Two-step Model Order Reduction for a Thermal Finite Element Model of a Power Electronics Module

Understanding the thermal behavior of power electronics is of critical importance in their design and development stage. Typical power losses are P loss > 2 kW, thus liquid cooling is often required in order to maintain acceptable temperatures. Due to the different thermal conductivities and heat capacities in the layered design, the system has multiple time constants and can not be modelled as a simple system with one time constant. However, this behavior can be well simulated using the finite element method. The transient thermal response is of special interest in the present case. Time constants spanning multiple order of magnitudes call for sufficiently small time steps. To speed up simulations, the original system can be compressed with model order reduction, lowering the state dimension to achieve higher performance, while retaining good accuracy of the simulation results. In this contribution, we apply these techniques to a typical power electronics use case and analyze their performance and accuracy. We also discuss a two-step reduction scheme combining the efficiency and error-bound of two state-of-the-art software packages.