Grounding Design Calculations – Part Fourteen


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.


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 


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#6: Determination Of Grid Current, IG

  




1- Terms Definitions for Step#6

  • DC Offset: Difference between the symmetrical current wave and the actual current wave during a power system transient condition. Mathematically, the actual fault current can be broken into two parts, a symmetrical alternating component and a unidirectional (dc) component. The unidirectional component can be of either polarity, but will not change polarity, and will decrease at some predetermined rate.


  • IF Effective Asymmetrical Fault Current: The rms value of asymmetrical current wave, integrated over the interval of fault duration.In cases where accounting for a possible dc offset component in the fault current is desired, an equivalent value of the symmetrical current, IF, will be used in above equations for Earthing Grid Conductor Sizing For Symmetrical Fault Currents as follows:


IF=  If x Df
Where:

If  is the symmetrical fault current,
Df is the Decrement Factor.





Notes:

  1. The resulting value of IF is always larger than If,
  2. The effect of dc offsets can be neglected if the duration of the current is greater than or equal to 1 s or the X/R ratio at the fault location is less than 5.


  • Decrement Factor: An adjustment factor used in conjunction with the symmetrical ground fault current parameter in safety-oriented grounding calculations. It determines the rms equivalent of the asymmetrical current wave for a given fault duration, tf, accounting for the effect of initial dc offset and its attenuation during the fault.


  • Symmetrical Ground Fault Current: It represents the rms value of the symmetrical component in the first half-cycle of a current wave that develops after the instant of fault at time zero. For phase-to-ground faults


I f = 3 I0

Where:

If is the initial rms symmetrical ground fault current,
I0 is the rms value of zero-sequence symmetrical current that develops immediately after the instant of fault initiation, reflecting the subtransient reactances of rotating machines contributing to the fault.

Note:

Not all of the Ground Fault Current will flow back through remote earth. A portion of the Ground Fault Current may have local return paths (e.g. local generation) or there could be alternative return paths other than remote earth (e.g. overhead earth return cables, buried pipes and cables, etc). Therefore a current division factor Sf must be applied to account for the proportion of the Ground Fault Current flowing back through remote earth.

  • Symmetrical Grid Current: That portion of the symmetrical ground fault current that flows between the grounding grid and surrounding earth. It may be expressed as:


Ig = Sf x I f = Sf (3 I0)

Where:

Ig is the rms symmetrical grid current in A,
If is the rms symmetrical ground fault current in A.
Sf  is the fault current division factor.

  • Fault Current Division Factor: A factor representing the inverse of a ratio of the symmetrical fault current to that portion of the current that flows between the grounding grid and surrounding earth.


S f = Ig / I f = Ig / 3I0

Where:

Sf is the fault current division factor,
Ig is the rms symmetrical grid current in A,
If is the rms symmetrical ground fault current in A.
I0 is the zero-sequence fault current in A.

Note:

The current division factor would change during the fault duration. However, for the purposes of calculating the design value of maximum grid current and symmetrical grid, the ratio is assumed constant during the entire duration of a given fault.

  • Maximum Grid Current: It is the worst case earth fault current that would flow via the earthing grid back to remote earth., defined as follows:


IG= Df x Ig = Df x Sf x I f

Where:

IG is the maximum grid current in A,
Df is the decrement factor for the entire duration of fault tf, given in sec,
Ig is the rms symmetrical grid current in A.

  • Subtransient Reactance: Reactance of a generator at the initiation of a fault. This reactance is used in calculations of the initial symmetrical fault current. The current continuously decreases, but it is assumed to be steady at this value as a first step, lasting approximately 0.05 s after a suddenly applied fault.

  • Synchronous Reactance: Steady-state reactance of a generator during fault conditions used to calculate the steady-state fault current. The current so calculated excludes the effect of the automatic voltage regulator or governor.

  • Transient Reactance: Reactance of a generator between the subtransient and synchronous states. This reactance is used for the calculation of the symmetrical fault current during the period between the subtransient and steady states. The current decreases continuously during this period, but is assumed to be steady at this value for approximately 0.25 s.

  • X/R Ratio: Ratio of the system inductive reactance to resistance. It is indicative of the rate of decay of any dc offset. A large X/R ratio corresponds to a large time constant and a slow rate of decay.






