It is the first paper where the electrical mode of an arc furnace (AF) is proposed to be considered as a state change. This work also proposes a methodology for calculating the time values of the probabilities of these states. The methodology is based on the representation of state-change processes by the Markov model of continuous time, discrete state (CDS) stochastic processes.

The state of electrical mode in each phase of an arc furnace is identified by the value of arc current that can be set for a given melting period, may be in the range of permitted deviations, or may get to the range of large operational or emergency deviations. Assuming that the system goes from state to state under the action of the Poisson flows of events, the concept of intensity of disturbance flows, and the intensity of flows of control actions are introduced. This makes it possible to form a system of Kolmogorov differential equations to change the state probabilities of the AF electrical mode. The solution of the system results in obtaining time dependencies of change in state probabilities.

When analyzing graphs of changes over time in the probabilities of AF electrical mode states, it is possible to choose the desired intensity of the flow of control actions, which ensures that the electrical mode is in a given state under the action of the corresponding disturbance flow.

**Keywords: **arc furnace, electrical mode, probability of the electrical mode state, Markov stochastic processes, intensity of disturbance flows, intensity of control actions.

- О. Lozynskyi and Y. Paranchuk, “Reduction of phase interactions in control processes of “arc steel-making furnace – power supply system” complex electrical technological system”,
*Computational Problems Of Electrical Engineering, vol. 6, no. 1, 2016.**ena.lp.edu.ua:8080/handle/ntb/35902*. - О. Lozynskyi and Ya. Marushchak, «A 3-D stochastic model of the system for controlling the electrical mode of an arc furnace”,
*Automation of manufacturing processes in m**achine building and instrument**making*, pp.7-11, Lviv, Ukraine: Issue 31, 1993. - О.Lozynskyi, Ya.Paranchuk, and А. Lozynskyi, “Optimization of dynamic modes of interdependent electromechanical systems”,
*Bulletin**of**Lviv Polytechnic National University “Electric power and electromechanical systems”*, no. 21, pp. 98-103, 2001 - О. Lozynskyi, Ya. Paranchuk, and V. Moroz, ”Synthesis of the process of control actions for electromechanical systems that are under the influence of random perturbations”, In
*Problems of automated electric drive. Theory and practice**,*pp. 104-106, Kharkiv, Ukraine: KHSPU, 1994. (Ukrainian) - О. Lozynskyi, Ya.Paranchuk, and V. Tsiapa, “Mathematical description of the dynamics of the system of regulation of the position of the AF electrodes by the state-space model”,
*Bulletin**of**Lviv**Polytechnic National University**“Electric power and electromechanical systems”**,*no. 840, pp.54 – 60, 2017. - Yu.Rudavskyi, P. Lostrubiy, О. Lozynskyi, and D. Ukhanska, “Elements of the theory of random processes”,
*Lviv:**Publishing House of Lviv Polytechnic National University*, p. 240, 2004. - .A. Nikolaev, E. Povelitsa, G. Kornilov, and A. Anufriev, "Research and Development of Automatic Control System for Electric Arc Furnace Electrode Positioning", In
*Applied Mechanics and Materials, Switzerland: Trans. Tech. Publications*, vol. 785, pp. 707-713, 2015.*doi.org/10.4028/www.scientific.net/AMM.785.707.* - L. Ghiormez and M.Panoiu, “Curent control of a 3-phase electric arc furnace using fuzzy logic”,
*ANNALS of Faculty Engineering Hunedoara*–*International Journal of Engineering,*pp. 237-242, |Fascicule 4 Tome XIII, 2015. - A. Nikolaev and P. Tulupov, “Method of setting optimum asymmetric mode of operation of electric arc furnace Sign In or Purchase” in
*Proc.**11th France-Japan & 9th Europe-Asia Congress on Mechatronics (MECATRONICS) /17th International Conference on Research and Education in Mechatronics*, 2016. DOI: 10.1109/MECATRONICS.2016.7547111 - T. Zheng and E.Makram, “An Adaptive Arc Furnace Model”,
*IEEE Transaction on power delivery*, no. 15, pp. 931 –939, 2000. DOI: 10.1109/61.871355 - H. Rahmatollah, B. Mahdi, and T. Mahdi, “A New Time Domain Model for Electric Arc Furnace”,
*Esfahani Journal of Electrical Engineering,*vol. 59, no. 4, pp. 195–202, 2008. - O. Lozynskyy, A. Lozynskyy, Y. Paranchuk, and R. Paranchuk, “Analysis and synthesis of intelligent system for electric mode control in electric arc furnace”,
*Lecture Notes in Electrical Engineering*, no. 452, pp. 111-130, 2018. DOI.org/10.1007/978-3-319-63949-9_7 - O. Lozynskyi, A. Lozynskyi, Y. Paranchuk, I. Holovach, V. Tsyapa, “Fuzzy extreme control and electric mode coordinates stabilization of arc steel-melting furnace”, in
*Proc. of the 11th International Scientific and Technical Conference – Computer Sciences and Information Technologies, CSIT 2016.*- pp. 49-54, 2016. 10.1109/STC-CSIT.2016.7589866 - O. Lozynskyy; Y. Paranchuk; R. Paranchuk, “Fuzzy Control Law of Electrode Travel in Arc Steelmaking Furnace”, in
*Proc. 16th International Conference on Computational Problems of Electrical Engineering (CPEE-2015)*. - Lviv, 2015. Pages: 103-106. 10.1109/CPEE.2015.7333349