all designed in exactly the same way only the regulation arrangement for the electrode 1 will be described in more detail in the same way as the other respective electrodes 2 and 3 the electrode 1 is mounted on a supporting arm 17 whose height is adjustable via a hydraulic positioning apparatus 10 having an electrohydraulic actuator 11 by means of which the arc length can be set the actuator 11 is connected to the output of an impedance regulator 12 the phase current i 1 flowing through the electrode 1 and the phase voltage u 1m between the associated secondary terminal of the furnace transformer 7 and the star point formed by the furnace vessel 5 with the material 6 to be melted are detected respectively via a current transformer 13 and a voltage transformer 14 and are converted in a measurement device 15 into an actual impedance value z 1 for the relevant furnace phase this actual impedance value z 1 is compared at an addition point 16 with a predetermined set impedance z 1 for the relevant phase the control error u03b4z 1 obtained in this way is supplied as an input variable to the impedance regulator 12 which produces an actuating signal s 1 in order to adjust the height of the electrode 1 as a function of the control error u03b4z 1 the set impedance values z 1 z 2 and z 3 are determined by means of an impedance optimizer 30 according to the invention the impedance optimizer 30 calculates the set impedance values z 1 z 2 and z 3 in such a manner that the power emission from the electrode 1 2 3 is a maximum the temperature t of the three phase arc furnace is monitored by means of a temperature.