Research On Stability Of Time-delay Power Systems Based On Load Frequency Control

Load Frequency Control(LFC)is an important method for controlling power systems,which aims to maintain the stability of the power grid frequency within a region and exchange power with neighboring areas.With the continuous expansion of power grids,multiple power systems are interconnected to form an interconnected power grid.In the interconnected power grid,open communication networks are cost-effective and flexible,allowing for real-time transmission and exchange of power systems state information to ensure the stability and reliability of the power systems.However,due to limited network resources,delays may occur during the transmission of information in the interconnected power grid,leading to a reduction in the dynamic performance of the power systems and even causing instability.To ensure the stable operation of the power grid,delays in information transmission must be considered and corresponding measures taken to reduce their impact.This paper further studies the stability issues of delay systems and delay LFC power systems based on Lyapunov theory.The main research contents are as follows:First:Research on robust stability of time-delay systems.Absolute stability criteria with finite sectorial intervals and robust absolute stability criteria with infinite open planes are proposed for the delayed Lur’e system based on two forms of its nonlinear functions.Firstly,a Lyaounov-Krasovskii functional is constructed with a delay-dependent matrix and four single-integral terms.It can fully utilize the information of system state variables and time-varying delays.Secondly,nonlinear matrix inequalities in the stability criteria are equivalently transformed into linear matrix inequalities using a new equivalent transformation lemma of indefinite inequality,leading to new stability criteria that are easy to solve using MATLAB.Finally,the effectiveness of the proposed stability criteria is verified through numerical examples,including the Chua’s circuit.This method improves the upper bound of the maximum allowable delay in delay systems and lays the foundation for expanding the stability margin of LFC power systems.Second:Research on stability of single-area LFC power systems with interval time-varying delays.Based on the stability criteria for time delay systems in the previous section.Firstly,a proportional-integral type model for the single-area LFC power system with interval time-varying delays is established.Secondly,under the conditions of lower bounds of the delays being zero and non-zero,an augmented Lyapunov-Krasovskii functional is constructed.New stability criteria are derived by using this functional.Applying new equivalent transformation lemmas to transform the nonlinear matrix inequalities in the stability criteria into linear matrix inequalities that can be easily solved using MATLAB.Finally,numerical examples are used to determine the maximum stability margin of the systems and to compare the obtained results with the latest published results.The results show that the stability criteria obtained in this paper are less conservative.The effectiveness of the results is verified by modeling and simulating the single-area LFC power system using the Simulink toolbox.Third,Stability and H∞ performance optimization of two-area LFC power systems with with interval time-varying delays.The section extends the content of the second part to the two-area time-varying and time-delayed LFC power system,focusing on the stability analysis and H∞performance optimization.Firstly,the stability of the two-area time-varying and time-delayed LFC power system is studied,and a conservative stability criterion based on Lyapunov stability theory is obtained.Secondly,the H∞ performance of the two-area LFC power system is optimized by designing a time-delay dependent PI controller to obtain a suboptimal controller gain matrix for a given set of H∞performance indicators.Finally,the maximum stability margin of the system is obtained using the MATLAB LMI toolbox and compared with the latest published results.The results show that the stability criterion obtained in this study has a lower conservatism,and the effectiveness of the results is verified by modeling and simulating the two-area LFC power system using the Simulink toolbox.