Abstract: In recent years, the system stability problem from line commutated converter based on high voltage direct current (LCC-HVDC) has been widely concerned. Several experts and scholars have suggested using linear periodic time-varying modeling methods such as harmonic state space (HSS) to analyze it. However, HSS inevitably increases the complexity and dimension of modeling and has limitations in the face of large-scale AC/DC systems. At the same time, LCC-HVDC contains multiple types of harmonic coupling, and the influence of each part of coupling on the stability has not been fully demonstrated. In this paper, the LCC-HVDC coupling impedance matrix is established based on HSS theory, and the mechanism of harmonic coupling in HVDC transmission system is revealed. Furthermore, through the idea of multi-frequency circuit equivalence, a dimension reduction model of multi-dimensional impedance of three-phase system is proposed. The coupling impedance matrix is lossless dimension reduction into single-input single-output impedance (SISO), and the influence of different harmonic coupling times on impedance characteristics and stability is analyzed. The results show that considering the 13th harmonic truncation can effectively improve the accuracy of the impedance model of HVDC transmission system, but the impact on the stability analysis results is less than the error caused by ignoring the change of working condition and simplifying the inverter side.