Resilient <i>H</i> <sub>∞</sub> Consensus-Based Control of Autonomous AC Microgrids With Uncertain Time-Delayed Communications
Mohammad Raeispour, Hajar Atrianfar, Hamid Reza Baghaee, Gevork B. Gharehpetian
Abstract
In this paper, a resilient distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus-based control scheme is proposed to be used in the secondary layer of the hierarchical control structure of AC heterogeneous autonomous microgrids (MGs). In the presented study, the external disturbance, the uncertainty on the communication links, and fixed time-delays (FTDs) are all considered as the destabilizing components of the time-varying topologies network. So, by applying <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> theory to the reduced-order model of the system, sufficient conditions for the stability and robustness of the proposed controller are outlined based on Lyapunov-Krasovskii theory (resulting in the feasibility of linear matrix inequalities (LMIs), which yields the upper bound of time-delay that guarantee the stability of system), so that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance index for uncertainty and disturbance are satisfied. Finally, to evaluate the performance of the control laws, offline digital time-domain simulation studies are performed on a test MG system in MATLAB/Simulink, and the obtained simulation results reveals the effectiveness, efficiency, authenticity, and accuracy of the proposed method in regulating MG voltage and frequency, providing accurate proportional active power-sharing, and state of charge (SoC) modification (balancing).