Dynamic Iteration for Coupled Problems of Electric Circuits and Distributed Devices

Abstract

Coupled systems of differential-algebraic equations (DAEs) may suffer from instabilities during a dynamic iteration. For a general dynamic iteration, we extend the existing analysis on recursion estimates, error transport and stability to a general DAE setting. In this context, we discuss the influence of certain coupling structures and the computational sequence of the subsystems on the rate of convergence. Furthermore, we investigate convergence and divergence for two coupled problems stemming from refined electric circuit simulation in detail. These are the semiconductorcircuit and field-circuit coupling. As a result of our analysis, we quantify the convergence rate and behavior also using Lipschitz constants and suggest an enhanced modeling of the coupling interface in order to improve convergence.

Multirate Coupling of Controlled Rectifier and Non-Linear Finite Element Model Based on Waveform Relaxation Method

“…This should be compared with the 3 months estimated to perform the simulation using the same time step for the control loop and the FEM. The WRM converges to the exact solution as proved in [9], so the solution is supposed to be close to the exact one. …”

“…A classic source coupling, as the one used in the previous section, does not allow to control the current i s into the secondary winding because it would be imposed as a source to the circuit rectifier part. Therefore, a parameter coupling is used [9], [10]. An equivalent circuit of the transformer is introduced into the rectifier circuit (Fig.7) with a resistance R and an inductance L. The resistance is the same than in the FEM, and the inductance is obtained by a calculation based on a linear FEM of the transformer.…”

“…The WRM approach is an iterative process which converges in theory to the solution of a strong coupling [3]. The method was used for many years for the simulation of circuits [4], [5] or transmission lines [6], and has been recently studied for the coupling of circuit equations and a FEM [7], [8], either by source coupling or by parameter coupling [9], [10].…”

Coupled Heat-Electromagnetic Simulation of Inductive Charging Stations for Electric Vehicles

“…A simple time-domain model consists of the magnetic vector potential equation (1) for the electromagnetic problem and the heat equation (2) to describe the heat diffusion. It can be stated as…”

“…Finally, iteration is still possible in this multirate approach, similar to dynamic iteration approaches, e.g. [1]. However, the main part of the computational costs is the integration of the EM equation, which still has not changed in comparison to the single rate approach.…”