This study presents a comprehensive analytical analysis of line start permanent magnet (LSPM) synchronous motors in both steady-state and transient domains. The PM flux, the back-EMF and the winding inductances are first calculated in the steady-state based on the hybrid solution of magnetic circuit and the magnetic islands. Next, the motor voltage relations are mapped into an arbitrary d-q reference frame to dynamically assess the transient speed response as well as the individual motor torque components. Based on the presented analytical modelling, the parameters of the motor are optimised via genetic algorithm to maximise the back-EMF voltage and the overall steady-state performance. Given the parabolic relation between the back-EMF and the braking torque, the starting capability of the motor is defined as the optimisation constraint. Finally, the analytical results are verified by using a finite element analysis software package.

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