3‐D calculations of leakage field and reactance for special transformers

K.Zakrzewski1, M.Lukaniszyn2, B.Tomczuk2
1Institute of Electrical Machines and Transformers, Technical University of Lodz, Lodz, Poland
2Department of Electrical Engineering and Automatic Control, Technical University of Opole, Opole, Poland

Tóm tắt

Two approaches to 3‐D magnetic field calculations for low‐power special transformers are presented in the paper. The application of fast calculation procedures based on the finite difference method, to direct solving of the Poisson and Laplace equations is given. The calculated example deals with the three‐phase leakage transformer. On the other hand, the iterative solution of regularized integral equations used for calculation of 3‐D field distribution and integral parameters of leakage field in current transformer is also presented. The software packages developed by the authors are useful for computer‐aided design of low‐power special transformers.

Từ khóa


Tài liệu tham khảo

1.Pawluk, K., Sikora, R., Sykulski, J. (Ed.), Stoll, R., Turowski, J. and Zakrzewski, K., Computational Magnetics, Chapman & Hall, London, Glasgow, Weinheim, New York, NY, Tokyo, Melbourne, Madras, 1995.

2.Lavers, J.D., “Electromagnetic field computation in power engineering”, IEEE Trans. on Magn., Vol. 29 No. 6, 1993, pp. 2347‐52.

3.Burridge, D. and Temperton, C., “Note‐A fast Poisson‐solver for large grids”, Journal of Comput. Physics, Vol. 30 No. 1, 1979, pp. 145‐8.

4.Lukaniszyn, M., Modelling of the Three‐dimensional Magnetic and Electric Fields by the Finite Difference Method Using Fast Calculating Subroutines, (in Polish), Studies and Monographs, No. 41, Technical University of Opole, Opole, 1990, p. 137.

5.Lukaniszyn, M. and Unbehauen, R., “The 3‐D calculations of the leakage magnetic field and the short‐circuit reactance in a transformer with disk windings”, Archiv für Elektrotechnik, Vol. 78 No. 3, 1995, pp. 151‐7.

6.Schumann, U. (Ed.), Computers Fast Elliptic Solvers and Applications, Proceedings of the GAMM ‐ Workshop on Fast Solution Methods for the Discretized Poisson Equation, Karlsruhe, March 3‐4, 1977, Advance Publications, London, 1978.

7.Swarztrauber, P., “A direct method for the discrete solution of separable elliptic equations”, SIAM J. Numer. Anal., Vol. 11, 1974, pp. s.1136‐50.

8.Wilhelmson, R. and Ericksen, J., “Direct solution for the Poisson′s equation in three dimensions”, Journal of Computational Physics, Vol. 25, 1977, pp. 319‐31.

9.Adams, J., Swarztrauber, P. and Sweet, R., FISHPAK a Package of Fortran Subprograms for the Solution of Separable Elliptic Partial Differential Equation, Research Report, NCAR, Colorado, 1979.

10.Mercier, P. and Deville, M., “A multidimensional compact higher‐order scheme for 3‐D Poisson’s equation”, Journal of Comput. Physics, Vol. 39 No. 2, 1981, pp. 433‐55.

11.Zakrzewski, K. and Lukaniszyn, M., “Three‐dimensional model of three‐phase transformer for leakage field calculation”, Archiv. für Elektrotechnik, Vol. 73, 1990, pp. 319‐24.

12.Zakrzewski, K. and Lukaniszyn, M., “Three‐dimensional model of one ‐ and three‐phase transformer for leakage field calculation”, IEEE Trans. on Magnetics, Vol. MAG‐28 No. 2, March, 1992, pp. 1344‐7.

13.Tomczuk, B., Three‐dimensional Modeling of Open Magnetic Fields in Transformers and Reactors by Means of Integral Methods, (in Polish), Studies and Monographs, No. 77, The Technical University of Opole, Opole, 1994, p. 150.

14.Tomczuk, B., “Analysis of 3‐D magnetic fields in high leakage reactance transformers”, IEEE Transactions on Magnetics, New York, Vol. 30 No. 5, 1994, pp. 2734‐8.

15.Zakrzewski, K. and Tomczuk, B., “3‐D calculation of zero‐component flux in three‐phase three‐column transformer”, COMPEL ‐ The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 13 No. 1, 1994, pp. 93‐6.

16.Zakrzewski, K. and Tomczuk, B., “3‐D calculation of magnetic field and inductance of a reactor with open magnetic core by integral equations method”, COMPEL ‐ The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1992, pp. 221‐4.

17.Zakrzewski, K. and Tomczuk, B., “Magnetic field analysis and leakage inductance calculation in current transformers by means of 3‐D integral methods”, COMPUMAG’95 Conference, Berlin, Germany, 10‐13 July 1995, pp. 320‐21.

18.Mikhlin, S.G. and Smolitsky, K.L., Approximate Methods for Solution of Differential and Integral Equations, Elsevier, New York, NY, 1967.

19.Tomczuk, B., “Three‐dimensional leakage reactance calculation and magnetic field analysis for unbounded problems”, IEEE Transactions on Magnetics, New York, Vol. 28 No. 4, 1992, pp. 1935‐40.