The focus of our work is the use of an energy storage system (ESS) to integrate solar energy generators into the electrical grid. Although, in theory, an ESS allows intermittent solar power to be shaped to meet any desired load profile, in practice, parsimonious ESS dimensioning is challenging due to the stochastic nature of generation and load and the diversity and high cost of storage technologies. Existing methods for ESS sizing are based either on simulation or analysis, both of which have shortcomings. Simulation methods are computationally expensive and depend on the availability of extensive data traces. Existing analytical methods tend to be conservative, overestimating expensive storage requirements. Our key insight is that solar power fluctuations arise at a few distinct time scales. We separately model fluctuations in each time scale, which allows us to accurately estimate ESS performance and efficiently size an ESS. Numerical examples with real data traces show that our model and analysis are tight