A Model Reduction Perspective on Thermal Models for Induction Machine Overload Relays

Full-order thermal models are often used by machine designers to analyze the induction machine thermal behavior. The real-time implementation of such models for the purpose of motor thermal protection is difficult because an extensive knowledge on motors and sufficient computational resource are required. This paper demonstrates that full-order thermal models can be systematically reduced via pole-zero cancellation or Hankel singular-values-based model reduction techniques without additional physical assumptions. As a result, a system of a substantially lower dimension, which has nearly the same response characteristics in the frequency band of interest, is obtained. Both the estimated rotor cage temperature, which is extracted from the voltage and current measurements by a sensorless rotor temperature estimator, and the measured stator winding temperature are used to evaluate the performance of low-order thermal models. Given a certain tolerance for the modeling error, a reduced low-order thermal model can be used to characterize the thermal dynamics of a small- to medium-sized line-connected induction machine and to provide proper protection against motor overheating.