Determination of Voltage Margin Decision Boundaries via Logistic Regression for Distribution System Operations

This paper presents a data-driven decision-support framework for distribution system operations using logistic regression (LR) on the Voltage Margin Index (VMI). Treating VMI as the sole explanatory feature, the proposed two-stage workflow first fits an inferential LR model to establish statistical significance and perform valid statistical inference on the coefficients. Next, it trains a performance-optimized LR classifier with class-balanced sample weighting to produce calibrated violation probabilities. LR maps VMI to violation probability and analytically converts a calibrated probability threshold into an operator-ready VMI decision boundary. Applying 5-fold group cross-validation to 8816 node-level samples generated from a 22.9 kV Jeju Island model yields performance- and safety-oriented probability thresholds (θopt = 0.7891, θsafe = 0.6880), which correspond to VMI decision boundaries VMIDB,opt = 0.7893 and VMIDB,safe = 0.8101. On an unseen 20% test set, the LR classifier achieves 99.94% accuracy (F1 = 0.9977) under θopt and 100% recall under θsafe. A random forest (RF) benchmark confirms comparable accuracy (=99.72%) but lacks analytical invertibility and transparency. This framework offers distribution system operators (DSOs) and virtual power plant (VPP) operators clear, evidence-based criteria for routine planning and risk-averse decision-making, and it can be applied directly to any distribution system with node-level voltage measurements and known regulation limits.