A stackelberg-generalized Nash equilibrium model for energy trading in distribution networks with novel two stage wasserstein distributionally robust reformulation

Microgrids (MGs) have attracted widespread attention due to their capability to effectively manage distributed energy resources. However, the large-scale integration of MGs introduces a complex coupling structure within distribution networks, involving multiple agents, multiple objectives, and multiple variables, thereby posing significant challenges to optimal system operation and market mechanism design. Moreover, the uncertainties associated with upstream electricity prices and renewable energy sources further exacerbate the complexity of energy interactions within distribution networks. To tackle these challenges, this paper presents a novel Stackelberg-generalized Nash equilibrium (Stackelberg-GNE) model for coordinated energy trading in distribution networks. First, a Stackelberg game between the distribution system operator (DSO) and MGs, together with a GNE model among MGs, is formulated to characterize multi-agent interactions and benefit allocation. Then, a two-stage Wasserstein distributionally robust optimization (WDRO) is employed to handle uncertainties. To overcome the high computational burden of conventional two-stage WDRO reformulations, a novel model reformulation is further proposed to enhance tractability and solution performance. We show that the GNE model among MGs can be equivalently reformulated as a centralized optimization problem. Based on this, a fully distributed algorithm combining fixed-point theory with the alternating direction method of multipliers (ADMM) and column-and-constraint generation (C&CG) is developed, and we prove that the proposed algorithm converges to the market equilibrium solution. We conduct case studies on modified IEEE 33- and 69-bus systems, which show that the proposed method reduces computation time by 48.6% and 46.5%, respectively, compared with the conventional two-stage WDRO reformulation algorithm, confirming the computational efficiency of the proposed approach.