In the conversion process from primary arc to secondary arc, there exists a 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. The results showed that with the increase in 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. The 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.
Index Terms-Arcing time, initial position, primary arc, secondary arc, stochastic model. Haoxi Cong received the B.Sc. (Hons.) degree in electrical engineering from Shandong University, Jinan, China, in 2011, where he is currently pursuing the Ph.D. degree in electrical engineering. His current research interests include secondary arcs with half-wavelength transmission lines and the interaction mechanism with the electromagnetic transients of power systems. Qingmin Li (M'07) received the B.Sc., M.Sc., and Ph.D. His current research interests include secondary arcs with half-wavelength transmission lines. W. H. Siew received the B.Sc. (Hons.) degree in electronic and electrical engineering, the Ph.D. degree in electronic and electrical engineering, and the M.B.A. degree from the University of Strathclyde, Glasgow, U.K.He is currently a Reader with the Department of Electronic and Electrical Engineering, University of Strathclyde. His current research interests include large systems electromagnetic compatibility, cable diagnostics, lightning protection, and wireless sensing systems. Dr. Siew is a Convener of the CIGRE WG C4.208, and a member of the Technical Advisory Panel of the IET Professional.