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This paper provides a review of two different mathematical arc models. The first one is based on the arc diameter variation, the second one is defined as cylindrically-symmetric channel model of a vertical arc with a variable radius. The arc model based on the arc diameter was introduced for high current setup, while the channel model was implemented in software for low current experiment. Both models performed well, and the simulated curves matched with the experimental data taken as a basis. However, the model considering the arc diameter impact on its conductance requires additional parameters that should be estimated using measured data. In contrast, the channel model does not impose the use of such parameters, which makes it more flexible.

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The article comprises the results of the research defining open-flame arcs self-quenching conditions in the event of a single phase-to-ground fault in overhead medium-voltage distribution networks according to existing theories of arc extinguishing. The calculations included metallic and arc faults modeling in a network with low phase-to-ground fault current. The arc gap simulation based on the mathematical channel model of a cylindrically symmetrical upright arc stabilized by rising convective gas flow was carried out in ATPDraw software program. The single phase-to-ground arc fault calculations results indicated an increase in high-frequency currents’ attenuation rate during transient processes as well as a reduce reduction in the electric arc lifetime from 8 ms to 2 ms in case of the breakdown voltage decrease from the peak value to zero. Notably, in case of low single phase-to-ground fault current the arc extinguishing took place at the first high-frequency current zero. For the cases of nonzero breakdown voltages, the electric arc extinguishing was detected at the fundamental frequency current component zero-crossing instant. The maximum overvoltage ratio of K = 2.8 was obtained as athe result of the single phase-to-ground fault at the peak phase voltage.