Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 Analysis of Stray Losses in Power Transformers by 3-D Magnetic Field Simulation Chetan C. Adalja, M.L. Jain, Technology Department, EMCO Limited, Thane, India Abstract—Transformer is a vital link in the power system, which is connected in the network at different stages right from the generating station to the user’s premises. The T&D losses in the Indian power system ranges from 10-50%, which is significantly high. In this, the contribution of transformers exceeds 6% of the total power generated. Although the transformer is the most energy efficient equipment in the system, yet it would be expedient to make an attempt to further reduce the losses in it to improve the overall system efficiency. In this context, a case study was undertaken to analyze various components of stray losses in power transformer and assess the scope for their optimization. The load losses in the transformer consist of I2R & stray losses. In large rating transformer, the stray losses constitute about 20-25% of the total load losses. Designers adopt various cost-effective measures to minimize the losses and make the transformer more efficient. These losses could be controlled to a level of 8-10% by means of magnetic shunts judiciously placed so as to canalize the leakage flux. However optimum location of these shunts calls for accurate knowledge of 3-D flux mapping. Some of the commercially available software programs support 3-D field simulation studies for estimation of stray losses with fairly good accuracy. Depending on the accuracy requirement, these programs could be exploited to a varying degree to achieve the desired results. This paper presents a case study involving estimation of stray losses in a 100 MVA, 220/66/11 kV system transformer using an Integral Equation Method (IEM) and Finite Element Method (FEM) based EDMAG-3D software program. To present a comprehensive picture of total stray losses, the winding stray losses due to axial and radial magnetic fields are also calculated using 2-D programs. II. CASE STUDY Accurate estimation of stray losses at design stage is a prerequisite for a cost-effective and reliable design of transformer. Towards this, a case study was carried out on a 100 MVA, 220/66/11 kV system transformer with S.C. impedance at maximum, normal and minimum tap positions of 10.46%, 10.20% and 10.04% respectively and load losses of 245 kW (at normal tap) involving 3-D magnetic field mapping and estimation of stray losses. As a first step, stray losses in the transformer were estimated by to-the-scale modeling of transformer and 3-D field mapping for a standard design. Moreover, the influence of shunt dimensions and edge stack construction in two halves on stray losses was also studied. The solution to the problem was attempted by plotting the 3-D magnetic field on both HV & LV sides. Fig. 1 below shows the modeled HV side 3-D geometry using software program. Similarly, the LV side geometry is modeled and analyzed. I. INTRODUCTION The stray losses in a transformer comprise winding stray losses, viz. eddy loss and circulating current loss; the loss in the edge stack (smallest packet of the core limb); and the loss in structural parts, viz. frame, flitch plate and tank. Core loss at the impedance voltage being insignificantly low, is not considered in the present analysis. In case of large generator transformers, stray losses due to high current carrying leads also become significant. As the total stray losses with shielding measures in large rating transformers are of the order of 20-25% of the total load losses, it is imperative to estimate stray losses accurately as control over these gives a competitive advantage. Measures like using judiciously designed magnetic shunts help reduce the stray losses effectively [1]. The estimation of stray losses in structural parts of transformer at design stage is generally carried out by using empirical formulae covering wide range of design variants and complicated asymmetrical geometries. These formulae therefore inherently suffer form unpredictable inaccuracies, which would be actually known only at final testing stage. However, with the availability of high speed and accurate computational tools and software programs [2] it is possible to simulate complex geometries for 3-D electromagnetic fields mapping