With the growing need for transitioning to clean energy, increasing the share of renewable energy sources has become a global priority. The integration of distributed energy resources (DERs), such as photovoltaic (PV) and wind turbine (WT) systems, is crucial for optimizing the current distribution systems. Despite its benefits, DER integration presents technical challenges. DERs can cause rapid power output changes, leading to voltage instability and overvoltage, thereby impacting the power quality and equipment reliability. Mitigating this instability often requires costly grid infrastructure upgrades. Therefore, optimizing existing networks is essential to reduce these costs. To achieve this, the voltage profile of the target area must be thoroughly assessed and locations suitable for DER integration must be identified to ensure stable operation and voltage stability. This study proposes a new evaluation index, the Voltage Margin Evaluation Index (VMEI), to address the limitations of the existing indices. This index evaluates voltage stability and promotes DER integration in a region. Using the VMEI, we assessed the suitability of DER integration in Jeju, South Korea. Results demonstrate that integrating a 0.5 MW DER at Node 37 in Feeder 5, the optimal point with a VMEI of 1.00066, maintained the maximum voltage at 22.97 kV within the regulated range and improved voltage stability. Conversely, Node 29 in Feeder 4, with the lowest VMEI of 0.97262, resulted in a maximum voltage of 23.84 kV, exceeding the voltage regulation range, demonstrating that VMEI effectively identifies suitable DER integration points. This study provides valuable insights for improving DER integration into distribution systems, aiding the global transition to sustainable energy.

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 (θ_opt = 0.7891, θ_safe = 0.6880), which correspond to VMI decision boundaries VMI_DB,opt = 0.7893 and VMI_DB,safe = 0.8101. On an unseen 20% test set, the LR classifier achieves 99.94% accuracy (F₁ = 0.9977) under θ_opt and 100% recall under θ_safe. 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.