The increasing deployment of stand-alone photovoltaic (PV) power supply systems is driven by their capability to convert solar irradiance into electrical energy. A typical application of such systems is solar-powered water pumping. However, since solar irradiance varies throughout the day, the maximum power output of PV panels may be lower than the load demand. A viable solution to this issue is the integration of hybrid energy storage systems (HESSs) combining batteries and supercapacitors (SCs). In this work, HESS charging and discharging control strategies were developed based on adaptive droop control, which regulates the power distribution between the SC and the battery and limits DC grid voltage deviations. In the developed method, the SC droop coefficient is adaptively adjusted in a stepwise manner depending on the SC state of charge (SoC), while the battery droop coefficient remains constant. The performance of the proposed strategies was evaluated through simulations, showing SC-battery internal loss minimization by up to 50% compared with the scenario without droop control when the SC is discharged first, and only then is the battery engaged. Step response of the converter was investigated experimentally, showing less than a 2 ms response time, and no undesired influence from the proposed control method was detected.