For large natural gas pipeline networks, it takes dozens of hours to complete one operation optimisation, in which the calculation time of the compressor power accounts for the vast majority of the run time. For centrifugal compressors that are widely used but extremely difficult to calculate power consumption, in order to improve the calculation efficiency and accelerate the speed of solving operation optimisation problems, three new fitting functions of centrifugal compressor power are proposed. The numerical performances of these three new fitting functions are tested with three types of compressors as experimental objects. The experimental results show that for the three types of compressors, the accuracy of the power calculation has improved a lot after using the three new fitting functions. In addition, these three new fitting functions are applied to operation optimisation of a virtual gas pipeline network and the results are compared with the traditional method for calculating the compressor power. The numerical results show that using three new fitting functions to calculate the compressor power can greatly reduce the solution time while ensuring the accuracy of the solution.