Hourly solar irradiance forecasting based on statistical methods and a stochastic modeling approach for residual error compensation

By reducing fossil fuel use, renewable energy improves the economy, quality of life, and environment. These impacts make renewable energy forecasting crucial for lowering fossil fuel utilization. This paper aims to mathematically improve time series forecasting literature by focusing on solar irradiance applications in Los Angeles, Denver, and Hawaii solar irradiance sites. A three-phased time series forecasting hybrid method is devised for this endeavor. The ARFIMA is used to forecast the original solar irradiance time series in phase I. Next, the dataset's residuals, are retrieved by subtracting the phase I results from the observed time series to prepare the scenario for the following phase. A novel enhanced fractional Brownian motion is used for residual forecasting in phase II. The parameter estimation in phase II is implemented adaptively to capture the dynamic statistical characteristics of the time series efficiently. Finally, the phases I and II results are numerically conglomerated to form the final forecasting results in phase III. The residual forecasting part, in phase II, reveals a substantial superiority. Also, when comparing the proposed hybrid algorithm results to other existing cutting-edge algorithms applied to the same solar irradiance applications, the output demonstrates that the suggested algorithm has a significantly improved performance.