Phase-shifting transformers in load flow and short-circuit analysis: modelling and control

Abstract

A new accurate model representing phase-shifting transformers for both load flow and fault analysis is introduced. The model is simple, efficient and numerically stable. The theoretical basis of the model and the practical procedures of implementation for the fast-decoupled load flow method and short-circuit calculation are presented. For load flow implementation the developed model requires no additional storage except for data; the number of iterations and the time per iteration is unchanged. The phase-shifting trans formers have been used for real power control in parallel circuits and the relative analyses and test results are presented. For short-circuit analysis, the asymmetry in the admittance matrix introduced by the phase-shifting transformers is dealt with in two stages. The network is first solved using symmetrical admittance matrix, fully exploiting sparsity, and subsequently the effect of the asymmetry is superposed using the diakoptical approach and effective programming, which optimises the calculation time and storage. To illustrate the process involved a small numerical example is given in Appendix 9.1. The model described was implemented in the Interactive Power System Analysis program [12], and the results of verification for various transformer arrangements in typical practical networks are presented.