Grounding Design Calculations – Part Eleven


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:

  1. Domestic, commercial and industrial premises,
  2. 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:





You can preview the following Articles for more info:












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. 


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 withthe 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)


In this Article and following Articles, I will explain these steps in detail.








Step#3: Calculation Of Tolerable Touch And Step Voltages






Terms Definition for Step#3

  • 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.
  • Mesh Voltage: The maximum touch voltage within a mesh of a ground grid.
  • Metal-To-Metal Touch Voltage: The difference in potential between metallic objects or structures within the substation site that may be bridged by direct hand-to-hand or hand-to-feet contact.
  • 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.
  • 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.
  • Transferred Voltage: A special case of the touch voltage where a voltage is transferred into or out of the substation from or to a remote point external to the substation site.








Typical Shock Situations

Fig(2) and Fig(3) show five basic situations involving a person and grounded facilities during a fault, the basic five shock situations are as follows:



Fig(2)



Fig(3)

  • Metal-To-Metal Touch Voltage: shock situation due to either hand-to-hand or hand-to-feet contact,
  • Touch Voltage: shock situation due to hand-to-feet contact,
  • Step Voltage: shock situation due to foot-to-foot contact,
  • Mesh Voltage: shock situation due to hand-to-feet contact,
  • Transferred Voltage: shock situation due to hand-to-feet contact, occurred when a person standing within the substation area touches a conductor grounded at a remote point,
  • Extended Transferred Voltage: shock situation due to hand-to-feet contact, occurred when or a person standing at a remote point touches a conductor connected to the substation grounding grid.








First: Calculations of Tolerable Step Voltage


In step#3, we will calculate the maximum tolerable limits for step voltage from its circuit equivalent as follows:


Fig(4)


The equivalent circuit for step voltage is as in fig(4):

From Thevenin theorem:


VTh = (RB + ZTh) x IB

And, ZTh = 2Rf

Where:

RB is the resistance of the human body in Ω
Rf is the ground resistance of one foot (with presence of the substation grounding system ignored) in Ω

So, the permissible total equivalent voltage becomes:


VTh = Estep = (RB + 2Rf) x IB


To get the Tolerable Step Voltage, you need to calculate the parameters RB, Rf &IB.






1- Calculation Of Resistance Of The Human Body (RB)

IEEE 80 assumes the following:

  • Resistances in series with the body resistance are as follows:


  1. Hand and foot contact resistances are equal to zero.
  2. Glove and shoe resistances are equal to zero.


  • The resistance of a human body which may be one of the following:


  1. From Hand-to-feet or,
  2. From Hand-to-hand or,
  3. From One foot to the other foot.


 Will equal 1000 Ω.

RB = 1000 Ω







2- Calculation of ground resistance of one foot (Rf)

For the purpose of circuit analysis, the human foot is usually represented as a conducting metallic disc and the contact resistance of shoes, socks, etc., is neglected.


For Theoretically Uniform Soil Resistivity:


The ground resistance in ohms of a metallic disc of radius b (m) on the surface of a homogeneous earth of resistivity ρ (Ω·m) is given by Laurent as follows:

Rf = ρ/ 4b

Traditionally, the metallic disc representing the foot is taken as a circular plate with a radius of 0.08 m. With only slight approximation, equations for ZTh can be obtained in numerical form and expressed in terms of ρ as follows.


Rf = ρ/ 4b = ρ/ (4 x 0.08) = 3 ρ

And, ZTh = 2 Rf = 6 ρ



But actually,it is common to apply a thin layer (0.08m - 0.15m) of high resistivity material (such as gravel, blue metal, crushed rock, etc) over the surface of the ground to help protect against dangerous touch and step voltages. This is because the surface layer material increases the contact resistance between the soil (i.e. earth) and the feet of a person standing on it, thereby lowering the current flowing through the person in the event of a fault.

