Analytical wind turbine wake models and wake superposition methods are prevailing tools widely adopted by the wind energy community to predict the power production of wind farms. However, none of the existing wake superposition methods conserve the streamwise momentum. In this study, a novel wake superposition method capable of conserving the total momentum deficit in the streamwise direction is derived theoretically, and its performance is validated with both particle imaging velocimetry measurements and large-eddy simulation results. Detailed inter-method comparisons show that the novel wake superposition method outperforms all the existing methods by delivering an accurate prediction of the power production and the centreline wake velocity deficit, with a typical error of less than 5% (excluding the near-wake region). Additionally, the momentum-conserving wake superposition method is extended to combine the transverse velocities induced by yawed wind turbines, and the secondary wake steering effect crucial to the power optimization in active wake control is well reproduced.