Design Methodologies for Variable-Flux Machines With Extra Torque–Speed Range

The design methodologies for variable-flux machines (VFMs), which can illustrate the relationship between the extra torque–speed range and the machine properties of VFMs, are proposed in this article based on the analytical and graphic methods. The operating principles of the VFMs with different salient ratios are analyzed. The influences of machine properties on torque–speed curves are comprehensively studied. Then, the magnetization-state boundary of the non-salient VFM with $i_{d} = 0$ control method is investigated by the analytical method. The design methodology for selecting suitable magnetization state is deduced. Due to the complexity of the transcendental equations for other type machines and control methods, the per unit system and the graphic method are used to obtain the boundary. The influence of the negative $d$ -axis current limit on the torque–speed curves is investigated. The methodology to remedy the influence is given. The proposed methodologies can fully exploit the machine properties and provide the reference guidance in the initial design stage of the VFMs.