Energy storage systems and devices are essential for the stable and secure operation of electrical grids with a high penetration of renewable energies. A broad system perspective may be necessary for adequately integrating DC storage systems, particularly when associated with grid-forming inverters. This paper introduces a comprehensive model for a bidirectional Buck-Boost DC-DC converter of type D1, characterized by continuous input current, designed to integrate sensitive DC sources subject to pulsating currents with grid-forming inverters. The focus is on a non-linear control strategy utilizing input-output feedback linearization to enhance the system’s dynamic response to sudden power shifts and direction changes. This approach ensures a wide operating range, especially when the converter transitions between power supply modes and absorbs power from the AC grid to the connected DC-side energy storage system.