Bivariate Polynomial Approximation of Flux Linkages Based on Measured Differential Inductances for Permanent Magnet Synchronous Motors

This paper introduces a novel method to obtain accurate high-order polynomial function approximations for the current-dependent electric flux linkages and inductances of per-manent magnet synchronous motors from differential inductance measurements at discrete current operating points. The proposed approach allows to take fundamental electromagnetic reciprocity properties into account such that they are exactly observed by the resulting characteristics. Moreover, the algorithm is robust against outliers and zero-mean stochastic errors in the measured values. Mathematically the procedure leads to a linear least-squares problem whose unique solution can reliably be found by means of standard solvers. The model is verified by fitting real measurements acquired in a industrial servo motor.