Highly penetrated rooftop solar photo-voltaic (PV) units might cause both slow and fast voltage fluctuations in the connected low voltage (LV) distribution feeder due to random variations in solar PV power output, in addition to the variations in load demand. These fluctuations in voltage can be mitigated with the use of distributed energy storage systems integrated in solar PV units. A novel methodology to determine the optimum sizing of a Battery Energy Storage System (BESS) for the simultaneous mitigation of fast and slow voltage fluctuations has been proposed in this paper. The proposed method is simulated on a practical distribution feeder in NSW, Australia. The simulation results show that the optimum sizing and optimum operating parameters can be obtained for various fast and slow PV output variations.