This paper presents a graphical, performance-based energy storage capacity sizing method for residential feeders with high solar penetration levels. The rated power and storage capacity of an energy storage device (ESD) are calculated to fulfill a specified operational requirement. Three locations for installing ESDs are investigated: 1) consumer-owned ESDs inside single-family households; 2) utility-owned distribution transformer-level ESDs; and 3) third-party owned ESDs in a community. First, historical solar radiation data, residential household load data, and residential load models are used for creating the net load (load minus solar generation) ensembles at the house level with resolution of 15 min. Then, a novel graphical capacity selection method using equal probability lines on compressed, composite cumulative distribution function curves is developed for sizing the energy storage needs at the house, distribution transformer, and community levels. Demand-side management methods are investigated for further reducing the need of energy storage. Simulation results demonstrate that the proposed method avoids over- or under-sizing ESDs and allows the users to compare the marginal benefit of increasing the capacity of the ESD.