aper presented at the 16 th International Conference on Electrical Machines, ICEM 004, Cracow, oland, eptember 5-8, 004. Fast ower Transformer Design Technique Validated by Measurements V.. Lazaris, M. A. Tsili and A. G. Kladas Faculty of Electrical & Computer Engineering, National Technical University of Athens, GR-15780, Athens, Greece, phone: (+30) 10-773765, fax: (+30) 10-773593 e-mail: kladasel@central.ntua.gr Abstract The present paper illustrates the development of a very fast computer software for the design of three-phase, stack core, power transformers. The program is based on a particular algorithm for the design methodology. It is applied in the design of a 1000 kva, 0/0.4 kv distribution transformer and the accuracy of the results is validated through comparison to the results of three and twodimensional finite element method and local field measurements on a constructed wound core transformer of the same rating. I. INTRODUCTION ower transformer design involves a compromise between cost and specified characteristics target. It is within the transformer manufacturer responsibility to implement a reliable design that maintains adequate margins for performances during normal operation, short circuit and other transient phenomena, while simultaneously being cost effective. The transformer modelling and design is therefore a complex task, widely encountered in the technical literature, as in [1]-[4]. In the present paper, a very fast computer software for the design of three-phase, stack core, power transformers is developed. The design methodology [5], [6] is implemented in computer code, enabling the development of a flexible and user friendly design software, providing fast and reliable ulation of the transformer performance characteristics and construction cost. The method is applied in the design of a 1000 kva, 0/0.4 kv distribution transformer and the accuracy of its results is validated through comparison to the results of threedimensional finite element method and local field measurements on a constructed wound core transformer of the same rating. The paper is organised as follows: ection II describes the proposed technique, presenting the steps followed during the design procedure along with its implementation on the computer software. ection III presents the technique validation by application to the design of a 1000 kva stack core transformer and comparison of its results to the characteristics of a constructed wound core power transformer of the same rating and to the results obtained by D and 3D FEM. ection IV includes the experimental verification of the method, by local field measurements on the constructed transformer. Finally, ection V concludes the paper. II. DECRITION AND IMLEMENTATION OF THE DEIGN TECHNIQUE The active part configuration of the three-phase stack core power transformer considered is illustrated in Fig. 1. by limbs bw W Ai yoke Figure 1. Active part configuration of the three-phase stack core power transformer considered. A. Design Algorithm The transformer design algorithm is depicted in the flowchart of Fig.. The required input data for the implementation of the algorithm are listed in Table I. reion of volts pur turn increase of volts per turn Calculation of new Ai if bw-*(lvwidth+hvwidth)=5mm modificati on of bw if Uk>1,1*UkGuar if Uk<0,9*UkGuar Data Input material Bm < 1.1 material 1 Core reion of Bm if Fe> no load losses 1,15*FeGuar Low Voltage Winding turn cross-section (copper sheet) number of turns LV winding mean diameter, length High Voltage Winding reion of J turn cross-section number of turns conor dimensions HV winding mean diameter, length copper losses losses hort circuit impedance Tank increase of lt,bt if dtubestotal> windings temperature dtank tubes if T>T rise if dtubestotal<dtank END if > 1,15*Guar if Total> 1,1*(Guar+FeGuar) L NO YE DFe> D Figure. Flowchart of the transformer design program.
