A holistic day-ahead distributed energy management approach: Equilibrium selection for customers' game

In this paper, a new holistic day-ahead distributed energy management approach with desired equilibrium selection capability in a smart distribution grid is proposed. The interaction between customers and the distribution company was modeled as a single-leader multiple-follower Stackelberg game. The interaction among customers was modeled as a non-cooperative generalized Nash game as they were faced with a common constraint. Customers held the average of the aggregate loads in the appropriate domain to reshape it and improve the Load Factor (LF). The strategy of the distribution company was day-ahead energy pricing through maximizing profit, which was formulated as a stochastic conditional value in risk optimization to consider the uncertainty in price of electricity in the wholesale market. Strategies of the customers were based on hourly consumption of deferrable loads and scheduled charge/discharge rates of energy storage devices in response to price. The generalized Nash game had multiple equilibria. Hence, the distributed proximal Tikhonov regularization algorithm is proposed here to achieve the desired equilibrium. The simulation results validated the performance of the proposed algorithm with 31.46% increase in the LF besides 45.89% and 14.23% reduction in the maximum aggregate demand and aggregate billing cost, respectively.