# This paper presents the application of

This paper presents the application of interval mathematics as a new method to address uncertainties associated with designing substation earthing grid system. Uncertainties in the parameters are integrated into the analysis, as interval numbers, determine the important factors for personnel safety in and around substations such as earth resistance, touch, step and mesh potentials of substation earthing grid. A comprehensive uncertainty level analysis is presented. The relative significance of each uncertain input is established through an interval sensitivity analysis. The method offers utilities with alternatives for selecting the standard conductor size to be used. In this study it is assumed that the system of ground electrodes has the form of a grid of horizontally buried conductors, supplemented by a number of vertical ground histone methyltransferase inhibitor connected to the grid. Based on IEEE STD 80-2000, this concept represents the prevailing practice of most utilities both in the USA and in other countries. The proposed method is tested for the design and configuration arrangement of a 115/13kV substation earthing rectangular grid with ground rods system and encouraging results are reported.

The governing equations
In order to account for uncertainties associated with the substation earthing grid system design, the following analysis is followed [7]. The input parameters’ uncertainties, in interval format, are integrated into the governing equations as follows:where is the interval grid resistance, ρ is the interval soil resistivity, is the total effective length of buried conductor, A is the grid area, and h is the depth of the grid burial.
Ignoring the station resistance, the interval symmetrical ground fault current (assuming single line to ground fault) iswhere E is the phase-to-neutral voltage, is the estimated resistance of the fault (normally it is assumed =0), R1, R2 are the positive and negative sequence equivalent system resistances respectively, is the zero sequence equivalent system resistance, X1, X2 are the interval positive and negative sequence equivalent system reactances (subtransient) respectively, is the interval zero sequence equivalent system reactance.
The values R1, R2, , X1, X2, and are computed looking into the system from the point of fault.
So, the interval maximum grid current is given bywhere is the decrement factor and is the division factor.
Assuming the use of cupper wire and ambient temperature of 40°C, the required interval conductor diameter (for fault duration =0.5) in mm is [7]
Consequently, at this stage, the designer may opt to check if, alternately, the use of a less conductive (30%) copper-clad steel wire and the imposition of a more conservative maximum temperature limit of 700°C will still permit the use of a conductor with the above diameter d. So, the minimum interval conductor diameter to be used can be calculated by;where TCAP is the thermal capacity per unit volume, is the current duration, is the thermal coefficient of resistivity at reference temperature, is the resistivity of the ground conductor, is the reciprocity of the thermal coefficient of resistivity at 0°C, is the maximum allowable temperature, and is the ambient temperature.
Assuming that for the particular station the location of grounded facilities within the fenced property is such that the person’s weight can be expected to be at least 70kg [7], the interval tolerable step and touch voltages for humans of 70kg, respectively, can be computed as follows:where is the interval crushed rock wet resistivity, is the reduction factor and can be approximated as [7]where is the thickness of crushed rock surfacing.
It is necessary to compare the interval ground potential rise (GPR) to the interval tolerable touch voltage (). GPR is calculated byThe interval mesh voltage () at the center of the corner mesh is computed as follows [7]where is the total length of the conductor in the horizontal grid, is the length of ground rod at each location, is the total length of ground rods, and are the length and the width of the substation respectively, is the correction factor for grid geometry, is the spacing factor for mesh voltage, and they are given bywherewhere D is the equally grid spacing, is the Corrective weighting factor that adjusts for the effects of inner conductors on the corner mesh and equals 1 for grid with ground rods, is the corrective weighting factor that emphasizes the effects of grid depth, is the grid reference depth, n is the geometric factor composed of factors , , , and , and is the peripheral length of the grid.