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A high-speed permanent magnet (PM) motor has been used extensively in flywheel energy storage, electric vehicles, high-speed rail, and other applications because of its advantages such as high power density, small size, light weight, and high efficiency. For high-speed electrical systems, various configurations are recommended. Specifically, a permanent magnet synchronous motor (PMSM), which is a PM-based motor, uses PMs on the rotor and conventional windings on the stator. In this case, the rotor spins synchronously with the rotating magnetic field of the stator. However, due to the high speed, the large carrier frequency of the PM, and the harmonics of the air-gap field, the eddy current loss in the PM increases. Additionally, due to limited internal space and insufficient heat dissipation conditions, the temperature of the rotor increases, and irreversible demagnetization of the PM may occur in severe cases, which reduces the reliability and safety of the motor. Therefore, accurate calculation of the rotor eddy current loss is crucial for the design and stable operation of a high-speed PM motor.

Question

A high-speed permanent magnet (PM) motor has been used extensively in flywheel energy storage, electric vehicles, high-speed rail, and other applications because of its advantages such as high power density, small size, light weight, and high efficiency. For high-speed electrical systems, various configurations are recommended. Specifically, a permanent magnet synchronous motor (PMSM), which is a PM-based motor, uses PMs on the rotor and conventional windings on the stator. In this case, the rotor spins synchronously with the rotating magnetic field of the stator. However, due to the high speed, the large carrier frequency of the PM, and the harmonics of the air-gap field, the eddy current loss in the PM increases. Additionally, due to limited internal space and insufficient heat dissipation conditions, the temperature of the rotor increases, and irreversible demagnetization of the PM may occur in severe cases, which reduces the reliability and safety of the motor. Therefore, accurate calculation of the rotor eddy current loss is crucial for the design and stable operation of a high-speed PM motor.

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Pulse width modulation current harmonics and space harmonics are some of the major factors affecting the rotor eddy current loss of the high-speed permanent magnet motor. In this study, based on the principle of the equivalent current sheet, a two-dimensional motor model in a rectangular coordinate system was established. Considering the armature reaction, the end effect, and the current harmonics generated by variable frequency power supply, the eddy current loss of the rotor at different frequencies was analyzed and calculated using the analytical and finite element methods (FEM). When the frequency is between 200 Hz and 600 Hz, the variation trend of the rotor eddy current loss with a frequency obtained by analytical calculation and FEM analysis is roughly the same, and the error is still within a reasonable range. However, as the frequency continues to increase, the error between the two becomes larger and larger. Furthermore, based on the two-dimensional FE model, the influence of the sleeve material, the thickness, and the composite structure on the rotor eddy current loss were studied and analyzed. It was found that adding a graphene shielding layer between the permanent magnet and the sleeve can effectively shield the harmonic magnetic field, greatly reduce the eddy current loss of the permanent magnet, and effectively prevent the temperature of the permanent magnet from being too high, which is conducive to the continuous and stable operation of the high-speed permanent magnet motor.

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A 400 V, 5- Hz, 3-phase delta connected, 6-pole induction motor has following standstillleakage impedances per phase referred to stator:z1 = 1.2 + 2.1j ohm , Z2 =1.32 + 2.2j ohm.Neglecting magnetizing impedance, determine(a) gross output power at a slip of 0.04,(b) thechange in line current when the stator terminals are switched from star to delta at a slip of0.4,(c) the resistance to be added in each rotor phase to obtain a starting torque of 350 Nm

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