aper presented at the 16 th International Conference on Electrical Machines, ICEM 004, Cracow, oland, eptember 5-8, 004. TABLE I REQUIRED INUT DATA FOR THE TRANFORMER DEIGN ALGORITHM ymbol Nominal output power (kva) V HV Nominal voltage of primary (High Voltage-HV) winding (V) V LV Nominal voltage of secondary (Low Voltage-LV) winding (V) f Nominal frequency (Hz) T Maximum winding temperature rise ( o C) U k Guaranteed short circuit impedance (%) Fe Guaranteed iron (no load) losses (W) Guaranteed copper (load) losses (W) Table I includes the nominal power, voltage and frequency of the designed transformer as well as the desired performance characteristics, which the considered design must meet in order to comply with customer requirements and international technical specifications, [7]. These characteristics involve the maximum permissible winding temperature rise and the anteed values of losses and short circuit impedance. The relation between the anteed and specified performance can be described as follows: the transformer users specify a desired level of load losses, no-load losses and short-circuit impedance (specified values) while the transformer manufacturer antees the values of losses and short-circuit impedance (anteed values: U, k and in Table I). Fe The objective of the algorithm is to provide a design within the permissible deviations of the anteed values from the ulated ones, listed in Table II, at the lowest possible construction cost. TABLE II ERMIIBLE DEVIATION BETWEEN GUARANTEED AND CALCULATED TRANFORMER ERFORMANCE CHARACTERITIC ACCORDING TO IEC 60076-1 ermissible Deviation (% percentage of the respective anteed value) hort circuit Impedance ± 10 No load losses +15 Load losses +15 Total Losses +10 In order to achieve the above objective, the design algorithm of Fig. proceeds to the following steps: 1) Design of the Magnetic Circuit (Core) In a first step, the magnetic circuit (core) design is realized: an initial value of magnetic inion (B m ) and current density (J) is considered and the volts per turn (E t ) are ulated with the use of the following equation: E t = K i (1) 3 where K i is a winding factor selected according to the transformer rated power and voltage. The program computes the core leg cross-section A i, the diameter D 1 of the circumscribed circle of the leg, the window area A w, the window length L, the window width b w and the overall core length W, as follows: E t Ai = () 4.44 f B A w m Ai D1 = K (3) = (4) 3.33 f B K J A m w L = A w (5) A w b w = (6) W = (b D ) + 0.9D (7) w + 1 The factors K and K w appearing in (3) and (4) are core leg and window factors respectively. The core leg factor derives from the transformer rated power and voltage while the window factor is given by: 80%, 5kVA < 50kVA 10 K w = 100%, 50kVA < 50kVA 30 + (VHV /1000) 10%, > 50kVA (8) The iron losses are then ulated for the core limbs and yoke, based on their weight and the core material specific loss curve. Their sum, increased by a factor of 7%, gives the no load losses: Fe = 1.07(lim bs + yoke ) (9) If the losses exceed the anteed value, with a margin greater than the specified one in Table II, the core is redesigned with the use of a new magnetic inion value. As shown in Fig., when the lowest possible value of B m is reached, the procedure continues with the selection of a new core material. ) Design of LV and HV winding In a second step, the program proceeds to the design of the Low Voltage and High Voltage winding: for the initial value of current density (J), the volts per turn value ulated above is used for the derivation of the number of the LV and HV winding turns, N LV and N HV, their cross-section, α LV and α HV, as well as the axial and radial space required by each winding. A minimum distance of the HV windings of two adjacent phases is also considered. Fig. 3 illustrates the radial arrangement of the HV and LV windings, along with their dimensional details. The LV winding is divided into two layers, for the achievement of more effective by interpolating a between them. Besides the s appearing in Fig. 3, spacers are located between the LV and HV windings, the LV winding and the core, as well as between the HV windings of two adjacent phases. 1 i
