Abstract As distributed generations (DGs) are occupying an increasing proportion in active distribution network, the fluctuation of bus voltage becomes severe because of their intermittent and stochastic characteristics. Energy Storage System (ESS) can be adopted as an effective means to mitigate this fluctuation. This paper proposes a methodology for the optimal allocation of ESSs based on the novel optimal affine power flow (OAPF) approach. Affine models of wind turbine generation (WTG), photovoltaic (PV) system, and ESS are built while considering uncertainty characters of their power outputs. The objective function is set to minimize the capital investment of ESSs and the penalty costs of bus voltage fluctuations. The complex affine arithmetic based distribution power flow is used to ensure that constraints on power flow limits, voltage limits, and ESS operational limits are satisfied. The optimization problem is solved by an improved immune genetic algorithm (IIGA). The proposed approach is verified via a modified IEEE 33-bus system with a high penetration of DGs. Results show that the optimal allocation of ESSs can satisfy both the technical and economic requirements under such an uncertain environment.