Arc equivalent resistance modeling of inductor-disconnected-discharged arc considering electrode breaking speed

When an open circuit fault occurs in electrical and electronic equipment working in an explosive environment,the arc generated by the inductor may ignite flammable and explosive gases,which seriously endangers the safety of personal and equipment in hazardous environments such as underground coal mines.As a non-electrical parameter, the electrode breaking velocity v has the same effect on the arc discharge characteristics as the electrical parameters such as the inductance ^L and the initial breaking current ^I₀.The IEC safety spark test procedure requires that electrodes should be separated at a constant speed of 25 cm/s,while the actual breaking speed of the fault point is random. Therefore,even the intrinsically safe circuit conforming to the IEC safety spark test procedure may ignite explosive gas at specific breaking speed. Based on IEC safety spark test apparatus (SSTA),the inductor-disconnected-discharged (IDD) arc was studied.It was found that the arc discharge time T decreases exponentially with the increase of the electrode breaking speed v and tends to be stable.However,T increases with the increase of inductance L and the initial breaking current I₀.The initial arc resistance R_arc0 decreases as the breaking initial current I₀ increases; the electrode breaking speed v mainly affects the growth rate of the arc resistance R_arc; the inductance L has no significant influence on the variation trend of the arc resistance R_arc.According to the tendency of arc power,it was divided into three stages:arcing,stable and declining stage.In the arcing stage,the maximum arc power P_arcmax increases with the increase of the breaking initial current I₀; in the stable stage,the larger the inductance L is,the slower the decreasing trend of arc power P_arc will be; the increase of the electrode breaking speed v accelerates the conversion of P_arc from the stable stage to the declining stage.Based on the function regression analysis and the linear superposition theorem,the relationship between the electrode breaking speed v and the arc discharge time T was established.Considering the electrode breaking speed v,an arc equivalent resistance model was proposed.The model parameters were determined by the LevinbergMarquart optimization algorithm,and the expressions of arc voltage,current,power,and energy were derived respectively.Simulation and experimental results show that the theoretical analysis and the proposed arc equivalent resistance model are valid and feasible.Theoretical calculations and experiments show that the arc power P_arc and the arc energy Warc both decrease with the increase of the electrode breaking speed v.That is,an increase in the electrode breaking speed v is helpful to reduce the arc energy during circuit fault.