and precise estimation of stray losses at drawing-board stage. Fig. 1. Modeled HV side geometry of Transformer III. METHODOLOGY The software tool, based on Integral Equation Method (IEM) and Finite Element Method (FEM) is used for stray losses analysis. This involves estimation of 3-D magnetic field intensity (H, A/m) and induction (B, Tesla) together with the eddy current losses in the structural parts and the resultant temperature rises. It calculates values of the magnetic field quantities at pre-defined locations in space, as a sum of field created by the current sources (windings, leads) with specified distribution of current using BiotSavart law and the field created by the fictitious magnetic charges on the interface of magnetic and nonmagnetic media (to account for ferromagnetic magnetization) using algebraization of integral equations. The complete transformer, comprising Core, Windings, Frames, Flitch plates, Tank, Wall shunts and the epures (pre-defined line on which magnetic field values are computed in all 3-directions) is modeled for stray losses estimation. The field quantities obtained at these epures are used for estimation of stray losses. 498 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 Table I & II show these values at normal and extreme tap positions on HV and LV side tank respectively. IV. ESTIMATION OF STRAY LOSSES TABLE I MAGNETIC FIELD STRENGTH ON HV SIDE TANK SURFACE Magnetic field Intensity Seff Mode (HV Side), A/m (mm2) Heff, Heff_w Hmax Max. Tap 414 501 1601 48.63 Nor. Tap 607 743 2455 48.63 Min. Tap 644 795 2846 48.63 This section explains the modeling of transformer geometries and estimation of stray losses in structural parts, viz. tank, wall shunts, frames, flitch plates and edge stack. The losses in different structural parts of transformer are computed as follows. A. Estimation of stray loss in Tank The tank is made of mild steel having a nonlinear permeability. The software tool first calculates the magnetic field value at the tank surface by decoupling the effect of nonlinearity. After estimation of the magnetic field, losses are calculated considering nonlinearity by an iterative estimation of coefficient of the tank influence factor. The geometry of the tank is modeled by slicing it at different heights and then connecting these levels using vertically defined epures. Fig. 2 shows the local coordinate system of the tank depicting the horizontal and vertical epures. TABLE II MAGNETIC FIELD STRENGTH ON LV SIDE TANK SURFACE Magnetic field Intensity Seff Mode (LV Side), A/m (mm2) Heff, Heff_w Hmax Max. Tap 422 478 1447 43.76 Nor. Tap 620 710 2337 43.76 Min. Tap 649 739 2453 43.76 The stray losses in tank computed from the above magnetic field intensity values are presented in Table III below. TABLE III STRAY LOSSES IN TANK Stray loss, kW Mode HV Side LV Side Max. Tap 6.54 7.06 Nor. Tap 6.48 7.00 Min. Tap 5.48 6.47 Total 13.60 13.48 11.95 The above trend of stray losses in tank follows the leakage impedance pattern. B. Estimation of stray loss in Wall Shunts Shunts are made of CRGO material and modeled as ferromagnetic bodies with linear permeability. The wall shunts modeled on HV side of transformer tank are shown in Fig. 1 above. The total 7 wall shunts are provided (viz. 3 on HV side, 3 on LV side and 1 on side wall) to reduce tank stray losses. The epures are pre-defined at HV & LV side wall shunts locations to estimate stray losses. Fig. 4 below shows the plot of the modulus of flux density components (Bx, By, Bz) along the height of the shunts (opposite to the winding on LV side at central phase) for normal tap position. The curves A, B & C indicate the components of flux density, i.e. normal, along the width and the height of the shunt respectively. Fig. 2. Local co-ordinate system for modeling of tank Fig. 3 below shows the variation of the modulus of flux density components (Bx, By, Bz) along the height of the tank surface (on HV side) opposite to the winding axis of central phase and considering all wall shunts in place. Fig. 3. Flux density variation on the HV Side tank surface at central phase (opposite to winding axis) In order to compute losses in the tank it is necessary to obtain the values of Heff, Heff_w, Hmax and Seff. Where, Heff: effective tangential magnetic field strength on the tank surface (A/m); Heff_w: effective tangential magnetic field strength (opposite to the winding axis) on the tank surface (A/m); Hmax: maximum tangential magnetic field strength on the tank surface (A/m) & Seff: loss emission area (mm2). Fig. 4. Flux density profile in shunts placed on LV side of tank wall For computation of stray loss in the shunts, it is necessary to obtain values of B1, B2, L1 and L2 as represented by notations in Fig. 4. The peak values of magnetic field at normal tap position for first triangle is 0.01035T (B1) with base 1025mm (L1) and second triangle is 0.01054T (B2) with base 1645 mm (L2) respectively. 