Sensitivity Analysis of Lumped-Parameter Thermal Networks for the Experimental Calibration of eMotor Models

Lumped-parameter thermal networks (LPTNs) are efficient computational models that can be used to replicate the thermal behavior of eMotors in a way that is compatible with real-time execution. The accuracy of the simulation results delivered by LPTNs relies on the selection of an appropriate topology and the accurate tuning of their parameters, namely resistances, capacities and heat sources. It is difficult, however, to obtain an accurate tuning of the parameters starting from theoretical expressions, and these often need to be adjusted based on experimental calibration. Several methods can be used to this end; among these, finite differences are a popular option. This article presents a methodology for the analytical determination of the sensitivity of LPTN dynamics with respect to its lumped parameters. The obtained analytical sensitivities provide information about the effect of the circuit parameters on the thermal dynamics of the overall system, and can be used to enable the use of gradient-based optimization methods to adjust the LPTN parameters. The proposed method overcomes several limitations of finite difference approaches, such as the computational load incurred when the number of parameters to be adjusted is large, and the variability of the results with the increment used to define the finite differences. The analytical sensitivities were tested in the analysis and optimization of a benchmark thermal model and the LPTN representation of a permanent-magnet synchronous motor (PMSM).