Energy management systems (EMS) are becoming increasingly important in order to utilize the continuously growing curtailed renewable energy. Promising energy storage systems (ESS), such as batteries and green hydrogen should be employed to maximize the efficiency of energy stakeholders. However, optimal decision-making, i.e., planning the leveraging between different strategies, is confronted with the complexity and uncertainties of large-scale problems. Here, we propose a sophisticated deep reinforcement learning (DRL) methodology with a policy-based algorithm to realize the real-time optimal ESS planning under the curtailed renewable energy uncertainty. A quantitative performance comparison proved that the DRL agent outperforms the scenario-based stochastic optimization (SO) algorithm, even with a wide action and observation space. Owing to the uncertainty rejection capability of the DRL, we could confirm a robust performance, under a large uncertainty of the curtailed renewable energy, with a maximizing net profit and stable system. Action-mapping was performed for visually assessing the action taken by the DRL agent according to the state. The corresponding results confirmed that the DRL agent learns the way like what a human expert would do, suggesting reliable application of the proposed methodology.