Non-linear power-voltage characteristics of Solar cell and frequently changing output power due to variation in solar irradiance caused by movement of clouds are the major issues need to be considered in photovoltaic penetration to maintain the power quality of the grid. In recent years several authors have developed the power smoothing approaches for solar photovoltaic system. This work proposes, a power smoothing control approach to smoothen out the power output variations of a Solar photovoltaic system using a supercapacitor energy storage device. Fuzzy logic - Proportional Integral (PI) charge controller are developed for Buck-Boost converter to deliver the constant current and suitable voltage for supercapacitor and to achieve better power smoothing. In this study, Boost converter is working as an MPPT converter to ensure the operation at available peak power point and the Fuzzy controller are developed for Boost converter switches to adjust the duty ratio of the Pulse-Width Modulation (PWM) generator. Three different case studies with variable irradiance and temperature are considered for this work and validated on mono-crystalline solar photovoltaic module. To confirm the accuracy of the proposed model comparison of results are studied by using three different case studies with and without the use of Energy Storage System (ESS). The proposed model is developed and examined on MATLAB/Simulink environment. Simulation outcomes shows that it can effectively smooth out the power output variations of the solar photovoltaic system.