Distributed peer-to-peer electricity-heat-carbon trading for multi-energy virtual power plants considering copula-CVaR theory and trading preference

• Copula-CVaR theory is developed to quantitatively characterize the operation risk of VPP to achieve accurate quantification of wind and solar forecast errors correlation and economic risk. • A distributed peer-to-peer electricity-heat-carbon trading model considering the trading preference for multi-energy VPPs based on CVaR is established. • An alternating direction method of multipliers with Gaussian back substitution is proposed to solve the model and an adaptive step size is adopted to accelerate the convergence speed. To promote clean and low-carbon energy development, distributed renewable energy resources are connected to power systems, which affects the stable operation of these systems. Virtual power plants can aggregate various distributed energy resources and have become an important way to improve power system stability. In response to the impact of renewable energy uncertainties and the advantages of virtual power plants in resource mutual sharing, a distributed peer-to-peer electricity-heat-carbon trading method for multi-energy virtual power plants is proposed based on conditional value-at-risk and copula theory in this paper. First, considering the wind and solar forecast errors correlation, the uncertainty loss is quantitatively modelled by conditional value-at-risk and copula theory. Second, considering the trading preferences of various resources and the multi-market coordination of electricity, heat, and carbon, a peer-to-peer trading model is established to achieve horizontal complementarity among multiple virtual power plants. Subsequently, the alternating direction method of multipliers with Gaussian back-substitution is applied to solve the optimization model, and an adaptive step is used to further accelerate convergence. Finally, case studies are performed to verify the effectiveness, rationality, and superiority. The results shows that prediction errors for the virtual power plant lead to a 23.8 % reduction in risk costs. At the same time, there is an 11.14 % decrease in total costs. Moreover, the model-solving time was reduced by 613 s, showing significantly improved efficiency of the solution method.