This paper presents a voltage-aware operational framework for active distribution networks using a mixed-integer linearized optimization model. Unlike conventional approaches that treat voltage limits as hard constraints, a linear voltage deviation penalty is incorporated directly into the objective function, enabling voltage conditions to influence operational decisions, particularly the charging and discharging schedules of energy storage systems. The proposed formulation jointly considers active and reactive power dispatch, storage operation, and network losses within a single computationally tractable framework. Simulation results on the IEEE 33-bus distribution system demonstrate that the proposed approach leads to a smoother voltage profile at critical buses over the scheduling horizon, while maintaining voltages within acceptable limits. Compared to the base case, the total network losses are reduced from 3028.48 kW to 3027.66 kW, corresponding to a relative reduction of approximately 0.03%. In parallel, the modified objective function value reflects the explicit consideration of voltage quality, resulting in an increase of about 9.2% in the objective value, which represents a trade-off between voltage performance and operational cost. The results confirm that incorporating voltage deviation into the optimization objective enables voltage-aware storage operation and provides a transparent mechanism to evaluate its impact on network performance.