Fast algorithm to obtain the torque characteristics with respect to load angle of synchronous machines using finite element method

Synchronous machines (SMs) have wide applications in many areas including industrial, agricultural, and domestic. The torque-load angle relationship is an essential parameter governing the characteristics of SMs. Conventionally, for each load angle, a transient magnetic field model using the time-domain finite element method (FEM) needs to be solved, and hence it is very time-consuming to obtain the complete characteristics of SMs. In this paper, a fast variable phase method, which computes the transient process of the time-domain FEM once only and not repeatedly, is proposed to find the entire torque-load angle curve of SMs. By adjusting the time-step size and the nonlinear iteration error tolerances, the proposed method can significantly reduce the computing time when compared with those of conventional methods.