As the high penetration of wind power increases intermittent generation in power systems, large-scale energy storage systems (ESSs) are necessary to mitigate this variable generation and increase operational flexibility. The variable power generation and the ESSs scheduling may affect voltage security issue of the power systems, making it important to include and assess static voltage stability (SVS) as an important aspect of security in the power system operation studies. Under this perspective, this paper proposes a stochastic security-constrained unit commitment (SCUC) model integrating the bulk ESSs in the power system with the high penetration of wind power. The modeled bulk ESSs are compressed air energy storages (CAESs). A practical criterion of the SVS is considered as an operational constraint to ensure that the stochastic SCUC decision is economically and technically optimal. The wind power uncertainty is handled using an adaptive point estimate method (APEM) due to its decreased computation time and acceptable accuracy, compared to other methods. Also, to reach more practical results, flexible reactive power capability of DFIG-based wind farm is modeled probabilistically. In order to effectively adjust the SVS margin, a two-stage approach is developed in the proposed stochastic SCUC model which includes voltage stability relaxed stochastic SCUC (VSR-SSCUC) as the first stage and voltage stability constrained stochastic SCUC (VSC-SSCUC) as the second stage. The proposed stochastic SCUC model is solved using a mixed-integer non-linear programming (MINLP) method and is applied to IEEE 30-bus and IEEE 57-bus test systems. Simulation results show that the SVS margin can be effectively adjusted using the proposed two-stage approach. In the stage of VSC-SSCUC, expected operation cost is higher than the other stage, whereas a considerable SVS margin is obtained. Proper scheduling of the CAESs can reduce the impact of wind generation uncertainty on supply side variability and improve the SVS of the power system, as well as decrease the expected operation cost. Moreover, the proposed APEM is compared with three conventional methods, namely, Monte Carlo simulation (MCS), scenario reduction method (SRM), and deterministic approach, in numerical studies that show the APEM is more efficient than the conventional methods for this analysis.