The integrated energy system(IES)has the characteristic of multi-energy coupling

which can realize the comprehensive utilization and maximize the synergistic effects and complementary benefits among different kinds of energy

such as electricity

heat and natural gas. In this context

this paper proposes a structure of IES to couple electricity

heat and gas. The energy coupling degree and other definitions used for quantitative analysis of the coupling of IES are presented. Besides

an IES optimal operation model using minimum cost as the target is developed

in which the electricity

heat and natural gas network constraints are taken into account. Considering the coupling problem among electricity

heat and natural gas

a collaborative optimization method based on Lagrangian relaxation(LR)is proposed to achieve multi-energy decoupling in the IES optimal operation. Finally

a 71-node IES test system is used to verify the effectiveness of the proposed model and method

and the mapping relationship between the IES optimization results and the system coupling is analyzed quantitatively.