This article presents a novel control algorithm for a three-level interleaved buck converter (TLIBC) to supply energy to a proton exchange membrane electrolyzer (PEMEL) in the presence of renewable energy sources. It leverages the main advantages of the TLIBC, i.e., a high voltage conversion ratio, low output current ripple, and the ability to operate in case of electrical circuit failures. The new control law, based on nonlinear improved sliding model-based control, offers a significant improvement of the performance for input power variation when renewable energy sources are used. The proposed controller exhibits further benefits, such as a faster dynamic response and greater robustness against parameter uncertainties when compared to traditional PI-based control. Experimental verification is carried out using a PEMEL dynamic emulator to preserve the real PEMEL performance during the tests. The obtained experimental results demonstrated that the proposed control technique overcomes current limitations in terms of performance usually characterized by PI controllers. Particularly, during operating conditions change when considering electrolyzers powered by renewable energy sources, a faster response is obtained. The rise time is imposed by the controller, and it does not depend on the operating point.