Stability Analysis Of Time-Varying Delay System Based On Integral Inequality

In recent years,with the expansion of the scale of modern interconnected power system and the continuous improvement of its structural complexity,the stability of the system is facing a severe test.Therefore,it is particularly important for the system to maintain stable operation for a long time.From the perspective of the overall situation,most power systems use the method of establishing a wide area measurement system to realize all-round real-time monitoring of the power grid,so as to analyze its stability and timely feedback control.In this process,it is essential to produce time delay.This phenomenon is one of the many factors affecting the stability of the system.Therefore,scientifically and objectively analyzing the phenomenon of system time delay and its impact on the stability of the whole power system,studying and discussing how to effectively improve the time delay margin of system stability,so as to obtain a less conservative stability criterion has very important scientific theoretical significance and engineering practice value.The main results of this paper are as follows:(1)For systems with single time-varying delay,according to the characteristics of time-delay systems,based on the auxiliary function integral inequality method,this paper studies the stability of time-varying delay systems with a single interval.Firstly,the system model with time-delay term is established,and a new Lyapunov Krasovskii functional is constructed based on Lyapunov Krasovskii theory.When estimating the functional derivative,the integral term in the functional derivative is divided by making full use of the system delay information,and then the auxiliary function integral inequality is introduced for estimation.Combined with the improved convex combination expansion and contraction method,the functional derivative has a tighter upper bound.Therefore,the stability criterion of interval time-varying delay system with less conservatism is derived,and the delay related sufficient conditions for judging the asymptotic stability of the system are established.Then the stability criterion is further applied to typical second-order timedelay power systems with single time-delay,single machine infinite bus systems,and two zone four machine power systems with multiple machines and single time-delay.The effectiveness and superiority of this method are verified by simulation and data comparison.(2)For systems with multiple time-varying delays,considering the coupling problem of transmission delays and multiple delays in multiple loops in wide area systems and the timevarying characteristics of time delays,a system model containing multiple time-varying delay terms is established,and a stability criterion suitable for multiple time-varying delay systems is proposed by using the theoretical analysis method of time-delay systems.In the derivation of the criterion,in order to use all possible information to study the relationship between the delayed state and the current state,an augmented Lyapunov Krasovskii functional is designed,and the functional derivative is reduced and expanded by using the second-order Bessel Legendre inequality and the interactive convex combination method,so as to reduce the conservatism of the stability criterion.Finally,a typical second-order power system with multiple time-varying delays is used to verify the effectiveness of the results.(3)For the single region time-varying time-delay power system based on PI load frequency control,this paper considers the time-varying time-delay characteristics,time-delay change rate and system state information of the system,constructs a new extended Lyapunov Krasovskii functional based on Lyapunov Krasovskii theory,and estimates the integral term in the functional derivative by using Bessel Legendre inequality method according to the time-delay constraints,Thus,the delay stability margin of time-varying delay power system is improved.Then,combined with numerical examples,the relationship between system delay stability margin and PI control gain is obtained.Through the comparison with the existing literature,the effectiveness and superiority of this method compared with the existing methods are verified.