Direct adaptive power system stabilizer design using fuzzy wavelet neural network with self-recurrent consequent part

Highlights

• The main disadvantage of FWNN is that the application domain is limited to static problems due to its feed-forward network structure. Therefore, we propose to use a self-recurrent wavelet neural network (SRWNN) in the consequent part of FWNN, solving the control problem for chaotic systems.

• Our proposed structure requires fewer wavelet nodes than the networks with feed-forward structure, due to the dynamic behavior of the recurrent network.

• Finding the optimal learning rates is a challenging task in the classic gradient-based learning algorithms. Hence, in our proposed framework, all of the learning rates are determined optimally based on Lyapunov stability theory.

• We develop a controller based on the proposed network structure and use it for damping the oscillations in the multi-machine power system.

Abstract

This paper aims to propose a stable fuzzy wavelet neural-based adaptive power system stabilizer (SFWNAPSS) for stabilizing the inter-area oscillations in multi-machine power systems. In the proposed approach, a self-recurrent Wavelet Neural Network (SRWNN) is applied with the aim of constructing a self-recurrent consequent part for each fuzzy rule of a Takagi-Sugeno-Kang (TSK) fuzzy model. All parameters of the consequent parts are updated online based on Direct Adaptive Control Theory (DACT) and employing a back-propagation-based approach. The stabilizer initialization is performed using an approach based on genetic algorithm (GA). A Lyapunov-based adaptive learning rates (LALRs) algorithm is also proposed in order to speed up the stabilization rate, as well as to guarantee the convergence of the proposed stabilizer. Therefore, due to having a stable powerful adaptation law, there is no requirement to use any identification process. Kundur's four-machine two-area benchmark power system and six-machine three-area power system are used with the aim of assessing the effectiveness of the proposed stabilizer. The results are promising and show that the inter-area oscillations are successfully damped by the SFWNAPSS. Furthermore, the superiority of the proposed stabilizer is demonstrated over the IEEE standard multi-band power system stabilizer (MB-PSS), and the conventional PSS.

Introduction

The nonlinear dynamics and the complex characteristics of a power system trigger low frequency oscillations when the power system is exposed to the disturbances. The power system stabilizer, a very efficient controller installed in the automatic voltage regulator of the generator, is extensively utilized for enhancing the stability of power systems. The parameters of conventional fixed structure PSS (CPSS) are determined based on a linearized model of the power system considering a single operating point. Factors such as the nonlinearity of the power system, changes in operating conditions or system topology, and deviations in system parameters all cause a degradation in the performance of the CPSS.

To address the abovementioned issues there is a need for a method to design a PSS that could demonstrate better performance compared to the conventional ones. Some methods in this field are adaptive control [1], [2], [3], [4], smart control [5], artificial intelligence [6], [7], robust control [8], [9], [10] and sliding mode control [11]. Among these, the methods based on adaptive control and robust control can be considered a good approach for the effects of uncertainty in the power system. In adaptive control, the controller's parameters are updated based on the identification of the plant parameters, while in robust control, a worst-case design scenario for the plant families is considered, which corresponds to the different uncertainties in the system.

Wavelet functions have recently attracted much attention in various engineering areas [12], [13], [14], [15], [16], [17]. Based on wavelet theory, any signal or function can be closely approximated by a finite sum of the weighted wavelet functions. Wavelet neural networks (WNNs), which incorporate wavelet functions into a neural network, have been proposed by Zhang and Benveniste [18], and used for identifying and controlling nonlinear systems [19], [20], [21]. The activation functions such as sigmoid and Gaussian functions which have non-local properties in time are swapped with the wavelet functions in the hidden layers of neurons in the WNN. The output of a WNN is localized in both the time and frequency domains, thus providing the time-frequency localization properties of the input signal. This means that the WNN is a local network. Therefore, in on-line training and corresponding to any given point of the input space, a small subset of the network parameters is active and can thus be updated. This means that the generalization ability of the WNN can be maintained while its flexibility is high, and its training can be performed in speeds higher than that of a non-local network. Furthermore, local minima can be eliminated in the WNN. The WNN, however, has a shortcoming too [22]: it has a feed-forward structure. To solve this problem, the self-recurrent wavelet neural network (SRWNN) has been proposed [22]. Due to having a mother wavelet layer with self-feedback wavelets, the SRWNN is able to record the previous data of the network, adapting very fast to sudden changes in configuration or conditions of the controlled plant.

A fuzzy wavelet neural network (FWNN) combines wavelet neural networks (WNN) with a Takagi-Sugeno-Kang (TSK) fuzzy model in order to enhance the function approximation accuracy, as well as the generalization ability in very complex processes. Several previous works have discussed the synthesis of an FWNN to solve such problems as forecasting, function approximation, fault diagnosis, system identification, and control problems [23], [24], [25], [26]. In [23], fault diagnosis for power transformers is discussed using a rough set (RS) and fuzzy wavelet neural network, integrated with a least square weighted fusion algorithm. A gradient-based update rule is employed to update all parameters of the FWNN in on-line mode, while an ALRs algorithm is also proposed to guarantees the convergence of the adaptive process in [24]. The constructed network is used for identification and control of dynamic plants. In [25], using a combination of TSK fuzzy models with wavelet transform and ROLS learning algorithm, a fuzzy wavelet network is proposed with the aim of approximating arbitrary nonlinear functions. A fuzzy wavelet neural network (FWNN) approach is introduced for forecasting long-term electricity consumption in a high energy consuming city, while the rate of training is raised compared with the prediction model based on the artificial neural network in [26].

In this paper, a stable fuzzy wavelet neural-based adaptive power system stabilizer (SFWNAPSS) is proposed for stabilizing the inter-area oscillations in a multi-machine power system. Considering the advantages of SRWNN, in our proposed approach we employ it as several distinct sub-networks to construct a flexible self-recurrent wavelet- based consequent part. By applying an efficient genetic algorithm, the optimal values of the proposed SFWNAPSS parameters are obtained. A back-propagation algorithm with LALRs is proposed in order to update all parameters of the consequent part of each fuzzy rule in on-line operation. Kundur's four-machine two-area benchmark power system and six-machine three-area power system are used with an aim of assessing the effectiveness of the proposed stabilizer. Studies demonstrate promising results and show that the inter-area oscillations are successfully damped by the SFWNAPSS. In brief, the main contributions of the paper are summarized as follows:

• The main disadvantage of FWNN is that the application domain is limited to static problems due to its feed-forward network structure. Therefore, we propose to use a self-recurrent wavelet neural network (SRWNN) in the consequent part of FWNN, solving the control problem for chaotic systems.

• Our proposed structure requires fewer wavelet nodes than the networks with feed-forward structure, due to the dynamic behavior of the recurrent network.

• Finding the optimal learning rates is a challenging task in the classic gradient-based learning algorithms. Hence, in our proposed framework, all of the learning rates are determined optimally based on Lyapunov stability theory.

• We develop a controller based on the proposed network structure and use it for damping the oscillations in the multi-machine power system.

The brief outline of this paper is as follows: a brief background of SRWNN structure is presented in Section 2; Section 3 describes the architecture of the proposed FWNN with self-recurrent consequent part; the design procedure of a stable fuzzy wavelet neural-based adaptive PSS is discussed in Section 4; in Section 5, a comprehensive stability study is provided; the initialization of the proposed stabilizer by GA is presented in Section 6; design validation and simulation results are provided in Section 7; finally, the conclusions are presented in Section 8.