Three Dimensional Flux Calculation on a Three-Phase Transformer

Increases in the ratings of large power transformers have demanded more accurate methods of predicting leakage fields which give rise to excessive losses in the devices. This paper addresses the issue, giving the development of a technique which can be used with minimal computing power to determine the distribution of the magnetic fluxes. Estimates for the additional stray load losses in the iron parts can be calculated with reasonable accuracy after the flux distribution has been found. For developing large transformers and reactors, it is necessary to know the distribution of the magnetic leakage field to calculate the electro-dynamic forces and the stray losses due to eddy currents in the winding conductors and in steel parts such as core, tank, pressing beams, etc. In general, the magnetic field in the transformer is calculated using the assumption that the structure is two-dimensional. But actual transformers are three-dimensional. Thus, the customary two-dimensional approximations are inadequate. In this paper, the three-dimensional magnetic flux distribution on the tank wall of a three phase transformer has been calculated. In order to perform the calculation, a finite element scheme has been adopted to obtain a two-dimensional solution at 15 meridian planes of the transformer coil of a single phase transformer for any arbitrary value of current density. Using the actual values of current densities, the magnetic field has been computed for each phase at two selected instants of time in the cycle. Then, the results are manipulated to obtain an overall solution.