Reciprocity relations for the mutual inductances between orthogonal axis windings in saturated salient-pole machines

Abstract

It has been demonstrated clearly in the literature that saturation in electrical machines leads to a flux linkage between orthogonal axis windings. Hence this magnetic coupling should be included in the mathematical model for the (small signal) dynamic analysis of saturated machines. Obviously, in smooth air-gap machines the resulting incremental mutual inductances must be equal because of symmetry. I n salient-pole-type machines, however, the assumed saturation models do not settle the question whether the reciprocity property, which is well-known for linear inductors, is still valid for these saturated mutual inductances. I t is shown that the reciprocity property can be extended to these cases, provided the losses are either negligible or modeled separately (as is usual in machine analysis). As a corollary, a condition is derived for the self-inductances of the orthogonal windings so that the total magnetizing current can be used to characterize the saturation level in both axes.

Modeling of Mutual Saturation in Induction Machines

“…This kind of saturation models always fulfill (4), but they cannot model the mutual saturation effect. Instead of the power function (6), a polynomial could be used [9], [7].…”

“…The goal is to find physically reasonable functions i m (ψ m , ψ rσ ) and i r (ψ m , ψ rσ ) fulfilling (9) and having a small number of parameters. It is convenient to consider functions of the form [15] …”

“…For the magnetizing curve, explicit functions have been used, e.g. polynomials [9], [7], power functions [10], [5], and rational power functions [11]. In these previously proposed models, the mutual saturation effect is omitted.…”

Modeling of Saturation Due to Main and Leakage Flux Interaction in Induction Machines

“…This kind of saturation models always fulfill (5), but they cannot model the mutual saturation effect. Instead of the power function (8), a polynomial could be used [10], [6].…”

“…For the magnetizing curve, explicit functions have been used, e.g. polynomials [10], [6], power functions [11], [4], and rational power functions [12]. In these previous models, the mutual saturation effect is omitted.…”