The Small Signal Stability Analysis For Power System With Time-delayed Load Frequency Control

With the expansion of the modern power system and the development of the power market,load frequency control(LFC)utilizes open communication network to exchange large amount of wide-area signals,while at the same time it also leads to the problem of time delay.Time delays will inevitably reduce the control performance of load frequency control without considering time delay and even causes the failure of controllers which makes the system unstable,affecting seriously the stable operation of the power grid.This paper studies the influence of time delay on the load frequency controller,which has important theoretical and practical significance.In the face of the LFC system with time-delay,the dissertation studies the small-interference stability analysis,proposing a characteristic analysis method based on the SOD-IRK(Solution Operator Discretization with Implicit Runge Kutta)method for the stability of power system with time-delay and a delay margin calculation method based on matrix pencil mathod.The two methods are seperately applied to the time delay LFC system.The influence of time delay on the system's small disturbance stability is analyzed.The main research work and achievements are as follows:(1)A mathematical model of the time-delayed LFC system for the analysis of small disturbance stability is established in both conventional and deregulated environments.The characteristics,including the sparsity of the system matrix and the essential characteristics of the LFC system,are analyzed.The time delay state matrices of the system are highly sparse.The state space models of the multi-area LFC system under the traditional environment and deregulated environment are in the same form,and thus have the same characteristic equation.Therefore,it can be shown that the various power consumption contracts of the LFC system under the market environment have no influence on the stability of the LFC system.(2)A critical eigenvalue calculation method for time delayed LFC system based on SOD-IRK method is proposed.This method adopts two core technologies including sparse eigenvalue calculation and Newton iteration correction and can obtain the critical eigenvalues of the system through once calculation.Finally,the characteristic distributions of single-area LFC and multi-area LFC in traditional and deregulated environment are obtained,and the effect of delays on the stability of LFC systems are analyzed.(3)An accurate calculation method of time delay margin for time delayed system is proposed based on matrix pencil theory.The stability type of system is determined by solving generalized eigenvalues and their corresponding system eigenvalues of a constructed matrix pencil.The accurate delay margin can be obtained if system is time-delay dependent.In order to apply this method to large-scale delayed system,scalability analysis of the method is performed.Finally,the effectiveness of this method and the accuracy of results are verified on a single-area LFC system.For multi-area LFC systems,the influence of the controller gain on the time-delay stability margin is analyzed.The critical eigenvalue calculation method for time delayed LFC system based on SOD-IRK method can obtain accurate eigenvalues by only once caculatin.The accurate calculation method of time delay margin for time delayed system can caculate accurate delay margin while it cannot be applied to large delayd system because of curse of dimension.