Embedded finite-element solver for computation of brushless permanent-magnet motors

This paper describes the theory underlying the formulation of a “minimum set” of finite-element solutions to be used in the design and analysis of saturated brushless permanent-magnet motors. The choice of finite-element solutions is described in terms of key points on the flux–MMF diagram. When the diagram has a regular shape, a huge reduction in finite-element analysis is possible with no loss of accuracy. If the loop is irregular, many more solutions are needed. This paper describes an efficient technique in which a finite-element solver is associated with a classical $d$– $q$-axis circuit model in such a way that the number of finite-element solutions in one electrical half-cycle can be varied between 1 and 360. The finite-element process is used to determine not only the average torque but also the saturated inductances as the rotor rotates