This paper is devoted to electric arc furnace (EAF) modeling using a random differential equation based on the power balance approach. It presents a method which enables the estimation of EAF model coefficients with the help of measurement data - voltage and current waveforms recorded during the melting stage of an EAF work cycle. The estimated coefficients have been analyzed with respect to their time variability as well as the probability distributions of their values and increments. Next, the identification of the stochastic processes representing the model coefficients has been carried out. The paper presents solutions validated with statistical tests.

Electric arc furnaces (EAFs) are important appliances in the steelmaking industry, but they are characterized by a nonlinear, dynamic, and stochastic nature. Due to this fact, EAFs can have a negative influence on power systems. Measures to mitigate such problems can be designed properly only with knowledge of the influence of the load on the system. Therefore, it is necessary to have accurate EAF models that reflect the complicated character of such loads. Researchers use different approaches for EAF modeling, such as stochastic process analysis, differential equation models, or neural networks. This article presents the application of three models based on artificial neural networks (ANNs) in EAF modeling along with an extension based on the stochastic moving average (MA) process. The goal was to provide ANN models that are simple in structure in comparison to, e.g., deep learning methods used by other researchers. The first two models are built on multilayer perceptron networks, and the third applies a nonlinear autoregressive exogenous model with the help of differential equation transformed into the Hammerstein–Wiener model. ANN models are improved by adding an MA ingredient. The article describes the measurement data, the design of each approach, and the results of the EAF modeling.

The paper proposes a solution for the problem of optimizing medium voltage power systems which supply, among others, nonlinear loads. It is focused on decision tree (DT) application for the sizing and allocation of active power filters (APFs), which are the most effective means of power quality improvement. Propositions of some DT strategies followed by the results have been described in the paper. On the basis of an example of a medium-voltage network, an analysis of the selection of the number and allocation of active power filters was carried out in terms of minimizing losses and costs keeping under control voltage total harmonic distortion (THD) coefficients in the network nodes. The presented example shows that decision trees allow for the selection of the optimal solution, depending on assumed limitations, expected effects, and costs.

The article introduces a fractional-order electric arc furnace (EAF) model. It is based on a power balance equation which, as has been shown, can be represented by a Hammerstein-Wiener model. Such a model includes a block described by a linear integer-order differential equation, in this case the order is equal to one, which can be extended to a fractional-order equation. The introduced fractional order is either constant or variable in time. The variable coefficients of the model have been identified by a genetic algorithm The proposed model has been tested using measurement data from two different EAFs and its accuracy has been compared with the classical integer-order model based on the RMS error between the model output and measurement waveforms. The results show that the fractional-order EAF model enables error reduction and consequently reflects more accurately the phenomena taking place in the furnace.

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 paper, 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.