Question
What is the best approach to control the segmentation of a conductor network in order to get accurate calculations of the earth potential?
Answer
It is difficult to give general statements regarding the validity of the computed scalar potential as a function of the segmentation of a conductor network. Basically, the potential will be accurate as long as the computed current distribution is accurate. MALZ approximates the real current distribution by a piece-wise constant distribution, with current leaking out of (or into) the conductors at their mid-point. MALT and HIFREQ use similar approximations. The potential is determined by this leakage current, and as such is more accurate close to the mid-points of conductors than to their extremities.
The potential at points close to the surface of a conductor is affected strongly by the local leakage current distribution. Several factors can affect the current distribution: the computation frequency, the soil resistivity, the presence of other conductors nearby, etc...
There are a few rules of thumb that can help here, especially as regards high-frequency calculations. First, the length of the conductor segments should be smaller than about 1/6 of the electromagnetic field propagation wavelength in the medium. In a conductive medium, an approximate formula for this wavelength (in meters) is 3160 * sqrt(rho / f) with rho the resistivity of the soil and f the frequency. At 50 kHz with a 0.5 Ohm-m soil, this is roughly 10 m. At 1 MHz in the same soil, it is closer to 2 m. Another rule is that the current distribution tends to vary more rapidly close to discontinuities such as intersection of conductors or end points of conductors, and so it can be advantageous to subdivide conductors more finely near those points. Finally, if can help to subdivide finely those conductors that are closer to the observation (computation) points .
On the other hand, the only way to really be sure that the segmentation level you used is detailed enough is to proceed experimentally: try a case with more segments and verify that the results are not appreciably affected. Note that in many cases, it is sufficient to subdivide finely only those conductors that are closer to the observation points: the other conductors have a much smaller impact on the end results.
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