A discrete‐time model including cross‐saturation for surface permanent‐magnet synchronous machines

Abstract

Purpose

To provide a discrete‐time nonlinear model for surface permanent‐magnet synchronous machines (SPMSMs) in order to discuss the stability of such machines.

Design/methodology/approach

Through differencing the co‐energy, obtained from a finite element method, the main flux path can be described by a complex reluctance. Furthermore, for a SPMSM, an equivalent circuit is presented that includes the eddy‐current losses and the voltage drops across stator resistance and leakage inductance. The model is transformed to a discrete‐time state‐space model by using a forward rectangular rule. By using a root locus technique, the stability of the new model is discussed.

Findings

From the calculated root locus it is concluded that the stability of a SPMSM is only guaranteed for certain values of the open loop gain. Moreover, by using the forward rectangular rule, it is concluded that a well‐considered time step has to be chosen.

Research limitations/implications

The model considers the fundamental space harmonic components only. Moreover, the saturation of the leakage flux path is neglected.

Practical implications

As the model is formulated in discrete time, it can be used in modern drives where a digital controller is used.

Originality/value

This paper presents an equivalent electrical circuit for SPMSMs that takes into account the saturation of the magnetizing flux paths as well as the magnetic interaction between the two orthogonal magnetic axes.

Citation

De Belie, F.M.L.L., Melkebeek, J.A.A., Vandevelde, L., Geldhof, K.R. and Boel, R.K. (2006), "A discrete‐time model including cross‐saturation for surface permanent‐magnet synchronous machines", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 25 No. 4, pp. 766-778. https://doi.org/10.1108/03321640610683980