The object of the invention is a device and self-controlling current arrangement for balancing or sharing of conductor current of parallel conductors or plurality of phase conductor of an alternating current line. Each of the asymmetrically charged parallel conductor (1,2,3...4) has a single current transformer (21, 22,23...24), which have the same turns of secondary windings, which are correctly connected in series by their current direction. Because of the serial connection of the secondary circuit, the secondary currents (13,14,15... 16) will be the same, therefore their excitations will be also identical The properly selected core provides a linear magnetic coupling between the primary and secondary excitations, therefore the primary excitations are also necessarily identical. The primary currents (25,26,27...28) are identical if the primary turns are identical. Which are equal to the current of the asymmetrically charged conductors in the present invention.