Temperature estimation in PMSMs via combined direct and indirect methods

• PMSM temperature estimation using observers that utilize available sensor data. • Electrical model-based observer estimates magnet temperature indirectly. • Thermal model-based observer uses measured stator temperatures and magnet temperature estimate. • Combines data-driven calibration with physics-based modeling. • Fusing both observers improves accuracy and error convergence speed. Accurate temperature monitoring is essential for the safe and efficient operation of permanent magnet synchronous machines (PMSMs), especially in automotive applications. However, due to cost and integration challenges, placing temperature sensors on critical components like permanent magnets is impractical. This paper proposes an observer-based approach that leverages available measurements to estimate temperatures throughout the machine without relying on full sensor coverage. Two observers are developed: one based on an electrical machine model, which estimates the permanent magnet temperature indirectly via the permanent magnet flux linkage, and another one based on a thermal model, which incorporates measured temperatures from the end winding and the estimate from the electrical observer. The approach combines data-driven calibration with physical modeling to achieve high estimation accuracy and robustness under varying cooling conditions. The proposed method is validated both experimentally and through dedicated simulation studies, that assess the observer’s robustness to model uncertainties, parameter variations, and measurement noise. The results demonstrate that fusing electrical and thermal observations enables more precise and responsive temperature estimation than using either model alone. The method provides a practical alternative to dense sensor placement while preserving reliability and safety.