Bivariate polynomial approximation of cross-saturated flux curves in synchronous machine models

Efficient control is always related to the quality and accuracy of the model describing the plant. The torque generated in synchronous machines is a function of flux linkage and stator currents. For efficiency improvements in torque, speed or position control, a precise knowledge of the relation between flux and current is thus essential. Magnetic saturation affects this relation and - if neglected - causes noticeable efficiency reductions, especially at high loads. This work presents an analytical methodology for describing the complete, saturated flux characteristics of synchronous machines by means of bivariate polynomials. An effective strategy for determining the polynomial coefficients is proposed and demonstrated exemplarily for a synchronous reluctance machine and an interior permanent magnet synchronous machine.