Social Optimal Energy Management with the Presence of the battery Storages in Smart Grid

In this paper, a new day ahead energy management system is proposed for a smart grid in which distribution company and residential customers are involved. The interaction between customers and the distribution company is modeled as a single leader-multiple followers Stackelberg game. The leader of Stackelberg game is the distribution company which calculates the price of energy by maximizing its profit in a stochastic optimization framework. The residential customers, who are the followers of Stackelberg game, consider the common constraint of maximum aggregated load regulating in their optimization problem and thus play a general Nash game with each other. It is proved the customers’ general Nash game is strongly monotone and consequently has a unique equilibrium. To achieve the unique Stackelberg equilibrium, the best response-based energy management algorithm is devised, and its convergence condition is proved. It is also proved that the Stackelberg equilibrium is an optimal social equilibrium, in which the sum of customers’ cost is minimized, and the profit of the distribution company is maximized. The proposed energy management mechanism decreases the maximum aggregated load by 21.89% and increases the load factor by 27.72%.