Proximity effect between an earthing grid and external electrodes in an earthing system of high-voltage installations

The paper presents an original analytical procedure for obtaining a relatively simple mathematical relation which can accurately include the influence that the surrounding ground potential of an earthing grid has on the nearby sections of continuously earthed cable sheaths or other, similar, earthing electrodes radiating from the main earthing grid. Its effect influences the distribution of fault current which flows in the sheath to ground and thus should be taken into account when calculating the overall earthing impedance of an earthing system. This influence, or `proximity¿ effect, always appears when the elements of an earth electrode system are too close together. It is manifested in an increase of the total earthing impedance, compared with the value obtained when those elements are sufficiently distant. In the case of the earthing grid and the cable sheaths acting as long earth electrode conductors, the effect is dependent on, inter alia, the dimensions of the grid, the soil resistivity and the design parameters of the cable sheath and on the length of the cable which may be infinite or finite. The numerical examples shown in the paper demonstrate that the proximity effect has appreciable significance for conditions which are regarded as standard and normal in the majority of high voltage installations.