Data-driven Thermal Modeling for Electrically Excited Synchronous Motors -- A Supervised Machine Learning Approach

TL;DR

This work addresses the challenge of online, accurate temperature estimation for electrically excited synchronous motors (EESMs) in EVs by adopting a data-driven, supervised learning approach based on ordinary least squares (OLS). The model uses a rich feature set that includes default sensor inputs, loss-related features (copper and iron losses), and memory of past conditions via exponentially weighted moving averages and standard deviations, with formulas such as $\hat{\boldsymbol{y}}=\boldsymbol{X}\hat{\boldsymbol{\beta}}$ and $\hat{\boldsymbol{\beta}}=(\boldsymbol{X}^{\mathbf{T}}\boldsymbol{X})^{-1}\boldsymbol{X}^{\mathbf{T}}\hat{\boldsymbol{y}}$, plus moving-average definitions $\mu_t$ and $\sigma_t$. The approach is validated on experimental data from a 190 kW EESM prototype, collected at 10 Hz over about 7 hours, and evaluated with 10-fold cross-validation using metrics such as MSE, MAE, and MaxAE. Results show that including loss inputs improves prediction accuracy (e.g., rotor MSE down to $2.8983$ and stator MSE down to $0.4664$), while the model remains computationally efficient and suitable for online use. Overall, the work demonstrates that a data-driven, memory-enabled OLS model can deliver accurate, online thermal estimations for EESMs, with practical benefits for safety, cooling, and performance in EV propulsion systems.

Abstract

This paper proposes a data-driven supervised machine learning (ML) for online thermal modeling of electrically excited synchronous motors (EESMs). EESMs are desired for EVs due to their high performance, efficiency, and durability at a relatively low cost. Therefore, obtaining precise EESM temperature estimations are significantly important, because online accurate temperature estimation can lead to EESM performance improvement and guaranteeing its safety and reliability. In this study, in addition to the default inputs' data, EESM losses data is leveraged to improve the performance of the proposed ML approach for thermal modeling. Exponentially weighted moving averages and standard deviations of the inputs are also incorporated in the learning process to consider the memory effect for modeling a dynamical thermal model. Using the experimental data of an EESM prototype, the performance of ordinary least squares (OLS) method is evaluated through a complete training, testing and cross-validation process. Finally, simulation results will provide the key performance metrics of OLS for EESM thermal modeling.

Figures (6)

• Figure 1: EESM in the test bench. The slip ring transferring the rotor temperature signal can be seen in the left of the image.
• Figure 2: EESM rotor and stator temperature sensors' positions depicted with red circles.
• Figure 3: Toque-speed values of three measurement cycles. In total these sets make up 276 min of 400 min of experimental data.
• Figure 4: $k$-fold cross-validation.
• Figure 5: MSE of OLS over 10-fold cross validation results incorporating different loss inputs.