Study on the secondary current characteristics of transmission lines coupling arc dynamics model with Mayr resistance model

•A complete dynamic model of secondary arc is established by coupling the arc dynamics model, the Mayr arc resistance equation and the three-phase high-voltage AC transmission line model.•The influence of various transmission line parameters and compensation measures on secondary current is discussed based on the above model.•The secondary arc is found to extinguish rapidly with the decrease of the transmission line resistance or the increase of the line length.•The amplitude of primary current is negatively correlated with the transmission line length and the line resistance, while the amplitude of secondary current is positively correlated with the line length.