Grounding Design Calculations – Part Fifteen

In Article Grounding Design Calculations – Part One ", I indicated the following:

 Grounding System Design Calculations according to type of the building The procedures for performing the Grounding System Design Calculations can differ slightly according to the type of the building as follows: Domestic, commercial and industrial premises, High and medium voltage electricity substations.

 First: Domestic, commercial and industrial premises We mean by domestic, commercial and industrial premises, all installations up to 1,000 V ac and 1,500 V dc - between phases, with some minor exceptions.

And I explained Methods of Grounding Design Calculations of Domestic, commercial and industrial premises in the following Articles:

 Second: High And Medium Voltage Electricity AC Substations

I began explaining Grounding Design Calculations for second type of buildings: AC Substations in Article
Grounding Design Calculations – Part Ten "  where I explained the following:

• Design Procedures for grounding system design as per IEEE 80: Guide for safety in AC substation grounding,
• Step#1: Field Data Collection,
• Step#2: Earthing Grid Conductor Sizing.

Also in " Grounding Design Calculations – Part Eleven ", I explained Step#3: Calculation Of Tolerable Touch And Step Voltages.

And in Article " Grounding Design Calculations – Part Twelve ", I explained Step#4: Preliminary Design of Grounding System for AC Substations.

And In Article " Grounding Design Calculations – Part Thirteen ", I explained Step#5: Calculation of the Preliminary Grid Resistance, Rg, Of the Grounding System in Uniform Soil

And In Article " Grounding Design Calculations – Part Fourteen ", I explained Step#6: Determination of Maximum Grid Current, IG.

Today, I will continue explaining other steps from the design procedures of grounding system for AC Substation.

 Design Procedures of Grounding System for AC Substations - Continued

Design Procedures

The design process of a substation grounding system requires many steps. The following steps were established by the IEEE Standard 80-2000 for the design of the ground grid:

Step#1: Field Data Collection,

Step#2: Earthing Grid Conductor Sizing,

Step#3: Calculation of tolerable touch and step voltages,
Step#4: Preliminary design of grounding system,
Step#5: Calculation of of the preliminary Grid Resistance, RG, of the grounding system in uniform soil.
Step#6: Determination of Grid current, IG.
Step#7: Calculation of maximum grid potential rise and comparing with the tolerable touch voltage from step#3. If the GPR of the preliminary design is below the tolerable touch voltage, move to step#12 (no further analysis is necessary). If not, continue to step#8.
Step#8: Calculation of mesh and step voltages.
Step#9: Comparing the computed mesh voltage from step#8 with the tolerable touch voltage from step#3. If the computed mesh voltage is below the tolerable touch voltage, continue to step#10. If not, move to step#11 for revising the preliminary design.
Step#10: Comparing the computed step voltage from step#8 with the tolerable step voltage from step#3.If the computed step voltages are below the tolerable step voltage, move to step#12. If not, move to step#11 for revising the preliminary design.
Step#11: Preliminary Design modification
If either the step or touch tolerable limits from step#3 are exceeded, revision of the grid design is required.
Step#12: Detailed final design. After satisfying the step and touch voltage requirements, additional grid and ground rods /conductors may be required. The final design should also be reviewed to eliminate hazards due to transferred potential and hazards associated with special areas of concern.

The block diagram in Fig (1) illustrates the Design procedures. Fig (1)

 Step#7: Calculation Of Maximum Grid Potential Rise And Comparing With The Tolerable Touch Voltage From Step#3

 7.1 Terms Definitions for Step#7 Ground Potential Rise (GPR): The maximum electrical potential that a substation grounding grid may attain relative to a distant grounding point assumed to be at the potential of remote earth. This voltage, GPR, is equal to the maximum grid current times the grid resistance. Touch Voltage: The potential difference between the ground potential rise (GPR) and the surface potential at the point where a person is standing while at the same time having a hand in contact with a grounded structure.

 7.2 Calculation of Maximum Ground Potential Rise (GPR) Maximum Ground Potential Rise (GPR) can be calculated by the following equation: GPR = IG x Rg Where: GPR is the maximum ground potential rise (V), IG is the maximum grid current found earlier in Step#6 (A), Rg is the earthing grid resistance found earlier in Step#5 (Ω).

