Convergence Behaviour of Newton-Raphson Method in Node- and Loop-Based Non-linear Magnetic Equivalent Circuit Analysis

Abstract

In this paper, the non-linear magnetic system equations are derived. The Newton-Raphson method is used to solve the system of non-linear equations. A simplified Jacobian is derived for both node- and loop-based magnetic equivalent circuit analysis. The partial derivative term is eliminated in this simplified Jacobian using differential relative permeability. The convergence behaviour of the Newton-Raphson method is studied. The loop analysis exhibits more stable convergence than that of the node analysis while solving non-linear magnetic equivalent circuit using the Newton-Raphson method.