The global shift towards renewable energy generation has led to a significant increase in renewable energy consumption, posing challenges in maintaining electricity balance due to the intermittent nature of sources like wind and solar power. To address this, the paper emphasizes the potential of hydrogen as a clean and efficient secondary energy source for balancing electricity consumption effectively. By integrating an Electric Hydrogen Hybrid Storage (EHHS) system, the study aims to mitigate wind power fluctuations. The research proposes utilizing improved wavelet characterization theory and deep reinforcement learning (DRL) technology to enhance wind power stability within the EHHS framework. Previous studies have primarily focused on energy storage systems using electrochemical storage and supercapacitors, with limited research on combining energy storage with hydrogen systems, highlighting the novelty and importance of this study. The paper introduces novel algorithms and strategies to optimize the performance of EHHS, showcasing the potential of DRL in effectively managing the nonlinearity and randomness of wind power fluctuations, ultimately contributing to the stability and reliability of renewable energy systems.