Analytical computation of the optimal reference currents for MTPC/MTPA, MTPV and MTPF operation of anisotropic synchronous machines considering stator resistance and mutual inductance

The derivation of analytical solutions for the optimal reference currents 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 is presented. The analytical solutions allow for a direct computation of the corresponding reference currents without neglecting stator resistance and/or mutual inductance (as usually done). Numerical approximations 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 measurement will illustrate.