A Novel Model for the Security Boundary Calculation of Distribution Systems Considering the Stochastic Characteristics of DG

In recent years, the concept of distribution system security region (DSSR) has been widely applied to the security analysis of distribution networks. However, with the large-scale integration of distributed generation (DG), the analysis results of existing security region models show significant discrepancies from actual conditions. To address this issue, the paper first establishes a probabilistic model of DG under the $\mathbf{N}-1$ security criterion, accounting for the volatility and randomness of DG. Then, by analyzing the $\mathrm{N}-1$ constraints of the main transformer and feeder, a model of DSSR considering the stochastic characteristics of DG is further developed. The random power flow indices of DG are applied to the power supply capability index system, addressing the limitations of the original static indices in performing random power flow simulations. Finally, this paper analyze the total supply capacity (TSC) considering the stochastic characteristics of DG and explore the impact of different DG penetration levels on the distribution network