The stochastic and nonlinear characteristics of electric arc furnaces (EAFs) lead to power quality challenges in the power system. In studying EAF behaviors, having optimized characteristics/models, selecting a suitable and optimum model that adapts to the actual characteristics of EAFs, and investigating simulation software’s capability for implementing EAF models are essential. However, the literature shows a research gap in investigating EAF simulations in various software products based on different models. This paper studies several time-domain models, such as piece-wise linear, modified piece-wise linear, hyperbolic, exponential, and exponential-hyperbolic models, for EAF modeling and simulation. The optimal estimation of parameters for the introduced models is necessary to adapt actual EAF characteristics. Thus, one of the studies taken in this paper is optimizing the EAF model’s characteristics. The proposed optimization problem is solved using the genetic algorithm (GA) and particle swarm optimization (PSO). Moreover, the optimized models are simulated in DIgSILENT and EMTP-RV to investigate different EAF models from the viewpoint of accuracy and efficiency. The optimization of different EAF models’ characteristics and comparison of EMTP-RV and DIgSILENT in simulating EAF behavior are the contributions of this paper. The proposed method is validated based on the actual data of a realistic EAF-based steel company in Iran. The obtained results show that the modified piece-wise linear model has the most accuracy in identifying the EAF behavior. The test results based on DIgSILENT and EMTP-RV simulations imply that the EAF could be simulated with high accuracy using modified piece-wise linear and piece-wise linear models. In general, EMTP-RV has expressed more accuracy in simulating different EAF models, and the simulation execution speed of EMTP-RV is around 2.5 times faster than DIgSILENT. In contrast, DIgSILENT is more suitable to facilitate the power system studies of EAF according to its extensive study tools and library.