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Real-time electricity pricing of a comprehensive demand response model in smart grids

This paper proposes a real-time interactional pricing scheme to maximize the social welfare of players in real-time demand response program in smart grids. Lagrangian relaxation–based dual decomposition is used to separate the social welfare optimization problem into a retailer's problem along with many consumers' subproblems, and the gradient projection method is adopted to solve them. First, the consumers' subproblems are solved to determine the optimal demand responses to the price announced by the retailer. To obtain the optimal demand response, a comprehensive mathematical function is developed on the basis of a combination of 5 costumer's utility functions reported in literature (ie, linear, potential, logarithmic, exponential, and hyperbolic). Afterward, the retailer calculates a real-time price in response to the consumers' reactions to maximize its profit. In terms of practical implementation, the consumers and the retailer interact with each other via a limited number of control messages exchanges to find the optimal solution at each hour. The proposed method is evaluated considering the various retailer's cost functions and the consumers' behaviors. Also, the results of elasticity sensitivity analysis are presented from the retailer and consumer viewpoints.