Loop Formulation in Hybrid Analytical Modeling for Solving 2-D Nonlinear Magnetostatic Problems

This article presents a novel formulation in hybrid analytic modeling (HAM) for solving 2-D nonlinear magnetic problems. This novel formulation, referred to as the loop formulation, solves the magnetic equivalent circuit (MEC) through Kirchhoff's voltage law, as opposed to the traditional node formulation, which uses Kirchhoff's current law. This allows one to solve the system iteratively using the Newton-Raphson method instead of the fixed-point method, providing a convergence rate up to four times faster. The novel HAM formulation also provides an excellent tradeoff between accuracy and computational time. It offers approximately one order of magnitude lower computation time for the same accuracy compared to finite-element analysis (FEA) on a slotless geometry.