 7.3 From Step#3: Tolerable Touch Voltage Equations Etouch (for 50 Kg Person) =  (RB + Rf/2) x IB = (1000 + 1.5 Cs ρs) x 0.116 / √ts And, Etouch (for 70 Kg Person) =  (RB + 2Rf) x IB = (1000 + 1.5 Cs ρs) x 0.157 / √ts Where: RB is the resistance of the human body in Ω = 1000 Ω, Rf is the ground resistance of one foot (with presence of the substation grounding system ignored) in Ω, Cs is the surface layer derating factor found earlier in Step#3, ρs is the resistivity of the surface layer material (Ω.m), ts is the duration of the current exposure in sec.

7.4 Comparing Maximum Ground Potential Rise (GPR) with the tolerable touch voltage (Etouch)

 If Action GPR < Etouch The Preliminary grid design is safe, Move to Step#12: Detailed final design (no further analysis is necessary) GPR > Etouch The Preliminary grid design is not safe , Continue to Step#8: Calculation of mesh and step voltages

Example#1:

For A small industrial facility with a network connection via a transmission line and a delta-wye connected transformer:

1- Calculate the erthing grid resistance using the simplified equation For a rectangular earthing grid (see fig.2) with the following parameters: fig.2

• Length of 90m and a width of 50m,
• 6 parallel rows and 7 parallel columns,
• Grid conductors will be 120 mm2 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.

2- Calculate the Tolerable Touch Voltages for 70 Kg person, if 120 mm thick layer of crushed rock is spread on the earth's surface above ground grid in a switchyard, noting that:

• Crush rock resistivity ρs = 3000 Ωm,
• Thickness of the crushed rock surface layer hs = 0.1 m,
• Shock duration in sec (exposure time) ts= 0.15 sec.
• The soil resistivity around the switchyard was measured with a Wenner four-pin probe and found to be approximately 300 Ω.m.

3-calculate the maximum grounding grid fault current IG, noting that:

• The maximum single phase to earth fault at the HV winding of the transformer = 3.1 KA,
• Current division dactor that flows between ground Sf=0.6,
• The X/R ratio at the fault is approximately 15,
• The maximum fault duration 150ms,
• The system nominal frequency is 50Hz,
• Cp Corrective projection factor =1.2.

4- Evaluate the preliminary design.

Solution:

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

2- Calculate the Tolerable Touch Voltages for 70 Kg person:

Step#1: Calculate The Surface Layer Derating Factor Cs

Step#2: Calculate The Tolerable Touch Voltage

Etouch (for 70 Kg Person) = (1000 + 1.5 Cs ρs) x 0.157 / √ts

= (1000 + 1.5 X 0.7207 X 3000) 0.157 / √0.15 = 1720.04 V

3-calculate the maximum grounding grid fault current IG

Step#1: For each fault, based on its duration time, tf, determine the value of decrement factor Df to allow for the effects of asymmetry of the fault current wave

Since, The X/R ratio at the fault is approximately 15, the maximum fault duration 150ms and the system nominal frequency is 50Hz.

Ta is then:

The decrement factor Df is then:

Step#2: apply the Cp Corrective projection factor =1.2.

So, the maximum grounding grid fault current IG is:

IG = Sf. Df. Cp. If

So, IG = 0.6 x 1.1479 x 1.2 x 3.1 KA = 2.562 KA

4- Evaluate The Preliminary Design:

This is done by Comparing Maximum Ground Potential Rise (GPR) with the tolerable touch voltage (Etouch):

Maximum Ground Potential Rise (GPR) can be calculated by the following equation:

GPR = IG x Rg = 2562 A X 2.2753 Ω = 5829.31 V

Since, GPR = 5829.31 V and Etouch = 1720.04 V

So, GPR > Etouch

The Preliminary grid design is not safe, a further design analysis is needed and we must Continue to Step#8: Calculation of mesh and step voltages.

 Step#8: Calculation Of Mesh And Step Voltages

 8.1 Terms Definitions for Step#8 Mesh Voltage: The maximum touch voltage within a mesh of a ground grid. Step Voltage: The difference in surface potential experienced by a person bridging a distance of 1 m with the feet without contacting any other grounded object.

