Composite Fractal Index for Assessing Voltage Resilience in RES-Dominated Smart Distribution Networks

This work presents a lightweight and interpretable framework for the early warning of voltage stability degradation in distribution networks, based on fractal and spectral features from flow measurements. We propose a Fast Voltage Stability Index (FVSI), which combines four independent indicators: the Detrended Fluctuation Analysis (DFA) exponent α (a proxy for long-term correlation), the width of the multifractal spectrum Δα, the slope of the spectral density β in the low-frequency range, and the c2 curvature of multiscale structure functions. The indicators are calculated in sliding windows on per-node series of voltage in per unit Vpu and reactive power Q, standardized against an adaptive rolling/first-N baseline, and anomalies over time are accumulated using the Exponentially Weighted Moving Average (EWMA) and Cumulative SUM (CUSUM). A full online pipeline is implemented with robust preprocessing, automatic scaling, thresholding, and visualizations at the system level with an overview and heat maps and at the node level and panel graphs. Based on the standard IEEE 13-node scheme, we demonstrate that the Fractal Voltage Stability Index (FVSIFr) responds sensitively before reaching limit states by increasing α, widening Δα, a more negative c2, and increasing β, locating the most vulnerable nodes and intervals. The approach is of low computational complexity, robust to noise and gaps, and compatible with real-time Phasor Measurement Unit (PMU) /Supervisory Control and Data Acquisition (SCADA) streams. The results suggest that FVSIFr is a useful operational signal for preventive actions (Q-support, load management/Photovoltaic System (PV) ). Future work includes the calibration of weights and thresholds based on data and validation based on long field series.