Motivation

CHAPTER 1 Introduction

1.1 Motivation

Recently, the study of power system stability has attracted lots of attention [6,28,34]. Among the possible instabilities, a serious type is the so-called “voltage collapse” [1,2,8,9,17,32]. This kind of instability in a power system is characterized by an initial slow progressive decline and then rapid decline in the voltage magnitude [17]. The voltage collapse behavior has been reported to be attributed to the increase of power demand that results in the operation of an electric power system near its stability limit [8,17].

In 1988, Dobson and Chiang [9] have presented a mechanism for voltage collapse and introduced a simple power system model containing a generator, an infinite bus and a nonlinear load. They claimed that the voltage collapse behavior might occur around a saddle node bifurcation point [8,9]. Abed et al. [1,2,32] have reported the oscillatory behavior of a power system using Hopf bifurcation theory.

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In addition to distinguishing the cause of voltage collapse, to detect such instability phenomena is also an important area of research. Traditional available methods have relied on utilizing system Jacobian matrix of power flow [4,16,21,37], by exploiting either its sensitivity by determining its vicinity to singularity or its eigenvalue behavior. These approaches have the drawback of time consuming computations. And with increased network size these Jacobian based methods will become very time consuming and therefore inappropriate for quick detection. Thus, the first goal in this thesis is to provide a means for quick detection of voltage collapse in the power system. Various techniques for fault detection of a control system have been developed (see e.g., [5,7]). Among these techniques, the so-called “fault identification filter’’ (FIDF) is one of the most effective [5,7]. The FIDF has been successfully applied to the detection of sensor fault [23], mobile robot [24] and compression systems [19]. In this thesis, we adopt the power system model proposed by Dobson and Chiang [9], and employ FIDF design technique to detect the voltage collapse. We will show how the FIDF may be used to detect the occurrence of voltage collapse in a power system without complex computations.

In practical, an efficient and reliable operation of power systems should have the property that the voltage and frequency should remain nearly constant. As is well known, the frequency of a system is dependent on active power balance while the voltage magnitude is dependent on reactive power balance [16,27]. From voltage stability analysis, we know that the lack of the reactive power in the power system may cause the voltage decrease, which may in the worst case lead to the voltage collapse. So, an important issue for power system control is to maintain a steady acceptable voltage under normal operation and disturbed conditions, which is referred as the problem of voltage regulation. Thus, the second goal in this thesis is to provide a voltage controller which can achieve voltage regulation purpose. Tap changer is

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known to be one of an effective device for voltage control. The effect of tap changer ratio in the power system has been studied in [20,22,39,16,27]. In this thesis, we will employ setting tap changer ratio to achieve voltage regulation. In practical, the power systems are large scale nonlinear systems. The simplest controller design for voltage regulation might be based on approximate linearization approach. However, this controller is usually effective around a neighborhood of operating point. In addition, the linearization approach might work well when a small disturbance occurs, but it usually cannot survive a large disturbance. Recently, nonlinear control theories have been employed to power systems voltage controller design. These designs are mainly based on the nonlinear feedback linearization technique [10,33,38], which transforms the power system into a linear and controllable one, and thus linear control theories can be applied to design an effective control law. Although the feedback linearization approach is a powerful tool for nonlinear controller design, it is only suitable for nonlinear affine systems (for definition, see e.g., [3]). Since in this thesis we take the tap changer as control input, the power system model is found to be a general nonlinear system form xç = f(x, u) in stead of being a nonlinear affine version.

Thus feedback linearization approach can not be applied. It is known that variable structure control (VSC) has many advantages including fast response and small sensitivity to system uncertainties and disturbances [25,29]. It then has been widely applied to a variety of control problem, such as power system stability control [13,34,36], robotic control [15,26], and so on. In this thesis, we will adopt the VSC technique in the controller design issues.

In many practical control problems, the controlled systems usually have parameter uncertainty. The uncertainty in power system may come from a large variation in loading condition during operation. It is known that the performance of a control system might not be acceptable or even result in unstable if it does not take the

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parameter uncertainty into account for controller design. Thus, the third goal in this thesis is to provide a parameter estimation scheme to help voltage controller dealing with the power system in the presence of uncertainty or unknown variation in the load.

Finally, we will develop a scheme of prevention of voltage collapse with the aid of prior analysis and design. It provides us a secure and reliable operation of the power system.