Worked Example Earthing Calculation

Worked Example In this example, the touch and step potential calculations for an earthing grid design will be  performed. The proposed site is a small industrial facility facility with a network connection via a transmission line and a delta-wye connected transformer.

Step 1: Soil Resistivity The soil resistivity around the site was measured with a Wenner four-pin probe and found to be be approximately 300 Ω.m.

Step 2: Surface Layer Materials A thin 100mm layer of blue metal (3,000 Ω.m) is proposed proposed to be installed on the site. The surface layer derating factor is:

Step 3: Earthing Grid Resistance

Figure 1. Proposed rectangular earthing grid A rectangular earthing grid (see the figure right) with the following parameters is proposed:   

Length of 90m and a width of 50m 6 parallel rows and 7 parallel columns 2 Grid conductors will be 120 mm  and buried at a depth of 600mm

 

22 earthing rods will be installed on the corners and perimeter of the grid Each earthing rod will be 3m long

Using the simplified equation, the resistance of the earthing grid with respect to remote earth is:

Step 4: Maximum Grid Current Suppose that the maximum single phase to earth fault at the HV winding of the transformer is 3.1kA and that the current division factor is 1 (all the fault current flows back to remote earth). The X/R ratio at the fault is approximately 15, the maximum fault duration 150ms and the system nominal frequency is 50Hz. The DC time offset is therefore:

The decrement factor is then:

Fianlly, the maximum grid current is:

kA

Step 5: Touch and Step Potential Criteria

Based on the average weight of the workers on the site, a body weight of 70kg is assumed for the maximum touch and step potential. A maximum fault clearing time of 150ms is also assumed. The maximum allowable touch potential is:

V The maximum allowable step potential is:

V

Step 6: Ground Potential Rise (GPR) The maximum ground potential rise is:

V The GPR far exceeds the maximum allowable touch and step potentials, an d further analysis of mesh and step voltages need to be performed.

Step 7: Earthing Grid Design Verification Mesh Voltage Calculation

The components of the geometric factor

,

,

and

for the rectangular grid are:

Therefore the geometric factor

is:

The average spacing between parallel grid conductors

where

is:

and

are the width and length of the grid respectively (e.g. 50m and 90m)

and

is the number of parallel rows and columns respectively (e.g. 6 and 7)

The geometric spacing factor

The irregularity factor

The effective buried length

is:

is:

is:

m Finally, the maximum mesh voltage is:

V The maximum allowable touch potential is 1,720V, which exceeds the mesh voltage calculated above and the earthing system passes the touch potential criteria (although it is quite marginal). Step Voltage Calculation

The geometric spacing factor

The effective buried length

is:

is:

m Finally, the maximum allowable step voltage is:

V

The maximum allowable step potential is 5,664V, which exceeds the step voltage calculated above and the earthing system passes the step potential criteria. Having passed both touch and step potential criteria, we can conclude that the earthing system is safe.