There is one important concept in the calculations of power transmission lines – this is the equivalent depth of current in the ground (Dg). In symmetrical operating modes (normal mode and three-phase short circuit), there is no electric current in the ground, and this depth is not interesting to us. However, in any unbalanced modes of operation, the current in the ground appears, and the depth Dg of the current in the ground has a significant impact on the processes.

The current depth determines the active impedance and self-inductance of a number of contours. For an overhead line, these may be “conductor-ground” or “shield-ground” contours. For a cable line, these may be the “core-ground”, “screen-ground”, “armour-ground” contours. In addition, the depth affects the mutual inductances between the specified contours.

In particular, for cable lines, all these inductances (self and mutual) influence on:
1️⃣ Parameters of the cable line for the zero sequence.
2️⃣ Induced voltages on cable screens in case of a single-phase short circuit, on which the selecting the bonding/grounding type of the cable screens depends (for example, the number of single-end grounded sections, the number for cross-bonding cycles).
3️⃣ Selection of surge arresters installed in the screens (sheath voltage limiter, SVL).
4️⃣ Calculation of induced voltages from one circuit to another (safety issues).

How can we calculate such a depth? Both overhead and cable lines (it doesn’t matter if they are underground or above ground) use the same formula shown in the photo. The formula can be written in different ways, but it gives approximately the same result – for a typical soil at a frequency of 50 Hz, the depth is about 930 m.

However, in my opinion, it can’t be like that. The fact is that the typical length of a cable line is only a few km, and for such short lines, the current simply will not be able to penetrate so deeply into the ground. No current will flow in the ground in a U-shaped circuit. Current in the ground will pass there more or less in a straight line, that is, for short cable lines, the current in the ground does not occupy such a thick layer of earth as for long overhead lines. Therefore, for cable lines of a typical length, the depth of the current in the ground cannot be 930 m, but must be less. This reduces the inductance (L) and increases the active impedance (R), and there are many other consequences.

Which depth should we take then? This depends on the length of the cable line and on some other conditions. All of this mean that, for instance, software for calculating the parameters of cable lines should make it possible not only to calculate the depth using a standard formula (which is wrong for short cable lines), but also to set the depth value in the way that the user considers the most correct.

Please read Item 2.3.2 of the book on cables.