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The heat and hydrogen balance of the hydrogen energy storage system’s intermittent operation becomes a key factor affecting the performance of the wind-hydrogen hybrid system (W-HHS). This work designed a hydrogen energy storage system (HESS), including waste heat utilization. Then, a dual state of charge (SOC) model is established, in which hydrogen and heat storage is considered. Furthermore, based on the distributionally robust method, an optimal dispatch method of W-HHS is proposed to reduce the operation cost of conventional units in the grid and increase the revenue of the W-HHS. The previously proposed dual SOC model of heat-hydrogen balance is regarded as a constraint in this cooperative dispatch. The effectiveness and efficiency of the dual SOC model were verified on the IEEE 30-bus system with an actual wind plant data set. The results show that the hydrogen-heat dual SOC model can fully reflect the influence of heat and hydrogen balance on the operation of the W-HHS. The cooperative dispatch method improves the reliability of the W-HHS operation under the premise of ensuring the heat-hydrogen balance. When the constraints of hydrogen balance SOC and heat balance SOC are met simultaneously, the available power of the wind plant is 6–8% lower than the ideal situation. Parameter analysis indicates that reducing the heat dissipation coefficient can reduce the influence of the SOC constraint of heat balance on the dispatch strategy and increase the power output of the wind plant. When the heat dissipation coefficient is less than 1/1,200, the heat balance SOC constraint fails.

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