Robust Energy Management of Residential Nanogrids via Decentralized Mean Field Control

Energy management systems (EMS) are viable techniques to reduce the customers billing cost as well as enhancing the grid reliability and efficiency. Uncertainty and information privacy of users are serious concerns in designing EMS of a residential nanogrid with renewable energy resources. This paper addresses a decentralized energy management algorithm for day-ahead scheduling of residential nanogrids using the concept of Mean Field (MF). The aim of each user is to find its optimal demand strategy by minimizing an objective function consisting of energy consumption cost, battery degradation cost, and cost of user discomfort while meeting a suite of constraints. The strategy of a user affects the objective functions of other users through the electricity price; such interaction among the users is hence modeled as a game problem. Each user, without any information exchange with other users, sends its electricity demand to the utility company. The utility company broadcasts the aggregated demand as a common information of the grid (MF term) to all users. The robustness of the algorithm in presence of uncertainties in decision making of the clients and non-residential load prediction error is analytically verified. In particular, it is shown that the algorithm converges to ε-Nash equilibrium point of the game and ε uniformly converges to its minimum value as the population size of the users goes to infinity. Simulation results show the advantages of the proposed method.