# SYNTHESIS AND ANALYSIS OF ARC FURNACE ELECTRICAL MODE CONTROL SYSTEM ON THE BASIS OF THREE-DIMENSIONAL PHASE CURRENTS VECTOR DISTRIBUTION

## Authors

• O. Y. Lozynskyi Lviv Polytechnic National University, Ukraine
• A. O. Lozynskyi Lviv Polytechnic National University, Ukraine
• Y. S. Paranchuk Lviv Polytechnic National University, Ukraine
• R. Y. Paranchuk Lviv Polytechnic National University, Ukraine

## Keywords:

arc furnace, electric mode, three-dimensional vector of phase currents, stochastic control, dispersion, optimization, adaptation, arc current control circuit

## Abstract

Goal. The purpose of the article is to create the method for the operative synthesis of an arc steel-melting furnace (ASF) electric mode (EM) control signal on the basis of a three-dimensional arc currents vector, which takes into account the stochastic nature of the processes in the melting space and power circuit and has low sensitivity to the control object parameters changes, as well as development of the control system structure for its implementation. Method. The basis of the created control method is formed on the statistical theory of dynamical systems, as well as the provisions of the statistical theory of optimal control based on the Fokker-Planck-Kolmogorov equation, which enables to synthesize operational control by the criterion of approaching the regulated coordinate distribution density to the d-function, that is to minimize the dispersion of the three-dimensional furnace phases arc currents vector. Results. The system of equations for operational real-time calculation of control influences of the thyristor switch of phase inductors, included in the power supply circuits of three-phase arcs, and the structural scheme of the adaptive contour for the formation of three-dimensional phase currents vector dispersion for the implementation of adaptive optimal control were obtained. Scientific novelty. For the first time, based on the Fokker-Planck-Kolmogorov equation, we obtain a system of equations representing a mathematical model of a stochastic adaptive optimal control of the arc furnace electric mode by the criterion of a minimum dispersion of three-dimensional phase (arcs) currents vector, which enables, in comparison with known methods, to increase dynamic precision of the arc currents stabilization at the level set by the criteria of energy efficiency and electromagnetic compatibility values. Practical value. The use of the proposed adaptive optimal control model and structural system scheme for its implementation allows, in comparison with the serial arc power regulators, to improve the dynamic accuracy of the arc current currents stabilization at the level of given optimal settings and, based on this, to improve the energy efficiency and electromagnetic compatibility indices of the arc furnace and power supply network.

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2019-08-18

## How to Cite

Lozynskyi, O. Y., Lozynskyi, A. O., Paranchuk, Y. S., & Paranchuk, R. Y. (2019). SYNTHESIS AND ANALYSIS OF ARC FURNACE ELECTRICAL MODE CONTROL SYSTEM ON THE BASIS OF THREE-DIMENSIONAL PHASE CURRENTS VECTOR DISTRIBUTION. Electrical Engineering & Electromechanics, (4), 26–34. https://doi.org/10.20998/2074-272X.2019.4.04

## Section

Electrotechnical complexes and Systems