Bidding strategy for the virtual power plant based on cooperative game participating in the Electricity-Carbon joint market

•VPP with CCER mechanism promotes the consumption of new energy, increases the total profit and reduces the carbon emissions in the joint market.•An improved PBDR combined with elastic coefficient is proposed, which enhances the impact of electricity price on electricity consumption.•An improved Shapley value method is proposed, which ensures the fairness of distribution and maintains the stability of cooperation alliance. With the proposal of “Dual-carbon” target, the electricity market and carbon market has been gradually improved. Establishing a deep coupling of electricity-carbon market to promote the in-depth development of two markets has become a new research focus. Based on the cooperative game theory, a bidding strategy for the virtual power plant (VPP) which considers Chinese certified emission reduction mechanism and demand response is proposed. Firstly, the framework of VPP participating in the electricity-carbon joint market is constructed. Secondly, an upper and lower iterative bidding strategy model is established. The upper model uses the whale optimization algorithm to obtain the optimal bidding strategy, and the lower model is optimized to obtain the optimal power consumption. Thirdly, the elastic influence weight is introduced into the price-based demand response, and then an improved Shapley value method about profit distribution considering prediction accuracy and environmental benefits is proposed. Finally, the examples and simulation results verify that the proposed model can increase the total profit, reduce the carbon emission and the peak-valley difference rate of load. Meanwhile, it’s demonstrated that the profit distribution method improves the enthusiasm of the cooperative operation of the internal units in VPP.