The Research Of Time Delay Stability For Power System Based On Free-weighing Matrices Theory

Electricity has become essential energy of human beings, to guarantee power system safety and stability operation is very important for modern society. In the past, some blackouts have happened in the world and have brought enormous economic loss and disastrous result. How to avoid such disasters is a big challenge for power system operation and stability studies. In recent years, PMU/WAMS (Phasor Measurement Unit/Wide Area Measurement System) based on GPS technology has been rapidly developed. It can greatly improve the observability of power system so that it is suitable for wide-area coordination control. However, according to the communication relay, there are significant time delays in the WAMS data, from tens of millisecond to hundreds of millisecond, which have great influence on the designing of wide-area coordination controller. So it is important to properly evaluate the impact of time delays on power system stability analysis and controller designing under wide area environment.In this paper, impact of time delays on power system stability analysis and controller designing are deeply studied. And, some improved time delay stability criteria are presented. Main work of this paper is as following:(1) According to the stability analysis of power system with time delays, a suitable TDAE (Time-delayed Differential Algebraic Equation) model is established. Further, the traditional free-weighting-matrices (FWM) method, which is used for stability analysis on ODE (Ordinary Differential Equation) model, is improved so that it can be used to analyze the stability of TDAE systems.(2) An improved delay-dependent stability criterion for power system with multiple time delays based on FWM method is presented. In this method, a Lyapunov function is constructed based on the Lyapunov-Krasovskii theory. To reduce the conservativeness of the method, some necessary slack variables are introduced to its derivative function. The derivative function is then expressed as a set of Linear Matrix Inequalities (LMI), which can be solved by the LMI toolboxes. Some time-delayed systems, such as single-machine-infinite-bus(SMIB) system and WSCC 3-generator-9 -bus system are employed to validate the presented method. Simulation results reveal its correctness and effectiveness.(3) An improved delay-dependent robust stability criterion for power system with uncertain time delays is presented. On the basis of time-delay stability analysis method for power system, by using Schur complement theory, power system robust stability criterion is proposed. The presented method is validated by using the SMIB system and WSCC 3-generetor-9-bus system. Impact of the uncertainties in the gain of the exciter on the system stability analysis is deeply discussed. Numerical studies reveal that the presented method is correct and effective.(4) In designing a wide-area controller for a power system, one problem cannot be neglected is the transmission time delay. The improved delay-dependent stability criterion is used to stabilize power system with time delays. By using the improved stability criterion, a memoryless state feedback controller and a wide-area controller based on wide area information are proposed. Simulation results reveal that the given controller can significantly improve the power system stability. And, the given method has less conservativeness and better performance in helping with wide-area controller designing.