Analytical Relationship between the Electrical Parameters of the PV Array and External Factors based on the Lambert W-Function

Mamadsho Ilolov, Khakim Ahmedov, Ahmadsho M. Ilolov, Anvar S. Qodirov, Jamshed Sh. Rahmatov, Narimon Sh. Yusufbekov

Abstract: The main goal of this research is to find and to analyze qualitatively, the current/voltage characteristics of the photovoltaic (PV) array. The proposed mathematical model is based on the single diode equivalent circuit; the analytical relationship between the electrical characteristics of the PV module and external environmental factors such as the intensity of solar radiation and temperature are taken into account. Mathematical and computer modeling are of the particular importance under the conditions of a significant spread in the values of external factors which occur in the mountain and remote desert areas in Central Asia. A mathematical analysis of the resulting transcendental equation is carried out using a Lambert W-function which has been the subject of a large number of publications.

Keywords: Mathematical model, solar cell, Lambert W-functions, maximum power point, photovoltaic module