Coupled Heat-Electromagnetic Simulation of Inductive Charging Stations for Electric Vehicles
Coupled electromagnetic-heat problems have been studied for induction or inductive heating, for dielectric heating, for testing of corrosion, for detection of cracks, for hardening of steel, and more recently for inductive charging of electric vehicles. In nearly all cases a simple co-simulation is made where the electromagnetics problem is solved in the frequency domain (and which thus is assumed to be linear) and the heat equation in the time domain. One exchanges data after each time step (or after some change in the heat profile). However, the coupled problem is non-linear in the heat variable. In this paper we propose to split the time domain in windows in which we solve the electromagnetics problem in frequency domain. We strengthen the coupling by iterations, for which we prove convergence. By this we obtain a higher accuracy, which will allow for larger time steps and also for higher order time integration. This fully exploits the multirate behavior of the coupled system. An industrial example illustrates the analysis.
KeywordsHeat Equation Electric Vehicle Eddy Current Loss Source Current Density Magnetic Vector Potential
This work is supported by the German BMBF in the context of the SOFA project (grant number 03MS648E). The fifth author is supported by the Excellence Initiative of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt.
- 2.Brachtendorf, H.G., Welsch, G., Laur, R., Bunse-Gerstner, A.: Numerical steady state analysis of electronic circuits driven by multi-tone signals. Electr. Eng. (Archiv fur Elektrotechnik) 79, 103–112 (1996)Google Scholar
- 3.Chen, H., Tang, J., Liu, F.: Coupled simulation of an electromagnetic heating process using the finite difference time domain method. J. Microw. Power Electromagn. Energy 41(3), 50–68 (2007)Google Scholar
- 4.Clemens, M., Gjonaj, E., Pinder, P., Weiland, T.: Numerical simulation of coupled transient thermal and electromagnetic fields with the finite integration method. IEEE Trans. Magn. 36(4), 1448–1452 (2001)Google Scholar
- 5.Clemens, M., Schöps, S., Cimala, C., Gödel, N., Runke, S., Schmidthäusler, D.: Aspects of coupled problems in computational electromagnetics formulations. ICS Newslett. (International Compumag Society) 19(2), 3–12 (2012)Google Scholar
- 6.COMSOL Multiphysics: Command Reference (2007). www.comsol.com
- 9.Kaufmann, C., Günther, M., Klagges, D., Knorrenschild, M., Richwin, M., Schöps, S., ter Maten, E.J.W.: Efficient simulation of frequency-transient mixed co-simulation of coupled heat-electromagnetic problems. Math. Ind. 4 (2014, to appear).Google Scholar
- 10.Rudnev, V.: Induction Hardening of Gears and Critical Components. Gear Technology pp. 58–63 (Sept/Oct) and 47–53 (Nov/Dec) (2008). Part I and IIGoogle Scholar
- 13.Will, J.: An optimal control problem in electromagnetic induction heating. Master’s thesis, Chemnitz University of Technology, Department of Mathematics (2010)Google Scholar