Grounding Design Calculations – Part Thirteen

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.

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 [4, pp. 88-89].

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

 Step#5: Calculation Of The Preliminary Grid Resistance, Rg, Of The Grounding System In Uniform Soil

 1- Terms Definitions for Step#5 Grounding System: it is the system that Comprises all interconnected grounding facilities in a specific area. Grounding Grid: A system of horizontal ground electrodes that consists of a number of interconnected, bare conductors buried in the earth, providing a common ground for electrical devices or metallic structures, usually in one specific location. Notes: Grids buried horizontally near the earth’s surface are also effective in controlling the surface potential gradients. A typical grid usually is supplemented by a number of ground rods and may be further connected to auxiliary ground electrodes to lower its resistance with respect to remote earth.

 2- Required Values of the Earthing Grid Resistance Rg for AC Substations Low values of resistance to remote earth are required in order to minimize the ground potential rise GPR and consequently avoid dangerous touch and step voltages, for example: For most transmission and other large substations, the ground resistance is usually about 1 Ω or less. In smaller distribution substations, the usually acceptable range is from 1 Ω to 5 Ω, depending on the local conditions.

 3- Factors Affecting The Earthing Grid Resistance Rg Values The earthing grid resistance mainly depends on: The area taken up by the earthing grid, The total length of buried earthing conductors The number of earthing rods / electrodes. The area of the grounding system, which is usually known in the early design stage, is the single most important geometrical factor in determining the resistance of the grid. The larger the area grounded, the lower the grid resistance and, thus, the lower the ground potential rise GPR.

 4- Calculations Methods of Earthing Grid Resistance, Rg, In Uniform Soil IEEE Std 80 offers two alternative options for calculating the earthing grid resistance (with respect to remote earth) as follows: The Simplified Method, The Schwarz Equations.

 4.1 The Simplified Method A- First approximation: Rg for a grounding system of circular metal plate at zero depth: As a first approximation, a minimum value of the substation grounding system resistance in uniform soil can be estimated by means of the formula of a circular metal plate at zero depth as follows: Where: Rg is the substation ground resistance in Ω, ρ is the soil resistivity in Ω·m, A is the area occupied by the ground grid in m2. B- Approximation Refining: Rg for a grounding system of a grid rod combination: An upper limit of the substation ground resistance in uniform soil can be obtained by Laurent and Niemann equation as follows: Where: LT is the total buried length of conductors in m. This equation states the fact that the resistance of any actual grounding system that consists of a number of conductors is higher than that of a solid metallic plate. The difference will decrease with the increasing length of buried conductors and will approach 0 for infinite LT, when the condition of a solid plate is reached. C- Final Equation: Finally, the simplified method equation as modified by Sverak to include the effect of earthing grid depth will be as follows: Where: Rg is the substation ground resistance in Ω, ρ is the soil resistivity in Ω·m, A is the area occupied by the ground grid in m2, LT is the total buried length of conductors in m, h is the depth of the grid in m.

Example#1:

For a rectangular earthing grid (see fig.2) with the following parameters is proposed:
• 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. Fig.2

Calculate the erthing grid resistance using the simplified equation.

Solution:

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

 4.2 The Schwarz Equations The Schwarz equations are a series of equations that are more accurate in modeling of grounding system in a homogeneous soil consisting of horizontal (grid) and vertical (rods) electrodes as follows: Where: R1 ground resistance of grid conductors in Ω, R2 ground resistance of all ground rods in Ω, Rm mutual ground resistance between the group of grid conductors, R1, and group of ground rods, R2 in Ω. A- Ground Resistance Of The Grid (R1): Where: ρ is the soil resistivity in Ω·m, Lc is the total length of all connected grid conductors in m, a' is √ (a x 2h) for conductors buried at depth h in m, or a' is a for conductor on earth surface in m, a is the cross-sectional radius  of conductor in m, A is the area covered by conductors in m2, k1, k2 are constant coefficients depending on the geometry of the grid. B- Ground Resistance Of The Rod Bed (R2): Where: Lr is the length of each rod in m, LR is the Total Length Of All Rods, b is the cross-sectional radius of an earthing electrode in m, nR number of rods placed in area A. C- Mutual Ground Resistance Between The Grid And The Rod Bed (Rm): Note: The combined ground resistance of the grid and the rod bed will be lower than the ground resistance of either component alone, but still higher than that of a parallel combination.

4.2.1 Determination Of Coefficients K1 and K2

Coefficients k1 and k2 can be determined by one of the following two methods:

Method#1: from Curves as follows: K1 Curve K2 Curve

Method#2: from Equations as follows:

A- For coefficient k1:

The coefficient k1 can be approximated by the following equations:

• For depth h = 0 : k1 = - 0.04 L/R + 1.41
• For depth h = √A /10 : k1 = - 0.05 L/R + 1.2
• For depth h = √A /6 : k1 = - 0.05 L/R + 1.13

A- For coefficient k2:

The coefficient k2 can be approximated by the following equations:

• For depth h = 0 : k2= 0.15 L/R + 5.50
• For depth h = √A /10 : k2= 0.10 L/R + 4.68
• For depth h = √A /6 : k2= 0.05 L/R + 4.40

Where in both cases, L/R is the length-to-width ratio of the earthing grid.

 Example#2: For a square  earthing grid with the following parameters is proposed: Length of  15 m and a width of 15 m, 6 parallel rows and 6 parallel columns, Grid conductors will be 70 mm2 and buried at a depth of 1.5 m, Grid conductors diameter will be 0.011 m, 10 earthing rods will be installed on the corners and perimeter of the grid, Each earthing rod will be 1.2 m long, Rod diameter will be 0.019 m, Soil resistivity 100,000 ohm.m. Calculate the erthing grid resistance using Schwarz Equations. Solution: Step#1: Calculating Ground Resistance Of The Grid R1 ρ= Soil resistivity = 100,000 ohm.m Lc = Total length of all connected grid conductors = 6 x 15 + 6 x 15 = 180 m a' = √ (a x 2h) = √(0.0055 x 2 x 1.5) = 0.1285 a  = the raduis of conductor in m = 0.011 /2 = 0.0055 m A = the area covered by conductors in m2 = 15 x 15 = 225 m2 L/R = length-to-width ratio = 15 / 15 = 1 Since, h = √A /10 ( because h = 1.5 m and √A /6 = 15/10 =1.5) then k1 = - 0.05 L/R + 1.2 = 1.15 k2= 0.10 L/R + 4.68 = 4.78  by applying R1 equation: So, R1 = 2.9989 ohm Step#2: Calculating Ground Resistance Of The Rod Bed (R2): Lr =  the length of each rod = 1.2 LR =  the Total Length Of All Rods = 1.2 x 10 rods = 12 m b =  the cross-sectional radius of an earthing electrode = 0.019 / 2 = 0.0095 m nR = number of rods placed in area = 10  by applying R2 equation: So, R2 = 2.1394 ohm Step#3: Calculating Mutual Ground Resistance Between The Grid And The Rod Bed (Rm):  by applying Rm equation: So, Rm = 2.3734 ohm Step#4: Calculating The Erthing Grid Resistance Rg  by applying Rg equation: So, Rg = 1.9995 ohm

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