A coordinated optimization strategy for EV clusters and soft open points based on carbon–electricity coupling drive

To enhance the hosting capacity and low-carbon operation level of active distribution networks with high-penetration renewable energy, this paper proposes a bi-level optimization framework that coordinates electric vehicle (EV) clusters with soft open points (SOPs). In the upper level, the framework aims to minimize the total system operating cost by optimizing the power output of distributed generators and SOPs. At the lower level, a generalized energy storage model for the EV cluster is formulated based on the Minkowski sum, with the objective of minimizing charging costs. This model responds to electricity price signals derived from dynamic carbon emission factors. Case studies on a modified IEEE 33-node system demonstrate that the proposed strategy effectively guides the vehicle–grid interaction through the carbon–electricity price signals. Consequently, it ensures distribution network voltage security while achieving a win–win outcome for both system economy and low-carbon objectives.