Under carbon emission constraints, to promote low-carbon transformation and achieve the aim of carbon peaking and carbon neutrality in the energy sector, this paper constructs an operational optimization model for the coordinated operation of a virtual power plant cluster (VPPC). Considering the resource characteristics of different virtual power plants (VPPs) within a cooperative alliance, we propose a multi-VPP interaction and sharing architecture accounting for electricity–carbon interaction. An optimization model for VPPC is developed based on the asymmetric Nash bargaining theory. Finally, the proposed model is solved using an alternating-direction method of multipliers (ADMM) algorithm featuring an improved penalty factor. The research results show that P2P trading within the VPPC achieves resource optimization and allocation at a larger scale. The proposed distributed ADMM solution algorithm requires only the exchange of traded electricity volume and price among VPPs, thus preserving user privacy. Compared with independent operation, the total operation cost of the VPPC is reduced by 20.37%, and the overall proportion of new energy consumption is increased by 16.83%. The operation costs of the three VPPs are reduced by 1.12%, 20.51%, and 6.42%, respectively, while their carbon emissions are decreased by 4.47%, 5.80%, and 5.47%, respectively. In addition, the bargaining index incorporated in the proposed (point-to-point) P2P trading mechanism motivates each VPP to enhance its contribution to the alliance to achieve higher bargaining power, thereby improving the resource allocation efficiency of the entire alliance. The ADMM algorithm based on the improved penalty factor demonstrates good computational performance and achieves a solution speed increase of 15.8% compared to the unimproved version.

To address the uncertainty and volatility of renewable energy while meeting the requirements of low-carbon economic operation, this paper proposes a two-stage robust optimal dispatch model for an integrated wind-solar-hydro-thermal-storage energy system with coupled power-to-gas (P2G) and carbon capture system (CCS). First, a mathematical model of the integrated wind-solar-hydro-thermal-storage energy system with P2G-CCS coupling is developed to promote internal carbon cycling and enhance the capability to accommodate renewable energy. Second, the scheduling problem is formulated as a two-stage robust optimization model. A cardinality-based uncertainty set is adopted to model deviations in renewable energy output, and a column-and-constraint generation (C&CG) algorithm is applied to efficiently solve the problem. Comparative case studies are conducted to quantify the performance differences between the proposed method and deterministic optimization and stochastic optimization. The results show that compared with conventional optimization methods, the proposed two-stage robust optimization model increases the carbon utilization rate of the IES to 24.38% and raises the renewable energy accommodation rate to 100%; the system’s intraday balancing cost and total operating cost are reduced by 94.54% and 4.49%, respectively, and the overall indirect carbon emissions decrease by 57.96%, thus achieving coordinated optimization of economic performance, robustness, and low-carbon characteristics. In addition, further analysis of the robustness parameter indicates that an overly conservative robust strategy leads to worse economic performance and higher carbon emissions. This study provides quantitative guidance for balancing robustness, economy, and environmental benefits in integrated energy system operation.