Dissipative Analysis for Multi-Area Power Systems in Multi-Delay Environments and PI-Type Load Frequency Controller Design via LMIs Method

This article focuses on the dissipative stability issue with load frequency control (LFC) in multiple time-varying delay (MTD) power systems. Firstly, the model is constructed considering the effects of MTD. Next, Lyapunov-Krasovskii functionals (LKF) are constructed which include delay-product-type terms (DPT) with MTD. Then, the low conservative stability criteria with respect to linear matrix inequalities (LMIs) are derived through the application of auxiliary function-based integral inequalities (AFBII) and improved reciprocal convex inequalities (IRCI) to handle the DPT. Next, an effective dissipative control strategy is developed based on the above criteria. Finally, simulation experiments are carried out, and the effectiveness of the proposed design method is highlighted by comparing with the previous results. Note to Practitioners—This paper focuses on the dissipative stability of LFC in power systems with MTD. It provides a new perspective for the control and optimization of power systems and other dynamic systems involving MTD. Specifically, when constructing LKF with DPT, this paper designs for different time-varying delay conditions, which can better deal with the uncertainty caused by time delay changes and help to improve the accuracy and reliability of system stability analysis. Then, the new stability criterion proposed in this paper provides more relaxed conditions, which reduces the conservatism of system stability analysis and makes the stability criterion more practical application value. Based on the new stability criterion, a dissipative controller design method is presented in this paper. This method can provide better control effect when dealing with complex multi-delay systems and help to improve the overall operating efficiency and stability of the power system. Finally, the effectiveness of the scheme is verified by simulating the multi-region power system.