In order to solve the influence of intermittent and fluctuating wind energy on the economy and reliability of the system, a day-ahead and real-time energy management strategy for islanded wind power hydrogen production system with energy storage battery is proposed. In the day-ahead energy management stage, the energy management strategy of alkaline electrolytic cell power classification is adopted, and the economic energy management model of isolated wind power hydrogen production system is established with the maximum daily profit of the system as the objective function. An improved grey wolf optimization algorithm is proposed to solve the system energy management model, optimize the system energy flow and improve the system economy. In the real-time energy management stage, in order to ensure that the system can maintain stable operation when unplanned power fluctuations occur, a real-time energy management strategy for island wind power hydrogen production system based on condition identification is designed, which can adjust the system operation status in time according to the real-time operating conditions of the system. The experimental results show that the day-ahead energy management based on the improved grey wolf optimization algorithm effectively increases the daily revenue of the system and improves the economy of the system. The real-time stage energy management based on condition identification can maintain the system power balance when the wind power fluctuates under the day-ahead plan, and realize the stable hydrogen production of the electrolytic cell throughout the day.