To realize the goal of “dual-carbon”, integrated energy systems (IES) have become an important research direction in recent years. However, the traditional IES energy flow calculation can no longer accurately reflect the impact of the parameter changes of the mixed gas after hydrogen injection into the natural gas network brought by the power-to-gas (P2G) technology on an IES. For this reason, the SRK (Soawk-Redlich-Kwong) gas equation of state is added to the traditional steady state analysis method for natural gas systems, and the compression factor is used as a state variable, so as to propose a steady state analysis method that can reflect the effect of hydrogen injection. A computational method for solving the electro-thermal-gas IES energy flow decomposition taking into account the hydrogen injection and compression factors is proposed. The proposed model and method are validated by an arithmetic example. This effectively reflects the effect of parameter variations of gas mixture on the IES.