499 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 The stray loss values in shunts, estimated based on above magnetic field values, are indicated in Table IV below. Mode Max. Tap Nor. Tap Min. Tap TABLE IV STRAY LOSSES IN SHUNTS Stray loss, kW HV Side LV Side Side Shunt 0.78 2.51 0.54 1.38 2.54 0.36 0.76 1.47 0.25 typically at normal tap position, obtained for top and bottom frame are as under. See Table V. TABLE V MAGNETIC FIELD CONCENTRATION IN FRAMES Magnetic field (B), T Top Frame Bottom Frame Maximum value (B1) 0.00744 0.02022 Minimum value (B2) 0.00032 0.00139 Total 3.83 4.28 2.48 It is observed that the stray loss values in HV side shunts are lower than those on LV side due to their smaller height and larger distance from the outer most winding. C. Estimation of Stray Loss in Frames Frames, also called yoke beams, are made of mild steel material and are used for clamping of yokes and supporting the windings. The frames are modeled as epures coinciding with their physical locations for magnetic field plotting and estimation of losses. Fig. 5 & 6 below show the plots of the modulus of flux density components (Bx, By, Bz) in top & bottom frames along the height of the frame (from bottom to top) on the HV side of the transformer at normal tap position. For estimation of loss in the frames, it is essential to obtain the maximum and minimum values of flux densities occurring along the height of the frames, which is represented by notations B1 & B2 in Fig. 5 & 6. The field concentration in the bottom frame is over 2.7 times of that in top frame. This is attributed to lesser distance between the winding bottom edge and the bottom frame. Similarly, the maximum and minimum field values are obtained for top and bottom frames both for HV and LV sides of transformer at extreme tap positions. The loss in the frames calculated from magnetic field values is as shown in Table VI below. Mode Max. Tap Nor. Tap Min. Tap TABLE VI STRAY LOSS IN FRAMES Stray loss, kW Top Frame Bottom Frame 0.98 1.74 0.82 1.43 0.58 1.24 Total 2.72 2.25 1.82 The loss in the bottom frame, which is higher as compared to the top frame, is commensurate with the higher flux concentration in the bottom frame. D. Estimation of Stray Loss in Flitch Plates Flitch plates, made of MS and with slots at top and bottom positions are used in the present case. The flitch plates are 200 mm wide and 12mm thick modeled to the scale, taking care of the slots and analysis carried out using FEM technique. It is important to note that the stray losses in such structural elements are quite low but the incident magnetic field on them can be quite high for the exposed area leading to unacceptable local hot spots. Fig. 7 & 8 shows the vector plot of eddy current density J (A/m2) and temperature rise profile (K) from minimum to maximum value differentiated by a colour band from blue to red, red being the highest. Fig. 5. Flux density variation along the height of the Top Frame Fig. 7. Vector plot of current density J (A/m2) in Flitch Plate Fig. 6. Flux density variation along the height of the Bottom Frame It is observed that owing to the proximity effect, the maximum flux density occurs in the bottom part of top frame and the top part of bottom frame. The maximum and minimum values of flux densities, The magnetic field impinging on flitch plates induces eddy currents. The eddy current loops are shown in both solid and slotted regions in Fig. 7. The magnitude of normal flux density being the highest at top and bottom winding edges, it results in higher losses and hotspots in those regions of the flitch plates. In order to avoid such situations, the slots are provided in the flitch plates at both top and bottom locations. 