient temperature, fl is the full load bottom oil temperature rise over ambient temperature obtaed from an off-le test; Rl is the ratio of load loss at rated load to no-load loss. The variable Ir is the ratio of the specified load to rated load. I Ir (14 I rated The eponent n depends upon the coolg state. The loadg guide recommends the use of n=0.8 for natural convection and n= for forced coolg. Results and Disssion A code has been provided for fite difference solution of energ and Navier-Stoes equations usg MATLAB 7.1. Figure 1 shows cross section of a 50KVA, 0KV/400V power transformer two dimensions. Dimensions and specifications of the power transformer have been summarized Table. Table 3 shows the power transformer losses. We assume that let oil temperature is the temperature base. Therefore, we have T Tb, oil T 100 (15 T b, oil FIGURE 1 THREE PHASE POWER TRANSFORMER IN TWO DIMENSIONS TABLE DIMENSIONS AND SPECIFICATIONS OF THE PROPOSED POWER TRANSFORMER Core diameter (cm 10 Width of each wdow (cm 1 Height of wdow (cm 8 Thicness of LV wdg (cm 1. Thicness of HV wdg (cm Rated power HV voltage LV voltage 50KVA 0V 400V HV rrent 1.44A LV rrent 7A TABLE 3 POWER TRANSFORMER LOSSES Losses (w Value Core 158 DC of LV wdgs 384 DC of HV wdgs 534 Edd rrents of LV wdgs 64 Edd rrents of HV wdgs - Where Tb,oil is the bottom oil temperature. Figure shows temperature distribution from LV wdg (ais smmetr height direction one per unit (p.u. load with oil natural coolg (ON. It can be poted out that for LV wdg, maimum temperature location is around 80% of wdg height 110

4 HST( C HST rise over bottom oil temperature(% HST rise over bottom oil temperature(% HST rise over bottom oil temperature(% International Journal of Material and Mechanical Engeerg Vol. 1 Iss. 6, November 01 from the bottom and at about 50% of radial thicness of the laer. Temperature distribution from HV wdg has been shown figure 3. It can be observed that the maimum temperature ocrs the neighborhood of 55% of the aial and 50% of the radial thicness of the laer. Figure 4 shows HST rise over bottom oil temperature versus load for two tpes of oils and figure 5 shows HST versus load at Tamb=5(C Transformer oil Silicon oil Load(p.u Height of LV wdg(m FIGURE TEMPERATURE DISTRIBUTIONS IN HEIGHT DIRECTION OF LV WINDING WITH TRANSFORMER OIL NATURAL COOLING Height of HV wdg(m FIGURE 3 TEMPERATURE DISTRIBUTIONS IN HEIGHT DIRECTION OF HV WINDING WITH TRANSFORMER OIL NATURAL COOLING FIGURE 4 HST RISE OVER BOTTOM OIL TEMPERATURE VERSUS LOAD AT Tamb=5(C WITH OIL NATURAL COOLING It can be poted out from figures 4 and 5 that the HST value is low when the transformer oil is used for coolg, therefore the transformer oil is better than silicon oil the coolg of the power transformer when load changes. Table 4 shows comparison of the proposed method with fite tegral transform used [10] for power transformer oil. HST locations at different loadg are given Table 5. TABLE 4 HST (C MAGNITUDES AT Tamb=5(C Load (p.u. Proposed Analtical [10] Transformer oil Silicon oil Load(p.u. FIGURE 5 HST VERSUS LOAD AT Tamb=5(C WITH OIL NATURAL COOLING Reference [10] has proposed an analtical method based on boundar value problem of heat conduction power transformer wdg usg fite tegral transform techniques. This technique uses Fourier transform and Hanel transform and fds 111

