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A novel fractional order grey Euler model and its application in clean energy prediction

Author

Listed:
  • Yang, Zhongsen
  • Wang, Yong
  • Fan, Neng
  • Wen, Shixiong
  • Kuang, Wenyu
  • Yang, Mou
  • Sapnken, Flavian Emmanuel
  • Narayanan, Govindasami
  • Li, Hong-Li

Abstract

The global imperative for sustainable energy solutions has intensified due to escalating energy demands and heightened environmental regulations, making clean energy adoption critical for strategic policymaking. This study introduces an advanced fractional grey Euler model (FEGEM(p,1)) incorporating a novel fractional-order accumulated generating operation with exponential kernel functionality (r-EAGO) to forecast clean energy production trends in hydroelectricity, nuclear power, and natural gas. The proposed r-EAGO mechanism demonstrates superior capability in extracting implicit patterns from historical data through its sophisticated accumulation process. The fractional-order modelling framework offers enhanced flexibility through its adjustable differential order, particularly effective in addressing the inherent non-linearity and complexity of clean energy systems. To ensure optimal performance, the model hyperparameters are optimised using a differential evolution algorithm. The results of Monte-Carlo simulation and probability density analysis reveal good robustness of the model. Comprehensive validation of the seven forecasting models revealed that the FEGEM(p,1) model is extremely accurate, achieving a mean absolute percentage error (MAPE) of 2.508 %, 3.489 %, and 2.343 % for the three energy cases, respectively. Projections of the next five years indicate distinct growth trajectories: Nuclear power generation and natural gas production are forecasted to maintain compound annual growth rates of 4.65 % and 5.46 % respectively through 2027, while hydropower exhibits cyclical growth patterns influenced by hydrological variations, ultimately reaching 1,429 billion kWh by the terminal forecast year. Finally, these findings yield strategic recommendations for optimising energy development framework.

Suggested Citation

  • Yang, Zhongsen & Wang, Yong & Fan, Neng & Wen, Shixiong & Kuang, Wenyu & Yang, Mou & Sapnken, Flavian Emmanuel & Narayanan, Govindasami & Li, Hong-Li, 2025. "A novel fractional order grey Euler model and its application in clean energy prediction," Energy, Elsevier, vol. 322(C).
    • Handle: RePEc:eee:energy:v:322:y:2025:i:c:s0360544225012514
    DOI: 10.1016/j.energy.2025.135609
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