Generally, large earth grids have very low impedance with high inductance.
IEEE Std 80-2000 defines touch voltage as the difference between the ground potential rise (GPR) and the surface potential where a person might be in contact with an earthed or grounded structure [1].
Sometimes, especially for large grids, calculating touch voltages is not simply a subtraction of GPR with surface voltages.
ELEK SafeGrid Earthing Software calculates the GPR and surface voltages, and consequently, it can also calculate touch voltages. Note these quantities are complex numbers.
Touch voltage calculations mostly use the GPR as the reference voltage, but the software can also consider reach distance, the faulted segment voltage, or a constant voltage as the reference.
There is an example below.
The GPR is 1185 V. The surface voltage at position x = 100 m, y = 250 m is 1148.8 V.
One might conclude that the touch voltage at this location is 1185 V - 1148.8 V = 36.2 V
However, the touch voltage plot shows the correct value of 242.5 V.
Why is there a large discrepancy between the touch voltage plot and GPR minus surface voltage?
Answer: You must take the difference of two complex numbers to get the correct touch voltage.
Fortunately, the software can export the surface, touch, and step voltages for the voltage calculation points. Below is a processed table showing the exported surface and touch voltages side-by-side.
It also includes the coordinates; the closest point to the example in the above figures has been highlighted.
The calculated touch and surface voltages are 242.05∠66.01° V and 1148.77∠-21.21° V, respectively.
As the screenshot highlights, the GPR is 1185∠-9.44° V.
To get the touch voltage manually, the complex difference must be taken between GPR and the surface voltage:
1185∠-9.44° V - 1148.77∠-21.21° V = 242.99∠ 66.11° V
It can be seen that the manually calculated touch voltage closely matches the software's touch voltage result, both the exported voltages and the voltage plot.
References:
[1] IEEE Guide for Safety in AC Substation Grounding, IEEE Standard 80-2013, IEEE Power and Energy Society, 2013. doi:10.1109/IEEESTD.2013.6515191.
[2] ELEK SafeGrid Earthing Software V8.5
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