500 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 normal tap position on the HV side of the transformer. The curves A, B and C indicate the component of flux densities normal to the edge stack, along the width of edge stack and along the height of edge stack respectively. As the magnitude of normal magnetic flux density is higher at the top and bottom winding edges, Fig. 9 represents first and second triangle with peak value flux densities 0.04270T & 0.04422T respectively (at winding edges) along the height of edge stack. The length covered by first and second triangle is represented by notations L1 & L2 in Fig. 9 is 635 & 710 mm respectively and distance between the peaks of two triangles represented by notation L12 in Fig. 9 is 1544 mm. Based on the magnetic field and eddy current density, the losses are calculated for principal and extreme tap positions in the flitch plates as shown in Table VII below. TABLE VII STRAY LOSS IN THE FLITCH PLATES Mode Stray loss, kW Max. Tap 0.65 Nor. Tap 0.62 Min. Tap 0.52 Fig. 8. Temperature profile in Flitch Plate The temperature profile in the flitch plate is estimated by specifying heat transfer co-efficient and using 3-D FEM. Well, in absolute terms, the stray losses in flitch plates may not form a significant part of the total losses of the transformer [3]. Nevertheless, it deserves designer’s attention as it could cause abnormal local hotspot rise in the flitch plates, and that in-turn disintegration of oil in the close vicinity, and consequential generation of fault gases, which could be misconstrued as fault / defect in the transformer. The effect of using non-magnetic material (stainless steel) for flitch plate with following combination of slots was studied and the results obtained are shown in Table VIII below. a) Flitch plate without slot b) Flitch plate with slots at top and bottom c) Flitch plate with slot(s) throughout winding height Fig. 9. Flux density variation along the height of the Edge Stack TABLE VIII STRAY LOSS IN FLITCH PLATE WITH DIFFERENT DESIGNS Stray loss, kW MS Plate SS Plate SS Plate SS Plate with Mode with slots at without with slots at slot(s) top & slot top & throughout bottom bottom winding height Max. Tap 0.65 1.416 0.485 0.291 Nor. Tap 0.62 1.324 0.458 0.286 Min. Tap 0.52 1.248 0.425 0.252 From the above, it is observed that for a given design of flitch plate, a) Loss in SS plate without any slot is the highest b) Loss in SS plate with slots at top and bottom is about 26% less than that with MS plate c) Loss in SS plate with slot(s) throughout the winding height is about 54% less than that with MS plate E. Estimation of stray loss in Edge Stack Stray loss in edge stack occurs due to flux impinging normally (radially) on the outermost packet of the core. For estimation of stay loss in edge stack it is essential to compute the 3-D magnetic field values along & across the height of the edge stack. Fig. 9 & 10 below show the plots of the modulus of flux density components (Bx, By, Bz) along and across the height of edge stack respectively, at Fig. 10. Flux density variation across the height of the Edge Stack at top winding edge position The average value of magnetic field across the length of edge stack is computed from Fig. 10. The maximum and minimum value of magnetic field at top winding edge position across the edge stack, represented by notations Bm1 & Bm2 in Fig. 10, is 0.07285T & 0.04379T respectively. Similarly, the maximum and minimum value of magnetic field at bottom winding edge is also obtained. These magnetic field values are estimated for all phases at principal & extreme tap positions on both HV & LV sides of transformer. The stray loss based on above magnetic field values estimated in edge stack is shown in Table IX below. 501 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 respect to the windings, type and material. In the present case study, the height of magnetic wall shunts was increased by 645 mm on HV side of tank wall to attract larger chunk of the leakage flux entering the tank and the results obtained with above modification are shown in Table XII below. TABLE IX STRAY LOSS IN EDGE STACK Mode Stray loss, kW Max. Tap 4.90 Nor. Tap 5.40 Min. Tap 4.38 F. Total stray load losses The stray losses in winding i.e. eddy losses are also measured as part of total stray losses during testing and are practically inseparable; hence same are calculated through another 