Application of the deterministic chaos in AC electric arc furnace modeling

Electric arc furnaces (EAFs) are widely used in the steel production and recycling process. However, their application is associated with various power quality problems whose mitigation requires a reliable model of the EAF. In this paper, we have proposed a model based on a power balance equation, where the coefficients are assumed to be responsible for the nonlinear and stochastic behavior of the EAF. These coefficients have been modeled with some variables derived from a chaotic system, while previously developed models mostly applied chaotic systems to modulate the arc length or the voltage signal itself. The paper presents the application and evaluation of four different chaotic systems: Chua, Lorenz, Rössler, and a four-wing attractor system. The parameters of each system have been fitted to the measurement data concerning the minimal discrepancy between the distribution and autocorrelation of the output data of the model and the measurements.