 First: Mesh Voltage Calculation The mesh voltage is the maximum touch voltage within a mesh of an earthing grid and is calculated as follows: Where: IG: the maximum grid current found earlier in Step#6 (A), LM: the effective buried length of the grid, Km :  the geometric spacing factor, Ki : irregularity factor,  which accounts for some of the error introduced by the assumptions made in deriving Km, ρ: the soil resistivity, (IG/LM): the average current per unit of effective buried length of the grounding system conductor. A- The geometric spacing factor Km is calculated as follows: Where: D is the average spacing between parallel grid conductors (m), h is the depth of buried grid conductors (m), d is the cross-sectional diameter of a grid conductor (m), Kh is a weighting factor for depth of burial = √(1+h), Kii is a weighting factor for earth electrodes /rods on the corner mesh, A.1 the average spacing between parallel grid conductors D is calculated as follows: Where: Wg  and Lg  are the width and length of the grid respectively (m), nr and nc  is the number of parallel rows and columns respectively. A.2 The weighting factor for earth electrodes /rods on the corner mesh Kii is calculated as follows: Kii = 1 for grids with earth electrodes along the grid perimeter or corners or a combination of both, Kii for grids with no earth electrodes or grids with only a few ground rods, none located on the corners or on the perimeter is: Where: n is a geometric factor. A.3 The geometric factor n is calculated as follows: n = na x nb x nc x nd Where: LC is the total length of horizontal grid conductors in m, Lp is the length of grid conductors on the perimeter in m, A is the total area of the grid (m2). And, nb = 1 for square grids, nc = 1 for square and rectangular grids, nd = 1 for square, rectangular and L-shaped grids. otherwise, Where: Lx and Ly are the maximum length of the grids in the x and y directions (m), Dm is the maximum distance between any two points on the grid (m). B- The irregularity factor, Ki, used in conjunction with the above defined n is Ki = 0.644 + 0.148 n C- the effective buried length of the grid LM  is found as follows: For grids with few or no earthing electrodes (and none on corners or along the perimeter): LM  = LC + LR Where: LC is the total length of horizontal grid conductors (m), LR is the total length of earthing electrodes / rods (m). For grids with earthing electrodes on the corners and along the perimeter: Where: LC is the total length of horizontal grid conductors (m), LR is the total length of earthing electrodes / rods (m), Lr is the length of each earthing electrode / rod (m), Lx and Ly are the maximum length of the grids in the x and y directions (m).

Second:  Step Voltage Calculation

The maximum allowable step voltage is calculated as follows:

Where :
ρs is the soil resistivity (Ω.m),
IG: the maximum grid current found earlier in Step#6 (A),
Ks  : the geometric spacing factor,
Ki : corrective factor,  which accounts for some of the error introduced by the assumptions made in deriving Km,
Ls : the effective buried length of the grid.

A- Geometric Spacing Factor Ks:
The geometric spacing factor Ks is applicable for burial depths (h) between 0.25m and 2.5m (0.25 m < h < 2.5 m) and is calculated as follows:

Where:

D is the spacing between parallel grid conductors (m),
h is the depth of buried grid conductors (m),
n is a geometric factor (as derived above in the mesh voltage calculation).

B- Effective Buried Length LS:
The effective buried length LS for all cases can be calculated as follows:

LS = 0.75 LC + 0.85 LR

Where:

LC is the total length of horizontal grid conductors (m),
LR is the total length of earthing electrodes / rods (m).

Example#2:

Using the same data of Example#1, calculate the Maximum Mesh and Step Voltages.

Solution:

First: Mesh Voltage Calculation

Step#1: calculate the geometric factor n
The components of the geometric factor na, nb, nc, and nd for the rectangular grid are:

Step#2: calculate the average spacing between parallel grid conductors D

Step#3: calculate the geometric spacing factor Km

Step#4: calculate the irregularity factor Ki
Ki = 0.644 + 0.148 n = 0.644 + 0.148 x 6.4939 = 1.605

Step#5: from the above steps, the maximum mesh voltage is:

Second: Step Voltage Calculation

Step#1: calculate the geometric spacing factor Ks

Step#2: calculate the effective buried length Ls
LS = 0.75 LC + 0.85 LR = 0.75 x 890 + 0.85 x 66 = 723.6 m

Step#3: from the above steps, calculate the maximum allowable step voltage

In the next Article, I will explain Other Steps from the Design Procedures of Grounding System Design for AC Substation. Please, keep following.