Feasible Region Modeling and Optimal Operation of Distribution Networks Based on the Holomorphic Embedding Method

With increasing distributed renewable energy (DG) in distribution networks, voltage stability and security challenges arise. Traditional optimization methods often struggle with convergence and efficiency in complex multi-DG scenarios. This study employs the Holomorphic Embedding Method (HEM) for feasible region modeling and optimal operation. First, a novel HEM-based model efficiently characterizes the voltage-secure feasible region of active distribution networks with DGs, enabling quantification of DG hosting capacity and integration boundaries. Second, leveraging relationships among voltage power series coefficients, a linearized power flow model is developed using first-order coefficients and power injection sensitivities. An optimization model minimizing voltage deviation is formulated, incorporating operational constraints of energy storage and reactive power compensation devices to enhance security. Finally, case studies on IEEE 33-bus and a practical 91-bus system validate the method’s effectiveness and engineering applicability.