Modeling study on the secondary arc with stochastic initial positions caused by the primary arc

In the conversion process from primary arc to secondary arc, there exists stochasticness phenomenon of the initial positions of secondary arc. However, the present simulation results of the arcing time with the arc chain model are constant, which is not consistent with the test results. In reaction to the above phenomenon, the stochastic simulation model was first established to calculate the relationship between the conductivity of the air and the temperature. Furthermore, the conductivity along the radius direction of the primary arc was acquired, and then the stochastic initial length of the secondary arc with different primary current was also obtained. Results showed that with the increase of primary current, the average value and dispersion of the initial secondary arc length also increased. Finally, the stochastic model of secondary arc with different initial positions was applied into the arc chain model to calculate the arcing time with dispersion, and the simulation results were compared with the experimental results. Results showed that the simulation results of the arcing time are consistent with the test results, and the relative errors are within 10%, which shows that the stochastic model is effective and reliable.