Adaptive RTRL based neurocontroller for damping subsynchronous oscillations using TCSC

Abstract

Modern interconnected electrical power systems are complex and require perfect planning, design and operation. Hence the recent trends towards restructuring and deregulation of electric power supply has put great emphasis on the system operation and control. Flexible AC transmission system (FACTS) devices such as thyristor controlled series capacitor (TCSC) are capable of controlling power flow, improving transient stability and mitigating subsynchronous resonance (SSR). In this paper an adaptive neurocontroller is designed for controlling the firing angle of TCSC to damp subsynchronous oscillations. This control scheme is suitable for non-linear system control, where the exact linearised mathematical model of the system is not required. The proposed controller design is based on real time recurrent learning (RTRL) algorithm in which the neural network (NN) is trained in real time. This control scheme requires two sets of neural networks. The first set is a recurrent neural network (RNN) which is a fully connected dynamic neural network with all the system outputs fed back to the input through a delay. This neural network acts as a neuroidentifier to provide a dynamic model of the system to evaluate and update the weights connected to the neurons. The second set of neural network is the neurocontroller which is used to generate the required control signals to the thyristors in TCSC. This is a single layer neural network. Performance of the system with proposed neurocontroller is compared with two linearised controllers, a conventional controller and with a discrete linear quadratic Gaussian (DLQG) compensator which is an optimal controller. The linear controllers are designed based on a linearised model of the IEEE first benchmark system for SSR studies in which a modular high bandwidth (six-samples per cycle) linear time-invariant discrete model of TCSC is interfaced with the rest of the system. In the proposed controller, since the response time is highly dependent on the number of states of the system, it is often desirable to approximate the system by its reduced model. By using standard Hankels norm approximation technique, the system order is reduced from 27 to 11th order by retaining the dominant dynamic characteristics of the system. To validate the proposed controller, computer simulation using MATLAB is performed and the simulation studies show that this controller can provide simultaneous damping of swing mode as well as torsional mode oscillations, which is difficult with a conventional controller. Moreover the fast response of the system can be used for real-time applications. The performance of the controller is tested for different operating conditions.

Introduction

The recent advances in power electronics have led to the development of reliable and high speed flexible AC transmission system (FACTS) devices. Thyristor controlled series capacitor (TCSC) is such a FACTS device which can compensate transmission line reactance and control power flow through the transmission system. The influence of conventional fixed series capacitor can cause growing subsynchronous oscillations between the electrical system and turbine-generators due to electrical resonance.

The phenomenon of SSR was brought to the general attention in connection with the two damages that occurred to the turbine — generator shafts at the Mohave Generating station in southern Nevada in the United States of America in December of 1970 and October of 1971. These two failures were analysed and found that the failures occurred in the shaft section between the generator and the exciter of the main generator collector was due to torsional fatigue (IEEE Committee Report, 1985, IEEE, 1992, Anderson et al., 1990). Torsional problems are most frequently encountered in rotor systems with long shafts and large inertias constituting a weakly damped mechanical system. Different methods of mitigating SSR are available in literature (Hingorani, 1981, Walker et al., 1981, IEEE SSR Working Group, 1982). The introduction of TCSC with fast and flexible control of effective reactance can improve the overall system performance of the series compensated systems (Padiyar, 1998, Ballance and Goldberg, 1973). In order to assess the flexibility of TCSC and hence to determine its appropriate control strategy, accurate models of TCSC are needed. Since the TCSC incorporates both continuous dynamics like capacitor voltage and discrete conditions like thyristor triggering, its modeling and analysis are complicated.

Attempts have been made in the past to obtain linearised time invariant continuous models or discrete sample invariant models suitable for eigenanalysis. A discrete linear time invariant analytical model based on Poincare mapping method is developed by Othman and Angquist (1996). The frequency range of this model is twice the system frequency. It incorporates thyristor triggering logic, synchronisation system and higher level control loop. A detailed derivation of the closed form TCSC dynamic model is presented in Rajaraman and Dobson's (1996) paper. In this, the steady state solution of the TCSC compensated network can be approximated by nominal quantities in the DQ reference frame. This can be applied to a system where the TCSC forms a relatively small proportion of the total series compensation which is the normal case of an existing TCSC line. The drawback of this method is that it cannot be used for systems with larger proportion of the compensation provided by TCSC. In this case there will be strong harmonic interactions between the TCSC and the network. Jalali and Hedin (1996) developed a dynamic TCSC model based on Poincare mapping technique with sampling time of a system cycle and also it considered the non-linearities due to both generator and TCSC. Kabiri et al. (2005) developed a discrete state space model of TCSC compensated system. They have discretised the system with sampling frequency six times that of the system frequency. Cheriyan and Kulkarni (2009) developed a linearised discrete-time model of a pre-firing NGH damper for damping SSR oscillations. A modular discrete model of TCSC with high bandwidth is developed by Joshi et al. (2009). The time invariance of this model is made by the transformation of zero sequence components. Six samples per cycle is selected. This methodology is adopted in the present work.

