Efficient frequency-transient co-simulation of coupled heat-electromagnetic problems

Daniel Klagges,Matthias Richwin,Christof Kaufmann,Sebastian Schöps,E ter Maten,Michael Günther,Michael Knorrenschild

doi:10.1186/2190-5983-4-1

Abstract

BackgroundWith the recent advent of inductive charging systems all major automotive manufacturers develop concepts to wirelessly charge electric vehicles. Efficient designs require virtual prototyping that accounts for electromagnetic and thermal fields. The coupled simulations can be computationally very costly. This is because of the high frequencies in the electromagnetic part. This paper derives a mixed frequency-transient model as approximation to the original problem. We propose a co-simulation such that the electromagnetic part is simulated in the frequency domain while the thermal part remains in time domain.ResultsThe iteration scheme for the frequency-transient model is convergent for high frequency excitation. The error bound improves quadratically with increasing frequency.ConclusionsThe frequency-transient model is very efficient for coupled heat-electromagnetic simulations since the time scales typically differ by several orders of magnitude. The time steps of the full system can be chosen according to the heat subsystem only.MSC: 35K05, 35Q61, 65Z05, 78A25, 78M12, 80M25.

Highlights

With the recent advent of inductive power charging systems and wireless power transmission in consumer and mobile phone technology, [ ], all major automotive manufacturers develop concepts to wirelessly charge electric vehicles, both plug-in and pure electric vehicles (EV)
The electromagnetic (EM) field is considered at high frequencies, where the time scale of the heat conduction is significantly lower than the time scale of the EM field
From Algorithm it can be seen that time steps are chosen according to the time constant of the heat equation and only one linear system is solved per iteration for the curl-curl equation in frequency domain

Summary

Conclusions

A frequency-transient model tailored for heat-electromagnetic problems was derived. The convergence analysis is presented in detail. The error bound for the iteration decreases quadratically with higher frequencies. This result applies to approaches by Driesen and Hameyer [ ] and similar implementations in Comsol [ ]. Competing interests The authors declare that they have no competing interests. Authors’ contributions All authors contributed to this paper as a whole. All authors read and approved the final manuscript. Author details 1Fachbereich Elektrotechnik und Informatik, Hochschule Bochum, Bochum, 44801, Germany. KG, Lüdenscheid, 58513, Germany. 4Graduate School of Computational Engineering, Technische Universität Darmstadt, Darmstadt, 64293, Germany. 5Department of Mathematics & Computer Science, TU Eindhoven, PostBox 513, MB Eindhoven, 5600, The Netherlands

Introduction

Maxwell’s equations Maxwell’s equations read

Convergence analysis We first verify that the Maxwell operator is bounded

Schneider D