Bidding strategies for virtual power plants under the electricity-carbon joint market taking into account wind and solar uncertainties

As China's electricity and carbon markets undergo coordinated reforms, the growing integration of distributed resources within virtual power plants (VPPs) is shifting their role in market participation. To explore bidding strategies that balance economic efficiency and carbon reduction under the electricity-carbon joint market, this paper models VPPs as price makers and proposes a bi-level bidding framework considering wind and solar uncertainty. The upper level maximizes the VPP's profit, while the lower level maximizes social welfare in the joint market. To handle renewable generation uncertainty, robust optimization is employed to transform the bi-level model into a two-stage robust problem. The model is then solved as a mixed-integer linear program using the column-and-constraint generation algorithm, strong duality and the Big-M method. Case studies confirm the feasibility and effectiveness of the proposed strategy.