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.