A special-case surface voltage gradient formula [for substation design]

In the electrical design of a high-voltage substation, the designer needs a simple and reliable tool, preferably a closed-form formula, when calculating the surface voltage gradient of line segments within the substation since the surface voltage gradient is the governing parameter of the corona performance. This paper presents a derivation of a closed-form formula for calculation of the maximum surface voltage gradient of a special line configuration, namely a horizontal AC three-phase Pine configuration with bundle conductors consisting of three sub-conductors in a horizontal arrangement. The formula has been verified against exact calculations and was found to have an error less than 5% for all practical combinations of the conductor radius, the sub-conductor spacing, the phase distance, and the height above earth.