2- Calculation Steps for Maximum Grid Current IG

The following steps are involved in determining the correct design value of maximum grid current IG for use in substation grounding calculations:

  • Step#1: Assess the type, location and Value of the worst ground fault producing the highest value of the maximum grid current IG,
  • Step#2: Determine, by computation, the fault current division factor Sf for the faults selected in step#1,
  • Step#3: Determine the corresponding values of symmetrical Short-Circuit Current If from the power systems studies or from manual calculation,
  • Step#4: 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,
  • Step#5: Apply a correction factor where appropriate to allow for future increase in fault current due to expansion of the system.







Step#1: Assess the type and location of the Worst ground fault producing the highest value of the maximum grid current IG.


A- Types of faults:

In three-phase networks a distinction is made between the following kinds of fault:

  1. Three-phase fault (I"k 3),
  2. Phase-to-phase fault clear of ground (I"k 2),
  3. Two-phase-to-earth fault (I"k 2 E; I"k E 2 E),
  4. Phase-to-earth fault (I"k 1),
  5. Double earth fault (I"k E E),



B- Determining the Worst Fault Type:

The worst fault type for a given grounding system is usually the one resulting in the highest value of the Maximum grid current IG.

Since, Ig = Sf x I f = Sf (3 I0And since the Fault Current Division Factor Sf is almost independent of the fault type,

So, the worst fault type can be defined as the one resulting in the highest zero sequence or ground fault current flow into the earth, 3I0.

As a general rule In a given location:

  • A single-line-to-ground fault will be the worst fault type if Z1 Z0 > Z22 at the point of fault,
  • A line-to-line-to-ground fault will be the worst type if Z1 Z0 < Z22 at the point of fault.


In the usual case where Z2 is assumed equal to Z1, the above comparisons reduce to:

  • A single-line-to-ground fault will be the worst fault type if Z0 > Z1,
  • A line-to-line-to-ground fault will be the worst type if Z0 < Z2.


Where:

Z1: the positive sequence equivalent system Impedance in Ω,
Z2: the negative sequence equivalent system Impedance in Ω,
Z3: the zero sequence equivalent system Impedance in Ω.



C- Location of the Worst Fault Type:

The worst fault location may be either on the high voltage side or on the low voltage side, and in either case may be either inside the substation or outside on a line, at a certain distance from the substation. There are no universal rules for the determination of the worst fault location.







Step#2: Determine, by computation, the fault current division factor Sf for the faults selected in Step#1

The split factor is used to take into account the fact that not all the fault current uses the earth as a return path. it is computed by the following equation:

S f = Ig / I f = Ig / 3I0

Where:

Sf is the fault current division factor,
Ig is the rms symmetrical grid current in A,
If is the rms symmetrical ground fault current in A.
I0 is the zero-sequence fault current in A.


Note:

The current division factor would change during the fault duration. However, for the purposes of calculating the design value of maximum grid current and symmetrical grid, the ratio is assumed constant during the entire duration of a given fault.


Sf is dependent on many parameters, some of which are:

  1. Location of the fault,
  2. Magnitude of substation ground grid impedance,
  3. Buried pipes and cables in the vicinity of or directly connected to the substation ground system,
  4. Overhead ground wires, neutrals, or other ground return paths.



Methods For Calculation Of Sf

We have methods for determining the percentage of the total fault current that flows into the earth which are:

1- Computer programs:

The most accurate method for determining the percentage of the total fault current that flows into the earth is to use a computer program such as EPRI’s SMECC, Substation Maximum Earth Current Computation which requires an involved data collection effort.

2- Detailed methods such as:

  • Dawalibi Method,
  • Meliopoulos Method.



3- Approximate methods such as:

  • Endrenyi Method,
  • Garrett and Patel Method.


In this Article, we will use the Garrett and Patel Approximate method as follows.


Garrett and Patel Approximate method

It provides a quick and simple method to estimate the current division factor that avoids the need for some of the simplifying assumptions of the other approximate methods, though the results are still only approximate. These curves, along with a few new curves and an impedance table added for this guide, are included in Annex C in IEEE 80.

