Robust Optimal Scheduling of Multi-Energy Virtual Power Plants with Incentive Demand Response and Ladder Carbon Trading: A Hybrid Intelligence-Inspired Approach

Aiming at the uncertainty in load demand and wind-solar power output during multi-energy virtual power plant (VPP) scheduling, this paper proposes a robust optimal scheduling method incorporating incentive-based demand response (IDR). By integrating robust optimization theory, a ladder-type carbon trading mechanism, and IDR compensation strategies, a comprehensive scheduling model is established with the objective of minimizing the operational cost of the VPP. To enhance computational efficiency and adaptability, we propose a hybrid approach that combines the Column-and-Constraint Generation (C&CG) algorithm with Karush–Kuhn–Tucker (KKT) condition linearization to transform the robust optimization model into a tractable form. A robustness coefficient is introduced to ensure the adaptability of the scheduling scheme under various uncertain scenarios. The proposed framework enables the VPP to select the most economically and environmentally optimal dispatching strategy across different energy vectors. Extensive multi-scenario simulations are conducted to evaluate the performance of the model, demonstrating its significant advantages in enhancing system robustness, reducing carbon trading costs, and improving coordination among distributed energy resources. The results indicate that the proposed method effectively improves the risk resistance capability of multi-energy virtual power plants.