Implicit Enhanced Distributed Heavy-Ball Energy Management Strategy for Microgrids With Time-Varying Social Welfare and Delay

Mingqi Xing, Dazhong Ma, Kai Ma, Qiuye Sun

Abstract: Diverse energy sources and fluctuating energy demands highlight the criticality of microgrid energy management (MEM). This paper develops a general model of social welfare maximization in the presence of time-varying social welfare with quadratic transmission losses, which implies that the fitting coefficients of the transmission losses, cost function, and utility function may vary over time. A significant difference with existing works is the dependence of the problem’s optimal solution on time variation, making higher requirements on the algorithm’s performance, especially the convergence rate. To address these challenges, we extend the conventional heavy-ball method and propose a novel implicit enhanced distributed heavy-ball algorithm. The algorithm incorporates multiple heavy-ball terms to accelerate convergence. Notably, the second heavy-ball term is implicitly implemented via an acceleration term that contains historical information and consensus error. Furthermore, the algorithm obviates the necessity for the sharing of additional auxiliary variables, thereby reducing the communication overhead. We demonstrate that the algorithm converges asymptotically to the neighborhood of the time-varying optimal solution even with arbitrarily large but bounded communication delays. Finally, detailed case studies illustrate that the algorithm can improve the convergence rate by 15.02% over conventional method, followed by the validation of its scalability and the discussion of the negative impact of delay.