Modeling the shadow effect over the photovoltaic power generation using first order nonlinear differential equation

We develop a mathematical model to analyze the performance of photovoltaic (PV) systems under various shadowing effects on solar panels, including cloud shadow, dust accumulation, panel's temperature and fluctuations in sunlight intensity. We will model the effects of these factors on the conversion process by a first order nonlinear differential equation. We will solve the derived nonlinear differential equation and combine it with the power formula to obtain the first nonlinear equation between voltage V and current I. The second well-known nonlinear equation is the characteristic equation obtained from Kirschoff laws. We will solve this nonlinear system for (V,I) mostly using some numerical methods like Gauss-Seidel iteration or Newton Method and study the proprieties of the solution.