Modelling the flux-linkage in permanent magnet synchronous machines

Neglecting magnetic saturation and cross-coupling effects in permanent magnet synchronous machines (PMSM), reduces the accuracy of tasks such as online parameter estimation, machine control and machine performance predictions. Taylor's theorem for multi-variable functions is used to express the direct-axis and quadrature-axis flux-linkages as power series in the PMSM model presented in this paper. Therefore, the model can be extended to a n-degree polynomial, where n determines how accurately the saturation and cross-coupling effects are represented in the model. In addition, the identification of the model coefficients is formulated as an optimization problem that can be solved using quadratic programming. The proposed identification method is applied to data obtained from finite element simulations and measurements. Furthermore, for measured data, the method is extended to identify the machines winding resistance.