Stability Analysis And Control Of Time-varying Power System Based On Reciprocally Convex Inequality

With the development of science and technology,the power system has become an important guarantee for social life.If the stability of the power system is disrupted,the grid cannot supply power normally or the power system collapses,it may cause damage to the national economy and even casualties.Therefore,it is particularly important to maintain the stability of the power system.Power system stability is affected by many factors,one of which is time lag.The research focus of scholars is how to improve the time-delay stability margin,obtain a less conservative time-delay stability criterion,and at the same time provide a robust and stable controller design for time-delay power systems.The main research contents of this thesis are as follows:The Lyapunov-Krasovskii functional for the extension of the Bessel-Legendre inequality is selected,and the inverse convex group and the inequality improved based on the Bessel-Legendre inequality are used to process the quadratic integral term contained in the functional derivative term to obtain the time-delay stability criterion.Compared with the original inverse convex combination inequality method,the improved inverse convex combination inequality method provides a higher upper limit of time delay with less slack matrix variables.The stability criterion is further applied to the stability analysis of typical second-order time-delay power systems,single-machine infinite time-delay power systems,and dual-area four-machine time-delay power systems.A higher upper limit of time delay is obtained and the time-delay stability criterion is reduced.The conservativeness of the data is proved by simulation and data comparison to prove its effectiveness and practicability.Combine the inverse convex combination inequality method and the free weight matrix method to design the state feedback controller.First,the effectiveness of the improved free weight matrix method is verified through the stability analysis of the PI load frequency control system.On the basis of the improved inverse convex combination inequality method,the free weight matrix term is introduced,and the derivative term of the Lyapunov-Krasovskii functional is derived to obtain a new stability criterion.On this basis,the state feedback controller is designed,and the nonlinear term generated by the controller is processed by the adjustment parameter method,and the models of the memoryless feedback controller and the memory feedback controller and their corresponding stability criteria are established respectively.The controller is applied to the typical second-order time-delay power system and the single-machine infinite time-delay power system,and the controller feedback gain value is obtained,which improves the stability margin of the time-delay power system.The simulation results and the literature comparison prove the controller The effectiveness and practicality of the design.