This article presents a successful simulink model by using the photovoltaic (PV) product along with DC/DC buck converter, lithium ion battery, maximum power point tracker (MPPT) along with loads. The current-voltage (I-V) and power-voltage (P-V) characteristics of a Kyocera KC200GT product is validated using single diode PV model in conjunction with Lambert W function. Fuzzy logic algorithm is incorporated in MPPT for high tracking accuracy at steady state and better performance to the varying atmospheric conditions. The complete model is simulated under two testing scenarios i.e., sunny and cloudy day conditions. Exact analytical solution technique by using Lambert W function is followed by expressing I-V and P-V characteristic of PV module by converting into discrete equations. The proposed Lambert W function based mathematical model is accurate and there is a good agreement between calculated and simulated outputs.