SlideShare a Scribd company logo
Grounding Simulation
using FEA Software
Camilo Chaves
Electrical Engineer and Physicist
https://de.linkedin.com/pub/camilo-chaves/11/323/a72
Ground modeling in Low Frequencies
Model of a filamentar conductor on the ground per unit length
For low frequencies
• For low frequencies, the principal parameter to be considered is the conductivity of the soil
Consider a copper semi-spherical electrode
-Consider also a homogeneous soil (same resistivity in all directions)
-The layers drawn in the soil are the voltage equipotentials, produced when the current passes through
each layer of soil.
-The total current in each surface layer is the same, but the current densities gets smaller when the
probe gets away from the current injection point (J= Current I /Surface Area of the layers of soil)
-The Ground Diference of Potential is therefore higher in the proximity of the conductor (Higher J)
Potential profile on the soil for the semi-sphere
The higher Rt , the
higher Vt for the
same current I
Potential
Radius Distance (m)
Calculus of the Surface Potential Distribution
Rt depends only on the resistivity and geometric shape!
Ground Resistance Formulas for simple types of electrodes
Semi-Spherical Electrode
Error of 0.01% from
FEA Simulation
Calculated RESULTS
Radius of 1m, ρ = 500 Ω.m
Rtot = 79.57 Ω
FEA RESULTS
Rtot = 74.26 Ω + 5.3 Ω (R Adj.)
Rtot = 79.56 Ω
R Adjust Calculation
Size of the modeled soil = 15m radius
R adjust = R of a semi-sphere of 15m of radius
R = 5.3 Ω
All FEA simulations were done
with a soil model of 15m of radius
For any electrode configuration, in a homogeneous soil , after 10-15 times the electrode size, the equipotentials
behave like if they were produced by a semi-spherical electrode.
When the equipotentials start to become semi-spherical, from this point on, the rest of the soil resistance can be
computed using the semi-spherical electrode formula, using the radius from this point in the formula.
Error of 0.01% from
FEA Simulation
Current of 1A injected
Ground Resistance Formulas for simple types of electrodes
Horizontal Electrode, Length L, burried
at a distance d from the surface, radius r
Calculated RESULTS
L=3m, ρ = 500 Ω.m, d=0.5m,
radius of the rod r = 0.008m
Rtot = 186.35 Ω
FEA RESULTS
Rtot = 172.23Ω + 5.3 Ω (R Adj.)
Rtot = 177.53 Ω
Vertical Electrode, Length L,
radius a
Calculated RESULTS
L=3m, ρ = 500 Ω.m
radius of the rod a = 0.008m
Rtot = 167.46 Ω
FEA RESULTS
Rtot = 160.5 Ω + 5.3 Ω (R Adj.)
Rtot = 165.8 Ω
Error of 4.96% from
FEA Simulation
Error of 1% from
FEA Simulation
For a 100V on the electrode
on the ground
Current of 1A injected
Horizontal ring at distance h
from the surface, radius r
Vertical square
Same resistance of a ring with same area,
burried at the same distance (d) from the
surface
Ground Resistance Formulas for simple types of electrodes
Calculated RESULTS
Radius r=1m, ρ = 500 Ω.m, h=1m,
diam. of cable (d)= 1.6e-2 m
Rtot = 105.04 Ω
FEA RESULTS
Rtot = 98.77 Ω + 5.3 Ω (R Adj.)
Rtot = 104.07 Ω
Error of 0.93% from
FEA Simulation
Calculated RESULTS
Radius r=1m, ρ = 500 Ω.m, h=2m
Rtot = 93.17 Ω
FEA RESULTS
Rtot = 92.4 Ω + 5.3 Ω (R Adj.)
Rtot = 97.7 Ω
Error of 4.63% from
FEA Simulation
100V on the
electrode
Vertical ring at distance h from the surface.
h is taken from the center of the ring
Ground Resistance Formulas for simple types of electrodes
Sphere (d≈r)
Calculated RESULTS
Radius r=1m, ρ = 500 Ω.m, d=2m,
Rtot = 79.57 Ω
FEA RESULTS
Rtot = 44.26 Ω + 5.3 Ω (R Adj.)
Rtot = 49.56 Ω
Error of 60.55% from
FEA Simulation
Ground Resistance Formulas for simple types of electrodes
Sphere (d>>r)
Calculated RESULTS
Radius r=1m, ρ = 500 Ω.m, d=10m,
Rtot = 47.74 Ω
FEA RESULTS
Rtot = 35.16 Ω + 5.3 Ω (R Adj.)
Rtot = 40.46 Ω
Error of 17.99% from
FEA Simulation
Condition to use the formula: d>>r
Comparative Analysis for Simple electrodes
Electrode Configuration
Rt(Ω)
Formula
FEA Rt(Ω)
Simulation
Adjustm.
Ω
Rt (Ω)
FEA final
% error
Horizontal Electrode of Length L, Diameter D
burried at distance h
186.35 172.23 5.3 177.53 4.96%
Vertical Electrode with Length L, Diameter D 167.46 160.5 5.3 165.8 1%
Horizontal Ring at depth R with Radius R 105.04 98.77 5.3 104.07 0.93%
Vertical Ring at depth 2xR with Radius R 93.17 92.4 5.3 97.7 4.63%
Semi-Sphere with Radius R at the surface 79.57 74.26 5.3 79.56 0.01%
Sphere at Depth R with Radius 10xR (use only if d>>>r) 47.74 35.16 5.3 40.46 17.99%
Parameters for the formulas
=500 Ω.m , L= 3m, D= 1.6cm, h = 50cm, R= 1m, Size of the modeled soil: 30m of diameter.
The size of the soil implies an automatic adjustment of the FEA resistance. The final simulated resistance must be
the FEA resistance plus 5.3Ω, which is the resistance of a semi-spheric electrode of 15m of radius.
From the results the conclusion is clear. The bigger the surface area , the lesser is the resistance.
Ground Resistance Formulas for multiple electrodes
4 Point Star with Length L, burried at
depth d, in a horizontal plane. Radius of
the electrode is a in the formula
Calculated RESULTS
Length r=3m, ρ = 500 Ω.m, d=0.5m, a=0.008m
Rtot = 72.71 Ω
FEA RESULTS
Rtot = 114.64 Ω + 5.3 Ω (R Adj.)
Rtot = 119.94 Ω
100V on the electrode
Error of 39.38% from
FEA Simulation
Could the resistance be approximated by 2 horizontal rods in paralell ? Not exactly
Calculated RESULTS
L=3m, ρ = 500 Ω.m, d=0.5m,
radius of the rod r = 0.008m
Rtot = 186.35 Ω
Best result that could be achieved
for 2 horizontal rods (R in paralell)
Rtot = 186.35 Ω /2 = 93.17Ω
Considering the rods are out of the
sphere of influence of each other
This result can only be achieved if the 2 rods are sufficiently apart from each other! So, the formula of the 4 point star
must be wrong because it has computed 72.71 Ω. This value is lesser than what could be achieved with 2 rods. It must be
wrong or it considers that it is correct only with some specific parameters. Let’s say if d is >>>> L (let’s run the simulation)
Ground Resistance Formulas for multiple electrodes
Simulating the resistance of 2 horizontal rods in
parallel, sufficiently apart from each other
Calculated RESULTS for 1 rod
L=3m, ρ = 500 Ω.m, d=0.5m,
radius of the rod r = 0.008m
Rtot = 186.35 Ω
Best calculated result that could be
achieved for 2 horizontal rods
Rtot = 186.35 Ω /2 = 93.17Ω
Considering the rods are out of the
sphere of influence of each other
FEA RESULTS for 2 Rods
Rtot = 87.19 Ω + 5.3 Ω (R Adj.)
Rtot = 92.49 Ω
2 rods out of the sphere of influence of each other
So, the 2 rods in
parallel agrees
with the
simulation. But
again, what about
the 4 point star if
d>>>L?
Error of 0.73% from
FEA Simulation
1 rod formula
Ground Resistance Formulas for multiple electrodes
4 Point Star Simulation when d=10m and L=3m
FEA RESULTS for a 4 Point Star
Rtot = 88.53 Ω + 5.3 Ω (R Adj.)
Rtot = 93.83 Ω
4 Point Star when d>>>L
Calculated RESULTS when d>>>L
Length L=3m, ρ = 500 Ω.m, d=10m, a=0.008
Rtot = 7.909 Ω
It is better to approximate the value using
two rods in parallel until a better formula for
a 4 point star is found. If you know it, please
send it to me.
Interesting result!
It almost reached the minimum
allowed value for 2 rods in
paralell, on the last slide
(as it should be!)
Error of 91.57% from
FEA Simulation
Ground Resistance Formulas for multiple electrodes
Conclusion for 4 point star electrode configuration
• Close to the surface, the formula in comparison to FEA
presented and error of 39.38%. When d>>>L, the formula
presented an error of 91.57% from FEA
• Prior formulas of simple electrodes achieved close proximity to
FEA, within an error of 1%, so a condition was set in order for
them to be used, which is, install the electrodes sufficiently
apart from each other.
