Zhi Gao

A Sensorless Rotor Temperature Estimator for Induction Machines Based on a Current Harmonic Spectral Estimation Scheme

This paper proposes a sensorless rotor temperature estimator for small- to medium-sized mains-fed induction machines. With measurements obtained only from voltage and current sensors, the proposed estimator can capture the rotor temperature online. The rotor speed is first extracted from the stator current harmonic spectrum based on the estimated rotor slot and eccentricity harmonic frequencies. Then the inductances are estimated according to the induction machine equivalent circuit developed from the rotor flux field orientation. The stator winding resistance at ambient temperature is the only motor parameter needed as input in this stage. Once the inductances are obtained, they are fed into the rotor resistance estimation algorithm to yield an estimate of the rotor resistance. Finally, the rotor temperature is calculated from the linear relationship between the temperature and rotor resistance. The experimental results from different motors are shown to validate the proposed algorithms. The whole scheme is efficient and reliable and is therefore suitable for implementation in a motor overload protection relay to provide thermal protection against rotor overheating.

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.

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 motors 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.

A Frequency Demodulation Approach to Induction Motor Speed Detection

Rotor slot harmonics are found in the stator current waveforms for most squirrel-cage induction motors. These harmonics are caused by the finite number of rotor slots in a motor, and their frequencies are inherently correlated with the motors rotational speed. A frequency demodulation approach is proposed in this paper to continuously and accurately track the rotational speed for induction motors that are operated at either dynamic or steady-state conditions from fixed-frequency power supplies. First, a complex current vector is synthesized from polyphase electrical current measurements. Second, a local oscillator and a mixer are cascaded with a digital filter to heterodyne a specific rotor slot harmonic and suppress adjacent interferences. A finite impulse response differentiator is then employed as a frequency demodulator to approximate the time derivative of the phase of this specific rotor slot harmonic and to resolve its instantaneous frequency. Finally, the induction motor speed is calculated from this resolved instantaneous rotor slot harmonic frequency. Experimental results demonstrate that the proposed scheme is capable of interleaving data acquisition with real-time computation, iteratively estimating motor speed on a sample-by-sample basis.

A Sensorless Adaptive Stator Winding Temperature Estimator for Mains-Fed Induction Machines with Continuous-operation Periodic Duty Cycles

An induction machines thermal behavior is determined by various machine components with dissimilar thermal characteristics. When a model with a single thermal time constant is used to characterize the machines thermal behavior under periodic duty cycles, the magnitude of the thermal time constant needs to be adjusted according to the duty cycles to reflect the machines dominant thermal dynamics during that specific interval. Based on the analysis of the internal heating effects of a small- to medium-sized mains-fed induction machine, a sensorless stator winding temperature estimator is proposed to compensate for the shift in the thermal time constant for motors with continuous- operation periodic duty cycles. First, the rotor temperature is estimated from the voltage and current measurements and is used as an indicator of the motors internal thermal operating condition. Then, a hybrid thermal model is employed to correlate the rotor temperature to the stator winding temperature. Finally, an observer is designed to take the estimated rotor temperature as a feedback signal into the hybrid thermal model. The correction provided by the feedback signal enables a reliable tracking of the stator winding temperature for motors with periodic duty cycles. The experimental results are given to validate the proposed method, and the overall scheme is shown to estimate the stator winding temperature efficiently without using any real temperature sensors.

Filter Design for Estimating Parameters of Induction Motors With Time-Varying Loads

Periodically time-varying loads such as reciprocating compressors produce torque and speed oscillations in grid-connected induction motors. In each compression cycle, the torque and speed oscillations manifest themselves through periodic pulsations in the induction motors stator currents. In resistance-based rotor temperature tracking and overheating monitoring, low- or bandpass filters are frequently used to estimate induction motor electrical parameters from stator currents that contain periodic pulsations. Design of such filters relies on comprehensive knowledge of the load-related periodic pulsations in the stator currents. In this paper, a narrow-band angle modulation concept is first formulated in the framework of complex vector analysis to explain the periodic pulsations in the stator current. Carsons rule is then introduced to establish an empirical relationship between the stator currents modulating frequency and the appropriate bandwidth for low- or bandpass filters. The proposed filter design rules are experimentally validated, and explanations are provided using the phase angle between the motors complex stator current and voltage vectors.

