Three-phase AC electric arc furnace (EAF) is a typical non-linear load, causing many power quality problems. Most of the researches on the voltage problems of EAF mainly focus on the voltage fluctuation, and less on the transient voltage problems caused by EAF short circuit and open circuit. In this paper, the relationship between voltage and current of EAF is obtained by combining hyperbolic function and exponential function, then the white noise and chaotic circuit are added to establish the EAF model which is suitable for the study of voltage fluctuation and transient voltage. This paper analyzes the causes of the transient voltage problem of the EAF, calculates the short-circuit current, reactive impact and the influence on voltage at the point of common coupling (PCC) in the three-phase short-circuit of the EAF, and compares the calculation results with the simulation results to prove the accuracy of this model. The results show that the reactive impact of three-phase short circuit is about twice as much as that of normal operation of EAF, resulting in about 30% voltage sag at the PCC, which is very unfavorable to the power grid. This paper provides reference for transient power quality evaluation and dynamic reactive power compensation of EAF.