A game theoretic and control theoretic approach to incentive-based demand management in smart grids

In this paper, we propose a demand side management approach for smart grids. Our approach is based on incentive design in noncooperative games and allows to control the behavior of grid users in an effort to achieve efficient energy utilization matching supply with demand. We design a smart grid by means of game theory. We show that this model guarantees the existence of a Nash equilibrium that corresponds to a strategy set users choose to minimize their cost-functions. A pricing mechanism is used as a tool to ensure that the Nash equilibrium in game reaches a value satisfying a global objective expressed by the minimum of deviations between energy supply and energy consumption in a smart grid system. We present two methods to find an efficient Nash equilibrium solution. The first one is based on the properties of a special class of potential games according to which the Nash equilibrium is the minimum of a potential function. The second one is a control theoretic approach based on game dynamics. In this case, a game is treated as a control system that should be stabilized around a desired equilibrium point.