A Robust Design of a Static VAR Compensator Controller for Power System Stability Improvement

A novel robust damping controller for a static var compensator (SVC) in a power system has been designed using a simple graphical technique. The graphical loopshaping method starts by selection of a nominal plant function satisfying the robust stability and performance criterion. The variations in operating conditions from the nominal values are modeled as multiplicative structured uncertainty. The robust controller designed was tested for a number of operating conditions and disturbances. It is observed that the robust controller provides extremely good damping for a good range of operating points. The advantage of the proposed controller is that the design is based on a simple graphical method avoiding complex mathematical computations normally encountered in such designs. INTRODUCTION Thyristor controlled reactors and capacitors, termed as static var compensators (SVC) are well known to improve power system properties such as steady state stability limits, voltage regulation and var compensation, dynamic over voltage and under voltage control, counteracting subsynchronous resonance, and damp power oscillations [Hamad 1986;Hosseini and Mirshekhar 2001; So and Yu 2000]. Voltage controlled SVC, as such, does not provide any damping to the power system [Oliviera 1994; Zhou 1993]. However, it can be used to increase power system damping by introducing supplemental signals to the voltage set point [So and Yu 2000; Zhao and Jiang 1995]. A large volume of literature is available on SVC control design for the nonlinear power system problem. Controls for the nonlinear system are often realized through EL (exact linearization), LQR (linear quadratic regulator) theory, DFL (direct feedback linearization). DFL was employed by Tso and Wang [So et. al., 1997; Wang et. al., 1997] to generate SVC and other flexible AC transmission systems (FACTS) controllers. The method presents a complex nonlinear control law derived through the solution of Matrix-Riccati equation. More complex methods of disturbances auto-rejection control (DARC) and variable structure adaptive fuzzy sliding mode control were presented by Zhang and Zhou [1998], and Ghazi et.al.,[2001]. Optimum feedback control of SVC for stabilization of a power system was presented in [Rahim and Nassimi 1996]. One of the important goals of the control engineers is to design ‘robust’ fixed parameter controllers which will be effective for a large range of operation. Farasangi et. al., [2000], and Zhao and Ziang [1995] proposed a robust controller for SVC using H∞-based techniques. The designs require complicated minimization procedures restricting the realization of the controllers. This article presents a simple and novel design technique of robust SVC susceptance control for damping power system oscillations. The variations of the operating conditions of the nonlinear power system have been taken into consideration by modeling them as multiplicative unstructured uncertainty. A loop-shaping technique [Doyle et. al., 1992] has been employed to design the controllers. Simulation results demonstrate that the controller designed effectively damps the electromechanical oscillations for a wide range of operating conditions. POWER SYSTEM DYNAMICS WITH SVC The single machine power system configuration shown in Fig. 1 is considered for this study. The generator is connected to the load center termed as ‘remote system bus’ through a long transmission network. The SVC is placed at the middle of the transmission line which is generally considered to be the ideal site. The generator also has a local load connected at its terminal. A 4th order nonlinear dynamic model for the power system including the second order electromechanical swing equation, the generator internal voltage equation, and an IEEE type-ST exciter model equation is considered. The static var compensator circuit, shown in Fig.2, contains the ISBN: 1-56555-268-7 107 SCSC '03 voltage measuring and the voltage regulator circuit, output of which is fed to the thyristor firing control circuit. Normally, the susceptance of the SVC (B) is varied to maintain the mid-bus voltage Vm within its pre-specified tolerance. The supplementary stabilizing signal is added to the output of the voltage regulator. Figure 1. Power system configuration Figure 2. The SVC controller block diagram The variation of the susceptance (B) can be related through the differential equation, c c o T / ] u K B B [B + + ∆ = ∆ & (1) Kc and Tc are the gain and time constants, respectively of the SVC firing angle control circuits; and u is the extra stabilizing signal. Combining (1) with the fourth order generator model, the dynamic equations of the generatorSVC system are expressed as, u] f[x, x = & (2) Here, vector x comprises of the states [ δ, ω, eq , Efd, B]. Linearizing the nonlinear equations around a nominal operating condition, the input-state-output equations are written as, Bu x A x + ∆ = ∆& (3)