Increasing wind and solar generation in power grids leads to more renewable power curtailments in some periods of time due to the fast and unpredictable variations of their outputs. The utilization of these sources for energy storage can unlock huge potential benefits. Therefore, aiming at minimizing the curtailments of renewable power from the viewpoint of an independent system operator (ISO), in this paper, we propose deep learning-driven optimal sizing and operation of alkaline water electrolyzers (AWE) and battery energy storage systems (BESS). For this purpose, a set of actual renewable power curtailment data of California ISO was fully investigated, and deep learning forecast methods were employed to determine the prediction error and its probability distribution function (PDF). Using the fitted PDF, a set of scenarios was generated and reduced to some accurate and probable ones. Consequently, a two-stage scenario-based stochastic model was proposed to determine the optimal planning of this system, and a penalty variable was defined in the second stage to maximize the utilization of curtailed renewable energy sources (RESs). The learning results showed that the prediction errors were minimized using the gated recurrent unit (GRU) method. It was also shown that 97% of curtailments were utilized using AWEs with annual costs of $233.55 million, which had 63.5% fewer costs than using BESSs. Furthermore, using AWEs reduced operational expenses by 89.1% compared with using BESSs, owing to their operational benefits.