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.

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