Saeed Jafarzadeh

State Estimation of Induction Motor Drives Using the Unscented Kalman Filter

This paper investigates the application, design, and implementation of unscented Kalman filters (KFs) (UKFs) for induction motor (IM) sensorless drives. UKFs use nonlinear unscented transforms (UTs) in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. The advantage of using UTs is their ability to capture the nonlinear behavior of the system, unlike extended KFs (EKFs) that use linearized models. Four original variants of the UKF for IM state estimation, based on different UTs, are described, analyzed, and compared. The four transforms are basic, general, simplex, and spherical UTs. This paper discusses the theoretical aspects and implementation details of the four UKFs. Experimental results for a direct-torque-controlled IM drive are presented and compared with the EKF. The focus of this study is on low-speed performance. It is concluded that the UKF is a viable and powerful tool for IM state estimation and that basic and general UTs give more accurate results than simplex and spherical UTs.

Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part I. Stability Analysis

This paper introduces sufficient conditions for the exponential stability of type-1 and type-2 Takagi-Sugeno-Kang (TSK) fuzzy systems. A major advantage of the new conditions is that they do not require the existence of a common Lyapunov function and are, therefore, applicable to systems with unstable consequents. In addition, our results include two classes of type-2 TSK systems with type-1 consequents for which no stability tests are available. The use of the conditions in stability testing is demonstrated using simple numerical examples that include cases where methods that are based on a common Lyapunov function fail. The application of the stability test to develop new controller design methodologies is presented in a separate paper (i.e., Part II).

Solar Power Prediction Using Interval Type-2 TSK Modeling

The random nature of solar energy resources is one of the obstacles to their large-scale proliferation in power systems. The most practical way to predict this renewable source of energy is to use meteorological data. However, such data are usually provided in a qualitative form that cannot be exploited using traditional quantitative methods but which can be modeled using fuzzy logic. This paper proposes type-1 and interval type-2 Takagi-Sugeno-Kang (TSK) fuzzy systems for the modeling and prediction of solar power plants. The paper considers TSK models with type-1 antecedents and crisp consequents, type-1 antecedents and consequents, and type-2 antecedents and crisp consequents. The design methodology for tuning the antecedents and consequents of each model is described. Finally, input-output data sets from a solar plant are used to obtain the three TSK models and their prediction results are compared to results from the literature. The results show that type-2 TSK models with type2 antecedents and crisp consequents provide the best performance based on the solar plant data.

Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part II. Control Design

This paper proposes a new control system design methodology for type-1 and type-2 Takagi-Sugeno-Kang (TSK) fuzzy systems that are based on new stability conditions. The stability conditions are discussed in a companion paper (Part I) and are used in the proofs of our main results. A major advantage of the new methodology is that it does not require a common Lyapunov function and is therefore applicable to systems with nonstabilizable consequents. Our controllers include fuzzy type-1 proportional and proportional-integral (PI) controllers, as well as constant state feedback for the same systems. The controller results in an exponentially stable system, and the designer can specify the rate of exponential convergence. The controller designs can be tested by the usage of linear matrix inequalities (LMIs). The design methodology is demonstrated by the usage of simple examples where methods that are based on a common Lyapunov function fail and physical systems where the new methodology provides better performance.

Square Root Unscented Kalman Filters for State Estimation of Induction Motor Drives

This paper investigates the application, design, and implementation of the square root unscented Kalman filter (UKF) (SRUKF) for induction motor (IM) sensorless drives. The UKF uses nonlinear unscented transforms (UTs) in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. The advantage of using the UT is its ability to capture the nonlinear behavior of the system, unlike the extended Kalman filter (EKF) that uses linearized models. The SRUKF implements the UKF using square root filtering to reduce computational errors. We discuss the theoretical aspects and implementation details of the SRUKF for IM drives. Experimental results for a direct-torque-controlled drive are presented for a wide speed range of operation, with focus on low-speed performance. A comparison with the conventional EKF and the UKF is included. Our results show that the SRUKF is a viable and powerful tool for IM state estimation.

On the Stability and Control of Continuous-Time TSK Fuzzy Systems

This paper introduces a new stability test and control design methodology for type-1 and type-2 continuous-time (CT) Takagi-Sugeno-Kang systems. Unlike methods based on a common Lyapunov function, our stability results apply for systems with unstable consequents, and our controllers can be designed for systems with unstabilizable consequents. The stability results are derived using the comparison principle with a discontinuous function and the upper right-hand derivative. The control results include CT fuzzy proportional controllers and fuzzy proportional-integral controllers that can be obtained by solving linear matrix inequalities. We provide several examples to demonstrate our stability testing and controller design and compare our results to available methods in the literature. Our results compare favorably with results available in the literature and provide stability tests and controllers where earlier approaches fail.

Fuzzy TSK approximation using type-2 fuzzy logic systems and its application to modeling a photovoltaic array

This paper presents a simple approach to the fuzzy approximation of input-output data with a type-2 fuzzy model. The approach allows fuzzy type-2 modeling using data with input uncertainty, output uncertainty, or input-output uncertainty. The approximation error associated with the fuzzy representation is specified by the modeler and is used in the procedure to obtain the fuzzy model. We provide an example where type-2 fuzzy models of the characteristics of a photovoltaic array are obtained from input-output data with input, output, and input-output uncertainty.

Hour-ahead wind power prediction for power systems using Hidden Markov Models and Viterbi Algorithm

This paper presents a new stochastic method for very short-term (1 hour) wind prediction in electrical power systems. The method utilizes Hidden Markov Models (HMM) and the Viterbi Algorithm (VA). Past wind farm power production data are required to develop the HMM model. The accuracy of the predictions improves drastically if hourly weather forecast data are used as pseudo-measurements. Computer simulations using Northwestern weather recordings from the Bonneville Power Administration (BPA) website show good correlation between our predictions and the actual data.

Stability Analysis of Positive Interval Type-2 TSK Systems With Application to Energy Markets

Positive systems play an important role in many fields including biology, chemistry, and economics, among others. This paper discusses the stability of interval type-2 discrete-time positive Takagi-Sugeno-Kang (TSK) fuzzy systems. It discusses positive TSK systems and their nonzero equilibrium point. It then provides sufficient conditions for their exponential stability and instability. All the proposed stability and instability conditions can be tested using linear matrix inequalities. The stability and instability tests are demonstrated through application to a TSK model of the electric power market under a variety of market conditions.

A Unified Approach for Power System Predictive Operations Using Viterbi Algorithm

A paradigm shift in the renewable energy proliferation in the U.S. necessitates a paradigm shift in power system operations to accommodate large-scale intermittent power while keeping the grid reliable and secure. Energy management systems (EMS) will benefit from an auxiliary function, which integrates the wind and load forecasting to state estimation and forecasting. This auxiliary function will create a predictive database for the power system states using the historical states as well as wind and load forecasts. The predictive database can be utilized to provide pseudo-measurements to a static state estimator in the case of loss of observability and bad data processing, or it can be used for short-term congestion and ramping predictions. This paper proposes an auxiliary tool for look-ahead power system state forecasting in electrical power systems with high intermittent renewable energy penetration. The method utilizes Markov models (MMs) and the Viterbi algorithm (VA) with a grid of feasible power system states obtained and updated by using the past states. The proposed algorithm is evaluated on the IEEE 14-bus and 118-bus systems using wind and load data available from the Bonneville Power Administration (BPA). The results show good correlation between the predictions and the actual power system states.