Stochastic Dynamic Game between Hydropower Plant and Thermal Power Plant in Smart Grid Networks

In this paper, we study the competitive interactions between an autonomous pumped-storage hydropower plant and a thermal power plant in order to optimize power generation and storage. Each type of power plant individually tries to maximize its own profit by adjusting its strategy: both types of plants can sell their power to the market at a price depending on the demand and supply, as well as the dynamics over different periods of time; or alternatively, the thermal power plant can sell its power at a fixed price to the pumped-storage hydropower plant by storing the energy in the reservoir. A stochastic dynamic game is formulated to characterize this competition. The instantaneous market price is modeled as a Cournot duopoly game. Here, the dynamics comes from the varying water volume in the reservoir, and the stochastic aspect captures the uncertain natural inflow to and losses from the reservoir. The solutions are derived using the stochastic Hamilton–Jacobi–Bellman equations. We also show that the proposed game can converge to a feedback Nash equilibrium. The simulation results demonstrate the properties of the proposed game and suggest how to optimize the amounts of generation in hydropower and thermal power plants over time with the fluctuations of price. The proposed framework and games can reduce the peak-to-average ratio and total energy generation for the thermal plant, which helps power plant operation and reduces $\hbox{CO}_{2}$ emission.