aper presented at the 16 th International Conference on Electrical Machines, ICEM 004, Cracow, oland, eptember 5-8, 004. core HVwidth 1st layer of LV winding LVwidth dhvext dlvext D1 dhvint dlvint b b nd layer of LV winding b b1 spacer 3mm 5mm HV winding design margin, the winding design process is repeated with a new value of current density. = 3(I R + I R ) (14) LV LV HV HV 3) Calculation of transformer losses In the following step, the value of transformer losses is ulated, increasing the sum of load and no load losses by a factor of 5%. If their value exceeds the anteed value more than 10%, the procedure must be repeated with the selection new design variables. In order to select the variables to be modified, a comparison between the ratio D DFe Fe Fe Fe = and = is performed, enabling the choice between the attempt to lower the load or the no load losses. imilarly to the design steps 1 and, for the decrease of no load losses, a new B m value is selected, while the decrease of load losses is achieved through modification of the current density value. Figure 3. Radial arrangement of LV and HV winding around the core leg. The symbols appearing in Fig. 3 are explained in the followings: dlv Int : internal diameter of LV winding dhv Int : internal diameter of HV winding dlv Ext : external diameter of LV winding dhv Ext : external diameter of HV winding b : width of LV conors (i.e. LV winding width without the spacers and s width), b 1 : width of HV conors (i.e. HV winding width without the spacers and s width), LV width : width of LV winding, : width of HV winding. HV width The mean length of LV and HV winding (LV lmean, HV lmean ) are then ulated and used for the derivation of the LV and HV winding resistance values R LV and R HV : dlvext + dlvint LVlmean = π (10) dhvext + dhvint HVlmean = π (11) LVlmean ρ N LV R = (1) LV α LV HVlmean ρ N HV R = (13) HV α where ρ is the copper density. Next, the copper losses of the windings are ulated, according to (14). If their value is not within the specified HV 4) Calculation of transformer short-circuit impedance The transformer short circuit impedance is ulated with the use of (15). U = IX + IR (15) where, πfµ ο IX = k HV + LV lmean lmean L E t b + b 1 dhv dlv + Int Int (16) IR = (17) If the short-circuit impedance value deviates more than ± 10 % from the specified value, the design algorithm returns to step 1, after reducing or increasing the volt per turn value E t (according to the negative or positive sign of the deviation) and modifying respectively the b w value. 5) Calculation of transformer tank dimensions After the transformer active part ulations, the transformer tank design is performed, with the ulation of its length l t, height h t and width b t (based on the active part dimensions). The distance of the active part from the transformer tank walls dl t, dh t and db t is defined with the use of Table III. l t b w + D + dhv 1 Ext + dl t = (18) b t dhvext + db t = (19)
aper presented at the 16 th International Conference on Electrical Machines, ICEM 004, Cracow, oland, eptember 5-8, 004. h = L + b y + (0) t dh t TABLE III DEFINITION OF ACTIVE ART DITANCE FROM TRAMFORMER TANK WALL High Voltage Level (kv) Transformer Rated ower (kva) dl t (cm) db t (cm) dh t (cm) <11 <1000 8 10 45 1000 < 5000 14 18 50 11 VHV 33 <1000 15 0 55 1000 < 5000 17 5 60 B. Interface of the Transformer Design oftware The interface of the developed transformer design software is shown in Fig. 4. The user must enter the technical specifications of the considered transformer (listed in Table I) in the respective fields of the upper part of the form. After the activation of the Calculate button, the proposed design procedure is implemented as described in ection II.A. The results of the design ulations, listed in Table IV, appear in the fields of the lower part of the form of Fig. 3. 