A simple innovative method to calculate the magnetic field generated by twisted three-phase power cables

This paper firstly examines the consolidated analytical methodologies available in literature for the calculation of the magnetic field generated by a twisted three-phase conductor arrangement carrying balanced three-phase currents. Such literature methodologies consist of an exact analytical expression of the rms magnetic induction given in the form of complicated Besselfunction series and of an approximation of such exact expression where only the first term of the series is considered. Subsequently, a simple innovative approximated formula for the rms magnetic induction generated by twisted three-phase power cables is obtained by means of an heuristic procedure. This formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by the case of a twisted three-phase power cable used for power distribution at the medium voltage level.