• The calculated results and the FEA results for 2 electrodes apart
from each other differs has only 0.73% of error, thus confirming
that for simple electrodes, the formulas can be used.
• A FEA analysis of a deep 4 point star (d>>>L) showed that its
value differs from the value of 2 electrodes for only 1.44%. As it
should be, because the minimum resistance is to be found were
the 2 horizontal electrodes are set far apart, off the sphere of
influence of each other.
• Conclusion: For the parameters chosen, the formula has failed
to return a value closed to a simulated one.
Ground Resistance Formulas for multiple electrodes
Calculated RESULTS
n=4, ρ = 500 Ω.m, d=0.5m,
a=0.008m,L=0.5m
Rtot = 217.09 Ω
FEA RESULTS (radius of circle 3.18m)
Rtot = 37.72 Ω + 5.3 Ω (R Adj.)
Rtot = 43.02 Ω
Error of 404.6% from
FEA Simulation
N vertical rods with Length L in a circle
Restriction: S >> L
Ground Resistance Formulas for multiple electrodes
FEA RESULTS (radius of circle 3.18m)
Rtot = 37.72 Ω + 5.3 Ω (R Adj.)
Rtot = 43.02 Ω
N vertical rods with Length L in a circle
Restriction: S >> L
Could the final resistance be approximated by the equivalent resistance
of a horizontal circle of 3.18m in parallel with the resistance of 4 rods ?
1 vertical rod of L=0.5m,
a=0.008m, ρ = 500 Ω.m
Rrod= 719.61 Ω
4 rods out of the sphere of
influence of each other
Rrods= 719.61/4=179.9 Ω
1 horizontal ring, of
h=0.5m, d=1.6e-2m,
ρ = 500 Ω.m , r=3.18m
Rring = 45 Ω
Calculated RESULTS
Rtot=(1/Rring+1/Rrods)^-1
Rtot= 35.99 Ω
Error of 16.34% from
FEA Simulation
This is the best value that could ever be
achieved in this configuration!
The diference is because of the mutual
resistance between the elements
Alternative method for calculation
Ground Resistance Formulas for multiple electrodes
Conclusion for N vertical rods with Length L in a circle
• Close to the surface, the formula in comparison to FEA
presented and error of 404.6%.
• Since S >>> L, and L<< Perimeter of the ring, an alternative
method was applied. The calculated result achieved a close
proximity to the FEA Simulation within an error of 16.4%
• Conclusion:
• For the parameters chosen, the formula has failed to return a
value closed to a simulated one (an alternative method was
provided within certain restrictions of use)
Ground Resistance Formulas for multiple electrodes
3 Rods in a triangular shape
(4 steps to calculation)
1
2
3
4
Calculated RESULTS
S=3m, L=3m, d=0.008m,
ρ = 500 Ω.m
Rt = 73.5 Ω FEA RESULTS (S=3)
Rt = 48.91 Ω+5.3 Ω
Rt=54.21 Ω
Error of 35.58% from
FEA Simulation
The elements from this
configuration are too close in
order to estimate the minimum
resistance using paralell
resistances.
Let’s try S=50m and L=3
Ground Resistance Formulas for multiple electrodes
3 Rods in a triangular shape
(4 steps to calculation)
4
Graph Parameters
L=3m, d=0.008m, ρ = 500 Ω.m
FEA Results (S=10)
Rt=23.62 Ω+5.3 Ω
Rt=28.92 Ω
Error of111% from
FEA Simulation
But now, the elements are
sufficiently apart for us to
try an alternative method
Ground Resistance Formulas for multiple electrodes
3 Rods in a triangular shape
(4 steps to calculation)
FEA Results (S=10)
Rt=23.62 Ω+5.3 Ω
Rt=28.92 ΩAlternative Method using same
parameters, but diferent method
3 vertical rods with L=3m in parallel:
Rrods= 55.82 Ω
3 horizontal electrodes with S=10m (S is L in the formula) in parallel:
Rhoriz = 75.06 Ω
Final equivalent Resistance
Rt=(1/Rrods+1/Rhoriz)^-1
Rt=32.01 Ω
Again, when the elements are close to be off the sphere of influence of
each other, the global resistance can be approximated by simple
electrodes configuration in paralell
Error of 10.7%
from FEA
Simulation
Ground Resistance Formulas for multiple electrodes
Conclusion for 3 Rods in a triangular shape
• Close to the surface, the formula in comparison to FEA
presented and error of 35.58%, considering S=3m and
L=3m.
• When S=10m, the error increased to 111%
• In the alternative method, the same calculation was
performed using well known formulas for simple
electrodes, and error reduced to 10.7%
• Conclusion:
• For the parameters chosen, the formula has failed to return a
value closed to a simulated one (an alternative method was
provided within certain restrictions of use)
Ground Resistance Formulas for multiple electrodes
Error of 209.1% from
FEA Simulation FEA RESULTS
Rtot = 24.36 + 5.3(Adj)= 29.66Ω
Rods with length L, radius a, burried
depth d, in line. Restriction: s >> L
Calculated RESULTS for 3 rods in line (n=3) in a soil with 500 Ω.m
L=3m (length of the rod), S=6m, a=0.008m, d=0.5m (depth)
Rtot = 91.67 Ω
Ground Resistance Formulas for multiple electrodes
FEA RESULTS
Rtot = 24.36 + 5.3(Adj)= 29.66Ω
Calculated Results for 3 rods in parallel
L=3m, a=0.008m, ρ = 500 Ω.m
Rtot = 167.46 Ω/3 = 55.82 Ω
Calculated Results for 1 horizontal electrode of 12m
L=12m, r=0.008m, d=0.5m, ρ = 500 Ω.m
Rtot = 64.97 Ω
Calculated Equivalent
Resistance of the configuration
Rt=(1/Rrods+1/Rhor)^-1
Rt=30.02 Ω
Error of 1.21% from
FEA Simulation
Alternative method for calculation
Ground Resistance Formulas for multiple electrodes
Conclusion for 3 Rods in line
• Close to the surface, the formula in comparison to FEA
presented and error of 209.1%
• In the alternative method, the same calculation was
performed using well known formulas for simple
electrodes, and error reduced to 1.21%
• Conclusion:
• For the parameters chosen, the formula has failed to return a
value closed to a simulated one (an alternative method was
provided within certain restrictions of use)
Ground Resistance Formulas for multiple electrodes
Simple Mesh without Rods
FEA SIMULATION
A Potencial of 100V was set for the mesh
Rtot = 37.83 + 5.3(Adj)=43.13 Ω
Error of 38.48% from
FEA Simulation
Error of 24.87% from
FEA Simulation
Ground Resistance Formulas for multiple electrodes
Conclusion for Simple Mesh without Rods
• Close to the surface, the formula in
comparison to FEA presented and error of
24.87%
• No alternative method was used because in a
mesh the mutual resistance is not negligible.
• Conclusion:
• More simulations must be done in order to
determine if this formula can be used within the
same range of error.
Ground Resistance Formulas for multiple electrodes
Mesh with Rods
Error of 24.87% from
FEA Simulation
This is the
Mesh without
rods formula
Ground Resistance Formulas for
multiple electrodes
Mesh with Rods
FEA RESULTS
Rtot = 20.55 + 5.3(Adj)= 25.83Ω
Error of 102.94%
from FEA Simulation
Error of 1% from FEA
Simulation
Error of 27% from
FEA Simulation
Ground Resistance Formulas for multiple electrodes
Conclusion for Simple Mesh with Rods
• Close to the surface, the formula in
comparison to FEA presented and error of
27% using Visacro formula.
• No alternative method was used because in a
mesh the mutual resistance is not negligible.
• Conclusion:
• More simulations must be done in order to
determine if this formula can be used within the
same range of error.
Final Conclusion
 For simple electrodes, all the expressions presented agree with FEA.
 For complex electrodes, none of the expressions presented, agree with FEA,
with exception of Mesh without rods, and Mesh with rods using Visacros
expression, that has an error of 27%.
 Subsequent studies will determine the precise expression to take account the
mutual resistance between complex electrodes, using FEA as tool to model
this equations.
Thank you for your time
 Please, let me know if you have any other expressions for the grounding
electrodes configurations. I will test them and insert them in another
presentation
 Any errors you found, incorrect expressions you find, wrong calculations,
suggestions that you want to share, please, leave a comment on my post.
 https://de.linkedin.com/pub/camilo-chaves/11/323/a72

