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New directions in electric arc furnace modeling

Grabowski Dariusz, Klimas Maciej

Archives of Electrical Engineering

2023

Vol. 72, nr 1

157--172

This paper presents new directions in the modeling of electric arc furnaces. This work is devoted to an overview of new approaches based on random differential equations, artificial neural networks, chaos theory, and fractional calculus. The foundation of proposed solutions consists of an instantaneous power balance equation related to the electric arc phenomenon. The emphasis is mostly placed on the conclusions that come from a novel interpretation of the equation coefficients.

Enhancing the possibilities in visualisation of the ferroresonance phenomenon

Klimas Maciej, Majka Łukasz

Poznan University of Technology Academic Journals. Electrical Engineering

2019

No. 98

115--124

Waveforms measured and recorded in a ferroresonant circuit are the base for many computations, including simulation of ferroresonance circuit over - current/voltage responses and modelling a nonlinear coil. During such a study of ferroresonance phenomenon, the time dependent nonlinear differential equations are derived from R – Ψ(i) – C ferroresonant circuit. The system of nonlinear equations is numerically solved using various algorithm applications. In applied mathematics, in particular the context of the nonlinear dynamical systems analysis, phase – plane/space graphs are a visual display of certain characteristics of kinds of differential equations. The aim of the paper is a full plane/space presentation of all possible states of a test circuit when the ferroresonance occurs. Poincare maps application is also mentioned in the paper.