Multiple energies including electricity, heat, cold and gas are coupled in the integrated energy system(IES). Energy conversion equipment and energy transportation equipment installed in the system feature nonlinear operation under variable conditions, leading to the magnificent gap between supply and demand. And the output allocation among multiple units of the same type is uneven under variable operating conditions. Therefore, a refined collaborative optimization method for the IES considering the non-linearity of equipment under variable operating conditions is proposed. Firstly, the cooperative optimized operation architectures for different types of units under nonlinear operation and variable working conditions are constructed. Then, nonlinear operation curves of the units under variable conditions are segmented and linearized. Taking the energy consumption of pumps and pipeline flow balance constraint into consideration can improve the supply-demand balance and the reliability of the IES. The optimization scheduling model takes the minimum daily operating cost as the optimization goal. The model is simulated on a IES under multiple scenarios. The simulation results show that considering the non-linear operation characteristic of different units of the same type under variable working conditions can effectively reduce the operating cost and supply-demand gap of power systems.