Low Computational Cost Thermal Modelling of High-Frequency Power Transformers using an Admittance Matrix Apporach

Thermal modelling of magnetic components in high-frequency power electronic systems is not trivial. This can be attributed to the complex non-uniform losses, heterogenous construction of magnetic components, and the temperature dependence of electrical and magnetic properties. Accurate thermal modelling of such magnetic components relies on the use of bi-directionally coupled electromagnetic-thermal numerical analysis. Although such bi-directionally coupled numerical models provide accurate results, the computational cost of such models can be restrictive. Hence, there is a need for low computational cost thermal models of magnetic components. In this paper, we develop a low computational cost thermal model of a power transformer using the admittance matrix approach. First, a bi-directionally coupled multiphysics model of a power transformer is developed and validated using experimental test results. Using the numerical model, low-cost thermal models are evaluated for surface heat transfer coefficients varying between 1 to $\mathbf{200}\ \boldsymbol{W}/\boldsymbol{m}^{\mathbf{2}}\cdot \boldsymbol{K}$, covering the typical thermal operating range of magnetic components housed in conventional power electronic systems. The final low-cost thermal model's surface temperature and heat flux predictions were within $\pm \mathbf{8}.\mathbf{2}\%$ of the numerical results, while the junction temperature error was $\pm \mathbf{6}.\mathbf{18}\ \%$. The simplified thermal model developed shows close to Boundary Condition Independence (BCI) behaviour and is a low computational cost alternative to the numerical model.