Hammerstein Models for Rotor and Winding Temperature Estimation of a Permanent Magnet Synchronous Motor

The temperature monitoring of the rotor of a permanent magnet synchronous motor (PMSM) is crucial to prevent magnetic damages such as demagnetization, which directly impacts the machine’s torque capability. In this regard, data-driven methods such as machine learning and deep learning algorithms have been used to generate models that allow for the estimation of the rotor temperature. Nevertheless, data-driven methods require large sample sizes and large training times to be used effectively. In addition, data-driven methods typically do not consider prior knowledge about the thermal dynamics of the system, making it a black-box approach. This paper proposes the use of Hammerstein models to estimate the temperature of the rotor and winding of a PMSM. Hammerstein models require a linear time-invariant (LTI) block that incorporate prior knowledge about the system dynamics and an input nonlinear static block to model a given system. The LTI block was generated by identifying a lumped parameter thermal network (LPTN) of the PMSM by assuming fixed parameter values, while the input nonlinear block was composed of 4 sigmoid neural networks of 1 neuron applied to the inputs of the LPTN associated with stator and magnet losses. The results show that the LPTN can estimate the temperature of the winding and magnet with an average mean-squared error of $31.6637^{\circ} \mathbf{C}^{2}$ and $6.0015{ }^{\circ} \mathbf{C}^{2}$, respectively. On the other hand, using the Hammerstein model produces an average mean-squared error of $1.1098{ }^{\circ} \mathrm{C}^{2}$ and $2.0431{ }^{\circ} \mathrm{C}^{2}$ for the winding and magnet, respectively.