Application of integral equations to the magnetic field analysis of rotating electrical machines

An integral equation (IE) method is applied to the magnetostatic field analysis of salient-pole synchronous machines. A brief description of the method and verification with a known analytical solution are given. The method requires discretization only in the steel regions and does not necessitate any special treatment of the boundary conditions. For a two dimensional solution, the machine cross section is discretized into small triangular elements over which the magnetization can effectively be assumed constant. The resulting nonlinear algebraic equations are solved using the Gauss-Seidel iterative procedure. Application of Ampere´s circuital law around the current carrying regions, combined with overrelaxation, is used to speed convergence. An open circuit analysis is performed on a synchronous motor, where, because of the field symmetry, only one half pole pitch need be discretized. The resulting open-circuit voltage characteristic shows very good agreement with the test curve.