The high cost of power quality monitoring makes it difficult to install them on a large scale in distribution network, resulting in incomplete information on nodal harmonic monitoring. The use of alternative monitor equipment (AME), such as intelligent fusion terminals, for harmonic monitoring and calculation is an inevitable way to solve the problem of network-wide observable power quality in distribution networks. However, due to the AME non-synchronous sampling, there is the problem of inaccurate harmonic calculation. This paper proposes a harmonic calculation method adapted to non-synchronous sampling data, which can be applied to AME to achieve extensive harmonic monitoring in distribution networks. Considering that the accuracy of AME sensing is lower than that of professional power quality monitoring terminals, resulting in significant data noise, a denoising method based on singular spectrum analysis on key point algorithm is proposed to reduce the interference of noise in data processing. A fundamental period calculation method based on variational mode decomposition and Newton interpolation is proposed to eliminate the negative effects of harmonic components and achieve high-precision fundamental period extraction. A quasi-synchronous sampling method based on Hermite interpolation is proposed to overcome the spectral leakage and fence effect when performing harmonic calculations based on the discrete Fourier transform. The simulation verifies the effectiveness, accuracy and adaptability of the proposed method under two scenarios of frequency offset and frequency variation.