The change in the operating state of the compressor will cause the variety of working conditions in gas network,affecting the steady-state power flow of electric-gas-heat integrated energy system. In order to calculate the gas network power flow of the comprehensive energy system under different operation states,the sub-networks and energy coupling links of integrated energy system are modeled respectively. Considering five working modes and two driving modes of the compressors,based on Newton-Raphson method,an integrated power flow calculation method which reserves the pipelines of compressors is proposed and an equivalent solution method which separates the pipelines of compressors is developed for gas network with multiple compressors under different operation states. The power flow of integrated energy system is calculated by distributed algorithm. The accuracy and effectiveness of the proposed integrated power flow calculation method are verified through two examples,which remedies the disadvantages of existing power flow calculation models of gas network that cannot deal with complex working conditions in gas network and lack convergence and universality. Then the impacts of the change in compressor operation states on power flow of integrated energy system are revealed.