 Energy and Power Engineering, 2013, 5, 1105-1108 doi:10.4236/epe.2013.54B211 Published Online July 2013 (http://www.scirp.org/journal/epe) Calculation of Eddy Current Loss and Short-circuit Force in SSZ11-50000/110 Power Transformer Yan Li1, Bo Zhang1, Longnv Li1, Tongxun Yang2, Ning Wang2 1Power Transmission Technology Research Institution, Shenyang University of Technology, Shenyang 2TBEA Shenyang Transformer Group Co., Ltd. Shenyang Email: solomon.zb@163.com Received April, 2013 ABSTRACT The method is used in this paper to calculate the leakage magnetic field of SSZ11-50000/110 Power trans-former, and by which the structures’ influences to the main leakage flux are analyzed. Through the combination of the product and TEAM Problem 21B, the surface impedance method shows its great advantage in the calculation of eddy current loss. T Keywords: Power Transformer; Finite Element; Short-circuit Force; Eddy Current Loss; Surface Impedance Method 1. Introduction With the rising of voltage level and transformer capacity , the leakage flux of transformer increased, therefore, the problem of structural part stray loss and short-circuit strength has became one of urgent key technical issues both in transformer companies and operation department. To solve this type of problem, intra-industry corre-sponding standards are already existed, and it changes with the products upgrade. The traditional analytical method cannot analysis the local overheating, short circuit mechanical force withstand capability and three-dimensional spatial distribution of leakage flux which the new standards request. Based on three-dimensional finite element numerical method, the paper introduced transformer design criterion to discuss the leakage flux distribution, short circuit strength, and eddy current loss of transformer, and the fitted engineer-ing design loss calculation numerical method is also pr-oposed [1,2]. 2. Mathematical Model The method which uses scalar magnetic potential and electric vector potential can reduce unknown number and save computer memory when high precision is re-quired. TThe governing equations in eddy zone is 1σε TμT0t(Ω)t  (1) penalty function is introduced, 1σε Tt , then 11σε Tσε TμT0tt()t     (2) 0B, then μ()T0 (3) The governing equations in non-eddy zone is μHs()0  (4) where, Hs is the magnetic field produced by source cur-rent in infinite space, T is electric vector potential,  is scalar magnetic potential, is conductivity, is di-electric constant, σεμ is permeability. The calculation process is treated as follows: 1) According to structural symmetry, the half trans-former model is taken into calculation (as shown in Fig-ure 1); 2) Circulation and eddy current in winding, and eddy current in core is neglected; Using wire winding, and the current density is uniform in the winding. NJIS (5) where J is winding current density, N is winding turns, S is sectional area, I is winding current; *This work was supported by NSFC, under Project 51177103 and Program for LNIRT in University (LT2011002). Copyright © 2013 SciRes. EPE Y. LI ET AL. 1106 3) Material of iron core is according to rolling direc-tion and orthogonal opposite treated. The material of tank, draw plate and clamping part are treated according to each direction same treated. The basic magnetization characteristic curve is used here and hysteresis charac-teristic is neglected. 4) The Newton-Raphson algorithm is used to solve the magnetization characteristic of core silicon steel sheet and tank steel plate for their characteristic are nonlinear relation. 5) The eddy zone produce skin effect, and mesh gen-eration should take current density radial distance. 1f (6) where  is penetration depth, f is frequency,  is conductivity,  is permeability. According to field value some gradient descent discipline to stratify, pene- tration depth chooses 0.22, 0.51, 0.92, 1.6 and 5 times to mesh generation. 3. Field Analysis To analysis short-circuit electromagnetic force, the flux leakage magnetic distribution should be studied first. As shown in Figure 2 that winding average flux den-sity along circumferential distribution, winding end magnetic density is affected by upper and lower iron yok, the inner magnetic density is higher than the outers’. The radiation component Br value is impacted greatly from 24.35mT to 27.8mT. The axis component Bz value varies from 58.4mT to 61.6mT, and both of their two sides are more than that at the middle part. The middle of the winding does not change greatly for its far distant form clamping part and iron yoke. For the anglicizing of the structure eddy current loss, the surface field and eddy current distribution are the emphases. As shown in Figure 3 that the magnetic curve of outer tank side winding end part is bend, and the vortex center is formed for the leakage flux concentrated into the tank surface. tankDraw Plate Pp champing Figure 1. Transformer calculation model. Figure 2. Winding average fl ux density along circumferential distribution. Vo rtex center ble stress requirements g7 Figure 3. The surface of the oil tank eddy current distribu-tion. According to the CIGRE recommended document , the transformer metal structure of local overheating criteria, through calculation, the tank surface magnetic field strength of the tangential component maximum value was 48.22A • cm-1, does not exceed the standard value of 60 A • cm-1, therefore, the additional fuel tank shield is not necessary. 