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

Abstract

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 (FEM) simulation. The results provided in this paper prove that FEM results can be easily applied to a wide diversity of conductors' configurations and frequencies, thus being more general and often more accurate than the results provided by the formulas.

Analytical–Numerical Solution for the Skin and Proximity Effects in Two Parallel Round Conductors

“…These currents add to the applied currents. Consequently, the total current densities in conductors become non-uniform and non-symmetrical, and significantly affect the electromagnetic field, power losses in the wires, and the impedance matrix of such a system of conductors [2][3][4][5]. Thus, the knowledge on the current density distribution is essential in determining the network properties of such lines.…”

Calculation of the inductance of conductive nonmagnetic conductors by means of finite element method simulations

“…14 The external inductance, which is the main component, 20 is due to the magnetic field distribution outside the conductor, whereas the internal inductance is owing to the distribution of the magnetic field within the conductor. 21 The external inductance is almost independent of the supply frequency, as it will be shown in next section, and it dominates the total inductance, especially at high-frequency operation. 22 Inductance in a loop can be calculated from…”

The Magnetic Field and Impedances in Three-Phase Rectangular Busbars with a Finite Length

“…and ∆t x = t N (5,k) tx (7) where A and B are the widths of two horizontal and two vertical cover plates, respectively, t is their thickness, and k = 1, 2. All elementary conductors have the same length l.…”

“…Hence, there is a complex electromagnetic coupling between phase busbars and the enclosure of the bus duct system. In the case of a parallel conductor system, the uneven distribution of current density in these conductors is caused by the skin effect as well as the proximity effect [6][7][8][9][10][11], which affect their self and mutual impedances [12][13][14][15][16][17]. Both the skin effect and proximity effect will generally cause the resistance of the busbars to increase and the inductance to decrease [18].…”