###### Abstract
The molten metal remains in a liquid state during the transfer to the ladle furnace because of the heat generated by the arc in this procedure [14]. Figure 1 illustrates the apparent power variation derived through experimental methods from a 60 MVA EAF facility, which depicts the operation of the EAF in these three phases. Despite the substantial benefits of EAFs, such as low production cost and high melting capacity, they also have numerous adverse effects on power systems due to the variation in arc length during the melting process. Rapid arc changes, particularly in the boring  
Figure 1: Measured variation of apparent power in boring, melting, and refining processes from the 60 MVA EAF furnace [14]. and melting processes, induce nonlinear load behavior in EAFs [15; 16]. The primary cause of power quality issues, including harmonics, flicker, voltage sag and swell, and voltage imbalances, is this nonlinear behavior in the electrical circuits to which EAFs are connected [17; 18; 19; 20; 21; 22]. Numerous researchers have explored the power quality issues caused by EAFs. In [23; 24], a single-phase equivalent circuit model of the EAF was created, and the operational characteristics of the boring, melting, and refining processes were assessed, alongside an interpretation of their impact on power quality. The power quality issues caused by the EAF were analyzed according to IEC-61400-4-30 standards in [25]. In [26], the effect of harmonic filter groups used in EAFs on power quality was studied. [PERSON] et al. examined the power quality of a 100-T EAF using experimental data in their study [27]. Research has also been conducted in [28; 29] on the remote monitoring of power quality parameters of EAFs in Turkey and the recording of power quality. Many researchers have also investigated the nonlinear characteristic behavior of the electric arc, which is responsible for power quality issues in EAFs. The nonlinear V-I characteristics of the EAF have been characterized by time-domain methods, as described by certain researchers [18; 19; 20; 23]. Differential equations have also been proposed as a method for defining the mathematical expression of the electric arc [30; 31]. Linearization methods are employed to convey the electric arc's characteristics [32; 33]. Beyond these studies, the literature has presented a variety of modeling techniques for defining the characteristics of EAF loads. These techniques include different time-domain approaches based on the current-voltage characteristic of the electric arc [15; 34; 35; 36], research that examines the EAF's characteristics stochastically [37; 38], time-domain methods based on the Cassie-Mary differential equations [17; 39; 40; 41], and a nonlinear resistance model and frequency domain model [42]. However, the mathematical expression of the relationship between the arc's current and voltage characteristics in defining the nonlinear behavior is a common thread in all these studies. The most effective approach to establishing the nonlinear relationship between arc current and voltage is to measure the arc current and voltage directly. A mathematical approach can be devised to define the nonlinear current-voltage characteristic of the arc with an adequate amount of measurement data. In this study, unlike previous studies, a stochastic mathematical approach is presented to characterize the EAF during the melting process. The proposed model establishes the V-I characteristics of the arc using the modified Heidler function and double S-curves. The arc current and voltage fluctuations that occurred during the melting process of the 60 MVA EAF have been recorded in real time to establish the mathematical model. The V-I characteristic of the EAF's melting process is formulated using third- and eighth-degree polynomial equations, derived through the curve-fitting method. However, due to the difficulty of solving high-degree polynomial expressions, rapid variations in the arc current and voltage characteristics are not adequately described.