Steelmaking is one of the most energy-intensive industries, so improving control efficiency helps to reduce the energy used to produce a tonne of steel. Mutual influences between the phases of an electric arc furnace in available electrode movement control systems cause unproductive electrode movements as a reaction to the redistribution of currents among the phases of a three-phase power supply system due to changes in arc length in one of the phases. The nonlinearity of the characteristics of an electric arc furnace significantly complicates the ability to provide autonomous electrode movement control. The approach proposed in this paper, based on the formation of a matrix of mutual influences with variable coefficients, significantly improves the per-phase autonomy of the electrode movement control system. Nonlinear dependences of the mutual influence coefficients as a function of the current increment in the phase in which the disturbance occurred are obtained. Thus, it is possible to practically eliminate unproductive electrode movements in existing control systems by avoiding the traditional use of a dead zone, which reduces the control quality in the zone of small disturbances. The complex of experiments performed using the mathematical model demonstrate that the mutual influence improves the dynamic properties of the electrode movement system in certain operating modes.