Piecewise Affine Maximum Torque per Ampere for the Wound Rotor Synchronous Machine

Power-efficient torque control of the wound rotor synchronous machine (WRSM) below base speed requires a minimization of electrical losses, namely, copper losses. In this article, the maximum torque per ampere (MTPA) optimization problem is presented and solved using a convex Pareto frontier of the simulated or measured data points. Three filtered solution sets are mapped to current space using piecewise affine (PWA) functions, which approximate the current using a piecewise linear function for a given torque. This set of piecewise linear functions enables a machine controller to implement MTPA online or as an offline lookup table. Simulated and experimental results are presented for a 65-kW, finite element analysis (FEA)-sampled WRSM. Compared with linear MTPA, the PWA MTPA functions are shown to reduce the torque error by >25% and reduce the average copper loss by >20%.