General Nash bargaining based direct P2P energy trading among prosumers under multiple uncertainties

This paper presents a transaction scheme for the direct peer-to-peer (P2P) energy trading problem among prosumers under uncertainties. Prosumers, in the distribution network, coordinate with neighbors to share the idle energy and maximize the cooperative benefit. Most of the existing researches focus on mechanism design with the assumption of accurate forecast. Nevertheless, the P2P energy trading problem is challenging due to multiple uncertainties, caused by the market price, intermittent power output and load demand variation. Although stochastic or robust optimization approaches are introduced and investigated to manage uncertainties, there are limitations for their application, such as large scenario sizes in the stochastic programming, coordination of the conservativeness and economy in the robust optimization. To address these challenges, a hybrid stochastic/robust optimization model is adopted to manage uncertainties which makes trade-offs between computational time and conservatism. The uncertain price is modeled via various scenarios based on forecast values while a robust optimization is developed to take into account the uncertainties of renewable generation and load. Based on the above uncertainties description, the direct P2P energy trading among prosumers is formulated as a general Nash bargaining (GNB) problem which is decomposed into two subproblem: operation cost minimization problem (P1) and bargaining problem (P2). As P1 and P2 are nonconvex problem, linearization techniques including KKT conditions and logarithmic transformation are employed to transform them as mixed-integer linear programming problem. A linear distflow model is formulated to address an OPF problem considering voltage limits of an AC network in a radial structure. Furthermore, a graph theoretic method is proposed to construct the incident matrix about buses and branches in the network constraints which considerably enhances the solution efficiency. Numerical case studies demonstrate that the constructed model can effectively incentivize direct P2P energy trading among prosumers, and multiple uncertainties affect the operation costs and energy transaction decisions. Additionally, the efficiency of the graph theory based modeling approach is proved for solving the energy trading model with OPF constraints.