6) Transformer study Following the definition of the transformer active part dimensions, a thermal study is implemented, including the temperature ulation and the number of tubes required to maintain the winding temperature rise under the specified value. The transformer area (area where the losses are dissipated) is equal to the lateral area of the transformer tank, t. It is ulated with the use of the following equation: t = (bt + lt) ht (1) The rise in the windings temperature is given by: Total T = () 1.5 t If T >T (maximum permissible rise in the windings temperature), the insertion of tubes is necessary in order to keep the temperature below the maximum level. The required tube area is given by: 1.5 T t = (3) tubes 8.775T Afterwards, a check is performed in order to verify that the ulated tubes can fit around the transformer tank, by comparing their diameter d = N d to the tank circumference tubes tubes tube tubes dtan k = (lt + bt ). In case that d > d tan k, the tank is redesigned by increasing l t and b t by 10 cm. This procedure is repeated until d tubes becomes less than d tan k. 7) Calculation of transformer cost Finally, the transformer cost derives with the use of the following equation: C = Cost + Cost + Cost Total Fe + Cost tan k + Cost insulation + C (4) In the above equation, variable C represents the transformer constructional costs that do not depend on its dimensions (related to Bucholz relay, thermostat, low and high voltage insulators). Their value is related to the power and voltage rating of the considered transformer. Oil ymbol Figure 4. Interface of the transformer design program. TABLE IV TRANFORMER DEIGN OFTWARE OUTUT DATA Fe Calculated iron (no load) losses (W) Calculated copper (load) losses (W) Total Calculated losses (W) U k Calculated short-circuit impedance value (%) D Fe D D Total DU k Deviation between ulated and anteed no load losses (%) Deviation between ulated and anteed load losses (%) Deviation between ulated and anteed losses (%) Deviation between ulated and anteed short-circuit impedance (%) I o Calculated no load current (A) M Fe Iron mass (kg) M Copper mass (kg) C Total Total transformer cost ( )
aper presented at the 16 th International Conference on Electrical Machines, ICEM 004, Cracow, oland, eptember 5-8, 004. III. ALICATION OF THE METHOD TO A 1000 KVA DITRIBUTION TRANFORMER The method has been applied to the design of a 1000 kva, 0/0.4 kv distribution transformer. The ulated characteristics have been compared to the ones of a constructed wound core three-phase power transformer, showing a good correlation of the results. Table V juxtaposes the results of the design technique to the characteristics of the constructed wound core transformer. Both transformers are 1000 kva, 0/0.4 kv distribution transformers. The active part configuration of the threephase wound core power transformer considered is illustrated in Fig. 5. TABLE V COMARION BETWEEN THE CHARACTERITIC OF A TACK CORE TRANFORMER DEIGNED WITH THE ROOED TECHNIQUE AND A CONTRUCTED WOUND CORE TRANFORMER tack Core Transformer Wound Core Transformer No load losses 1766 W 148 W Load losses 869 W 131 W Total losses 10035 W 14550 W hort circuit impedance 6.5 % 6.13 % Iron mass 1055 kgr 780.9 kgr Copper mass 31 kgr 346.5 kgr Volts per turn Ε t 1.3 V/turn 16.5 V/turn Core leg cross-section 380.13 cm 439.93 cm Window length 60 cm 36 cm Core length 95.7 cm 11.48 cm Core width 19.8 cm 8.66 cm Core thickness 0 cm 5.4 cm Window width 18.9 cm 14.4 cm Distance between the center of two adjacent 37.9 cm 31.7 cm phases Low Voltage Turns 18 14 High Voltage Turns 1559 11 LV conor crosssection 80.8 mm 311. mm HV conor crosssection 6.315 mm 3.94 mm HV winding width 3.18 cm 6.4 cm LV winding width 5.68 cm 7.18 cm Tank length 1.4 m 1. m Tank width 0.7 m 0.67 m Tank height 1.6 m 0,965 m Cost 415 361 The main differences appearing in the characteristics of Table V are explained in the followings: i) Although the magnetic inion of both transformers is equal to 1.75 T and the core material is similar, the B m value is uniform in the wound core of the second transformer, while in the stack core transformer this value is different in the core yoke, where it is equal to 1.68 T. This fact justifies the greater value of the stack core iron mass and no load losses. ii) The active part of the stack core transformer is higher than the one of the wound core transformer (and the tank dimensions, respectively), resulting to smaller radial width of the HV and LV windings and smaller cross section of the core leg. The smaller width of the windings leads to lower value of load losses for the designed stack core transformer. iii) The stack core transformer short circuit impedance value is 1.96 % greater than the wound core transformer value. This difference is explained by the greater leakage field of the stack core transformer, due to the arrangement of the windings around the core (the three-limb core does not provide return path for the flux of the two extreme phases). IV. VALIDATION BY D AND 3D FEM A D and a 3D finite element simulation of the constructed transformer under short circuit test has been coned for the analysis of its leakage field and the ulation of its short circuit impedance (Uk). Table VI compares the short circuit impedance values ulated by FEM and the proposed design technique. Figure 5. Active part configuration of the three-phase wound core power transformer considered. TABLE VI COMARION BETWEEN D FEM, 3D FEM AND ROOED DEIGN hort circuit Impedance METHODOLOGY D FEM 3D FEM roposed methodology 6.8 6.19 6.5 From the results of Table VI, the deviation of the impedance ulated with the use of the proposed methodology to the ones
aper presented at the 16 th International Conference on Electrical Machines, ICEM 004, Cracow, oland, eptember 5-8, 004. given by D and 3D FEM is 0.5% and 1% respectively. Both methods validate the result given by the adopted design technique. D FEM is based on similar geometry configuration to the analysis proposed but it involves more important memory space and execution time resources. The 3D FEM model provides better representation of the real transformer geometry but its complexity and execution time is considerably greater from the proposed technique. V. EXERIMENTAL VERIFICATION The field values computed by 3D FEM have also been compared to those measured by a Hall effect probe during short-circuit test. Fig. 8 gives the variation of the perpendicular flux density component B n along the line AB, positioned as shown in Fig. 7. This figure illustrates the good correlation of the simulated results with the local leakage field measurements. VI. CONCLUION In the present paper, a fast stack core power transformer design technique was presented, based on a particular design methodology. The method was implemented in a transformer design program and it was applied to a 1000 kva distribution transformer. Its results were compared to the characteristics of a constructed wound core transformer, showing good agreement. The leakage field ulated by the method was also compared to the results of D and 3D FEM and local field measurements, proving that the proposed design methodology involves very reduced computational means and provides sufficient accuracy, at least for the stack core distribution transformer cases considered. Figure 6. Variation of the magnetic inion magnitude under short-circuit test for the 1000 kva wound core transformer (D FEM). Figure 7. Variation of the magnetic inion magnitude under short-circuit test for the 1000 kva wound core transformer (3D FEM). Bn (mt) 14 1 10 8 6 4 0 core Bn along the line AB short-circuit at 0 kv l.v winding 0 50 100 150 00 50 300 A r (mm) B h.v winding phase a phase b 3D FEM VII. REFERENCE [1] W. M. Grady, R. Chan, M. J. amotyj, R. J. Ferraro, J. L. Bierschenk, A C-Based Computer rogram for Teaching the Design and Analysis of Dry-Type Transformers, IEEE Trans. ower ystems, Vol. 7, No, pp. 709-717, May 199. [].. Georgilakis, N.D. Doulamis, A.D. Doulamis, N.D. Hatziargyriou,.D. Kollias, A novel iron loss reion technique for distribution transformers based on a combined genetic algorithm-neural network approach, IEEE Trans. ystems, Man, and Cybernetics, art C: Applications and Reviews, vol. 31, no. 1, pp. 16-34, Feb. 001. [3]. Georgilakis, N. Hatziargyriou, D. aparigas, "AI Helps Reduce Transformer Iron Losses," IEEE Computer Applications in ower, Vol. 1, Nr. 4, pp. 41-46, 1999. [4] L. H. Geromel, C. R. ouza, The application of intelligent systems in power transformer design, roceedings of the 00 International Joint Conference on Neural Networks, IJCNN 0, Vol., pp. 1504-1509, 1-17 May 00. [5] V. N. Mittle, A. Mittal, Design of Electrical Machines, tandard ublishers Distributors, Delhi 1998. [6] A. Dymkov, Transformer Design, English Translation from the Russian by A. Gavrilovets, Moscow 1975. [7] IEC 60076-1, ower Transformers art 1: General, 000. Figure 8. Comparison of measured and computed field values along the line AB.