## 3 Proposed V-I Characteristic Model of Electrical Arc
### Grey Wolf Optimization (GWO) Algorithm
To assess the effectiveness of the model, its results were compared with conventional exponential, hyperbolic, exponential-hyperbolic, and nonlinear resistance models, as well as real-time measurement data. The mathematical formulation of the proposed method was developed by demonstrating that the V-I characteristic of the electric arc melting process can be represented using polynomial equations of the third- and eighth degrees via the curve-fitting method. These polynomial expressions served as a benchmark for determining the appropriate equation parameters of the model. By integrating the GWO algorithm, the model successfully enhanced accuracy in predicting arc voltage and current variations, providing a more realistic representation of the arc melting process. The main advantage of the proposed model is its ability to more accurately characterize voltage and current fluctuations, improving the understanding of arc dynamics in EAF operations. The model effectively accounts for flicker effects, which are a crucial factor in dynamic arc behavior, making it a valuable tool for power quality analysis. The results indicate that the proposed methodology provides a more precise representation of the arc

Figure 28: Comparison of the proposed model with experimental data: (**a**) EAF arc voltage waveform, (**b**) EAF arc current waveform. melting process compared to the exponential, hyperbolic, exponential-hyperbolic, and nonlinear resistance models existing in the literature. Furthermore, a comparison of the harmonic components derived from the model with real-time FFT spectra demonstrates that the model is compatible with the current and voltage harmonics, highlighting its potential application in harmonic mitigation strategies for EAF systems. Additionally, the proposed methodology offers a versatile framework for evaluating power system disturbances, as it can be used to analyze harmonic distortion, voltage fluctuations, and arc stability. Although this methodology is specifically designed for the melting phase, it can be adapted to develop a mathematical model for other EAF operational stages using alternative mathematical frameworks. Conceptualization, M.S. ; Methodology, M.S. ; Software, E.U. and A.A.; Formal analysis, A.A.; Resources, A.A.; Data curation, M.S. ; Writing--original draft, M.S. and E.U. ; Writing--review & editing, M.D. ; Supervision, M.D. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The original contributions presented in this study are included in the article. Dataset available on request from the corresponding author. We would like to express our sincere gratitude to SIDEMIR and TEIAS for their valuable support during the data collection process. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} EAF & Electric arc furnace \\ FFT & Fast Fourier transform \\ GWO & Grey wolf optimization algorithm \\ IF & Induction furnaces \\ PPC & Point of common coupling \\ SVC & Static VAR compensator \\ THD & Total harmonic distortion \\ \end{tabular} 

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