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A method of arc voltage gradient calculation for an electric arc furnace (EAF) is presented. The arc voltage gradient is the basic characteristic in study and simulation of an automatic power control system of an EAF. This characteristic is a strongly nonlinear multifactorial function that depends on electrical parameters of a power supply system, thermal conditions, and processes of arc heat exchange in an EAF melting bath. The method of arc voltage gradient calculation considers the relation between the electric and thermal conditions of an EAF in order to describe feasible nonlinear properties and to improve expressions for voltage and current transfer ratios as nonlinear multifactorial functions in particular. An EAF is regarded as a subject of control. Multifactorial properties are defined by the parameters of an equivalent electrical circuit of a furnace and by variable conditions of arc heat exchange in a melting chamber during steel melting. The method is effective for overcoming the uncertainty of the arc length in simulation of an EAR power controller. The unstable behavior of the furnace at a high impedance was explained using the obtained functions of the arc current and the arc voltage for various electrodes and the arc length. The minimum allowed arc current was found. The automatic power controller becomes unstable and the arc is extinguished under this value.

The method of universal characteristics of an electric arc is described as a mathematical basis for the heat exchange model of an electric arc in the processes of electric arc heating in electrical engineering. Application of this method for calculation of the temperature characteristics of an arc column compressed by the walls of the discharge channel in the stabilization zone of a laminar plasma torch operating in air is considered. An example of the temperature profile calculation of a wall-stabilized arc for a plasma generator with a discharge channel diameter of 5 mm operating in air at an arc current of 60 A is presented. Calculated results are compared with the results of experimental studies of this plasma generator.