More Related Content

What's hot

Lecture 6
Lecture 6Lecture 6
Lecture 6
Forward2025
 
Electrical formulas
Electrical formulasElectrical formulas
Electrical formulas
ramkumar198603
 
Topic 2a ac_circuits_analysis
Topic 2a ac_circuits_analysisTopic 2a ac_circuits_analysis
Topic 2a ac_circuits_analysis
Gabriel O'Brien
 
Electrical formulas
Electrical formulasElectrical formulas
Electrical formulas
Rasheeth Ptech
 
Transmission line By Lipun
Transmission line By LipunTransmission line By Lipun
Transmission line By Lipun
Nanigopal Jena
 
519 transmission line theory
519 transmission line theory519 transmission line theory
519 transmission line theory
chanjee
 
ECNG 6509 Switchgear Technology
ECNG 6509    Switchgear TechnologyECNG 6509    Switchgear Technology
ECNG 6509 Switchgear Technology
Chandrabhan Sharma
 
7 slides
7 slides7 slides
7 slides
Gopi Saiteja
 
Rectangular waveguides
Rectangular waveguidesRectangular waveguides
Rectangular waveguides
khan yaseen
 
TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks
 TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks
TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks
Dr.SHANTHI K.G
 
Chap2 s11b
Chap2 s11bChap2 s11b
Chap2 s11b
Ibrahim Khleifat
 
Lecture Notes: EEEC6430310 Electromagnetic Fields And Waves - Transmission Line
Lecture Notes:  EEEC6430310 Electromagnetic Fields And Waves - Transmission LineLecture Notes:  EEEC6430310 Electromagnetic Fields And Waves - Transmission Line
Lecture Notes: EEEC6430310 Electromagnetic Fields And Waves - Transmission Line
AIMST University
 
Topic 2b ac_circuits_analysis
Topic 2b ac_circuits_analysisTopic 2b ac_circuits_analysis
Topic 2b ac_circuits_analysis
Gabriel O'Brien
 
Performance Analysis of Actual Step and Mesh Voltage of Substation Grounding ...
Performance Analysis of Actual Step and Mesh Voltage of Substation Grounding ...Performance Analysis of Actual Step and Mesh Voltage of Substation Grounding ...
Performance Analysis of Actual Step and Mesh Voltage of Substation Grounding ...
Editor IJCATR
 
transmission line theory prp
transmission line theory prptransmission line theory prp
transmission line theory prp
Dr. Pravin Prajapati
 
Impedance Matching
Impedance MatchingImpedance Matching
Impedance Matching
Yong Heui Cho
 
Lecture 5
Lecture 5Lecture 5
Lecture 5
Forward2025
 
EC6503 TLWG - Types of Transmission Lines
EC6503 TLWG - Types of Transmission LinesEC6503 TLWG - Types of Transmission Lines
EC6503 TLWG - Types of Transmission Lines
chitrarengasamy
 
Impedance Matching
Impedance MatchingImpedance Matching
Impedance Matching
Yong Heui Cho
 
