Energy storage devices are collocated with conventional solar photovoltaic (PV) systems to tackle the intermittency of solar irradiance and maintain the power quality of supplied energy. The energy storage system usually has its own conversion devices that may incur an extra capital cost of installation. This paper proposes an integrated and cost-effective photovoltaic-supercapacitor (PVSC) system in which the energy storage functionality of the supercapacitor (SC) is merged into the PV array where the power flow bidirectionally takes place to maintain the system stability under grid disturbances during the daytime, nighttime, and cloudy weather. A nonlinear mathematical model (NMM) was developed to conduct the stability analyses and to design the controller parameters, which facilitates a faster and more accurate numerical analysis compared to existing average models. The effectiveness of the proposed system was evaluated by simulation analysis and compared to that of the basic PV and a conventional SC system in which full energy storage is connected in parallel with the PV. The results demonstrate that the proposed PVSC system is effective in improving the dynamic performance of the connected power grid system. In addition, the proposed PVSC system fulfills the functionality of the conventional SC with merged conversion devices; that is, the performance of the proposed PVSC system is comparable to the conventional SC system.