Steady-state Temperature Calculation of Transistors using Harmonic Balance

Accurate calculation of semiconductor losses and temperature is the foundation of any design methodology for a power electronic converter. Computation accuracy and speed play a vital role if a large set of parameters needs to be considered. Averaged loss models often neglect the temperature dependence of transistors, leading to fast, but inaccurate results. In contrast, iterative methods and simulation tools, which can include temperature dependence, take significantly longer to compute, but yield more precise results. This paper presents a best of both worlds approach, by using the harmonic balance method to obtain the steady-state solution for any inverter topology including temperature dependent conduction and switching losses. The proposed method solves for the discrete Fourier series of the device temperature, by expressing the temperature dependence and operating parameters in the frequency domain. The set of equations for each coefficient is solved by a single matrix inversion, resulting in very fast computation for steady-state temperature cycles. The steady-state operation of over one thousand possible inverter designs is calculated within less than one minute, matching iterative simulation in device temperature, conduction and switching losses, at a fraction of the computation time. In addition, the method shows good agreement with temperature measurements of a three-phase silicon-carbide inverter.