Most of the controllers designed for the oscillation damping are based on a linearised model of the system in which the system is linearised about an operating point to give good performance. Since the electrical power system is highly non-linear with configurations and parameters that change with time, the conventional controller based on the linearised model cannot guarantee its performance in a practical operating environment. Moreover, the performance of these linear controllers will deteriorate with a wide variation of operating condition and in the presence of large disturbance. To accommodate the changes in the operating conditions, periodical retuning of the controller is needed to maintain the desired performance. Design of a linear or non-linear controller requires an accurate mathematical model of the system, which is practically difficult. Recently, various adaptive control techniques have been proposed for dealing with large parameter variations. Basically, adaptive control systems can be classified into two categories, namely the self-tuning regulators and the model reference control systems. The self-tuning regulator is based on explicit identification of the system transfer function has the difficulty of designing an efficient on-line identifier whereas, for the model reference control the requirement of satisfying the perfect model following conditions and the state information of the system, it is rather difficult to be applied to power system in the sense of practical implementation. In adaptive control methods, the model parameters are updated periodically to represent the actual system. But this control technique requires a good knowledge about the process, which requires an accurate mathematical modeling of the system which is very difficult.

Hence an intelligent controller with adaptive learning capabilities in the presence of unknown disturbances, unmodeled dynamics and unstructured uncertainties is required to replace the conventional controllers. Artificial neural network can be an intelligent controller to control non-linear, dynamic systems through learning. The variation of plant parameters and plant structures can be effectively updated in the neural network based control strategy and hence the robustness of the control system is improved. Since the accuracy in the plant modeling or the explicit parameter identification is not significant in the proposed neurocontroller, it can be used for non-linear control. The learning ability of the neural network and properties such as the ability to map non-linear functions, generalisation capabilities and fast response makes it attractive for control applications (Ender and Maciel Filho, 2000; Al-Zohary et al., 2002; Semino and Pannocchia, 1999).

In all the reported works, a fully connected recurrent neural network (RNN) is seldom used for the control of subsynchronous oscillations. In this paper, a new adaptive neurocontroller is proposed for the damping of subsynchronous resonance oscillations. The critical issue in the application of RNN is the choice of the network architecture, i.e., the number and type of neurons, the location of feedback loops and the development of a suitable training algorithm. Most of the training techniques available for neural network (Linkens and Nyongesa, 1996; Narendra and Parthasarathy, 1990, Jin et al., 1995, Zhang et al., 1992, Stephen and Pich, 1994) are unable to retain the informations about the infinite past which is essential for the real-time applications. A dynamic recurrent neuron with a feedback connection from output to input is the suitable architecture for the real-time learning. Different training methods are available for recurrent neurons (Pearlmutter, 1995, Williams and Zipser, 1989). Sindhu et al. designed a neurocontroller trained by RTRL algorithm (Sindhu Thampatty et al., 2009) which is used for the control of single-input single-output systems (SISO). In this work, the proposed neurocontroller architecture is suitable for any type of non-linear systems which can be trained by RTRL algorithm. Furthermore, the proposed controller can be designed by using a reduced plant model to simplify the controller design without degrading much the performance. It follows that the proposed controller is very attractive as far as the practical implementation is concerned. The system we considered in this study is a single-input multi-output (SIMO) system. RTRL algorithm is an optimal algorithm which minimises the instantaneous squared error at the output of RNN for every discrete time instants, while the network is running. Number of neurons in the output layer of RNN is equal to the number of states of the system and the number of neurons in the controller network must be same as the number of control inputs.

The paper is organised as follows. Section 2 briefly explains the subsynchronous phenomenon and Section 3 explains the mathematical modeling of modular time-invariant discrete model of TCSC. Section 4 explains the interconnection of the modular TCSC with the rest of the system in IEEE first benchmark model. Section 5 discusses the detailed design of the proposed adaptive neurocontroller. Simulation results are discussed in Section 6 followed by conclusion in Section 7.