This research study uses a computer simulation based on real input data to examine the impact of a supercapacitor module working as a fast response energy storage unit in renewable energy systems to increase energy self-consumption and self-sufficiency. The evaluated system includes a photovoltaic system with a capacity of 3.0 kWp and between 0 and 5 supercapacitor units with a capacity of 500 F per module. The study was carried out using experimental data for electrical load, solar irradiance, and ambient temperature for the year 2020, with a 1 min temporal resolution. The daily average ambient temperature was 10.7 °C, and the daily average solar irradiance was 3.1 kWh/m2/day. It is assumed that the supercapacitor could only be charged from a photovoltaic system using renewable energy and not from the grid. The simulation results showed that using the supercapacitors to feed the short and large peaks of the electrical load significantly increases energy self-consumption and self-sufficiency. With only five supercapacitor modules, yearly energy self-sufficiency increases from 28.09% to 40.77%.