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To enhance the utilization of clean energy sources, such as wind power and photovoltaic within virtual power plants, and mitigate carbon emissions, this paper proposes a virtual power plant participation in the electricity carbon joint market optimization operation model based on ensemble empirical mode decomposition–improved bat algorithm (IBA)–Markov chain new energy output prediction. First, complementary set empirical mode decomposition is performed on historical data to construct a Markov chain based wind power and photovoltaic prediction model optimized by IBA. Second, this prediction model is used to predict the daily generation power of wind power and photovoltaic power. Finally, with the optimization goals of maximizing the benefits and minimizing the carbon costs of virtual power plants, a virtual power plant system participating in the electricity carbon joint market model based on wind power and photovoltaic output prediction results is constructed. At the same time, demand response factors are introduced and solved using the NSGA-II algorithm. Taking a certain park as an example for simulation analysis, the research results show that the combined effect of carbon market and demand response can achieve 99.82% of new energy consumption in virtual power plants without significantly reducing profits, basically achieving complete new energy consumption, demonstrating the effectiveness of the proposed model in this paper.