The proposal of dual carbon target has significantly accelerated the integration of green production and low-carbon development.Addressing the challenges of energy sharing and low-carbon operations in commercial parks, an electricity-carbon trading model tailored for charging stations, commercial buildings, and photovoltaic energy storage power stations is proposed. It highlights the complex energy and information flow dynamics among park entities, power trading centers, microgrid operators, and carbon trading centers. Distributed robust optimization is utilized to address the non-convex chance constraint problem in the electricity-carbon scheduling model for commercial parks, reformulating it as a semidefinite programming problem. The proposed method’s effectiveness in cost reduction and carbon emissions mitigation is validated using three distinct schemes. Finally, the proposed method is compared with the Conditional Value at Risk（CVaR）based linear programming approach. Results demonstrate that the distributed robust approach achieves superior alignment with actual scheduling scenarios in terms of decision-making accuracy.