Coordinated optimization operation model of virtual power plant and distribution network in the electricity-carbon coupled market

To address the challenges of high-dimensional nonlinearity, multi-agent privacy protection, and computational efficiency in the collaborative optimization of VPP and distribution networks under an electricity-carbon coupled environment, this paper proposes a distributed collaborative operation model based on epigraph theory. First, a framework for electricity-carbon coupled market operations is established, incorporating the modeling of diverse distributed energy resources, including renewable energy units and carbon capture systems. Secondly, a quantitative bi-level mathematical model is formulated: the upper level aims to maximize the comprehensive benefits of the VPP within the electricity-carbon market, while the lower level focuses on minimizing system power purchase and carbon quota costs, with clearly defined constraints for each level. Finally, by leveraging epigraph theory, the original problem is converted into an efficient distributed solving form through function transformation and equivalent projection modeling. This approach effectively bypasses nonlinear constraint bottlenecks while safeguarding the privacy of participating entities. Simulation results on the IEEE 33-node system demonstrate that the proposed method achieves a 3.04% increase in total operating profit compared to traditional bi-level model solutions, validating its effectiveness in enhancing both economic performance and computational efficiency.