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This paper presents a closed-form solution to optimize surface permanent magnet (PM) machines using concentrated windings. An analytical model is developed to predict the electromagnetic performances of fractional-slot PM machines. The model can be used to evaluate open-circuit magnetic field distribution with stator slotting effects, armature reaction field distributions, back-EMF waveform, winding inductance, cogging torque, electromagnetic ripple torque, efficiency, specific power, radial force density, and vibration mode order. Particle swarm optimization technique is applied to the proposed model in order to search for solutions that are a good compromise between conflicting objectives. The performances of the optimized machine are verified using finite element analysis. Finally, the analytical and finite element results have been validated with the experimental data, demonstrating a strong correlation between key machine parameters.
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Min et al. (2017) studied this question.
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