Reciprocity relations for the mutual inductances of orthogonal axis windings in saturated electrical machines

It has been demonstrated 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 the saturated machines. In salient-pole-type machines, the assumed saturation models do not answer the question of whether the reciprocity property, which is well known for linear inductors, is still valid for these saturated mutual inductances. It 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.<>