Core Concepts
A novel strategy is proposed for the systematic coupling of magnetic field and electric circuit equations, preserving the underlying geometric structure and power balance of the coupled system.
Abstract
The paper presents a novel approach for the coupling of magnetic field and electric circuit equations when modeling power devices in the low-frequency regime. The key aspects are:
The authors consider a vector potential formulation for the magneto-quasistatic field equations and couple it with a magnetic-oriented nodal analysis for the electric circuit. Both models share the same geometric structure, which is preserved when coupling them appropriately.
The resulting coupled system of differential-algebraic equations has a particular structure that explicitly encodes the energy storage, dissipation, and transfer mechanisms. This allows the authors to derive a power balance on the continuous level, which can be preserved under appropriate discretization in space and time.
The theoretical findings are demonstrated through numerical results for a full-wave rectifier circuit coupled to a transformer model. The discrete power balance is shown to be satisfied with high accuracy, and the expected convergence rates are observed.
The authors discuss how the proposed approach can be extended to handle nonlinear constitutive models and more general coupling mechanisms. They also highlight the potential benefits in terms of numerical stability due to the reduced differential-algebraic index of the coupled system.