To enhance the efficiency of renewable energy utilization and minimize operational costs within the source- grid-load-storage system with electro-hydrogen hybrid energy storage, this paper presents an optimal operation method of electro- hydrogen hybrid energy storage system considering an SOC optimization setting to realize the day-ahead real-time optimal scheduling of the system. First, a method for SOC optimization setting of high-capacity energy storage systems is proposed to determine the day-ahead SOC optimization settings at the start and end of each day for the energy storage system. Subsequently, based on a twin delayed deep deterministic policy gradient algorithm, a day-ahead real-time optimal scheduling model training method is proposed. A real-time model for source-network-load energy storage system is established based on the optimized set points of energy storage SOCs and day-ahead operation data to achieve day-ahead real-time integrated optimal scheduling. Finally, the effectiveness of the proposed method is validated through case study results. The result indicates that the method proves to be efficient in enhancing system revenue, while the day-ahead real-time optimal scheduling model mitigates the impact of prediction errors.