Abstract: When a single-phase arc-grounding fault occurs in a medium voltage distribution network, the arc radius and length geometric parameters are affected by the dynamic coupling of the arc field strength, ambient air disturbance, temperature and other factors, showing nonlinear and time-varying characteristics, and the establishment of an accurate dynamic model of the arc is the basis of fault characterization, fault location, fault isolation, etc. of the distribution network. A magnetohydrodynamic model of AC arc coupled with electromagnetic field, temperature field and flow field is established. It’s revealed that the arc radius and current are nonlinear hysteresis relationship, and the influence of electrode spacing change on the arc voltage and current characteristics is analyzed. The improved Mayr arc model is proposed to address the problems of simplified heat dissipation mechanism and ignoring the randomness of arc length in the traditional arc model, the model integrates the effects of conduction heat dissipation and convection heat dissipation on the arc radius, introduces the randomly varying arc length in the arc time constant, and couples the parameters of the dynamic arc radius and the random arc length in the power constant, so as to achieve the dynamic mapping of the arc geometrical parameters under the environmental perturbation and the arc channel field strength change. The mapping can accurately and intuitively characterize the evolution and randomness of arc combustion and extinguishing. The voltage and current waveforms of the improved Mayr arc model are basically consistent with the simulated waveforms, and the deviation of the arc-firing voltage is 2%. By comparing and analyzing the voltage and current waveforms and key parameters of Mayr and cybernetic arc models with the improved model in this paper, the improved model introduces stochastic length fluctuation and radius change to make the periodic arc voltage fluctuate dynamically by 7.3%, and the current generates over-zero distortion and zero rest extension phenomenon, which characterizes the stochastic characteristics of the arc and the coupled hysteresis effect of multi-physical fields effectively. Finally, based on the heat dissipation mechanism, the model reveals the ability to characterize the arc characteristics under different grounding media and wind speed.