A security-constrained optimal energy flow calculation model for integrated power and gas energy sys-tems (IPGES) was established，considering the coupling of gas generators and motor driven compressors between power system and natural gas system． The model takes the total operating cost of the IPGES，that is，the sum of the cost of coal consumption by coal-fired generating units and the cost of natural gas consumption by gas sources of natural gas networks，as the objective function，and the security constraints of multiple N-1 contingencies in power systems and natural gas systems were considered． Firstly，the objective function of the original optimization model was divided by considering the influence of the transaction between the power network and the natural gas network．And the coupling equations of the gas generators and the motor-driven compressors were linearized by the first-order Taylor series expansion，respectively． Thus makes it possible to use the synchronous alternating direction multipli-er method (ADMM) for distributed solution of security-constrained optimal energy flow calculation model． Then the CONOPT solver in GAMS software was used to solve the optimal energy flow of power system and natural gas
system，respectively． Finally，the modified IEEE-39 bus power system and Belgium 20-bus natural gas system were taken as an example to validate the proposed model and solution algorithm． The results show that the proposed model and algorithm are correct and effective．