Maximum Reachable Torque, Power and Speed for Five-Phase SPM Machine With Low Armature Reaction

In this paper, the study of the torque and power versus speed characteristics for a family of five-phase surface-mounted permanent magnet machine is carried out. With considering hypotheses [linear magnetic modeling, only first and third harmonic terms in the back electromotive force (EMF) and current spectrums], an optimization problem that aims to maximize the torque for given maximum peak voltage and root mean square (RMS) current is formulated: the optimal torque sharing among the two virtual machines (the two dq-axis subspaces) that represent the real five-phase machine is thus calculated for any mechanical speed. For an inverter and a dc voltage sized with only considering the first harmonic of back EMF and current, the problem is solved with changing the virtual machine back EMFs and inductances ratios. With the introduction of the maximum torque/speed point, maximum power/speed point, and maximum reachable speed, it can be shown that, if the inductance ratio is large enough for given Volt-Ampere rating, the machine can produce higher torque without reducing its speed range, thus meaning that the capability of the inverter to work is improved with the use of the third harmonic. This property is all the truer as the base armature reaction is large. A particular five-phase machine is sized and numerically analyzed to check this property.