This paper proposes a key vulnerable node identification method based on the trend of short-circuit capacity change, and establishes a complete set of node vulnerability evaluation index system by analyzing the change of node short-circuit capacity before and after distributed power supply access. At the same time, this paper improves the traditional port compensation method, fully considering the influence of parallel branches and the nonlinear characteristics of distributed power supply. Combined with complex network theory, this study introduces indicators such as the proportionality coefficient and the association Q-function to deeply analyze the topological destruction resistance of active distribution networks. The results show that the short-circuit capacity varies from 17.39% to 21.95% at distributed power access points and their neighboring areas, which constitute the key vulnerable nodes of the system. This paper also proposes a stochastic model node-equivalent voltage crossing probability calculation method to simplify the impact analysis of multi-point stochastic modeling of power distribution networks through node equivalence. The probabilistic security analysis method based on Latin hypercube-Monte Carlo sampling considers multiple uncertainties and establishes a time series probabilistic tidal current calculation model. The results show that the penetration rate of distributed power supply is the main factor affecting system safety. In addition, the complex affine analysis and operation optimization method proposed in this paper effectively solves the affine approximation problem of suboperations such as trigonometric and inverse trigonometric functions, and reduces the network loss and voltage deviation. This study provides important theoretical value and engineering application significance for the planning and design, operation control and fault handling of active distribution networks.
