The earthing system shall consist of a network of buried conductors forming the earth grid, providing the earthing connections to equipment ground terminals, equipment housings and structures. If the  calculated Mesh and Step potentials for this earthing system is less than the attainable mesh and step potentials, then the design is considered to optimum one.

The earth grid shall encompass all of the area of the sub-station within the fencing and also shall extend for approximately one meter outside the fencing. 

The resistivity of the soil is then tested by any suitable method. As mentioned in the previous post titled "Earthing", the Wenner method is the most adopted.

The size of the conductor is chosen keeping in mind the fault current in the system and the entire area within the fencing and one meter outside the fencing has to be covered with crushed rock possessing a minimum resistivity of 3000ohm-m
The earth grid consists of horizontal conductors placed about 0.6m to 1.5m below the earth forming a checkerboard pattern. The depth of the earth grid is to be considered excluding the layer of the crushed rock put.

Vertical earth rods or the earth electrodes are to be buried at the grid corners and at the junction points along the perimeter of the earth grid. Electrodes (Earth Pits) may also be installed at the major equipment such as Transformers, Lightning Arresters, Towers / Structures, Lightning Masts. In the case of a Transformer, the transformer body has to earthed to a separate earth electrode and the neutral has to be connected to a separate earth electrode (Neutral Pit). 

Calculation of Tolerable Mesh Voltage

The Tolerable Touch or Mesh potential can be calculated from the below mentioned formula

E touch = (1000 + 1.5 Cs * ps) * 0.157 / SQRT( t * s ) (Ref: IEEE 80-2000 section 8)

Where, Etouch = Mesh Voltage 
           Cs = Surface Layer Derating Factor
           ps = Top layer resistivity of the soil
           ts = fault clearing time

Cs = 1 - a * [ (1-p/ps) / (2*hs + a) ]; where a =0.09  (Ref: eqn.27 of IEEE 80-2000)

With the above details, the Tolerable Touch potential can be calculated.

Calculation of Tolerable Step Potential

The tolerable Step potential can be calculated form the below formula
 
                           E step = (1000 + 6 Cs * ps) * 0.157 / SQRT( t * s ) (Ref: IEEE 80-2000 section 8)

Where, Etouch = Mesh Voltage 
           Cs = Surface Layer Derating Factor
           ps = Top layer resistivity of the soil
           ts = fault clearing time

Calculation of Design Mesh Voltage (Attainable Mesh Voltage)

The attainable Mesh voltage can be calculated form the below mentioned formula

Em = (p * Km * Ki * Ig) / Lm 

                                                                 (Ref: IEEE 80-2000 section 16)

Where, Em =       Attainable Mesh Voltage
            p =         Soil Resistivity ohm-meter
            Km =      Spacing Factor for Mesh Voltage
            Ki =        Correction Factor for Grid geometry
            Ig =        Maximum Earth Fault Current
            Lm =      Effective length for Lc and Lr for Mesh Voltages
            Lc =       Total length of grid conductors
            Lr =        Total length of earth rod (earth electrodes)

The geometrical factor Km can be expressed as below.

Km = (1/2*Pi) * [ ln(D^2/16.h.d + (D+2h)^2/8D*d - h/4d) + Kii/Kh * ln(8/Pi(2*(n-1)) ]

Where, D = Spacing between parallel conductors
            d = Diameter of the grid conductors
            h = Depth of earth grid condcutors
            n = Geometric factors
           Kh = Corrective weight factor that emphasizes the effects of grid depth
           Kii =  Corrective weight factor that emphasizes the effects of inner conductors

Most of the earthing design has earth electrodes at corners of the earth grid or along the perimeter. In such cases, the value of 'Corrective weight factor that emphasizes the effects of inner conductors' will be unity.

i.e. Kii = 1

The corrective factor that emphasizes the effects of grid depth can be expresses as below.

Kh = SQRT(1+(h/h0) ); h0 is 1m (ref depth)


Effective number of parallel conductors (n) in a grid can be made applicable to both rectangle layout and other irregular layout. 

n = na*nb*nc*nd

Where, na = 2Lc/Lp
            nb = 1 for square grids
            nc = 1 for square and rectangular grids
            nd = 1 for square, rectangular and 'L' shaped grids

Otherwise;

nb= SQRT ( Lp/(4SQRT(A) )
 
nc= SQRT [ Lx.Ly/A ]^(0.7*A/Lx*Ly)

nd= Dm/(SQRT(Lx^2 + Ly^2) )

Where; Lc = Total length of the conductors in horizontal grid
            Lp = Peripheral Length of the grid
            A = Area of the grid
            Lx = Maximum length of the grid in x direction
            Ly = Maximum length of the grid in y direction
            Dm = Maximum distance between any two points in the grid
            D = Spacing between the parallel conductors
            d = Diameter of the grid conductors
            h = depth of ground conductors

The irregularity factor is expressed as 
Ki = 0.644 + 0.148*n 

For grids with no earth rods, or with a few earth rods ( none located in corner or along the perimeter of the earth grid), the effective buried length is expressed as;
Lm = Lc + Lr 

Lr is the total length of all rods

For grids with earth rods in the corners and the perimeter of the grid, the effective buried length is expressed as;
Lm = Lc + [ 1.55 + 1.22 ( Lr / SQRT (Lx^2 + Ly^2) ) ] * Lr 

Calculation of Design Step Voltage ( Attainable Step Voltage )

The attainable Step Voltage is calculated form the below formula;
Es = p*Ks*Ki*Ig / Ls  


Where, p = soil resistivity
            Ks = Spacing factor for Step voltage
            Ki = Correction factor for grid geometry
            Ig = Maximum Earth fault current
            Ls = Effective buried length

For grids without earth rods or few earth rods, Ls is expressed as;
Ls = 0.75 Lc + 0.85 Lr   

Lc = Total length of grid conductors
Lr = Total length of ground rods

The spacing factor is expressed as; 

Ks = 1/Pi ( 1/2h + 1/D+h + 1/D (1-0.5^n-2) )

Where, D = Spacing between parallel conductors 
            h = Depth of earth grid conductors
            n = geometric factor

If the Designed Mesh and Step Potential are less than the tolerable Mesh and Step potentials, the design is an apt one. But, if the calculated mesh and step potential are more than the tolerable potentials, the grid design has to be modified.

To reduce the grid mesh and step potential, the mesh size has to be decreased, by increasing the number of parallel conductors in each direction.