4. Short Circuit Strength The national standard GB1094.5-2008, in the new ver-sion, the allowable stress requirements of .conventional, non - viscous, sticky wire and CTCs (continuous trans-posed conductor) are different from the original design. Now, take average ring stress t1, warping free limit stress cr, the inner winding radial bending stress sav, axial compressive stress act, conductor axial bending stress AL, and wire inclination critical stress _cr tilt for example [3,4] According to the national standard GB1094.2-2008, the first peak of asymmetric short-circuit current is 2kikIU峰 (7) where, i is rated current effective value, kU is short circuit impedance, 2k is peak factor, in this paper Copyright © 2013 SciRes. EPE Y. LI ET AL. 1107the transformer is valued 2.55. According to the Lorenz formula, the winding elec-tromagnetic force can be calculated., The SSZ11-50000/ 110 transformer short-circuit force calculated values and national standard GB1094.5-2008 requirements short- circuit mechanical strength are shown in Table 1. Through calculation, the low-voltage windings of power transformer SSZ11-50000/110 meet the national standard GB1094.5-2008 to withstand short-circuit me-chanical strength requirements. 5. Eddy Current Loss Eddy current density can be calculated by the following formula e(σVt AJ) (8) Eddy current loss 2eeσvpJdv (9) where, Je is eddy current density，pe is Eddy current loss, Ais magnetic vector potential，V is electric scalar po-tential. As shown in Figure 4, the maximum point appears in the main empty path up(down) direction, base on design experience ,the structural overheating criterion is shown in Table 2 Table 1. SSZ11-50000/110 anti short-circuit stability. t1(MPa) cr(MPa) sav(MPa) Calculation value 38.24 11.70 66.01 National standard ≤49 ≤98 ≤126 act(MPa) AL(MPa) tiltcr_(MPa)Calculation value 50 75.51 28.32 National standard ≤80 ≤126 ≤98 inside outside Figure 4. The eddy current loss density distribution of Clamp part. Table 2. Large transformer partial overheat judgment. Structure part maximum loss density / kW·m-3 tank 1800 champ 1800 Through calculation, the highest tank eddy current loss density is 1066.3 kW • m-3. And the clamp part maxi-mum loss density is 2100.5 kW • M-3, which exceed the empirical criterion. Through taking effective measures, the possible overheating is prevented. 6. Surface Impedance Method When eddy current loss in transformer is under calcula-tion, if more structures exists namely the vortex area ac-counts for a larger proportion of the solution domain, it will lead to a large amount of computer memory occu-pied. After taking into the consideration of the skin effect, the refinement of mesh in the penetration depth is also needed. Even using hierarchical subdivision method, a smaller grid is still needed to meet the needs of accuracy. Taking TEAM Problem 21B as an example , the relations of steel plate maximum length and the calcu-lated value eddy current loss is shown as Figure 5. When the maximum length of the element is 5 mm, it will cost one hour to reach the experimental values to meet the precision need, and the method can not be ap-plied in the calculation model because the structure size growth several times which makes the calculation up to tens of hours. When the skin depth is small, the surface of eddy re-gion is regarded as the impedance boundary conditions for solving domain, and the finite element method are still used in other domains that can obviously reduce the problem scale. The surface impedance eddy zone definition 11tstEfjZjH (10) where sZ is surface impedance, is tangential component of electric field intensity, tEtH is tangential component of magnetic field intensity,  is penetration depth. Solid line: the calculated values; dotted line: measured value Figure 5. 21B relations of maximum element length and calculation value. Copyright © 2013 SciRes. EPE Y. LI ET AL. Copyright © 2013 SciRes. EPE 1108 Table 3. Eddy current loss calculation. Unit: W SSZ11-50000/110 transformer problem21Btank champ draw champ Calculation value 9853.9 13054.57 4369.9 8.14 Measured value —— 8.09 After using surface impedance method, the calculation time has been significantly decreased, and the eddy cur-rent loss calculation is shown in Table 3. 7. Conclusions The method is used in this paper to calculate the parameters of SSZ11-50000/110 transformer, and the conclusion can be summarized as follows: T1) The short-circuit mechanical strength meets the new requirements; the tangential component of structure sur-face field is lower than the local overheating criterion. According to the design experience, surface eddy current density of the clamp part greatest is too high, and there is a risk of local overheating, for which the shielding equipment is considered installing in the clamps. 2) The end winding leakage flux along the circumfer-ential distribution is not uniform for the effect of iron yoke. The calculation of the winding end axial magnetic flux density is influenced by structure and should not be ignored when the short-circuit force is calculated. 3) By using hierarchical subdivision method for the calculation of transformer structure eddy current losses is time-consuming and difficult to ensure the accuracy. And using the finite element method of surface impedance boundary can solve this problem effectively. REFERENCES  “Transformer design principle of,” China Electric Power Press.  C. Y. Liu, “Calculation Method and Practice of Trans-former Design,” Liaoning Science and Technology Press.  J. Liu and A. H. Zhang, “Transformer Simulation and Evaluation of Power Winding Short-circuit Dynamic Sta-bility,” Transformer, Vol. 49, No. 6, 2012, pp.14-25.  GB1094.5-2008. Requirements Short-circuit Mechanical Strength  S. M. Yang, Z. G. Cheng and X. Q. Zhu, “The Stray Loss in Steel Measurement Technology,” Chinese Journal of Scientific Instrument.