Fractal-Informed Risk Modeling in Energy Systems: From Extreme Events to Resilience-Oriented Control

Extreme events, renewable-generation variability, and high-impact low-probability disturbances challenge energy-system risk assessment under nonstationary operating conditions. This paper critically reviews fractal and multifractal methods relevant to energy-system risk analysis and proposes a Fractal-Informed Risk Modeling (FIRM) architecture linking data acquisition, fractal feature extraction, probabilistic risk inference, AI-based prediction, and resilience-oriented control. Fractal descriptors, including the Hurst exponent, fractal dimension, and multifractal-spectrum measures, are treated as complementary indicators rather than deterministic predictors of failure. Their operational value depends on estimation uncertainty, window selection, threshold calibration, and validation against strong conventional baselines. FIRM is therefore presented as a conceptual reference architecture rather than an implementation-ready or experimentally validated model. The framework specifies inter-layer interfaces, uncertainty propagation, and the distinction between literature-demonstrated applications and proposed extensions. A validation roadmap is also provided, covering candidate datasets, baseline models, extreme-event scenarios, predictive and calibration metrics, and resilience indicators. Overall, this study identifies where fractal information may add value to established risk methods and defines the methodological safeguards required before such information can support operational decision-making.