Transmission Lines
Transmission LinesTransmission Lines
Transmission Lines
spmtsairam
 

What's hot (20)

Lecture 6
Lecture 6Lecture 6
Lecture 6
 
Electrical formulas
Electrical formulasElectrical formulas
Electrical formulas
 
Topic 2a ac_circuits_analysis
Topic 2a ac_circuits_analysisTopic 2a ac_circuits_analysis
Topic 2a ac_circuits_analysis
 
Electrical formulas
Electrical formulasElectrical formulas
Electrical formulas
 
Transmission line By Lipun
Transmission line By LipunTransmission line By Lipun
Transmission line By Lipun
 
519 transmission line theory
519 transmission line theory519 transmission line theory
519 transmission line theory
 
ECNG 6509 Switchgear Technology
ECNG 6509    Switchgear TechnologyECNG 6509    Switchgear Technology
ECNG 6509 Switchgear Technology
 
7 slides
7 slides7 slides
7 slides
 
Rectangular waveguides
Rectangular waveguidesRectangular waveguides
Rectangular waveguides
 
TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks
 TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks
TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks
 
Chap2 s11b
Chap2 s11bChap2 s11b
Chap2 s11b
 
Lecture Notes: EEEC6430310 Electromagnetic Fields And Waves - Transmission Line
Lecture Notes:  EEEC6430310 Electromagnetic Fields And Waves - Transmission LineLecture Notes:  EEEC6430310 Electromagnetic Fields And Waves - Transmission Line
Lecture Notes: EEEC6430310 Electromagnetic Fields And Waves - Transmission Line
 
Topic 2b ac_circuits_analysis
Topic 2b ac_circuits_analysisTopic 2b ac_circuits_analysis
Topic 2b ac_circuits_analysis
 
Performance Analysis of Actual Step and Mesh Voltage of Substation Grounding ...
Performance Analysis of Actual Step and Mesh Voltage of Substation Grounding ...Performance Analysis of Actual Step and Mesh Voltage of Substation Grounding ...
Performance Analysis of Actual Step and Mesh Voltage of Substation Grounding ...
 
transmission line theory prp
transmission line theory prptransmission line theory prp
transmission line theory prp
 
Impedance Matching
Impedance MatchingImpedance Matching
Impedance Matching
 
Lecture 5
Lecture 5Lecture 5
Lecture 5
 
EC6503 TLWG - Types of Transmission Lines
EC6503 TLWG - Types of Transmission LinesEC6503 TLWG - Types of Transmission Lines
EC6503 TLWG - Types of Transmission Lines
 
Impedance Matching
Impedance MatchingImpedance Matching
Impedance Matching
 
Transmission Lines
Transmission LinesTransmission Lines
Transmission Lines
 

Viewers also liked

Curso de aterramento elétrico
Curso de aterramento elétricoCurso de aterramento elétrico
Curso de aterramento elétrico
Katia Ribeiro
 
Aterramento rápido
Aterramento rápidoAterramento rápido
Aterramento rápido
Camilo Chaves
 
ATERRAMENTO & SPDA - Sistemas de Proteção contra Descargas Atmosféricas.
ATERRAMENTO & SPDA - Sistemas de Proteção contra Descargas Atmosféricas.ATERRAMENTO & SPDA - Sistemas de Proteção contra Descargas Atmosféricas.
ATERRAMENTO & SPDA - Sistemas de Proteção contra Descargas Atmosféricas.
Jean Paulo Mendes Alves
 
Para raios
Para raiosPara raios
Para raios
Gilramalho
 
Guia de aterramento
Guia de aterramentoGuia de aterramento
Guia de aterramento
Aldarci Marques da Silva
 
Sistemas de Proteção Contra Descargas Atmosféricas
Sistemas de Proteção Contra Descargas AtmosféricasSistemas de Proteção Contra Descargas Atmosféricas
Sistemas de Proteção Contra Descargas Atmosféricas
Edhy Torres
 

Viewers also liked (6)

Curso de aterramento elétrico
Curso de aterramento elétricoCurso de aterramento elétrico
Curso de aterramento elétrico
 
Aterramento rápido
Aterramento rápidoAterramento rápido
Aterramento rápido
 
ATERRAMENTO & SPDA - Sistemas de Proteção contra Descargas Atmosféricas.
ATERRAMENTO & SPDA - Sistemas de Proteção contra Descargas Atmosféricas.ATERRAMENTO & SPDA - Sistemas de Proteção contra Descargas Atmosféricas.
ATERRAMENTO & SPDA - Sistemas de Proteção contra Descargas Atmosféricas.
 
Para raios
Para raiosPara raios
Para raios
 
Guia de aterramento
Guia de aterramentoGuia de aterramento
Guia de aterramento
 
Sistemas de Proteção Contra Descargas Atmosféricas
Sistemas de Proteção Contra Descargas AtmosféricasSistemas de Proteção Contra Descargas Atmosféricas
Sistemas de Proteção Contra Descargas Atmosféricas
 

Similar to Grounding simulation slides

713_Transmission_Lines-F15.ppt
713_Transmission_Lines-F15.ppt713_Transmission_Lines-F15.ppt
713_Transmission_Lines-F15.ppt
DOAFCLF
 
713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt
yash919530
 
713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt
HalarMustafa1
 
713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt
AnandKumar689627
 
Earthing Types and role in power substation.ppt
Earthing Types and role in power substation.pptEarthing Types and role in power substation.ppt
Earthing Types and role in power substation.ppt
wazakify
 
ECGR4121_P2_LaPlant_J-edited
ECGR4121_P2_LaPlant_J-editedECGR4121_P2_LaPlant_J-edited
ECGR4121_P2_LaPlant_J-edited
Joshua LaPlant
 
N 5-antenna fandamentals-f13
N 5-antenna fandamentals-f13N 5-antenna fandamentals-f13
N 5-antenna fandamentals-f13
15010192
 
Elestrical Conduction
Elestrical ConductionElestrical Conduction
Elestrical Conduction
ianalaba06
 
Transmission lines, Waveguide, Antennas
Transmission lines, Waveguide, AntennasTransmission lines, Waveguide, Antennas
Transmission lines, Waveguide, Antennas
Kumar Pawar
 
Fault location for transmission line
Fault location  for transmission lineFault location  for transmission line
Fault location for transmission line
mohammed shareef
 
Antenna PARAMETERS
Antenna PARAMETERSAntenna PARAMETERS
Antenna PARAMETERS
AJAL A J
 
Ohm law i
Ohm law iOhm law i
Ohm law i
umammuhammad27
 
Polytechnic of namibia ...
Polytechnic of namibia                                                       ...Polytechnic of namibia                                                       ...
Polytechnic of namibia ...
Evandro Conceicao
 
