Improved Results on Delay-Dependent Stability of LFC Systems with Multiple Time-Delays
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Improved Results on Delay-Dependent Stability of LFC Systems with Multiple Time-Delays K. Ramakrishnan · G. Ray
Received: 27 August 2014 / Revised: 22 January 2015 / Accepted: 16 February 2015 © Brazilian Society for Automatics–SBA 2015
Abstract In this paper, the problem of delay-dependent robust stability of uncertain load frequency control (LFC) systems with multiple time-delays and exogenous power system disturbance has been considered. Using Lyapunov– Krasosvskii functional method, less conservative delaydependent stability criteria are proposed in linear matrix inequality formulation to compute the maximum value of the time-delays within which the LFC system under consideration remains asymptotically stable in the sense of Lyapunov. Compared to the existing result in the literature, the proposed result takes into account the effect of unknown exogenous load disturbance into the stability analysis, imparting more applicability and usefulness to the resulting stability criterion in real-time conditions. Keywords Load frequency control · Delay-dependent stability · Lyapunov stability analysis · Linear matrix inequality · Multiple time-delays
1 Introduction and Problem Formulation It is well known that load frequency control of multi-area power systems through communication network introduces time-delays in the feedback path Bevrani (2009). In realtime condition, these delays account for the transfer of system information (output or state variables) from power plant K. Ramakrishnan (B) Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Pillaichavady 605014, Pondicherry, India e-mail: [email protected] G. Ray Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, West Bengal, India
(RTUs) to the control center at remote where the control algorithm is embedded and the subsequent transfer of the control effort from the controller back to the plant. The presence of time-delays in a physical system is detrimental to the system performance as well as stability. Excessive timedelays often pave way to system instability Gu et al. (2003). Hence, it becomes necessary to compute the maximum value of the time-delays within which the closed-loop LFC system remains asymptotically stable in the sense of Lyapunov. This is called delay-dependent stability of time-delayed LFC systems Jiang et al. (2012). Generally, a power system is subjected to sudden unknown load disturbances that perturb the system from its equilibrium point. If system is capable of regaining the same equilibrium point where it was operating at and before the time of perturbation, then it is said to be asymptotically stable (in the sense of Lyapunov). On the other hand, in an unstable system, any perturbation from equilibrium point drifts the system completely away from it. If the system, by itself, regains the equilibrium point upon perturbation from it, then the system is said to be autonomously stable or open-loop stable; else, if it does regain the original
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