2-D package and added to the structural losses to get the total stray losses. The total stray losses in all structural parts and windings are computed at normal and extreme tap positions and the details are as summarized in Table X below. Sr. No. 1 2 3 4 5 6 TABLE X TOTAL STRAY LOAD LOSSES IN TRANSFORMER Component Stray losses, kW Max. Tap Nor. Tap Min. Tap Tank 13.60 13.48 11.95 Shunts 3.83 4.28 2.48 Frames 2.72 2.25 1.82 Flitch Plates 0.65 0.62 0.52 Edge Stack 4.90 5.40 4.38 Winding eddy losses 27.67 27.03 21.86 Total Stray + Eddy losses 53.37 53.06 43.02 TABLE XII COMPARISON OF ESTIMATED TANK LOSS WITH MODIFIED SHUNT Reduction in Tank stray loss, kW Mode loss (%) Standard Shunt Modified Shunt Max. Tap Nor. Tap Min. Tap 13.60 13.48 11.95 12.13 11.68 10.59 It is observed that increase in shunt height results in reduction in the tank loss significantly. This in turn does have the effect of increasing the loss in the shunts, which is marginal and hence ignored while reporting the total stray losses with modification. B. Modification in Edge Stack In large transformer, the radially incident flux may cause considerable eddy current loss in the edge stack, resulting in abnormal local hot spots, thereby increasing the risk of bubbling of oil in the local vicinity. Effect of division of the edge stack on the stray loss was studied and the estimated results are reported in Table XIII below. Distribution of component stray losses, calculated as percentage of the total stray load losses at normal tap position is represented in Fig. 11 below. Mode Max. Tap Nor. Tap Min. Tap TABLE XIII COMPARISON OF LOSS IN EDGE STACK Reduction in Edge Stack stray loss, kW loss (%) Standard design Modified design 4.90 2.18 55.51 5.40 2.57 52.42 4.38 2.09 52.27 The temperature profile of the edge stack is also analyzed. The losses in the core blade packets including edge stack and flitch plates are estimated and corresponding loss density values entered into the program. The various heat transfer co-efficients at outer core boundary surface are also specified to solve planar temperature field in core blade packets. Fig. 12 & 13 show the temperature profile of core cross-section without & with division of the edge stack. The temperature profile is differentiated from minimum to maximum by blue to red colour band. Fig. 11. Component stray losses as percentage of the total stray losses The estimated values of stray losses are compared with the tested values to validate the above results. V. COMPARISON OF STRAY LOSS RESULTS Comparison of the stray losses estimated by software program and the measured test results is shown in Table XI below. Sr. No. 1 2 10.80 13.33 11.41 TABLE XI COMPARISON OF TOTAL STRAY LOSSES Total Stray losses, kW Component Max. Tap Nor. Tap Min. Tap Tested values 52.98 49.95 46.93 Estimated values 53.37 53.06 43.02 Deviation -0.74 % -6.22 % 8.33 % Fig. 12. Temperature profile in standard edge stack design The reference tested values vis-à-vis the estimated values show a deviation of -0.74%, -6.22% & 8.33% at maximum, normal and minimum tap positions respectively. VI. CONTROL OF STRAY LOSSES A. Shunt design modification Magnetic shunts are effective in controlling the structural stray losses as they offer high permeable path to the leakage flux. The design of magnetic shunts depends on various factors, viz. length, width and height, placement with 502 Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 losses in the flitch plates. VIII. FURTHER WORK Precise estimation of stray losses is a subject in itself. It may not be prudent to attempt very precise simulation for computation of stray losses in routine designs disregarding the economic considerations. However, application of modern high speed and accurate computation tools offer deep insight into the complex field phenomena in asymmetric transformer geometries. There is a wide scope to exploit these tools for development of new cost-effective designs, exploring possibilities for improvements in certain areas like shunt materials, use of yoke shunts, use of widthwise wall shunts [4] etc. Fig. 13. Temperature profile in modified edge stack design It is observed that in the present case the stray loss is reduced by 52% at normal tap position and hotspot temperature rise is reduced by 14 K after the division of edge stack in two halves, which is quite