In this case, this thin layer affects the value of the soil resistivity ρ by a derating factor Cs which can be obtained with the analytical method (Thapar, Gerez, and Kejriwal) as follows:



Where:

Cs is the surface layer derating factor,
ρ is the soil resistivity (Ω.m),
ρs is the resistivity of the surface layer material (Ω.m),
hs is the thickness of the surface layer (m).



so, The effective ground resistance of one foot Rf can be calculated as follows:


Rf = 3 Cs ρs

And, ZTh = 2 Rf = 6 Cs ρs








3- Calculation of Tolerable body current IB

As stated by Dalziel and others, the non-fibrillating current of magnitude IB at 50Hz or 60Hz and at durations ranging from 0.03–3.0 s is related to the energy absorbed by the body as described by the following equation:

SB = (IB)2 x ts

Where:

IB is the rms magnitude of the current through the body in A,
ts is the duration of the current exposure in sec,
SB is the empirical constant related to the electric shock energy tolerated by a certain percent of a given population.


Note:

  • The above Equation is based on tests limited to a range of between 0.03 s and 3.0 s, it obviously is not valid for very short or long durations.


From the above equation, the current through the body IB will be calculated as follows:

IB = √SB / √ts

And given that: k = √SB

So, IB = k / √ts 


Dalziel found the following Data by tests:


Persons Weighing
Shock Energy (SB)
K Factor
IB Equation for the specified Persons Weighing
50 kg (110 lb)
0.0135
k50 = √SB = √0.0135 = 0.116
IB = 0.116 / √ts
70 kg (155 lb)
0.0246
k70 = √SB = √ 0.0246 = 0.157
IB = 0.157 / √ts








Tolerable Step Voltage Equation

So, from 1, 2 &3, the Tolerable Step Voltage equation becomes:


Estep (for 50 Kg Person) = (RB + 2Rf) x IB = (1000 + 6 Cs ρs) x 0.116 / √ts

And,

Estep (for 70 Kg Person) = (RB + 2Rf) x IB = (1000 + 6 Cs ρs) x 0.157 / √ts







Second: Calculations of Tolerable Touch Voltage


In step#3, we will calculate the maximum tolerable limits for touch voltage from its circuit equivalent as follows:



Fig(5)


The equivalent circuit for step voltage is as in fig(5):

From Thevenin theorem:


VTh = (RB + ZTh) x IB

And, ZTh = Rf/2

Where:

RB is the resistance of the human body in Ω
Rf is the ground resistance of one foot (with presence of the substation grounding system ignored) in Ω

So, the permissible total equivalent voltage becomes:


VTh = Etouch = (RB + Rf/2) x IB


To get the Tolerable Step Voltage, you need to calculate the parameters RB, Rf &IB.






4- Calculation Of Resistance Of The Human Body (RB)

Same as for calculation of Tolerable Step Voltage, so:

RB = 1000 Ω







5- Calculation of ground resistance of one foot (Rf)


Same as for calculation of Tolerable Step Voltage. so, The effective ground resistance of one foot Rf can be calculated as follows:

Rf = 3 Cs ρs

And, ZTh =  Rf/2 = 1.5 Cs ρs







6- Calculation of Tolerable body current IB

Same as for calculation of Tolerable Step Voltage, So:

IB (for 50 Kg Person) = 0.116 / √ts

IB (for 70 Kg Person) = 0.157 / √ts






Tolerable Touch Voltage Equation

So, from 4, 5 &6, the Tolerable Touch Voltage equation becomes:


Etouch (50 Kg Person)= (RB + Rf/2) x IB = (1000 + 1.5 Cs ρs) x 0.116 / √ts

And,

Etouch (70 Kg Person) = (RB + 2Rf) x IB = (1000 + 1.5 Cs ρs) x 0.157 / √ts








Example:

Calculate the Tolerable Step and 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.



Solution:

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


Step#3: Calculate The Tolerable Step Voltage

Estep (for 70 Kg Person) = (1000 + 6 Cs ρs) x 0.157 / √ts

= (1000 + 6 X 0.7207 X 3000) 0.157 / √0.15 = 5664.03 V






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




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