Comparison of four methods for computing positive-sequence reactances of three-phase core-type transformers

This study compares four methods for computing the positive-sequence reactances of three-phase core-type transformers: traditional basic formulae (TBF); two-dimensional (2D) finite difference method (FDM); and 2D and 3D finite element methods (FEM). A computer program was coded for the FDM, and a commercial software was applied for the FEM. The four applied methods are magnetostatic, and they were applied for computing the three positive-sequence short-circuit reactances of a three-winding transformer. The results of these methods were compared among themselves and with the measured values. In comparison with the measured values: (a) the TBF are relatively accurate, although they are based on an approximate representation of a simple 2D cross-section for the transformer window; (b) the results with different 2D cross-sections are also relatively accurate; (c) the results with the 3D modelling are more accurate than the TBF. These facts confirm that the space between the windings determines the value of the transformer positive-sequence reactance. Therefore the tank-winding distance and the tank magnetic permeability have little effect on the results. A weighted average of the results of different 2D cross-sections was computed with the FDM and with the FEM, and the obtained values are very close to the result with the 3D modelling. Although the results are relatively accurate, the main simplifications related to the performed magnetostatic analysis are highlighted.