Fractal-Based Digital Twins for Energy Systems: A Multi-Scale Modeling Paradigm for Real-Time Optimization

Modern energy systems are increasingly shaped by renewable integration, distributed generation, and dynamic demand, creating nonlinear and multi-scale behaviors that are difficult to capture using conventional digital twin models. This paper reviews digital twin technologies and fractal-based modeling approaches in energy systems and proposes a novel Fractal-Based Digital Twin (FDT) framework. The proposed framework integrates fractal feature extraction, real-time digital twin synchronization, AI-driven prediction, and optimization-oriented control within a unified multi-layer architecture. Its novelty lies in using fractal descriptors, such as the Hurst exponent, fractal dimension, and multifractal features, to enrich system representation and support adaptive decision-making under dynamic operating conditions. Key challenges related to data quality, computational complexity, implementation barriers, and real-world validation are critically discussed. The findings indicate that fractal-enhanced digital twins can improve the scalability, robustness, and adaptability of digital twin applications for next-generation energy system optimization.