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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 EAF model. In this article, we have proposed a model based on a power balance equation with coefficients 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 EAF models mostly applied chaotic systems to modulate the arc length or the arc voltage signal itself. The paper presents the application and evaluation of four different chaotic systems, i.e. Chua, Lorenz, Rössler, and a four-wing attractor system. The parameters of each system were fitted to the EAF measurement data concerning the minimal discrepancy between the distribution and autocorrelation of the output data of the model and the measurements. The measurement data originate from two differently sized installations - an industrial and a laboratory EAFs.