An Efficient Iterative Method for the Analysis of Electrical Circuits with Nonlinear Inductive Elements

This paper proposes and analyzes a modified version of the Hănțilă Method (HM) for solving electrical circuits with nonlinear inductive elements. The method replaces the nonlinear inductor with a generator comprising a nonlinear source and a linear impedance. The value of the nonlinear source is determined by defining a Picard–Banach fixed-point sequence that converges to the solution. This approach transfers the nonlinearity from the inductance to the generator’s source. The resulting circuit consists of linear and nonlinear sources and only linear components. It is solved in the harmonic domain using classical theorems and algorithms. A comparative analysis is performed on an RL circuit (a transformer primary winding at no-load). Both accuracy and computational effort are evaluated. The proposed iterative method is compared against steady-state time-domain transient analysis and frequency-domain approaches (Harmonic Balance Method) implemented in commercial software. This method is particularly suitable for analyzing circuits with nonlinear inductive components, such as iron-core coils and equivalent circuits for electrical machines.