Analytical Modeling of a Permanent-Magnet Synchronous Machine in a Flywheel

We develop an analytical model for a radial-flux external-rotor permanent-magnet synchronous machine (PMSM) without slots in the stator iron and with a shielding cylinder. The machine is part of an energy storage flywheel, to be used as the peak-power unit in a hybrid electric passenger bus. To reduce the induced no-load losses due to the high rotational speed of the flywheel, the slots in the stator are made not of iron but of a nonmagnetic plastic material. This results in an air gap winding with a stator yoke consisting of stacked circular laminations. The analytical model includes the effect of the winding distribution on the field, the fact that it is in the air gap, and the effect of the eddy-current reaction field of the shielding cylinder. The two-dimensional magnetic field is solved in six defined machine layers and useful machine quantities are derived directly from it, leading to the machine voltage equation. We built a prototype flywheel machine. The locked-rotor machine resistance and inductance predicted by the analytical model was compared with the experimentally determined values. The values showed good agreement, thereby validating the analytical model of the machine. Index Terms—Analytical modeling, energy storage, flywheels, permanent-magnet machines. I