Bi-Level Optimal Planning of Soft Open Points Integrated with Energy Storage in Distribution Networks Considering Dynamic Electro-Carbon Factors

To address the deepening electro-carbon coupling and flexibility shortages in active distribution networks with high renewable energy penetration, this paper proposes a bi-level collaborative planning strategy considering dynamic electro-carbon factors. First, considering the spatial–temporal correlation of wind and solar outputs, typical renewable energy scenarios are generated using the Frank-Copula function and clustering algorithms. Second, a bi-level planning model for the Soft Open Point integrated with an Energy Storage System (E-SOP) is established: the upper level optimizes the siting and sizing of E-SOPs to minimize the annualized comprehensive cost; the lower level incorporates a dynamic stepped carbon trading mechanism and a continuous price-based demand response (PBDR) mechanism to achieve optimal operational economy. For model solving, a hybrid bi-level decomposition strategy combining the Dhole Optimization Algorithm (DOA) and second-order cone programming (SOCP) is adopted, utilizing a coordinated dual-level solution interaction to favorably support numerical stability. Case studies on a modified IEEE 33-node system demonstrate that the proposed scheme reduces the annualized comprehensive cost by 12.3% and transforms the carbon trading expenditure into a net revenue, thereby significantly enhancing the low-carbon economic efficiency and operational flexibility of the distribution network.