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A special thanks to Yateendra Deshpande for his valuable help during the course of the project. I also thank all my friends who made life in College Station a little easier. Finally, I thank my parents and brother for all their emotional and monetary support and guidance. vi

Excellence of line start synchronous reluctance motors (LS-SynRM) such as their high efficiency amongst other types of line start motors necessitates the existence of analytical methods in their design. The start-up period of these motors is of high importance and regarding this, the cage design needs to be discussed thoroughly since the squirrel cage is responsible for speeding up the motor to reach at synchronism. One of the issues in this sense is the rich harmonic content of the air-gap MMF arising from irregular bars configuration which afterwards could lead to creation of the torque dips in the torque-speed characteristic of the machine and making it incapable of synchronization under load. An analytical approach to calculate these harmonic effects while also considering the reluctance rotor contribution on them is proposed in this paper. This scheme starts from the stator winding configuration as a known parameter, obtaining the air gap MMF due to only the stator magnetic field, calculating the current and voltages induced through the rotor bars considering the effect of saliency using the model proposed in [1, 2]. Next, harmonic contribution of the rotor cage in the air gap MMF is derived. Finally, probable harmonic cusps and consequently torque dips is found in the torquespeed characteristic of the motor which is helpful in anticipating the synchronization capability under various loads. The results have been verified with a sample 4-pole, two flux barriers per pole LS-SynRM which suffers crawling due to the existence of the torque dips in its torque-speed characteristic. All simulations have been done by finite element analysis (FEA) software and a comprehensive program was written in Matlab to implement the proposed algorithm.

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