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Optimal waveforms for maximum torque per ampere control of Permanent Magnet Synchronous Machines were explored via numerical techniques in the past. This paper introduces an analytical approach for computation of the optimal stator excitation in Permanent Magnet Synchronous Machines including surface mount and interior permanent magnet configurations. Furthermore, a unified solution for optimal current excitation of Permanent Magnet Synchronous Machines and Synchronous Reluctance machines are presented. The developed analytical solutions enable the online calculation of optimal excitation for minimum copper loss. It also provides guideline for multi-objective optimization when efficiency is of interest. Simulation results are provided for validation.
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Wang et al. (2012) studied this question.