Operational Feasible Region of Active Distribution Networks Based on the Holomorphic Embedding Method

With the increasing penetration of distributed energy resources (DERs) in distribution networks, voltage stability issues are becoming increasingly prominent, making the accurate characterization of the system’s security boundaries crucial. Traditional methods, such as the Continuation Power Flow (CPF) method, suffer from limitations, such as low efficiency and poor convergence when calculating high-dimensional feasible regions. This paper proposes a fast characterization method for the distribution network feasible region based on the Holomorphic Embedding Method (HEM). Firstly, the embedding approaches for the holomorphic embedding model at different types of nodes are presented, and the recursive relations for solving the power series coefficients are derived, noting that the model’s initial solution corresponds to the power flow solution of the system. Secondly, a distributed generator power injection space is introduced, and a holomorphic embedding model oriented towards limit violation point tracking is constructed. This model can efficiently characterize the operational feasible region of active distribution networks and quantify the hosting capacity and integration boundaries for DERs. Finally, case studies on the IEEE 33-node distribution system are conducted. Simulation results demonstrate that the proposed method effectively characterizes the security-constrained operational feasible region of active distribution networks, exhibits significant engineering practicality, and achieves markedly improved computational efficiency compared to the traditional CPF method. The method provides an important theoretical foundation and a practical tool for the planning and operation of active distribution networks.