A diffusion-enhanced active learning framework for static voltage stability region numerical characterization in DC networks

With the increasing grid integration of photovoltaic generation, energy storage systems, and electric vehicle fast charging stations in DC networks, source-and load-side uncertainties are becoming more pronounced. These uncertainties, which are modeled as fluctuations in nodal power injections, pose challenges to the static voltage stability in DC networks. This paper aims to characterize the Static Voltage Stability Region (SVSR), defined as the set of uncertain power injection profiles under which the DC power flow equations remain solvable. Analytical methods provide direct SVSR approximations but tend to introduce conservativeness. Numerical methods, while more accurate, require extensive simulation sampling, resulting in high computational burden. To address this, we propose a diffusion-enhanced active learning approach for efficient and accurate SVSR boundary characterization. First, we develop a closed-loop active learning algorithm that quantifies uncertainty based on classifier posterior probabilities and selectively queries the most informative samples for labeling. Then, a diffusion model is introduced to expand the high-value samples obtained by active learning into a dense set of reliable boundary samples, effectively accelerating the learning process. Case studies based on a DC 14-bus benchmark system demonstrate that the proposed approach reduces simulation cost by about 50% compared to conventional numerical methods.