Supercapacitors complement the limitations of battery storage technologies, and therefore, a battery-supercapacitor hybrid storage device (HSS) has established as a viable option for mitigating the renewable energy variability. For optimal sizing of both batteries and supercapacitors, batteries are treated as low-frequency variation mitigation device and supercapacitors as high-frequency variation mitigation device. However, the maximum amount of current injected or extracted from the battery for a given capacity rating is limited, failing which, supercapacitors would replace batteries to mitigate low-frequency variability. Both slow and fast varying components are defined respecting a cutoff frequency, and in this problem, the objective is to minimize the annualized cost of HSS with optimal cut-off frequency. The sizing of the HSS should also minimize the variability for a given statistical significance. The cut-off frequency is iterated over the solution space using mode pursuing sampling method to obtain the optima. The proposed method is illustrated with a sample dataset and results are discussed. Additionally, an additional problem where the frequency of operation of the supercapacitors is limited to two hours to limit the self-discharge rate of the supercapacitors is also discussed.