Carbon Economic Dispatching for Active Distribution Networks via a Cyber–Physical System: A Demand-Side Carbon Penalty

To address the challenges of climate change mitigation and operational flexibility in active distribution networks (ADNs) amid high renewable energy penetration, this paper proposes a low-carbon economic dispatch framework integrating demand-side carbon regulation and cyber–physical system (CPS)-enabled shared energy storage. First, a consumer-side emission penalty mechanism is developed by fusing a carbon emission flow (CEF) model with price elasticity coefficients. This mechanism embeds carbon costs into end-user electricity pricing, guiding users to adjust consumption patterns (e.g., reducing usage during high-carbon-intensity periods) and shifting partial carbon responsibility to the demand side. Second, a CPS-based shared energy storage mechanism is constructed, featuring a three-layer architecture (physical layer, control decision layer, security layer) that aggregates distributed energy storage (DES) resources into a unified, schedulable pool. A cooperative, game-based profit-sharing strategy using Shapley values is adopted to allocate benefits based on each DES participant’s marginal contribution, ensuring fairness and motivating resource pooling. Finally, a unified mixed-integer linear programming (MILP) optimization model is formulated for ADNs, co-optimizing locational marginal prices, DES state-of-charge trajectories, and demand curtailment to minimize operational costs and carbon emissions simultaneously. Simulations on a modified IEEE 33-bus system demonstrate that the proposed framework reduces carbon emissions by 4.5–4.7% and renewable energy curtailment by 71.1–71.3% compared to traditional dispatch methods, while lowering system operational costs by 6.6–6.8%. The results confirm its effectiveness in enhancing ADN’s low-carbon performance, renewable energy integration, and economic efficiency.