To address the issue of insufficient flexibility in integrated energy systems (IES) caused by output uncertainties on both supply and demand sides

this paper constructs a hydrogen-enriched compressed natural gas (HCNG)-based IES with deep gas-hydrogen coupling

and proposes a distributionally robust capacity optimization strategy considering a flexibility penalty mechanism and a tiered carbon trading mechanism. First

based on the characteristics of HCNG

a cooperative optimization framework for HCNG units

gas turbines

gas boilers

and natural gas pipelines is established to fully exploit hydrogen utilization potential. Second

to facilitate low-carbon system transition

a tiered carbon trading mechanism

featuring energy users and carbon operators as the main participants

is constructed within the carbon trading market to effectively constrain system carbon emissions. Finally

by quantifying source-load uncertainties using probability distributions

a flexibility supply-demand model is established

and a distributionally robust capacity optimization model is developed. Through scenario-based comparisons in an IES consisting of the IEEE 9-bus power system

a 7-node natural gas system

and a 6-node thermal system

the proposed model’s effectiveness in improving the low-carbon performance

economic efficiency

and flexibility of IES is validated.