A high penetration of rooftop solar photo-voltaic (PV) units can cause both slow and fast voltage fluctuations when connected to the low voltage (LV) distribution feeder due to the random variations in the solar PV power output versus load demand. These unacceptable fluctuations can be alleviated by using energy storage systems integrated with the solar PV units. In this paper, a novel heuristic control strategy is proposed to alleviate both the slow and fast voltage fluctuations in the connected LV distribution feeder; using a hybrid energy storage system. In the proposed method; the integrated battery storage will be dynamically charged to mitigate the voltage rise during mid-day, and discharged during the evening peak hours, and the integrated super capacitor storage will be simultaneously charged or discharged to control the fast fluctuations in the PV inverter to be within a specified magnitude. An energy sharing method between the battery storage and the super capacitor storage is proposed to provide undisrupted control for the fast fluctuations during passing cloud. The proposed control strategies have been verified on a distribution feeder system and the results have been reported.