An Online Adaptive Stator Winding Temperature Estimator Based on a Hybrid Thermal Model for Induction Machines

Conventional thermal models with a single thermal capacitor and a single thermal resistor are incapable of giving an accurate stator winding temperature estimate tailored to the specific motors cooling capability. A hybrid thermal model is presented in this paper to account for the disparities in thermal operating conditions for different motors of the same rating, and of the same totally enclosed fan-cooled design. Through theoretical analysis as well as simulation, the change in the motors thermal behavior under impaired cooling conditions, is found to be closely related to the change in this models thermal resistance, R 1. An online parameter tuning algorithm is proposed in this paper. By updating R1 based on the rotor temperature estimated from the rotor resistance, the tuning algorithm adapts the hybrid thermal model to the changes in the motors thermal operating conditions. Once the hybrid thermal model is properly tuned, an adaptive stator winding temperature estimator is established. It is capable of tracking the stator winding temperature for a motor with specific cooling capability to insure complete overload protection. Experimental results validate this temperature estimator based on the hybrid thermal model and the online parameter tuning algorithm

An adaptive Kalman filtering approach to induction machine stator winding temperature estimation based on a hybrid thermal model

The stator winding temperature of an induction machine is estimated from either a thermal model-based or an induction machine parameter-based temperature estimator. The thermal model-based temperature estimator is simple and robust, but it is usually incapable of giving an accurate temperature estimate tailored to a specific motors thermal capacity. The induction machine parameter-based temperature estimator is accurate and machine-dependent, but it is often too sensitive to the machines parametric changes. For small to medium size mains-fed induction machines with TEFC design, a hybrid thermal model is proposed to unify these two temperature estimators. Based on this hybrid thermal model, an adaptive Kalman filter is then formulated to track the stator winding temperature with increased accuracy and robustness. Noise identification and input estimation techniques are used in the Kalman filter to obtain an optimal estimate of the stator winding temperature. The experimental results are given to validate the proposed scheme. The overall algorithm provides efficient and accurate tracking of the stator winding temperature, ensures safe and reliable motor operation and avoids nuisance overload trips, all without using any real temperature sensors.

Robust neuro-identification of nonlinear plants in electric power systems with missing sensor measurements

Fault tolerant measurements are an essential requirement for system identification, control and protection. Measurements can be corrupted or interrupted due to sensor failure, broken or bad connections, bad communication, or malfunction of some hardware or software. This paper proposes a novel robust artificial neural network identifier (RANNI) by combining a sensor evaluation and (missing sensor) restoration scheme (SERS) and an ANN identifier (ANNI) in a cascading structure. This RANNI is able to provide continuous on-line identification of nonlinear plants when some crucial sensor measurements are unavailable. A static synchronous series compensator (SSSC) connected to a power system is used as a test system to examine the validity of the proposed model. Simulation studies are carried out with single and multiple phase current sensors missing; results show that the proposed RANNI continuously tracks the plant dynamics with good precision during the steady state, the small disturbance, the transient state after a large disturbance and the unbalanced three-phase operations. The proposed RANNI is readily applicable to other plant models in power systems.

Continuous on-line identification of nonlinear plants in power systems with missing sensor measurements

A novel robust artificial neural network identifier (RANNI) model is proposed in this paper. This RANNI can continuously track the dynamics of the plant model on-line when some sensor measurements are unavailable. A static synchronous series compensator (SSSC) connected to a small power system is used as a test system to examine the validity of the proposed model. In the simulation, one sensor is assumed to be missing; simulation results show that the proposed RANNI tracks the plant dynamics with good precision during the steady state, the small disturbance, and the transient state after a large disturbance. The proposed RANNI is readily applicable to other plant models in power systems.