Direct Steady-State Calculation of Electromagnetic Devices Using Field-Circuit Models

Field-circuit models are very often used to model electromagnetic devices with conductive and non-linear magnetic materials. The numerical calculations of the field in the magnetic material must be combined with an equation of an external coil placed in the magnetic circuit. This means that the partial differential equations of the electromagnetic field in non-linear conductive materials and the non-linear ordinary differential equations must be solved together. Effective algorithms for solving such problems are still being developed. The article presents an algorithm directly providing the steady state solution without the simulation of transients. The basic assumption is that the solution can be predicted as a periodic time and space function, which is represented by appropriate Fourier series. The developed algorithm uses discrete partial differential operators for time and space derivatives. It allows us to create finite difference equations directly from the field and circuit equations, which take the form of algebraic equations, generally non-linear. This is a unique approach developed by us, which till now did not exist (and is not mentioned) in the literature. That algorithm is tested on a simple case of a solenoid coil with a ferromagnetic and conductive cylindrical core, in 2D space of radius and time. The calculation results confirm the effectiveness of the proposed approach both qualitatively, with regard to physical phenomena in ferromagnetic and conductive material, and quantitatively, in comparison with the results from specialized commercial software.

Automated summary

This article introduces an algorithm that directly provides a steady state solution by representing the predicted periodic time and space function with appropriate Fourier series. The algorithm uses discrete partial differential operators for time and space derivatives and allows for the derivation of finite difference equations directly from the field and circuit equations. The effectiveness of the proposed approach is confirmed through testing on a simple case of a solenoid coil with a ferromagnetic and conductive cylindrical core, both qualitatively in terms of physical phenomena and quantitatively in comparison with results from specialized commercial software.