This paper presents a planning framework to find the minimum storage sizes (power and energy) at multiple locations in distribution networks to reduce curtailment from renewable distributed generation (DG), specifically wind farms, while managing congestion and voltages. A two-stage iterative process is adopted in this framework. The first stage uses a multi-period AC optimal power flow (OPF) across the studied horizon to obtain initial storage sizes considering hourly wind and load profiles. The second stage adopts a high granularity minute-by-minute control driven by a mono-period bi-level AC OPF to tune the first-stage storage sizes according to the actual curtailment. Congestion and voltages are managed through the optimal control of storage (active and reactive power), on-load tap changers (OLTCs), DG power factor, and DG curtailment as last resort. The proposed storage planning framework is applied to a real 33-kV network from the North West of England over one week. The results highlight that by embedding high granularity control aspects into planning, it is possible to more accurately size storage facilities. Moreover, intelligent management of further flexibility (i.e., OLTCs, storage, and DG power factor control) can lead to much smaller storage capacities. This, however, depends on the required level of curtailment.