Tunnel_FET_-_Learning_Module_Draft.pptx
Tunnel_FET_-_Learning_Module_Draft.pptxTunnel_FET_-_Learning_Module_Draft.pptx
Tunnel_FET_-_Learning_Module_Draft.pptx
SivaGovind2
 
1 ECE 6340 Fall 2013 Homework 8 Assignment.docx
 1 ECE 6340 Fall 2013  Homework 8 Assignment.docx 1 ECE 6340 Fall 2013  Homework 8 Assignment.docx
1 ECE 6340 Fall 2013 Homework 8 Assignment.docx
joyjonna282
 
Currentelectricity
CurrentelectricityCurrentelectricity
Currentelectricity
Conferat Conferat
 
Polytechnic of namibia ...
Polytechnic of namibia                                                       ...Polytechnic of namibia                                                       ...
Polytechnic of namibia ...
Evandro Conceicao
 
L25 resonance
L25 resonanceL25 resonance
L25 resonance
Satyakam
 
Tunnel_FET_-_Learning_Module_Draft.pptx
Tunnel_FET_-_Learning_Module_Draft.pptxTunnel_FET_-_Learning_Module_Draft.pptx
Tunnel_FET_-_Learning_Module_Draft.pptx
TPOVITSKARIMNAGAR
 
236793460 ee6361-electric-circuit-lab-docx
236793460 ee6361-electric-circuit-lab-docx236793460 ee6361-electric-circuit-lab-docx
236793460 ee6361-electric-circuit-lab-docx
homeworkping3
 

Similar to Grounding simulation slides (20)

713_Transmission_Lines-F15.ppt
713_Transmission_Lines-F15.ppt713_Transmission_Lines-F15.ppt
713_Transmission_Lines-F15.ppt
 
713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt
 
713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt
 
713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt713_Transmission_Lines-F21.ppt
713_Transmission_Lines-F21.ppt
 
Earthing Types and role in power substation.ppt
Earthing Types and role in power substation.pptEarthing Types and role in power substation.ppt
Earthing Types and role in power substation.ppt
 
ECGR4121_P2_LaPlant_J-edited
ECGR4121_P2_LaPlant_J-editedECGR4121_P2_LaPlant_J-edited
ECGR4121_P2_LaPlant_J-edited
 
N 5-antenna fandamentals-f13
N 5-antenna fandamentals-f13N 5-antenna fandamentals-f13
N 5-antenna fandamentals-f13
 
Elestrical Conduction
Elestrical ConductionElestrical Conduction
Elestrical Conduction
 
Transmission lines, Waveguide, Antennas
Transmission lines, Waveguide, AntennasTransmission lines, Waveguide, Antennas
Transmission lines, Waveguide, Antennas
 
Fault location for transmission line
Fault location  for transmission lineFault location  for transmission line
Fault location for transmission line
 
Antenna PARAMETERS
Antenna PARAMETERSAntenna PARAMETERS
Antenna PARAMETERS
 
Ohm law i
Ohm law iOhm law i
Ohm law i
 
Polytechnic of namibia ...
Polytechnic of namibia                                                       ...Polytechnic of namibia                                                       ...
Polytechnic of namibia ...
 
Tunnel_FET_-_Learning_Module_Draft.pptx
Tunnel_FET_-_Learning_Module_Draft.pptxTunnel_FET_-_Learning_Module_Draft.pptx
Tunnel_FET_-_Learning_Module_Draft.pptx
 
1 ECE 6340 Fall 2013 Homework 8 Assignment.docx
 1 ECE 6340 Fall 2013  Homework 8 Assignment.docx 1 ECE 6340 Fall 2013  Homework 8 Assignment.docx
1 ECE 6340 Fall 2013 Homework 8 Assignment.docx
 
Currentelectricity
CurrentelectricityCurrentelectricity
Currentelectricity
 
Polytechnic of namibia ...
Polytechnic of namibia                                                       ...Polytechnic of namibia                                                       ...
Polytechnic of namibia ...
 
L25 resonance
L25 resonanceL25 resonance
L25 resonance
 
Tunnel_FET_-_Learning_Module_Draft.pptx
Tunnel_FET_-_Learning_Module_Draft.pptxTunnel_FET_-_Learning_Module_Draft.pptx
Tunnel_FET_-_Learning_Module_Draft.pptx
 
236793460 ee6361-electric-circuit-lab-docx
236793460 ee6361-electric-circuit-lab-docx236793460 ee6361-electric-circuit-lab-docx
236793460 ee6361-electric-circuit-lab-docx
 

Recently uploaded

Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
shadow0702a
 
IEEE Aerospace and Electronic Systems Society as a Graduate Student Member
IEEE Aerospace and Electronic Systems Society as a Graduate Student MemberIEEE Aerospace and Electronic Systems Society as a Graduate Student Member
IEEE Aerospace and Electronic Systems Society as a Graduate Student Member
VICTOR MAESTRE RAMIREZ
 
Engineering Drawings Lecture Detail Drawings 2014.pdf
Engineering Drawings Lecture Detail Drawings 2014.pdfEngineering Drawings Lecture Detail Drawings 2014.pdf
Engineering Drawings Lecture Detail Drawings 2014.pdf
abbyasa1014
 
Null Bangalore | Pentesters Approach to AWS IAM
Null Bangalore | Pentesters Approach to AWS IAMNull Bangalore | Pentesters Approach to AWS IAM
Null Bangalore | Pentesters Approach to AWS IAM
Divyanshu
 
Applications of artificial Intelligence in Mechanical Engineering.pdf
Applications of artificial Intelligence in Mechanical Engineering.pdfApplications of artificial Intelligence in Mechanical Engineering.pdf
Applications of artificial Intelligence in Mechanical Engineering.pdf
Atif Razi
 
Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...
bijceesjournal
 
An improved modulation technique suitable for a three level flying capacitor ...
An improved modulation technique suitable for a three level flying capacitor ...An improved modulation technique suitable for a three level flying capacitor ...
An improved modulation technique suitable for a three level flying capacitor ...
IJECEIAES
 
Seminar on Distillation study-mafia.pptx
Seminar on Distillation study-mafia.pptxSeminar on Distillation study-mafia.pptx
Seminar on Distillation study-mafia.pptx
Madan Karki
 
Certificates - Mahmoud Mohamed Moursi Ahmed
Certificates - Mahmoud Mohamed Moursi AhmedCertificates - Mahmoud Mohamed Moursi Ahmed
Certificates - Mahmoud Mohamed Moursi Ahmed
Mahmoud Morsy
 
132/33KV substation case study Presentation
132/33KV substation case study Presentation132/33KV substation case study Presentation
132/33KV substation case study Presentation
kandramariana6
 
