Q230 : Computing the Potential at Points Close to a Conductor

Question
When I try to compute the earth potential at points very close to the surface of a conductor, I sometimes get values that are larger than the GPR of the conductor. What is wrong?

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Answer
The potential very close to a conductor's surface is strongly affected by the detailed current distribution in the vicinity of the observation point. This, in turn, is usually strongly affected by the length of the conductor segments (especially at higher frequencies).

The boundary condition satisfied by the scalar potential is imposed only at the mid-point of the conductor segments. In between those points, the boundary condition may or may not be well satisfied, depending on the nature of the current distribution. Therefore, the computation of the scalar potential at the surface of a conductor at a point other than its mid-point can be inaccurate in some cases. Note that this does not affect the computation accuracy for points which are located further away from the conductor: the scalar potential at points located at a distance equal to a few conductor radii away from the conductor is mainly affected by the average current distribution in the system, and is not very sensitive to the exact position of the observation point.

The question is, then, how short should the segments be in order for the potential at any point at the surface of a conductor (or close to it) to be accurate? In extreme cases, the length of the segments should be as small as the distance of the observation point from the axis of the conductor. This is usually a huge overkill, however, and is certainly not practical as it would generate too many conductor segments. In practice, the conductor segments can usually be considerably longer than this, but it is difficult to say by exactly how much. Basically, the segments should be short enough that the basic assumption in MALT/MALZ/HIFREQ (to the effect that the leakage current is uniform along a segment) is satisfied to the desired accuracy. This, in turn, depends strongly on the presence of intersections of conductors or of "floating nodes" (where the current distribution tends to vary more rapidly) close to the observation points as well as on the type of soil (to a lesser degree).

It is difficult to be give more explicit guidance without going into a detailed analysis of the conductor network. One approach that can be used (and should always be used whenever a network segmentation issue arises) is to repeat the calculations using a finer segmentation, to verify whether the results are stable or not.

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