Magnetic Field Modeling of Permanent Magnet Type Electronically Operated Synchronous Machines Using Finite Elements

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Abstract
The finite element method is applied to the analysis of electronically operated permanent magnet type synchronous machines. In this class of machines, the armature MMF is a discretely forward stepping one of high harmonic content. The discretely stepping MMF is accounted for by a series of finite element field solutions as the rotor moves throughout one complete cycle of the ac armature current. Because of the discretely forward travelling MMF, a series of finite element grids depicting the rotor at various equally spaced locations, covering its movement during one cycle of the armature current, is required. This is accomplished by means of an automated algorithm for generation of the required finite elemennt grids. This allows one to match any stator grid to any rotor grid for any given displacement between the two grids. This matching is done in the air gap region by fitting it with a suitable row of triangular elements. In addition, a permanent magnet model is developed based upon the magnet geometry and material properties. This method was applied to the analysis of a 15 hp samarium cobalt machine at both rated and no load conditions. The calculated results were in excellent agreement with search coil measurements at both of these operating conditions. These solutions were then used to determine the midgap EMF waveforms. The calculated midgap EMF was in excellent agreement with an oscillogram of the actual EMF in both waveshape and magnitude.