significant. ACKNOWLEDGEMENTS The authors are grateful to the EMCO Management for granting permission to publish this paper. C. Total stray losses in transformer after modification The total stray losses estimated in the transformer with modified shunt and divided edge stack are presented in Table IXV below. REFERENCES [1] Ramaswamy E, Sarma D V S, Lakhaini V K, “Design of magnetic and non-magnetic shunts for a power transformer using EDMAG-3D”, XI International Scientific Conference, Transformer Building-2005, September 2005, pp. 70-77. [2] Turowski, J., Turowski, M., and Kopec, M., “Method of threedimensional network solution of leakage field of three-phase transformers”, IEEE Transactions on Magnetics, Vol. 26, No. 7, September 1990, pp. 2911-2919. [3] D A Koppikar, S V Kularni, PN Srinivas, S A Khaparde, R. Jain, “Evaluation of flitch plate losses in power transformers”, IEEE Transections on Power Delivery, Vol. 14, No. 3, July 1999. [4] Prof. S V Kulkarni & Prof. S. A. Khaparde, Transformer Engineering – Design and Practice, Marcel Dekker, New York 2004, pp. 169-230. Sr. No 1 2 3 4 5 6 TABLE IXV TOTAL STRAY LOAD LOSSES WITH MODIFIED SHUNT AND DIVIDED EDGE STACK Stray losses, kW Component Max. Tap Nor. Tap Min. Tap Tank 12.13 11.68 10.59 Shunts 3.83 4.36 1.35 Frames 2.72 2.25 1.82 Flitch Plate 0.65 0.54 0.62 Edge Stack 2.18 2.57 2.09 Winding eddy losses 27.67 27.03 21.86 Total Stray + Eddy losses 49.18 48.43 38.33 About the Authors: Mr. Chetan C Adalja, born in April 1982, a gold medalist from Nirma University, completed his graduation in Electrical Engineering from CKPCET, Surat, South Gujarat University in 2003, followed by postgraduation in 2005 in PAS-Power Apparatus and Systems from Nirma University, Ahmedabad. He started his professional career as Lecturer at D. Comparison of total stray losses after modification The comparison of stray losses after modification in shunt and edge stack is shown in Table XV below. Sr No. 1 2 TABLE XV COMPARISON OF STRAY LOSSES AFTER MODIFICATION Total stray losses, kW Design Max. Tap Nor. Tap Min. Tap Standard 53.37 53.06 43.02 After Modification 49.18 48.43 38.33 Reduction 4.19 4.63 4.68 The results show that the modification in shunts and edge stack effect reduction in the total stray losses by 4.19 kW, 4.63 kW & 4.68 kW at maximum, normal and minimum tap positions respectively. VII. CONCLUSIONS 1. Stray losses in a transformer can be precisely estimated using EDMAG-3D software program that is a powerful tool to aid fairly accurate 3-D field mapping of complex transformer asymmetries. 2. The loss in the bottom frames is higher than the top frames because of its close proximity with bottom edge of the winding. It was observed that lowering of the bottom frame height resulted in reduced frame losses. This is attributed to its reduced interaction with the leakage field returning to the bottom yoke. 3. The stray loss in edge stack is significant, leading to localized hotspot. Division of the edge stack effects substantial reduction in loss as well as the temperature. 4. Choosing appropriate material for flitch plate and judicious slot dimensioning could effect reduction in stray Engineering College in Surendranagar, Gujarat.He has been associated with EMCO Limited from 2006 and working as a senior engineer in Technology Department. He has authored 3 technical papers. Mr. M.L. Jain, born in December 1945, completed his graduation in Electrical Engineering from MNNIT, Allahabad University in 1968, followed by post-graduation in 1970 in Design and Production Engineering – Heavy Electrical Equipment from MANIT Bhopal. He started his professional career as transformer design and development engineer in BHEL Bhopal in 1971. From 1979 onwards upto 1996, Mr. Jain was associated with testing of transformers and other HV equipments. He has authored a chapter on testing of transformers and reactors in BHEL monograph ‘Transformers’ published by Tata McGraw-Hill. Since 1996, Mr. Jain has been associated with EMCO Limited. Having worked as Head of Testing & Quality disciplines, he is presently Vice President – Technology, responsible for up-gradation of transformer technology. He has authored over 20 technical papers in the field of transformer design analysis, testing and diagnostics. He is representing EMCO on professional bodies like BIS and CBIP, and is a member of CIGRE(I). 503