The bi-directional energy conversion components such as gas-fired generators (GfG) and power-to-gas (P2G) have enhanced the interactions between power and gas systems. This paper focuses on the steady-state energy flow analysis of an integrated power-gas system (IPGS) with bi-directional energy conversion components. Considering the shortcomings of adjusting active power balance only by single GfG unit and the capacity limitation of slack bus

a multi-slack bus (MSB) model is proposed for integrated power-gas systems

by combining the advantages of bi-directional energy conversion components in adjusting active power. The components are modeled as participating units through iterative participation factors solved by the power sensitivity method

which embeds the effect of system conditions. On this basis

the impact of the mixed problem of multi-type gas supply sources (such as hydrogen and methane generated by P2G) on integrated system is considered

and the gas characteristics-specific gravity (SG) and gross calorific value (GCV) are modeled as state variables to obtain a more accurate operational results. Finally

a bi-directional energy flow solver with iterative SG

GCV and participation factors is developed to assess the steady-state equilibrium point of IPGS based on Newton-Raphson method. The applicability of proposed methodology is demonstrated by analyzing an integrated IEEE 14-bus power system and a Belgian 20-node gas system.