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


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.


Lozinskyi O.Yu., Maruschak Y.Yu. Three-dimensional stochastic model of the electric mode regulation of an arc furnace. Industrial Process Automation in Engineering and Instrumentation, 1993, no.31, pp. 7-11. (Ukr).

Lozinsky O.Yu., Parancuk Ya.S., Lozinsky A.O. Optimization of dynamic regimes of interconnected electro-mechanical systems. Bulletin of Lviv Polytechnic National University, «Electric Power and Electromechanical Systems» series, 2001, no.421, pp. 98-103. (Ukr).

Lozynskyi O.Yu., Parancuk Ya.S., Moroz V.I. Synthesis of the control process for electromechanical systems that are under the influence of random perturbations. Bulletin of NTU «KhPI». Series: Problems of automated electric drive. Theory and practice, 1994, pp. 104-106. (Ukr).

Lozinsky O.Yu., Parancuk Ya.S., Tsyapa V.B. Mathematical description of the dynamics of the regulation of the position of the electrodes of the chipboard model in the space of states. Bulletin of Lviv Polytechnic National University, «Electric Power and Electromechanical Systems» series, 2017, no.840, pp. 54-60. (Ukr).

Nikolaev A., Povelitsa E., Kornilov G., Anufriev A. Research and Development of Automatic Control System for Electric Arc Furnace Electrode Positioning. Applied Mechanics and Materials, 2015, vol.785, pp. 707-713. doi: 10.4028/

Ghiormez L., Panoiu M. Current control of a 3-phase electric arc furnace using fuzzy logic. ANNALS of Faculty Engineering Hunedoara – International Journal of Engineering, 2015, Fascicule 4 Tome XIII, pp. 237-242.

Nikolaev A.A., Tulupov P.G. Method of setting optimum asymmetric mode of operation of electric arc furnace. 2016 11th France-Japan & 9th Europe-Asia Congress on Mechatronics (MECATRONICS) / 17th International Conference on Research and Education in Mechatronics (REM), Jun. 2016. doi: 10.1109/mecatronics.2016.7547111.

Zheng T., Makram E.B. An adaptive arc furnace model. IEEE Transactions on Power Delivery, 2000, vol.15, no.3, pp. 931-939. doi: 10.1109/61.871355.

Hooshmand R., Banejad M., Torabian Esfahani M. A New Time Domain Model for Electric Arc Furnace. Journal of Electrical Engineering, 2008, vol.59, no.4, pp. 195-202.

Pugachov V.S. Teoriia sluchainykh funktsii i ee primenenie k zadacham avtomaticheskogo upravleniia [The theory of random functions and its application to problems of automatic control].Moscow, Fizmatizdat Publ., 1960. 883 p. (Rus).

Kazakov V.A. Vvedenie v teoriiu markovskikh protsessov i nekotorye radiotekhnicheskie zadachi [Introduction to the theory of Markov’s processes and some radio engineering problems].Moscow, Soviet radio Publ., 1973. 232 p. (Rus).

Lozynskyy O., Lozynskyy A., Paranchuk Y., Paranchuk R., Marushchak Y., Malyar A. Analysis and Synthesis of Intelligent System for Electric Mode Control in Electric Arc Furnace. Part of the Lecture Notes in Electrical Engineering book series (vol.452). Analysis and Simulation of Electrical and Computer Systems, 2017, pp. 111-130. doi: 10.1007/978-3-319-63949-9_7.

Lozynskyi O., Lozynskyi A., Paranchuk Y., Paranchuk R., HolovachI., Tsyapa V. Fuzzy extreme control and electric mode coordinates stabilization of arc steel-melting furnace. 2016 XIth International Scientific and Technical Conference Computer Sciences and Information Technologies (CSIT), Sep. 2016. doi: 10.1109/stc-csit.2016.7589866.

Lozynskyy O., Paranchuk Y., Paranchuk R. Fuzzy control law of electrode travel in arc steelmaking furnace. 16th International Conference on Computational Problems of Electrical Engineering (CPEE), Sep. 2015. doi: 10.1109/cpee.2015.7333349.

Lozinskyy O.Yu., Paranchuk Y.S. Optimization of the modes of the process control system for electric steel-melting in arc steel-smelting furnaces. Electrical engineering, 2004, no.6, pp. 50-54. (Rus).

Krasovskyi A.A. Statisticheskaia teoriia perekhodnykh protsessov v sistemakh upravleniia [Statistical theory of transient processes in control systems].Moscow, Nauka Publ., 1968. 240 p. (Rus).

Lozynskyi O.Y., Paranchuk Y.S., Paranchuk R.Y., Matico F.D. Development of methods and means of computer simulation for studying arc furnace electric modes. Electrical engineering & electromechanics, 2018, no.3, pp. 28-36. doi: 10.20998/2074-272X.2018.3.04.

Lozynskyy O., Paranchuk Y., Stakhiv P. The Study of Dynamics of the Two-Loop Arc Furnace Electric Mode ACS on a Simulink-model. Przegląd Elektrotechniczny, 2018, vol.1, no.12, pp. 24-27. doi: 10.15199/48.2018.12.06.



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.



Electrotechnical complexes and Systems