Analytical Approach and Solution for Line-Start Permanent Magnet Synchronous Machines with Anisotropic Rotor Reluctance

In this paper the derivations of transient current and torque of a line start permanent magnet synchronous motor are described. Using the detailed analytical formulas, the dependencies of the current and torque on machine parameters and internal state quantities can be determined. This type of machines have an anisotropic rotor design and so the reluctance in direct axis and in quadrature axis have to be considered. For derivation the stator resistance and the initial angle of mains voltage are considered. The derived equations were validated due to a comparison with a numeric solution. Finally, the applicability of the derived torque as an approximation for the start-up is evaluated.