A Novel Voltage–Current Characteristic Model for Understanding of Electric Arc Furnace Behavior Using Experimental Data and Grey Wolf Optimization Algorithm

The control of nonlinear systems cannot be effectively achieved using linear mathematical methods. This paper introduces a novel mathematical model to characterize the voltage–current (V–I) characteristics of the electric arc furnace (EAF) melting process, incorporating experimental field data for validation. The proposed model integrates polynomial curve fitting, the modified Heidler function, and double S-curves, with the grey wolf optimization (GWO) algorithm applied for parameter optimization, enhancing accuracy in predicting arc dynamics. The performance of the model is compared against the exponential, hyperbolic, exponential–hyperbolic, and nonlinear resistance models, as well as real-time measurement data, to assess its effectiveness. The results show that the proposed model significantly reduces voltage and current harmonic distortion compared to existing models. Specifically, the total harmonic distortion (THD) for voltage is reduced to 2.34%, closely matching the real-time measured value of 2.30%. Similarly, in the current spectrum, the proposed model achieves a significant reduction in third harmonic distortion and a THD of 11.40%, compared to 13.76% in real-time measurements. Consequently, a more precise characterization of the EAF behavior enables more effective mitigation of harmonics and vibrations, enhancing the stability and power quality of the electrical networks to which they are connected.