Design of the most efficient excitation for a class of electric motor

Three basic concepts often used in circuit and system theory are innovatively combined to design the minimum power excitation that produces smooth torque in a popular class of electric motor. First, the exponential Fourier series is used to represent currents and voltages in three-phase permanent magnet motors. Second, the developed torque is modeled by convolutions of current and voltage harmonics. The torque model can be compactly written as a set of linear equations, in which the currents must be solved to yield smooth torque. However, the set of linear equations is underdetermined, so there is an infinite number of solutions. Hence, the solution that is chosen is the “minimum norm” solution. In practical terms, the resulting current waveforms are optimal in the sense of minimum average power. An example calculation for an actual motor is presented, and theoretical efficiency and torque ripple performance results are compared to that achieved by the popular rectangular current excitation