Hybrid Forecasting Techniques for Renewable Energy Integration in Electricity Markets Using Fractional and Fractal Approach

The integration of renewable energy sources into electricity markets presents significant challenges due to the inherent variability and uncertainty of power generation from wind, solar, and other renewables. Accurate forecasting is crucial for ensuring grid stability, optimizing market operations, and minimizing economic risks. This paper introduces a hybrid forecasting framework incorporating fractional-order statistical models, fractal-based feature engineering, and deep learning architectures to improve renewable energy forecasting accuracy. Fractional autoregressive integrated moving average (FARIMA) and fractional exponential smoothing (FETS) models are explored for capturing long-memory dependencies in energy time-series data. Additionally, multifractal detrended fluctuation analysis (MFDFA) is used to analyze the intermittency of renewable energy generation. The hybrid approach further integrates wavelet transforms and convolutional long short-term memory (CNN-LSTM) networks to model short- and long-term dependencies effectively. Experimental results demonstrate that fractional and fractal-based hybrid forecasting techniques significantly outperform traditional models in terms of accuracy, reliability, and adaptability to energy market dynamics. This research provides insights for market participants, policymakers, and grid operators to develop more robust forecasting frameworks, ensuring a more sustainable and resilient electricity market.