A Stochastic Modeling and Characterization of Solar Energy Variability Using a Gamma Distribution Approach

Abstract

Energy intermittency and variability of solar energy presents a crucial challenge to the stability of the grid and its operational reliability. This study x-rays the statistical distribution of Direct Normal Irradiation. An hourly analysis of DNI data was conducted using a probabilistic model, relying on gamma distribution, fitted to method of moments. An hourly analysis of DNI was conducted using data derived from a solar facility located in Enugu state, Nigeria. The goodness of fit was analyzed using the Kolmogorov-Smirnov (KS) and Anderson darling tests. The result of the analysis showed that gamma distribution sufficiently represents DNI for the majority of daylight hours (Ks P>0.05 for 16 out of 24 hours), proving the strongest fit during mid-day and the weakest during the sunrise and sunset transition. A strong linear correlation of (r =0.94, p>0.001) was observed between monthly DNI and solar energy generation, thereby validating that the availability of solar resources is the major factor influencing energy output. However, a straightforward operational cost model comparing strategies without forecasting against those informed by forecasting suggests a potential reduction in grid back-up cost of about 18% under assumption of constant demand and a local tariff of #65/kwh. The study concluded that while gamma ray offers a valuable probabilistic framework for understanding DNI variability, integrated complementary energy storage solutions and more advanced forecasting techniques are essential for robust grid integration.