5 International Journal of Material and Mechanical Engeerg Vol. 1 Iss. 6, November 01 temperature based on polnomials with fite order (sequential series of space variables and time, and then approimates temperature with fite order. Analtical method [10] is suitable for cldrical wdg with rectangle cross-section, but this limitation is not for fite difference method. In the other hand, if we assume that we can crease order of polnomial, solution time will rise and analtical method will not differ with numerical method. Load (p.u. TABLE 5 HST LOCATIONS AT Tamb=5(C Proposed (radial thicness%-height% Analtical [10] (radial thicness%- height% / / / / / / / / / / / / / / / / / / / / 55.5 Conclusion A numerical stud was conducted to vestigate temperature distribution laer-tpe power transformer for a variet of load conditions and tpe of oil. Heat transfer partial differential equations were solved numericall with fite difference method. The heat source function has been taen as temperature dependent and has been directl corporated the heat conduction equation for core and wdgs. The purel numerical approach followed this paper seems to correspond reasonabl well with results of analtical callations [10]. In addition, it can be poted out that transformer oil is better than silicon oil coolg of the power transformer when load changes. ACKNOWLEDGEMENTS The fancial support b the Imam Khomei International Universit, Iran, under grant no for the wor is gratefull acnowledged. Nomenclature Cp : specific heat of oil (J.g -1.K -1 g: gravitational acceleration (m.s - Ir: ratio of the specified load to rated load : thermal conductivit of oil (W.m -1.K -1 K: equivalent thermal conductivit (W.m -1.K -1 : thermal conductivit of copper (W.m -1.K -1 : thermal conductivit of sulation (W.m -1.K -1 : thermal conductivit direction (W.m -1.K -1 : thermal conductivit direction (W.m -1.K -1 n : temperature rise eponent due to bottom oil P: pressure (N.m - Q : volumetric heat source function (W.m -3 Q0: reference volumetric heat source (W.m -3 ri s : radius of sulation and conductor laers (m Rl : loss ratio = load loss/no load loss T: temperature (K Tref : reference temperature (K Tb,oi : bottom oil temperature (K t: thicness of conductor (m t : thicness of sulation (m V: velocit direction (m.s -1 V: velocit direction (m.s -1 Abbreviations HST: hottest spot temperature HV: high voltage LV: low voltage ON: oil natural coolg p.u.: per unit Gree smbols : coefficient of volumetric epansion of oil (K -1 u : bottom oil temperature rise over ambient temperature (K fl: bottom oil temperature rise over ambient temperature at rated load (K : densit of oil (g.m -3 0: reference densit of oil (g.m -3 c : temperature coefficient of electrical resistance (K -1 : viscosit of oil (g.m -1.s -1 11

6 International Journal of Material and Mechanical Engeerg Vol. 1 Iss. 6, November 01 REFERENCES [1] L. W. Pierce, An vestigation of the thermal performance of an oil filled transformer wdg, IEEE Transactions on Power Deliver, 7(3, (199 pp [] L. W. Pierce, Predictg liquid filled transformer loadg capabilit, IEEE Transactions on Industr Applications, 30(1, (1994 pp [3] IEC Standard, IEC (006 "Loadg guide for oil immersed transformers". [4] IEEE Standard, C (1996 "IEEE guide for loadg meral oil immersed transformer". [5] IEEE Standard, (000 "IEEE guide for determation of maimum wdg temperature rise liquid-filled transformers". [6] Z. Radaovic, K. Feser, A new method for the callation of the hot-spot temperature power transformers with ONAN coolg, IEEE Transactions on Power Deliver, 18(4, (003 pp [7] G. Swift, T. Molsi, W. Lehn, R. Bra, A fundamental approach to transformer thermal modelg Part I: Theor and equivalent cirit, IEEE Transactions on Power Deliver, 16(, (001 pp [8] W. H. Tang, O. H. Wu,Z. J. Richardson, Equivalent heat cirit based power transformer thermal model, IEE Electric Power Application, 149(, (00 pp [9] F. P. Incropera, D. P. DeWitt, Fundamentals of heat and mass transfer, 4th edition, New Yor/USA: J. Wile & Sons, [10] M. K. Pradhan, T. S. Ramu, Prediction of hottest spot temperature (HST power and station transformers, IEEE Transactions on Power Deliver, 18(4, (003 pp [11] M. A. Taghihani, A. Gholami, Temperature Distribution Power Transformer Wdgs with NDOF and DOF Coolg, PES General Meetg, Pittsburgh, PA, USA, 0-4 Jul, 008. [1] M.A.Taghihani, A.Gholami,"Estimation of hottest spot temperature power transformer wdgs with oil natural coolg", Australian Journal of Electrical and Electronics Engeerg (AJEEE, 6(1, (009 pp Author Introduction Mohammad Ali Taghihani was born Tehran, Iran, He received the B.Sc. and M.Sc. degrees electrical engeerg from Amirabir Universit of Technolog, Tehran, Iran, 1997 and 000, respectivel. He received the Ph.D. degree electrical engeerg from Iran Universit of Science and Technolog, Tehran, Iran, 008. He was with the falt of Azad Universit, Tehran, Iran for 8 ears. He is rrentl an assistant professor and with the falt of Imam Khomei International Universit, Qazv, Iran. His terests are power sstem, numerical analsis, fite element and fite difference method, heat transfer and fluid mechanics. 113