An innovative nonlinear grey system model with generalized fractional operators and its application

Accurate electricity generation forecasting is essential for optimizing energy management, ensuring grid stability, and supporting sustainable development. This study presents a novel approach for forecasting electricity generation using a conformable fractional nonlinear grey Bernoulli model (ACFNGBM). The model integrates fractional-order calculus, nonlinear mechanisms, and Particle Swarm Optimization (PSO) to address challenges posed by small sample sizes, nonlinear relationships, and volatile energy data. The hyperparameters of the model are optimized to minimize prediction errors, improving the accuracy of the forecasts. The research uses electricity generation data from four regions in China (2004–2021) to compare the performance of the ACFNGBM with traditional grey models, advanced grey systems, and machine learning methods. The experimental results reveal that the proposed model outperforms the benchmark models in terms of prediction accuracy and stability. A sensitivity analysis further examines the influence of fractional order and power index on the model’s performance, highlighting the importance of hyperparameter optimization. Forecasts for 2024–2029 suggest a steady increase in electricity generation across all regions, with Jiangxi and Liaoning exhibiting the highest outputs, while Xizang shows gradual growth. The ACFNGBM proves to be a robust tool for energy forecasting, offering significant potential for sustainable energy planning and management.