This method includes:

  1. Garrett and Patel’s table of split factor equivalents,
  2. Garret and Patel’s split factor curves.


A- Garrett and Patel’s table of split factor equivalents (see part of Table C.1)


Table C.1


  • It called " Garrett and Patel’s table of split factor equivalents ",shows the equivalent transmission and distribution ground system impedance at 1Ω for 100% remote contribution with X transmission lines and Y distribution feeders.
  • The first column of impedances is for transmission line ground electrode resistance Rtg of 15 Ωand distribution feeder ground electrode resistance Rdg of 25Ω .
  • The second column of impedances is for Rtg of 100Ωand Rdg of 200Ω.
  • To determine the GPR with current splits, parallel the grid resistance with the appropriate impedance from the table and multiply this value by the total fault current.


B- Garret and Patel’s split factor Curves (see Curve C.1)






It called " Garret and Patel’s split factor curves ", the graphs are divided into the following four categories:

  • Category A: 100% remote and 0% local fault current contribution, representing typical distribution substations with delta-wye transformer, with X transmission lines and Y feeders (Figure C.1 through Figure C.16),
  • Category B: 75% remote and 25% local ground fault current contribution (Figure C.17 and Figure C.18),
  • Category C: 50% remote and 50% local ground fault current contribution (Figure C.19 and Figure C.20),
  • Category D: 25% remote and 75% local ground fault current contribution (Figure C.21 and Figure C.22).


For method of using these graphs and equivalent impedance table, limitations on this method and examples, please Refer to Annex C in IEEE 80.







Step#3: Determine the corresponding values of symmetrical Short-Circuit Current If from the power systems studies or from manual calculation


Calculation of worst fault type’s current value:

Initial symmetrical short-circuit currents are calculated with the equations in Table-1:



Table-1







Step#4: 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

The following Equation can be used to compute the decrement factor for specific X/R ratios and fault durations:





Where:

Ta is the dc offset time constant in sec,
tf is the time duration of fault in s.

Ta = (X/R )(1/ω) = (X/R)(1/2∏f)
 For 60 Hz, Ta = (X/R)(1/120π)

Where:

X/R is the X/R ratio at the fault location,
f is the system frequency (Hz).

Typical values of the decrement factor for various fault durations and X/R ratios are shown in Table-2.



Table-2


Note:

A decrement factor of 1.0 can be used for fault durations of 30 cycles or more.







Step#5: Apply a correction factor where appropriate to allow for future increase in fault current due to expansion of the system.

  • It is a common experience for maximum fault currents at a given location to increase as system capacity is added or new connections are made to the grid.
  • While an increase in system capacity will increase the maximum expected fault current IF, new connections may increase or decrease the maximum grid current IG. The future growth in a grid will be accounted by the Corrective projection factor Cp.


Cp Corrective projection factor : A factor to account for increase in fault current due to system growth during life span of grid.


Note:

Typical values of Cp assumed in design, lie in the range of 1.2 to 1.5 depending on the rate of growth of the system.







Final Equation Of The Maximum Grid Current IG

The maximum grounding grid fault current is calculated using Eq.

IG = Sf. Df. Cp. If

Where:

IG = maximum grid current,
Sf = fault current division factor,
Df = decrement factor for the entire duration of fault tf,
Cp = Corrective projection factor, if applicable,
If = rms value of symmetrical ground fault current.







Example:

A substation S/S-132/11kV, 1X30/40MVA with the following data:

  • Positive sequence impedance at the fault location Z1 =2.661 Ω,
  • Ratio of zero-sequence impedance to positive sequence lZ0/Z1l=3,
  • 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.


Calculate the maximum grounding grid fault current IG.


Solution:


Step#1: As a general rule in a given location and in the usual case where Z2 is assumed equal to Z1 and since lZ0/Z1l=3, so Z0 > Z1. So, A single-line-to-ground fault will be the worst fault type.

Step#2: the fault current division factor Sf is given = 0.6

Step#3: Determine the corresponding values of symmetrical short-circuit current by using the formulas of Table-1 in above:

Firstly, calculate the Symmetrical three phase short-circuit current (r.m.s.) Ik3




Where:
Nominal system voltage Un=132 kV

Secondly, calculate the Single phase to earth fault current Ik1 noting that Z2 is assumed equal to Z1




Step#4: 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#5: 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 18.9 Ka = 15.62 KA






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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