Mean-field-type games for distributed power networks in presence of prosumers

In this paper we study distributed power networks using Bayesian mean-field-type game theory. A prosumer (producer-consumer) is a user that not only consumes electricity, but can also produce and store electricity. We identify and formulate the key interactions between consumers, prosumers and producers. Based on forecasted demand, each operator determines its production quantity, its mismatch cost, and engages an auction mechanism to the prosumer market. All the operators together are engaged in a competitive energy market share. The resulting supply is completed by the prosumers auction market. This determines a market price, and the consumers react to the price and generate a demand. The consistency relationship between demand and supply of the three components provides a fixed-point system, whose solution is a mean-field equilibrium.