Inductance Estimation of Electrically Excited Synchronous Motor via Polynomial Approximations by Least Square Method

Electrically excited synchronous motors are designed to have high power density for electric vehicle applications. During a high-torque operation, severe nonlinearities associated with a saturation are observed: change of inductances, emergence of cross-coupling effects, variation of back EMF coefficient, etc. A flux linkage map over the current plane is obtained via finite-element analysis (FEA), and it is fitted by a third-order polynomial with the use of the least square method. Then, by grouping terms of the polynomial, the inductances are expressed as functions of currents. The validity of inductance fitting is shown by comparing with FEA and experimental results. This enables us to predict inductances online instead of using premade lookup table. The torque equation is expanded by incorporating the cross-coupling inductances, for which an extended maximum torque per ampere (MTPA) is developed by using Ferrari's method to a quartic equation. The extended MTPA locus is compared with the experimental optimal results.