Abstract Knowledge of the breakdown voltage of air gaps when subjected to positive switching impulse voltage is fundamental to the design of insulation coordination for power transmission systems. However, the length of phase-to-phase air gaps in ultra-high voltage power transmission lines has reached more than 30 m. It is very difficult, costly, and impossible to conduct full-scale test experiments to obtain the breakdown voltage of these gaps. Here, the numerical simulation method based on the self-consistent leader inception and propagation model was first used to simulate the air gap discharge process at four different scales and to obtain the gap breakdown voltage. The simulated data was compared with the measured data to verify the validity of the model. Then, the numerical simulation method was used to simulate the discharge process of phase-to-phase air gap for ultra-high voltage transmission lines with 30.3 m in length. The current and the development trajectory of the leader tip were obtained for the discharge process. More importantly, the breakdown voltage, which could not be obtained by full-scale testing, was obtained by simulation.
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