In this paper, an effective, three-stage day-ahead (DA) scheduling strategy for a wind farm (WF) with integrated multi-unit battery energy storage systems (BESSs) is proposed. In the first stage, a statistical flexible dispatch margin (FDM) based on the long-term wind forecast error-data is calculated to deal with the uncertainty of the wind power forecast. The FDM is modeled in such a manner that it not only compensates for the shortage of the wind power but also takes in account the expected excess amount of the wind power due to forecast errors. The conservativeness of the margin-based solution is addressed through the dynamic reliability evaluation of FDM. This FDM is realized using the multi-unit BESSs. At the second stage, a robust optimization formulation is presented that makes this strategy cost-effective in terms of revenue. Finally, at the third stage, a multi-unit BESS scheduling algorithm is presented that ensures equal cycles of charge and discharge avoiding the abrupt switching between the charging and the discharging modes to enhance the lifetime of BESS. The proposed scheduling strategy is compared with scenario-based stochastic and worst-case realization based robust optimization scheduling frameworks. The simulation studies, utilizing the real data, suggest that the proposed strategy is better in terms of the uncertainty mitigation, the total revenue obtained, the enhanced BESS lifetime and the computational time.