Distortions of current and voltage waveforms from a sinusoidal shape are, not only a source of technical problems, but also have serious economic effects. Their occurrence is related to the common use of loads with nonlinear current-voltage characteristics. These are both high-power loads (most often power electronic switching devices supplying high-power drives), but also widely used low-power loads (power supplies, chargers, energy-saving light sources). The best way to eliminate these distortions is to use active power filters. The cost of these devices is relatively high. Therefore, scientists all over the world are conducting research aimed at developing techniques for the proper placement of these devices, in order to minimize their investment costs. The best solution to this problem is to use optimization techniques. This paper compares the methods and criteria used by the authors of publications dealing with this topic. The summary also indicates a possible direction for further work.

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 article is devoted to modelling and analysis of linear time‐varying (LTV) filters with periodically variable coefficients. A transmission model of such filters has been described. Equations expressing the filter response for a given class of periodic parametric functions have been obtained and presented in a closed form. The results have been illustrated by an example.

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.