22CYT12-Unit-V-E Waste and its Management.ppt
22CYT12-Unit-V-E Waste and its Management.ppt22CYT12-Unit-V-E Waste and its Management.ppt
22CYT12-Unit-V-E Waste and its Management.ppt
KrishnaveniKrishnara1
 
cnn.pptx Convolutional neural network used for image classication
cnn.pptx Convolutional neural network used for image classicationcnn.pptx Convolutional neural network used for image classication
cnn.pptx Convolutional neural network used for image classication
SakkaravarthiShanmug
 
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.pptUnit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
KrishnaveniKrishnara1
 
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
171ticu
 
Mechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering on AAI Summer Training Report-003.pdfMechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering on AAI Summer Training Report-003.pdf
21UME003TUSHARDEB
 
Data Control Language.pptx Data Control Language.pptx
Data Control Language.pptx Data Control Language.pptxData Control Language.pptx Data Control Language.pptx
Data Control Language.pptx Data Control Language.pptx
ramrag33
 
Curve Fitting in Numerical Methods Regression
Curve Fitting in Numerical Methods RegressionCurve Fitting in Numerical Methods Regression
Curve Fitting in Numerical Methods Regression
Nada Hikmah
 
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
学校原版美国波士顿大学毕业证学历学位证书原版一模一样学校原版美国波士顿大学毕业证学历学位证书原版一模一样
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
171ticu
 
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURSCompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
RamonNovais6
 
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
insn4465
 

Recently uploaded (20)

Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
 
IEEE Aerospace and Electronic Systems Society as a Graduate Student Member
IEEE Aerospace and Electronic Systems Society as a Graduate Student MemberIEEE Aerospace and Electronic Systems Society as a Graduate Student Member
IEEE Aerospace and Electronic Systems Society as a Graduate Student Member
 
Engineering Drawings Lecture Detail Drawings 2014.pdf
Engineering Drawings Lecture Detail Drawings 2014.pdfEngineering Drawings Lecture Detail Drawings 2014.pdf
Engineering Drawings Lecture Detail Drawings 2014.pdf
 
Null Bangalore | Pentesters Approach to AWS IAM
Null Bangalore | Pentesters Approach to AWS IAMNull Bangalore | Pentesters Approach to AWS IAM
Null Bangalore | Pentesters Approach to AWS IAM
 
Applications of artificial Intelligence in Mechanical Engineering.pdf
Applications of artificial Intelligence in Mechanical Engineering.pdfApplications of artificial Intelligence in Mechanical Engineering.pdf
Applications of artificial Intelligence in Mechanical Engineering.pdf
 
Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...
 
An improved modulation technique suitable for a three level flying capacitor ...
An improved modulation technique suitable for a three level flying capacitor ...An improved modulation technique suitable for a three level flying capacitor ...
An improved modulation technique suitable for a three level flying capacitor ...
 
Seminar on Distillation study-mafia.pptx
Seminar on Distillation study-mafia.pptxSeminar on Distillation study-mafia.pptx
Seminar on Distillation study-mafia.pptx
 
Certificates - Mahmoud Mohamed Moursi Ahmed
Certificates - Mahmoud Mohamed Moursi AhmedCertificates - Mahmoud Mohamed Moursi Ahmed
Certificates - Mahmoud Mohamed Moursi Ahmed
 
132/33KV substation case study Presentation
132/33KV substation case study Presentation132/33KV substation case study Presentation
132/33KV substation case study Presentation
 
22CYT12-Unit-V-E Waste and its Management.ppt
22CYT12-Unit-V-E Waste and its Management.ppt22CYT12-Unit-V-E Waste and its Management.ppt
22CYT12-Unit-V-E Waste and its Management.ppt
 
cnn.pptx Convolutional neural network used for image classication
cnn.pptx Convolutional neural network used for image classicationcnn.pptx Convolutional neural network used for image classication
cnn.pptx Convolutional neural network used for image classication
 
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.pptUnit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
 
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
 
Mechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering on AAI Summer Training Report-003.pdfMechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering on AAI Summer Training Report-003.pdf
 
Data Control Language.pptx Data Control Language.pptx
Data Control Language.pptx Data Control Language.pptxData Control Language.pptx Data Control Language.pptx
Data Control Language.pptx Data Control Language.pptx
 
Curve Fitting in Numerical Methods Regression
Curve Fitting in Numerical Methods RegressionCurve Fitting in Numerical Methods Regression
Curve Fitting in Numerical Methods Regression
 
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
学校原版美国波士顿大学毕业证学历学位证书原版一模一样学校原版美国波士顿大学毕业证学历学位证书原版一模一样
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
 
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURSCompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
 
