The electric power sector is undergoing profound transformations due to the increasing penetration of distributed generation and intermittent renewable sources, heightening uncertainties in distribution companies planning and making the contracting of the transmission system usage amount (TSUA) a significant technical and economic challenge with major financial implications. Within this context, this work proposes an integrated stochastic optimization model for the optimal contracting of TSUA, considering the strategic operation of battery energy storage systems (BESS) as a tool for flexibility and risk mitigation. The developed approach employs stochastic linear programming with an objective function that combines expected cost and conditional value-at-risk, enabling a risk-averse decision-making framework. The operation of the BESS is co-optimized, incorporating its technical constraints and modeled using monthly typical days. Case studies, performed on the IEEE RTS 24-bus test system, evaluate the impact of the battery s location, configuration, and ramp constraints on the total system cost and the contracted TSUA. The results demonstrate that BESS can substantially reduce contractual costs and financial risks, establishing the optimized integration of storage as a valuable tool to enhance the contractual and financial management of distribution companies in a dynamic and uncertain energy landscape