Boundary Analysis of the Limit Penetration Rate for Large-Scale Distributed Photovoltaic Systems

With the proposal of the “dual carbon” targets and the rapid development of distributed photovoltaic (PV) systems, large-scale PV integration into distribution networks has led to emerging issues such as voltage limit violations, equipment overloading, and reverse power flows. To scientifically evaluate the hosting capacity of distribution networks for distributed PV, this paper proposes a boundary analysis method for the limit capacity penetration rate based on second-order cone relaxation (SOCR) and mixed-integer second-order cone programming (MISCOP). The model aims to maximize the PV penetration capacity while comprehensively considering node voltage, branch current, transformer power flow, and operational constraints, thereby establishing a quantifiable framework for secure access assessment. A 10 kV distribution network in a certain area is used as a case study, where three access scenarios—multi-point, partial-node, and single-node—are simulated. The results show that the system’s maximum PV integration capacity is approximately 676.58 kW (about 120% of the load capacity). The node voltage distribution remains stable, the system operates safely and reliably, and the differences in network loss rates among the access scenarios are small. The proposed model effectively characterizes the system operation boundary under high PV penetration and provides a scientific basis for PV access planning and capacity optimization.