Analysis of formulas to calculate the AC inductance of different configurations of nonmagnetic circular conductors

The inductance of single- and multi-conductors intended for electronic devices, power transmission and distribution, or grounding, lightning, and bonding systems greatly depends on the specific geometry and the supply frequency. It is also influenced by skin and proximity effects. The inductance is an important design parameter, since it significantly influences the voltage drop in the conductor, thus raising reactive power consumption and limiting the conductors’ current-carrying capacity. Although there exist some internationally accepted approximated and exact formulas to calculate the AC inductance of conductors in free air, its accuracy and applicability has been seldom analyzed in detail in the technical literature, which is done in this paper. Since such formulas can be used for a wide diversity of conductors’ configurations and under different operating conditions, it is highly desirable to evaluate their applicability. This evaluation is carried out by comparing the results provided by the formulas with data provided by finite-element method simulation.