A Generalized Nash Equilibrium analysis of the interaction between a peer-to-peer financial market and the distribution grid

Abstract

We consider the interaction between the distribution grid (physical level) managed by the distributed system operator (DSO), and a financial market in which prosumers optimize their demand, generation, and bilateral trades in order to minimize their costs subject to local constraints and bilateral trading reciprocity coupling constraints. We model the interaction problem between the physical and financial levels as a noncooperative generalized Nash equilibrium problem. We compare two designs of the financial level prosumer market: a centralized design and a peer-to-peer fully distributed design. We prove the Pareto efficiency of the equilibria under homogeneity of the trading cost preferences. In addition, we prove that the pricing structure of our noncooperative game does not permit free-lunch behavior. Finally, in the numerical section we provide additional insights on the efficiency loss with respect to the different levels of agents' flexibility and amount of renewables in the network. We also quantify the impact of the prosumers' pricing on the noncooperative game social cost.