To stabilize the electrical mode of an arc steelmaking furnace in the initial stages of melting, it is advisable to use a high-speed current-limiting system, in addition to the traditional electrode movement control system. This system is implemented by including the primary winding of the furnace transformer choke, controlled by thyristors. The use of such a system, on the one hand, reduces the negative impact of the arc steel furnace on the the power supply network operation and, on the other, affects the operation of the electrode movement system, built on the principle of an impedance regulator. In order to analyze the mutual influences between such systems, a mathematical model for the power supply and control system of the arc steelmaking furnace was created. The developed model can work in real time, which corresponds to the world trends of modern control system synthesis for complex technological objects. In the created model, the work of the combined control system with different approaches to the formation of the control effect in the high-speed circuit and the effect of the combined control system on the power supply system of the ASF are analyzed.