Delay-Dependent Stability Analysis For Load Frequency Control Systems With Electric Vehicles

Frequency is one of the important indexes to measure the power supply quality of power grid.One of the necessary conditions for the stable operation of power system is that the frequency of power grid can be maintained at a fixed value or has a small range of fluctuations around it.Load frequency control(LFC)Is the most common way to achieve this goal,and the stability of LFC system also directly determines whether the power system can run stably.The general LFC system first detects the change of frequency in the power grid,and then adjusts the output power of the generator according to the change,so as to achieve the effect of load frequency control.However,with the continuous expansion of the power grid and the application of wide area measurement system(WAMS),time-delay is an inevitable factor in LFC systems.Usually,the existence of time-delay may lead to instability and oscillation of systems,so the stability analysis and controller design of LFC systems with time-delay has become hot topics.In addition,in order to reduce carbon emissions,new energy electric vehicles(EVs)have been vigorously developed,and the number of EVs is increasing.With the concept of vehicle to grid(V2G)proposed,EV has great application value in power grid,and EV auxiliary frequency regulation is one of the potential applications.However,the introduction of EVs makes the analysis of time-delayed LFC system more difficult as more factors need to be considered.Therefore,this paper mainly analyzes the stability of the time-delayed LFC system with EVs,and designs of the controller.The main research results are as follows:(1)Stability analysis of one-area time-delayed LFC system with EV.In this chapter,an improved delay dependent stability criterion is proposed for one-area time-delayed LFC system with EV.based on matrix reconstruction technique and a new method to determine the negative definite condition of quadratic function.It reduces the conservatism without bringing much computational complexity.Some case studies are proposed to show the superiority of the proposed method.At the same time,some time-domain simulations are carried out.Besides,considering the effect of state of charge(SOC)on EV gain,a state space model with uncertain parameters is proposed and the stability analysis is carried out based on generalized free-weight-matrix inequality.Finally,some numerical examples are given to verify the effectiveness of the proposed method.(2)Stability analysis of multi-area interconnected LFC systems with EV considering time-delays.In this chapter,the problem of power exchange among the interconnected multi-area LFC systems is considered,and the system model is established.Based on Bessel-Legendre inequality and matrix reconstruction technique,two improved delay dependent stability criteria are proposed to reduce the conservatism and the computational complexity brought by high-dimensional system matrices.Finally,several case studies are given,including the superiority of the proposed method,the interaction of time-delays between areas and the influence of EV gain on the delay stability margin.(3)Design of delay-dependent H_∞ controller.In this chapter,a state space model with wind disturbance is established for a one-area time-delayed LFC system with EV.Based on Jessen inequality and convex combination inequality,the design conditions of delay dependent H_∞ controller are established,and the nonconvex problem in the controller solving process is transformed into a nonlinear minimization problem based on LMI.The controller with optimal H_∞ performance under given time delay is obtained by using improved cone complementary linearisation algorithm.Finally,some numerical examples show the good H_∞ performance of the designed controller and the H_∞ control performance index of the designed controller under different time delays.