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
 

Grounding simulation slides

  • 1. Grounding Simulation using FEA Software Camilo Chaves Electrical Engineer and Physicist https://de.linkedin.com/pub/camilo-chaves/11/323/a72
  • 2. Ground modeling in Low Frequencies Model of a filamentar conductor on the ground per unit length For low frequencies • For low frequencies, the principal parameter to be considered is the conductivity of the soil
  • 3. Consider a copper semi-spherical electrode -Consider also a homogeneous soil (same resistivity in all directions) -The layers drawn in the soil are the voltage equipotentials, produced when the current passes through each layer of soil. -The total current in each surface layer is the same, but the current densities gets smaller when the probe gets away from the current injection point (J= Current I /Surface Area of the layers of soil) -The Ground Diference of Potential is therefore higher in the proximity of the conductor (Higher J)
  • 4. Potential profile on the soil for the semi-sphere The higher Rt , the higher Vt for the same current I Potential Radius Distance (m)
  • 5. Calculus of the Surface Potential Distribution Rt depends only on the resistivity and geometric shape!
  • 6. Ground Resistance Formulas for simple types of electrodes Semi-Spherical Electrode Error of 0.01% from FEA Simulation Calculated RESULTS Radius of 1m, ρ = 500 Ω.m Rtot = 79.57 Ω FEA RESULTS Rtot = 74.26 Ω + 5.3 Ω (R Adj.) Rtot = 79.56 Ω R Adjust Calculation Size of the modeled soil = 15m radius R adjust = R of a semi-sphere of 15m of radius R = 5.3 Ω All FEA simulations were done with a soil model of 15m of radius For any electrode configuration, in a homogeneous soil , after 10-15 times the electrode size, the equipotentials behave like if they were produced by a semi-spherical electrode. When the equipotentials start to become semi-spherical, from this point on, the rest of the soil resistance can be computed using the semi-spherical electrode formula, using the radius from this point in the formula. Error of 0.01% from FEA Simulation Current of 1A injected
  • 7. Ground Resistance Formulas for simple types of electrodes Horizontal Electrode, Length L, burried at a distance d from the surface, radius r Calculated RESULTS L=3m, ρ = 500 Ω.m, d=0.5m, radius of the rod r = 0.008m Rtot = 186.35 Ω FEA RESULTS Rtot = 172.23Ω + 5.3 Ω (R Adj.) Rtot = 177.53 Ω Vertical Electrode, Length L, radius a Calculated RESULTS L=3m, ρ = 500 Ω.m radius of the rod a = 0.008m Rtot = 167.46 Ω FEA RESULTS Rtot = 160.5 Ω + 5.3 Ω (R Adj.) Rtot = 165.8 Ω Error of 4.96% from FEA Simulation Error of 1% from FEA Simulation For a 100V on the electrode on the ground Current of 1A injected
  • 8. Horizontal ring at distance h from the surface, radius r Vertical square Same resistance of a ring with same area, burried at the same distance (d) from the surface Ground Resistance Formulas for simple types of electrodes Calculated RESULTS Radius r=1m, ρ = 500 Ω.m, h=1m, diam. of cable (d)= 1.6e-2 m Rtot = 105.04 Ω FEA RESULTS Rtot = 98.77 Ω + 5.3 Ω (R Adj.) Rtot = 104.07 Ω Error of 0.93% from FEA Simulation Calculated RESULTS Radius r=1m, ρ = 500 Ω.m, h=2m Rtot = 93.17 Ω FEA RESULTS Rtot = 92.4 Ω + 5.3 Ω (R Adj.) Rtot = 97.7 Ω Error of 4.63% from FEA Simulation 100V on the electrode Vertical ring at distance h from the surface. h is taken from the center of the ring
  • 9. Ground Resistance Formulas for simple types of electrodes Sphere (d≈r) Calculated RESULTS Radius r=1m, ρ = 500 Ω.m, d=2m, Rtot = 79.57 Ω FEA RESULTS Rtot = 44.26 Ω + 5.3 Ω (R Adj.) Rtot = 49.56 Ω Error of 60.55% from FEA Simulation
  • 10. Ground Resistance Formulas for simple types of electrodes Sphere (d>>r) Calculated RESULTS Radius r=1m, ρ = 500 Ω.m, d=10m, Rtot = 47.74 Ω FEA RESULTS Rtot = 35.16 Ω + 5.3 Ω (R Adj.) Rtot = 40.46 Ω Error of 17.99% from FEA Simulation Condition to use the formula: d>>r
  • 11. Comparative Analysis for Simple electrodes Electrode Configuration Rt(Ω) Formula FEA Rt(Ω) Simulation Adjustm. Ω Rt (Ω) FEA final % error Horizontal Electrode of Length L, Diameter D burried at distance h 186.35 172.23 5.3 177.53 4.96% Vertical Electrode with Length L, Diameter D 167.46 160.5 5.3 165.8 1% Horizontal Ring at depth R with Radius R 105.04 98.77 5.3 104.07 0.93% Vertical Ring at depth 2xR with Radius R 93.17 92.4 5.3 97.7 4.63% Semi-Sphere with Radius R at the surface 79.57 74.26 5.3 79.56 0.01% Sphere at Depth R with Radius 10xR (use only if d>>>r) 47.74 35.16 5.3 40.46 17.99% Parameters for the formulas =500 Ω.m , L= 3m, D= 1.6cm, h = 50cm, R= 1m, Size of the modeled soil: 30m of diameter. The size of the soil implies an automatic adjustment of the FEA resistance. The final simulated resistance must be the FEA resistance plus 5.3Ω, which is the resistance of a semi-spheric electrode of 15m of radius. From the results the conclusion is clear. The bigger the surface area , the lesser is the resistance.
  • 12. Ground Resistance Formulas for multiple electrodes 4 Point Star with Length L, burried at depth d, in a horizontal plane. Radius of the electrode is a in the formula Calculated RESULTS Length r=3m, ρ = 500 Ω.m, d=0.5m, a=0.008m Rtot = 72.71 Ω FEA RESULTS Rtot = 114.64 Ω + 5.3 Ω (R Adj.) Rtot = 119.94 Ω 100V on the electrode Error of 39.38% from FEA Simulation Could the resistance be approximated by 2 horizontal rods in paralell ? Not exactly Calculated RESULTS L=3m, ρ = 500 Ω.m, d=0.5m, radius of the rod r = 0.008m Rtot = 186.35 Ω Best result that could be achieved for 2 horizontal rods (R in paralell) Rtot = 186.35 Ω /2 = 93.17Ω Considering the rods are out of the sphere of influence of each other This result can only be achieved if the 2 rods are sufficiently apart from each other! So, the formula of the 4 point star must be wrong because it has computed 72.71 Ω. This value is lesser than what could be achieved with 2 rods. It must be wrong or it considers that it is correct only with some specific parameters. Let’s say if d is >>>> L (let’s run the simulation)
  • 13. Ground Resistance Formulas for multiple electrodes Simulating the resistance of 2 horizontal rods in parallel, sufficiently apart from each other Calculated RESULTS for 1 rod L=3m, ρ = 500 Ω.m, d=0.5m, radius of the rod r = 0.008m Rtot = 186.35 Ω Best calculated result that could be achieved for 2 horizontal rods Rtot = 186.35 Ω /2 = 93.17Ω Considering the rods are out of the sphere of influence of each other FEA RESULTS for 2 Rods Rtot = 87.19 Ω + 5.3 Ω (R Adj.) Rtot = 92.49 Ω 2 rods out of the sphere of influence of each other So, the 2 rods in parallel agrees with the simulation. But again, what about the 4 point star if d>>>L? Error of 0.73% from FEA Simulation 1 rod formula
  • 14. Ground Resistance Formulas for multiple electrodes 4 Point Star Simulation when d=10m and L=3m FEA RESULTS for a 4 Point Star Rtot = 88.53 Ω + 5.3 Ω (R Adj.) Rtot = 93.83 Ω 4 Point Star when d>>>L Calculated RESULTS when d>>>L Length L=3m, ρ = 500 Ω.m, d=10m, a=0.008 Rtot = 7.909 Ω It is better to approximate the value using two rods in parallel until a better formula for a 4 point star is found. If you know it, please send it to me. Interesting result! It almost reached the minimum allowed value for 2 rods in paralell, on the last slide (as it should be!) Error of 91.57% from FEA Simulation
