As a form of hybrid multi-energy systems, the integrated energy system contains different forms of energy such as power, thermal, and gas which meet the load of various energy forms. Focusing mainly on model building and optimal operation of the integrated energy system, in this paper, the dist-flow method is applied to quickly calculate the power flow and the gas system model is built by the analogy of the power system model. In addition, the piecewise linearization method is applied to solve the quadratic Weymouth gas flow equation, and the alternating direction method of multipliers (ADMM) method is applied to narrow the optimal results of each subsystem at the coupling point. The entire system reaches its optimal operation through multiple iterations. The power-thermal-gas integrated energy system used in the case study includes an IEEE-33 bus power system, a Belgian 20 node natural gas system, and a six node thermal system. Simulation-based calculations and comparison of the results under different scenarios prove that the power-thermal-gas integrated energy system enhances the flexibility and stability of the system as well as reducing system operating costs to some extent.