With the integration of a high penetration of wind power into distribution system, the ability to cope with the voltage fluctuation issue arising from the intensified uncertainty should be improved. Energy storage system (ESS) with effective control strategies keeps a key role in smoothing the voltage fluctuation caused by the uncertainty of wind turbine generators (WTGs). Considering the constraints of state of charge (SOC), charge-discharge efficiency and continuous operation of ESS, this paper proposes a novel approach to determine the minimum capacity of ESS to satisfy the voltage fluctuation limit based on unbalanced three-phase interval power flow. An unbalanced forward-backward sweep interval power flow considering the constraints of ESS and the voltage fluctuation limit is proposed. The interval model of uncertain WTG output is established on basis of wind speed fluctuation curve. The interval model of the practical ESS output is obtained on basis of the present SOC, nominal capacity and comprehensive efficiency. The output voltages of power flow can directly demonstrate the voltage fluctuation rate due to their interval forms. Therefore, a feedback mechanism is established between the output voltage fluctuation rate and the input ESS practical power, which is used to determine the minimum capacity of ESS to satisfy the fluctuation limit. A modified IEEE 33-bus system with high penetration of WTGs is implemented to test the proposed method. Results demonstrate the validity and effectiveness of the proposed approach.