In the presence of a catenary infrastructure, the transition from fossil fuel-based bus fleets to electric-powered ones can be facilitated through conventional trolleybuses or In-Motion-Charging trolleybuses, offering environmentally friendly and cost-effective solutions. However, grid congestion at traction substations (TSs) can limit this transition as the grid operator is incapable or unwilling to provide more capacity. As grid connection contracts are typically tallied and billed in periods of 15 minutes, stationary energy storage devices can prove useful in short-term buffering of the power demand. Consequently, more electrification projects can be rolled out under the same, or minimally extended grid contract. In this aim, this paper looks at validating energy storage as a means of enabling bus fleet electrification. It presents a power management strategy that controls the power exchange between the energy storage system (ESS) within the TS, specifically to manage the 15-minute average power. This strategy also serves as a tool for sizing the ESS with the minimum capacity required for the application. A case study for the city of Bologna, Italy, has been considered to validate the proposed approach. The findings indicate that billing contract power can be reduced by up to 41.7% when a storage device actuates in high-energy-demand substations. Furthermore, different types of Lithium-ion cells, including their second-life versions, are compared to determine the most beneficial options under limited cost and volume constraints. Recommendations are drawn on the exact scenarios where each type of cell is most beneficial.