Analytical solutions for the optimal reference currents for MTPC/MTPA, MTPV and MTPF control of anisotropic synchronous machines

Analytical solutions for the optimal current references during maximum torque per current (MTPC; or maximum torque per Ampere (MTPA)), maximum torque per voltage (MTPV) and maximum torque per flux (MTPF) operation of anisotropic synchronous machines with non-negligible stator resistance and mutual inductance are presented. The analytical solutions allow for an (almost) instantaneous computation of the corresponding reference currents without neglecting stator resistance and/or mutual inductance (as usually done). Numerical methods (approximating these solutions only) are no longer required. The derived analytical solutions for MTPC, MTPV and MTPF operation are suitable for any anisotropic synchronous machine; even for nonlinear reluctance synchronous machines, as the presented measurement results illustrate.