To face the intensive use of natural gas and other fossil fuels to generate hydrogen, water electrolysis based on renewable energy sources (RES) seems to be a viable solution. Due to their fast response times, and high efficiency, proton exchange membrane electrolyzer (PEM EL) is the most suitable technology for long-term energy storage, combined with RES. Like fuel cells, the development of fit DC-DC converters is mandatory to interface the EL to the DC grid. Given that PEM EL operating voltages are quite low and to meet requirements in terms of output current ripples, new emerging interleaved DC-DC converter topologies seem to be the best candidates. In this work, a three-level interleaved DC-DC buck converter has been chosen to supply a PEM EL from a DC grid. Therefore, the main objective of this paper is to develop a suitable control strategy of this interleaved topology connected to a PEM EL emulator. To design the control strategy, investigations have been carried out on energy efficiency, hydrogen flow rate, and specific energy consumption. The obtained experimental results validate the performance of the converter in protecting the PEM EL during transient operations while guaranteeing correct specific energy consumption.