Safety Assessment of Loop Closing in Active Distribution Networks Based on Probabilistic Power Flow

To investigate the security issues of loop-closing operations in medium–low-voltage distribution networks under the influence of stochastic fluctuations from distributed generators (DGs) and loads, probabilistic power flow is introduced for analyzing loop-closing currents in active distribution networks. A novel method combining Latin Hypercube Sampling (LHS) and the Gram–Charlier (GC) series, termed the LHS-GC method, is proposed to calculate the probability distribution of loop-closing currents. By modeling DGs and loads as random variables, their cumulants are efficiently obtained through LHS. Based on a linearized formulation of loop-closing current equations, the cumulants of loop-closing currents are calculated, ultimately reconstructing the probability distribution function of loop-closing currents in active distribution networks. Subsequently, a security assessment framework for loop-closing operations is established using the probability distribution of loop-closing currents. This framework provides a quantitative evaluation from two dimensions: preliminary loop-closing success rate and the severity of current limit violations, offering data-driven decision support for loop-closing operations. Taking the IEEE 34-node distribution network as an example for feeder loop-closing current assessment, the proposed LHS-GC method achieves results with less than 4% deviation from simulation values in terms of cumulative probability distribution of loop-closing currents and safety assessment metrics. Under a sampling scale of 500 points, the computational time is 0.76 s, demonstrating its efficiency and reliability. These outcomes provide actionable references for decision-making support in loop-closing operations of active distribution networks.