Balancing cost and demand in a smart grid - a mean-field game analysis
In a smart grid, consumers can also play the role of producers and sellers of energy. Therefore, the control of a smart grid over time becomes a dynamic game with a large number of small players and one or several large players. This is much more complicated than the control of an energy system with a single producer. The framework of mean-field games with common noise allows the transformation of such a complicated model into a control problem for a typical prosumer (producer and consumer in one) optimizing his behavior against a flow of other such prosumers. In our model, we introduce 2 decision variables for such a controller: one describing the amount of electric energy bought from the grid (or sold to it), and the second one describing the charging rate for our battery. The cost function is designed to satisfy two goals: satisfying the demand of the consumer (a single home) and minimizing the payment for energy. Players are allowed to sell/buy energy from the grid. Common noise is hidden in price volatility and sun irradiance, which influence all the players. We compute the optimal controls for our model and simulate solutions on real data. The novelty of our construction, compared to other works on smart grid control, lies in combining the minimization of the cost of energy and sustaining some level of demand satisfaction. We analyze the impact of battery usage on achieving a balance between these two criteria. We also take into account that the smart grid is only part of the energy market, which makes consumer strategies dependent on energy consumption outside the grid.