A Nash–Stackelberg–Nash game for collaborative operation of a coupled microgrid-transportation network

With the increasing adoption of electric vehicles (EVs) and the advancement of dynamic wireless charging, the transportation network (TN) and multi-microgrid (MMG) are gradually transitioning from independent operations to a tightly coupled mode. This paper proposes a Nash–Stackelberg–Nash (N–S–N) game to optimize the collaborative operation of a coupled microgrid-transportation network (CMTN). The follower problem refers to the traffic assignment of the TN, which is established as a dynamic user equilibrium (DUE) model with elastic demand. Traffic demand changes in response to the operational and congestion states of the TN. This DUE model is transformed into variational inequalities for solving, and the obtained charging demand is then transmitted to the MMG. The leader problem concerns the cooperative scheduling of the MMG, where direct electricity trading among microgrids is allowed, which can be formulated as a cooperative game. The cooperative game can be decomposed into two sequential subproblems for solving, and the determined charging prices are then released to the TN. The leader and follower problems form an N–S–N game through this feedback dependency between charging prices and charging loads. This paper transforms the N–S–N game into a fixed-point problem and develops a best response algorithm to solve it. Moreover, an improved fixed-point algorithm and alternating direction method of multipliers with adaptive penalty factor are proposed to obtain the DUE of the TN and the cooperative scheduling of the MMG, respectively. The numerical results demonstrate that the proposed N–S–N game can not only effectively realize the collaborative operation of the CMTN but also improve energy efficiency, reduce costs, and lower carbon emissions.