## 1 Introduction  
The global energy transition is significantly challenged by the volatility of renewable energy sources and the uncertainty of multi-energy loads [1, 2]. Integrated energy systems (IESs) have emerged as a key solution, coordinating multiple energy networks, such as electricity and heat [3]. However, the reliance on traditional Combined Heat and Power (CHP) systems on fossil fuels and the integration challenges of renewable energy sources have limited IES flexibility, making hydrogen energy a crucial element. Through power-to-gas (P2G) and hydrogen-compressed natural gas (HCNG) technologies, hydrogen serves as both an energy storage medium and a facilitator of carbon recycling [4]. Early P2G technologies successfully coupled hydrogen production via water electrolysis and methane synthesis with the power system, enhancing renewable energy absorption and economic benefits [5]. However, their dependence on external carbon sources and low two-stage conversion efficiency necessitates a trade-off between cost and carbon emissions. Consequently, research has shifted towards combining P2G with carbon capture and storage (CCS) technologies. Reference [6] utilized CCS to capture CO2 emissions from gas turbines, converting the captured carbon into feedstock for a methane reactor. This closed-loop system established an internal carbon cycle, resulting in an 8.4% reduction in overall processing costs. Reference [7] integrated P2G with CCS in IESs containing wind and solar energy, achieving renewable energy absorption rates of 22.48% for wind and 30.28% for solar. Reference [8] further proposed a joint operation framework based on P2G, CCS, and Hydrogen Fuel Cells (HFCs), enhancing the coupling of various energy sources and improving system low-carbon performance and economic efficiency. To reduce the dependence on carbon sources, an alternative approach focuses on the direct utilization of hydrogen. HCNG technology blends hydrogen with natural gas for use as fuel in gas turbines, promoting coupling and complementarity between different energy sources [9]. However, HCNG technology requires further consideration to strike a balance between pipeline durability and emission reduction benefits. Reference [10] achieved good scheduling results by compensating for economic factors through low-carbon mechanisms. Reference [11] dynamically adjusted the hydrogen blending ratio at different times, improving the economic and environmental benefits of the system by 44.1% and 47.8%, respectively. Despite these advances, a research gap remains regarding the distribution pattern of dynamic hydrogen blending ratios and their ability to regulate system uncertainties. Specifically, considering the complexity of real-time control of the hydrogen blending ratio, there is a need to explore more simplified engineering solutions. With the deep integration of hydrogen energy and multi-energy networks, the spatiotemporal correlation between wind and solar output fluctuations and load variations has further intensified uncertainty in integrated energy systems (IESs). Traditional stochastic optimization (SO) and robust optimization (RO) methods struggle to strike a balance between computational feasibility, conservativeness, and distributional accuracy. Traditional SO relies on precise probability distributions [12; 13]; however, due to the scarcity of data for emerging hydrogen technologies, the cost of scenario enumeration becomes prohibitively high. Meanwhile, RO methods ensure system scheduling reliability by considering worst-case scenarios [14], but their overly conservative nature may lead to cost overestimation. To address this, distributionally robust optimization (DRO) has emerged, reducing the conservativeness of RO while ensuring computational feasibility. Research on Wasserstein-based DRO models [15] and unimodal transformation frameworks [16] indicates that DRO can achieve a better balance between conservatism and economic efficiency in IES scheduling compared to traditional SO and RO methods.