Widespread deployment of large-scale photovoltaics (PVs) and energy storage systems (ESSs) in distribution networks necessitates the development of methods to assess their possible system impacts. One of the primary concerns related to the integration of these systems is short-circuit overcurrent protection problems. Present techniques use simulations of full and detailed distribution circuit models with a large number of scenarios to estimate the PV and ESS sizes a distribution feeder can accommodate without causing adverse impacts. As this process requires considerable time and effort, this paper develops a practical and simplified analytical approach to conservatively estimate a utility distribution feeder's accommodation limits without causing protection problems. Sympathetic tripping and relay insensitivity problems are considered in this paper under both symmetrical and unsymmetrical fault conditions. Using the analysis presented, the factors influencing these protection problems are determined to provide insights into relay settings. The feeder accommodation limits obtained using the proposed analytical approach are compared with those obtained using simulations of an actual detailed distribution circuit model. The findings show that the proposed approach is accurate in estimating the feeder's accommodation limits for integrating large-scale PV and ESS.