For the harmonic instability problem with the multi-bridge converter caused by direct current(DC)magnetic bias in a high voltage direct current(HVDC)transmission system under different operating conditions

based on the switching function and modulating theory of the single-bridge 6-pulse converter

given the superposition characteristics of the converter transformer

the mathematical model of multi-bridge converter under different operating conditions is developed. Then

the modulation of harmonic between the AC/DC system sides through the obtained model is analysed

the magnification of harmonic and reliable criteria for determining harmonic instability of the multi-bridge converter are quantitatively deduced. By comprehensively going over various factors affecting the criterion

some effective measures to improve system harmonic stability by reasonably designing the AC/DC system impedance and arrangement of operating conditions of the system are proposed. A simulation model for the multi-bridge converter based on PSCAD/EMTDC is built

the results verifying the correctness and effectiveness of the proposed criteria and measures.