Collaborative Operation Strategy of Virtual Power Plant Clusters and Distribution Networks Based on Cooperative Game Theory in the Electric–Carbon Coupling Market

Against the backdrop of global low-carbon transition, the integrated development of electricity and carbon markets demands higher efficiency in the optimal operation of virtual power plants (VPPs) and distribution networks, yet conventional trading mechanisms face limitations such as inadequate recognition of differentiated contributions and inequitable benefit allocation. To address these challenges, this paper proposes a collaborative optimal trading mechanism for VPP clusters and distribution networks in an electricity–carbon coupled market environment by first establishing a joint operation framework to systematically coordinate multi-agent interactions, then developing a bi-level optimization model where the upper level formulates peer-to-peer (P2P) trading plans for electrical energy and carbon allowances through cooperative gaming among VPPs while the lower level optimizes distribution network power flow and feeds back the electro-carbon comprehensive price (EACP). By introducing an asymmetric Nash bargaining model for fair benefit distribution and employing the Alternating Direction Method of Multipliers (ADMM) for efficient computation, case studies demonstrate that the proposed method overcomes traditional models’ shortcomings in contribution evaluation and profit allocation, achieving 2794.8 units in cost savings for VPP clusters while enhancing cooperation stability and ensuring secure, economical distribution network operation, thereby providing a universal technical pathway for the synergistic advancement of global electricity and carbon markets.