The integration of renewable energy sources has significantly advanced sustainability efforts, yet their intermittent nature poses challenges to grid stability. Electricity-Hydrogen (EH) storage systems have emerged as promising solutions to store surplus renewable energy. Existing studies often overlook the technical disparities between Hydrogen Energy Storage Systems (HESS) and Battery Energy Storage Systems (BESS), highlighting the critical importance of considering Time-of-Use (TOU) hydrogen market prices in optimizing EH storage, as TOU pricing schemes incentivize efficient storage resource utilization and grid operation optimization. This paper addresses the pressing need for optimal scheduling strategies for EH storage systems in the context of renewable energy integration. The mathematical model is formulated by conducting comprehensive analyses to assess the economic aspects of EH storage under TOU hydrogen pricing scenarios. Additionally, a solution methodology based on Mixed-Integer-Linear Programming (MILP) and rolling optimization is employed to solve the problem. Through the comparative analysis, the results suggest that considering TOU prices of hydrogen can enhance the profitability of hydrogen trading, thereby improving the economic viability of the integrated power system.