Stand-alone power systems based on renewable energy sources are used to replace generators based on fossil fuels. Those renewable power systems also require Energy Storage Devices (ESD) interfaced by a charger/discharger power converter, which consist of a bidirectional DC/DC converter, and a DC bus. This paper proposes a single sliding-mode controller (SMC) for the charger/discharger DC/DC converter to provide a stable DC bus voltage in any operation condition: charging or discharging the ESD, or even without any power exchange between the ESD and the DC bus. Due to the non-linear nature of the power converter, the SMC parameters are adapted on-line to ensure global stability in any operation condition. Such stability of the adaptive SMC is mathematically demonstrated using analytical expressions for the transversality, reachability and equivalent control conditions. Moreover, a design procedure for the adaptive SMC parameters is provided in order to ensure the dynamic response required for the correct operation of the load. Finally, simulations and experimental tests validate the proposed controller and design procedure.