Modeling of Commercial Photovoltaic Modules using Fractional Order and Stochastic Differential Equations

This work presents an improved modeling approach using fractional differential equations (FDE) and stochastic processes for the I-V characteristics of commercial photovoltaic (PV) modules. Through the application of the Grünwald-Letnikov approach, the shortcomings of conventional integer-order models in a variety of meteorological scenarios can be overcome. By altering the sequence of differentiation and comparing accuracy, the suggested model makes use of fractional derivatives to increase FDE order flexibility. Stochastic white noise is also integrated to account for random fluctuations and create a more realistic model. Numerous scenarios are used to test the model in multiple circumstances for the derivative's order and determine which order provides the best accuracy under different weather conditions. The white noise effect is incorporated; thus, several runs were performed before the module current's mean and standard deviation were determined. Results indicate that, compared to standard models, the fractional stochastic model offers greater accuracy and realism, under different weather conditions of temperature and irradiance. Finally, improved energy management and optimization are made feasible by this work, which advances the field of renewable energy by providing a more accurate mathematical framework for estimating PV module performance.