Mathematical model for predicting the performance of photovoltaic system with delayed solar irradiance

Photovoltaic systems convert solar irradiance into electricity. Due to some factors, the amount of solar irradiance arriving at the solar photovoltaic collector at a specific location varies. The goal of this study was to develop a mathematical model for predicting the performance of a photovoltaic system, which depends on the amount of solar irradiance. A novel model for solar irradiance in the form of a delay differential equation is introduced by including the factor of delayed solar irradiance, hour angle and the sun's motion. The simulation study is carried out for the three scenarios of weather conditions: a clear day, a slightly cloudy day, and a heavily overcast day. The numerical solution is obtained by adopting the 4th-order Runge Kutta method coupled with a parameter fitting technique, the Nelder Mead algorithm, which is implemented by using MATLAB software. The data from a solar plant in Pahang, Malaysia, was used for model validation and it is found that the prediction profile for solar irradiance aligns well with the intermediate and decay phases, but deviates slightly during the growth phase. The output current and power for the solar photovoltaic panel were treated as time-dependent functions. As the solar irradiance increases, the output current and power of the solar panel will increase. The result showed that the maximum output current and output power of STP250S-20/Wd crystalline solar module decreased by 42% and 76%, respectively, during slightly cloudy and heavily overcast conditions when compared to clear days. In other words, the performance of a photovoltaic module is better on clear days compared to cloudy days and heavily overcast. These findings highlight the relationship between delayed solar irradiance and the performance of the solar photovoltaic system.