Bi-Level Low-Carbon Scheduling of Active Distribution Networks with Multiple Technical Virtual Power Plants in the Integrated Electricity and Carbon Markets

As the integration of distributed energy resources (DERs) accelerates, optimizing active distribution networks (ADNs) for low-carbon operations has become essential for decarbonizing power systems. This paper proposes a bi-level optimization model aimed at achieving low-carbon scheduling of ADNs interacting with multiple technical virtual power plants (TVPPs) in the integrated electricity and carbon markets. The upper-level problem seeks to minimize ADN costs, including expenses associated with energy procurement and carbon emissions. The lower-level problem maximizes VPP economic benefits by optimizing their power generation, demand response, and trading strategies. To enhance carbon accountability, the dynamic emission factors (DEFs) are developed, encompassing both generation-based and trading-based emission factors. The generation-based DEF quantifies emissions based on the output of distributed generators, while the trading-based DEF allocates emissions for ADNVPP power exchanges, preventing double-counting and ensuring accurate carbon cost assessments. The bi-level model is then reformulated as a single-level mixed-integer linear programming (MILP) problem using Karush–Kuhn–Tucker (KKT) optimality conditions, Fortuny-Amat transformation, McCormick Envelop method, and the strong duality theorem. Case studies conducted on a modified IEEE 33-bus test system demonstrate that the proposed approach can effectively reduce carbon emissions by 7.93% and further reduce total operational cost considering carbon price, achieving both economic and environmental objectives. These findings underscore the potential of integrating low-carbon strategies into ADN management for more sustainable and resilient power systems.