Impact of cross-saturation on accuracy of saturated induction machine models

Cross-saturation in smooth air-gap AC machines has been a subject of controversy in the 1980s. The discussions were based on the model of a saturated AC machine with d-q axis winding currents acting as state-space variables. The recently introduced concept of generalised flux and generalised inductance has enabled the derivation of a series of models of saturated smooth air-gap AC machines for various selections of state-space variables. All the models, except for the winding flux model, contain explicit terms that describe cross-saturation. The aim of this paper is to compare behaviour of various models when cross-saturation is neglected. Two transients of a single-cage induction machine are analysed: motor starting with increased voltage; and induction generator self-excitation. Some experimental results are included. It is shown that the impact of cross-saturation on accuracy depends on the type of the model. All the models that ask for a time derivative of the generalised inductance yield poor results if cross-saturation is neglected. However, the models that require a time derivative of the inverse of the generalised inductance are basically unaffected. Thus these models can be simplified without any loss of accuracy.