Method of Parameters Determination for Multi-Winding Transformer Equivalent Circuit in the Form of Multi-Beam Star

A technique is known for elaboration of equivalent schemes for transformers with two or three windings in the form of two or three beam stars (without electromagnetic coupling between the beam elements). Schemes usually contain the magnetization branch, connected to a common point. For the case of transformer with the number of windings four or more, the number of pair short-circuit impedances (which basically determined the main properties of transformer) is bigger than the number of beams of the corresponding star. This makes it impossible to obtain a sufficiently correct equivalent scheme in the form of a multi-beam star without electromagnetic coupling between the elements of the beams. An equivalent circuit in the form of complete polygon is also used; the number of polygon vertices is equal to the number of transformer windings. Also are used tree-like equivalent schemes that are approximate by nature. Besides, equivalent schemes of chain type are known, which have mutual electromagnetic coupling between the elements. However, for them the arrangement of the elements of the replacement circuit depends on the mutual arrangement of the transformer windings in the magnetic core window. In all these cases the problem arises of choosing the location of the magnetization branch connection point. In addition, these schemes (with the exception of the complete polygon scheme) are not universal, and the methods for determining their parameters are complex. In this paper, we propose a technique for determining the elements of the equivalent circuit for the replacement of a multi-winding transformer in the form of multi-beam star with mutual electromagnetic coupling between the elements of the beams with one magnetization branch. The basis for it is a formula, that connects the pair short-circuit impedance of the two windings with their full own and mutual impedances. Using the matrix pseudo-inversion procedure, a technique was developed for finding the own and mutual impedances, constituting the star's beams. This scheme is universal and did not depend on the specific mutual arrangement of the windings. Besides, it is possible to determine the parameters of the proposed multi-beam equivalent circuit in exact accordance with the values of the pair short-circuit impedances of the transformer. It is a logical continuation of the conventional equivalent scheme of three-winding transformer. In addition, the proposed algorithm ensures the positive values of the own inductive reactance of the beams (windings).