In the present trend, the grid-connected solar photovoltaic systems are playing a major role in supporting the utility peak power and providing the quality of power supply. The installation of solar photovoltaic system is reasonable cost for producing the power. But the solar power may not meet the utility peak demand continuously due to the intermittent nature of solar power. To make continuous supply, the battery storage system is proposed with the bidirectional convert using PI controller. In this work, the grid integration of solar photovoltaic with battery storage system is proposed using the hysteresis current controller for conditioning the electrical power. The solar power is extracted using fuzzy-based maximum power point tracking methods under dynamic variations in the irradiance and temperature. The extracted power is integrate with DC link, and the voltage at DC link is stabilized with the help of battery storage system. The DC link is integrated with the grid through the inverter using a hysteresis current control technique with the PI controller. The inverter and battery storage controllers are used for providing quality of power supply and can meet the necessary peak demand. The performance of the grid-connected solar photovoltaic and battery storage systems is simulated in MATLAB–Simulink software under the dynamic irradiance and the temperature variations. © 2019, Springer Nature Singapore Pte Ltd.