In order to cope with the potential failure risk of energy supply equipment in an integrated energy system, an equipment failure probability model based on operating conditions and an equipment failure severity model based on load ratios are established, characterizing the relationship between different operating conditions of equipment and system safety risks. An IES multi-objective optimization operation model is established by taking the operating cost and risk as the optimization objectives, considering comprehensively different constraints of a power network, natural gas pipeline networks, thermal pipeline networks, unit output, etc. Then, the model is processed into a mixed-integer second-order cone programming model using the second-order cone relaxation, piecewise linearization and tolerant hierarchical sequence method, and the tolerance is used to characterize the system's acceptance of risk. The analysis of a calculated example shows that the operating strategy derived from the model can take into account the safety and economy of the system. This verifies the rationality and effectiveness of the model and method. This work is supported by the Science and Technology Program of Sichuan Province (No. 2021YFSY0019).