Decentralized optimization of multi-area power-transportation coupled systems based on variational inequalities

Current urban transport and energy systems are gradually being integrated and developed towards a state of multi-area interconnection. Based on this change, this paper proposes a decentralized optimization approach of multi-area power-transport coupled systems (PTCSs). To begin with, the models concerning the optimal power flow and mixed equilibrium flow are defined to describe the flow patterns, respectively. Considering that the traffic assignment model is non-linear and challenging to solve, this paper converts it into an equivalent variational inequality (VI). With this foundation, a decentralized optimization model is proposed, alongside which the decoupling strategies are investigated. To solve the problem effectively, an improved algorithm applicable to the decentralized optimization of PTCSs, supported by the VI tool, is proposed. In addition, rigorous convergence analysis of the proposed algorithm was conducted. Simulations indicate that the proposed algorithm solves the problem with good results and can guarantee convergence within a reasonable time frame.