High-impedance ground faults on high-voltage transmission lines are mostly accompanied by arc discharge. The traditional Cassie and Mayr dynamic arc models are described with arc differential equations

while the numerical solution of every moment arc voltage should be calculated with iterations

hence these models cannot be directly used in relay protection and fault location. For lack of an accurate dynamic arc model

the model is generally considered a static resistant or steady arc voltage square wave model

and that results in loss of the most valuable dynamic characteristic. To solve this problem

based on the air discharge nature description of the Thompson theory

the directional movement of a large number of electrons is used to represent arc current; and the coupling relation between electric field and electronic avalanche motion in air space is utilized to create a function of arc voltage and current

thus establishing a dynamic arc model of high-impedance ground faults for the application in single terminal fault location in transmission lines. The traditional arc differential equations are complex to calculate and hard to be directly applied in current fault location and relay protection algorithms. Nevertheless

the model has overcome the defects and laid the foundation for high-impedance ground fault detection

protection and location. This work is supported by National Natural Science Foundation of China(No. 51477084)

Beijing Natural Science Foundation(No. 3152016)and State Grid Corporation of China.