Hydrogen, as a clean, efficient, and high-quality energy source, is recognized as a crucial solution for decarbonizing the energy system and mitigating climate change. The electricity and hydrogen energy system, which uses electricity and hydrogen as energy carriers, represents a key pathway for integrating power systems with hydrogen energy. It helps overcome the developmental limitations of renewable energy, fosters the interconnection and complementarity of multiple energy modes, and promotes deep integration across generation, grid, load, and storage. The electro-hydrogen coupling process, central to this system, can lower operating costs through peak shaving and valley filling. However, the efficiency of electrolyzers and fuel cell remain suboptimal, resulting in significant exergy losses alongside economic benefits during the coupling process. Striking a balance between economic viability and energy saving continues to be a challenging task. Moreover, the substantial forecasting errors caused by the uncertainty of renewable energy outputs can negatively impact the supply-demand balance and the operating conditions of electrolyzers. Therefore, the uncertainty risks associated with renewable energy must be thoroughly considered in optimal scheduling. In response to the above problems, a robust optimal scheduling model based on exergoeconomic analysis is proposed, with the uncertainty set defined by the confidence interval to reduce the conservatism of robust optimization.

Firstly, considering the dynamic efficiency characteristics of the electrolyzer, piecewise linearization was applied to handle the non-convex terms introduced by this relationship. The operation model of the electrolyzer including hydrogen production power allocation and operation models of fuel cell and energy storage equipment were constructed. Secondly, the energy quality coefficients were employed to analyze the exergy loss distribution based on the equipment operation model. A cost accounting method for exergy losses, including both internal and external factors, was proposed. Internally, the cost allocation method was used to price unit exergy losses, enabling the calculation of operational loss costs based on the distribution of exergy losses. Externally, the cost of transmission line losses and penalties of wind curtailment were calculated according to current electricity prices and relevant policies. Thirdly, taking into account constraints such as electrolyzer start-stop cycles, ramping power, and energy balance, an optimal scheduling model was developed with the goal of minimizing total exergy loss costs in the electricity and hydrogen energy system. Then, the model was reformulated into a robust optimization problem based on the uncertainty set of the confidence interval，and a dual transformation method for solving the model was proposed.

In the case simulation, four cases are set up for comparative analysis, leading to the following conclusions: (1) By setting the wind curtailment penalty coefficient appropriately, with the goal of minimizing exergy loss costs, a balance can be achieved between the economic benefits and the exergy losses associated with the electricity-hydrogen coupling process, while ensuring the efficient absorption of wind power. (2) The proposed model can further improve the overall hydrogen production efficiency of the electrolyzer array by taking advantage of the flexibility of hydrogen production power allocation. (3) The confidence interval is used as the uncertainty set of robust optimization, which can take into account the probability characteristics of random variables, and reduce the conservative degree of system operation under the premise of ensuring robustness.