Improved Harmonic Model Method for Electrical Machine Magnetic Field Modeling

The harmonic model (HM) method is widely applied for accurate linear/nonlinear magnetic field calculations; however, the harmonic truncation effect contributes to the error and slows down the convergence. The low-rank property of the coefficient factor matrix of the boundary conditions, moreover, results in an extremely time-consuming inverse matrix calculation. In this article we presented a simple but effective method that applies the Hanning window into HM method (HMHW) to achieve faster convergence and higher accuracy. To avoid the time-consuming inverse of the low-rank coefficient factor matrix, the coefficient factor matrix was analyzed, and a simplification method of the coefficient factor matrix in HM (SHM) was proposed. This article includes a detailed description of SHM method and HMHW method, improvements in time consumption and iterative calculation of the SHM and HMHW method, and finite element simulations to verify their magnetic field calculation accuracy. The HMHW method was found to reduce the rms error of the nonlinear magnetic field in the mid-air gap by an average of 18%, and the SHM method has reduced the magnetic field calculation time by an average of seven times when compared to the general HM method.