A complex space vector approach to rotor temperature estimation for line-connected induction machines with impaired cooling

Thermal models used in overload protection relays often fail to predict the rotor temperature for motors with impaired cooling conditions. In this case, the temperature estimated from the rotor resistance can be used as an indicator of the motor's cooling capability. However, this estimated rotor temperature is often corrupted by estimation error due to the asymmetry in the power supply. A detailed analysis of the trajectories of the complex current and voltage space vectors in a synchronous reference frame is presented in this paper, and the negative sequence fundamental frequency components are identified as the major cause of the estimation error. Based on this analysis, a fast and efficient algorithm is proposed to calculate the rotor temperature for line-connected induction machines. By applying the Goertzel algorithm to the complex current and voltage space vectors, constructed directly from the motor terminal measurements, the positive sequence fundamental frequency components are extracted, and the rotor temperature is then estimated with significantly reduced estimation error. Compared to the conventional scheme based on the fast Fourier transform, the proposed algorithm is faster and more efficient, and is therefore more suitable for implementation on a low-cost hardware platform. Index Terms--Complex space vector, condition monitoring, Goertzel algorithm, impaired cooling, induction machine, rotor temperature estimation, unbalanced supply.