  • 15. Ground Resistance Formulas for multiple electrodes Conclusion for 4 point star electrode configuration • Close to the surface, the formula in comparison to FEA presented and error of 39.38%. When d>>>L, the formula presented an error of 91.57% from FEA • Prior formulas of simple electrodes achieved close proximity to FEA, within an error of 1%, so a condition was set in order for them to be used, which is, install the electrodes sufficiently apart from each other. • The calculated results and the FEA results for 2 electrodes apart from each other differs has only 0.73% of error, thus confirming that for simple electrodes, the formulas can be used. • A FEA analysis of a deep 4 point star (d>>>L) showed that its value differs from the value of 2 electrodes for only 1.44%. As it should be, because the minimum resistance is to be found were the 2 horizontal electrodes are set far apart, off the sphere of influence of each other. • Conclusion: For the parameters chosen, the formula has failed to return a value closed to a simulated one.
  • 16. Ground Resistance Formulas for multiple electrodes Calculated RESULTS n=4, ρ = 500 Ω.m, d=0.5m, a=0.008m,L=0.5m Rtot = 217.09 Ω FEA RESULTS (radius of circle 3.18m) Rtot = 37.72 Ω + 5.3 Ω (R Adj.) Rtot = 43.02 Ω Error of 404.6% from FEA Simulation N vertical rods with Length L in a circle Restriction: S >> L
  • 17. Ground Resistance Formulas for multiple electrodes FEA RESULTS (radius of circle 3.18m) Rtot = 37.72 Ω + 5.3 Ω (R Adj.) Rtot = 43.02 Ω N vertical rods with Length L in a circle Restriction: S >> L Could the final resistance be approximated by the equivalent resistance of a horizontal circle of 3.18m in parallel with the resistance of 4 rods ? 1 vertical rod of L=0.5m, a=0.008m, ρ = 500 Ω.m Rrod= 719.61 Ω 4 rods out of the sphere of influence of each other Rrods= 719.61/4=179.9 Ω 1 horizontal ring, of h=0.5m, d=1.6e-2m, ρ = 500 Ω.m , r=3.18m Rring = 45 Ω Calculated RESULTS Rtot=(1/Rring+1/Rrods)^-1 Rtot= 35.99 Ω Error of 16.34% from FEA Simulation This is the best value that could ever be achieved in this configuration! The diference is because of the mutual resistance between the elements Alternative method for calculation
  • 18. Ground Resistance Formulas for multiple electrodes Conclusion for N vertical rods with Length L in a circle • Close to the surface, the formula in comparison to FEA presented and error of 404.6%. • Since S >>> L, and L<< Perimeter of the ring, an alternative method was applied. The calculated result achieved a close proximity to the FEA Simulation within an error of 16.4% • Conclusion: • For the parameters chosen, the formula has failed to return a value closed to a simulated one (an alternative method was provided within certain restrictions of use)
  • 19. Ground Resistance Formulas for multiple electrodes 3 Rods in a triangular shape (4 steps to calculation) 1 2 3 4 Calculated RESULTS S=3m, L=3m, d=0.008m, ρ = 500 Ω.m Rt = 73.5 Ω FEA RESULTS (S=3) Rt = 48.91 Ω+5.3 Ω Rt=54.21 Ω Error of 35.58% from FEA Simulation The elements from this configuration are too close in order to estimate the minimum resistance using paralell resistances. Let’s try S=50m and L=3
  • 20. Ground Resistance Formulas for multiple electrodes 3 Rods in a triangular shape (4 steps to calculation) 4 Graph Parameters L=3m, d=0.008m, ρ = 500 Ω.m FEA Results (S=10) Rt=23.62 Ω+5.3 Ω Rt=28.92 Ω Error of111% from FEA Simulation But now, the elements are sufficiently apart for us to try an alternative method
  • 21. Ground Resistance Formulas for multiple electrodes 3 Rods in a triangular shape (4 steps to calculation) FEA Results (S=10) Rt=23.62 Ω+5.3 Ω Rt=28.92 ΩAlternative Method using same parameters, but diferent method 3 vertical rods with L=3m in parallel: Rrods= 55.82 Ω 3 horizontal electrodes with S=10m (S is L in the formula) in parallel: Rhoriz = 75.06 Ω Final equivalent Resistance Rt=(1/Rrods+1/Rhoriz)^-1 Rt=32.01 Ω Again, when the elements are close to be off the sphere of influence of each other, the global resistance can be approximated by simple electrodes configuration in paralell Error of 10.7% from FEA Simulation
  • 22. Ground Resistance Formulas for multiple electrodes Conclusion for 3 Rods in a triangular shape • Close to the surface, the formula in comparison to FEA presented and error of 35.58%, considering S=3m and L=3m. • When S=10m, the error increased to 111% • In the alternative method, the same calculation was performed using well known formulas for simple electrodes, and error reduced to 10.7% • Conclusion: • For the parameters chosen, the formula has failed to return a value closed to a simulated one (an alternative method was provided within certain restrictions of use)
  • 23. Ground Resistance Formulas for multiple electrodes Error of 209.1% from FEA Simulation FEA RESULTS Rtot = 24.36 + 5.3(Adj)= 29.66Ω Rods with length L, radius a, burried depth d, in line. Restriction: s >> L Calculated RESULTS for 3 rods in line (n=3) in a soil with 500 Ω.m L=3m (length of the rod), S=6m, a=0.008m, d=0.5m (depth) Rtot = 91.67 Ω
  • 24. Ground Resistance Formulas for multiple electrodes FEA RESULTS Rtot = 24.36 + 5.3(Adj)= 29.66Ω Calculated Results for 3 rods in parallel L=3m, a=0.008m, ρ = 500 Ω.m Rtot = 167.46 Ω/3 = 55.82 Ω Calculated Results for 1 horizontal electrode of 12m L=12m, r=0.008m, d=0.5m, ρ = 500 Ω.m Rtot = 64.97 Ω Calculated Equivalent Resistance of the configuration Rt=(1/Rrods+1/Rhor)^-1 Rt=30.02 Ω Error of 1.21% from FEA Simulation Alternative method for calculation
  • 25. Ground Resistance Formulas for multiple electrodes Conclusion for 3 Rods in line • Close to the surface, the formula in comparison to FEA presented and error of 209.1% • In the alternative method, the same calculation was performed using well known formulas for simple electrodes, and error reduced to 1.21% • Conclusion: • For the parameters chosen, the formula has failed to return a value closed to a simulated one (an alternative method was provided within certain restrictions of use)
  • 26. Ground Resistance Formulas for multiple electrodes Simple Mesh without Rods FEA SIMULATION A Potencial of 100V was set for the mesh Rtot = 37.83 + 5.3(Adj)=43.13 Ω Error of 38.48% from FEA Simulation Error of 24.87% from FEA Simulation
  • 27. Ground Resistance Formulas for multiple electrodes Conclusion for Simple Mesh without Rods • Close to the surface, the formula in comparison to FEA presented and error of 24.87% • No alternative method was used because in a mesh the mutual resistance is not negligible. • Conclusion: • More simulations must be done in order to determine if this formula can be used within the same range of error.
  • 28. Ground Resistance Formulas for multiple electrodes Mesh with Rods Error of 24.87% from FEA Simulation This is the Mesh without rods formula
  • 29. Ground Resistance Formulas for multiple electrodes Mesh with Rods FEA RESULTS Rtot = 20.55 + 5.3(Adj)= 25.83Ω Error of 102.94% from FEA Simulation Error of 1% from FEA Simulation Error of 27% from FEA Simulation
  • 30. Ground Resistance Formulas for multiple electrodes Conclusion for Simple Mesh with Rods • Close to the surface, the formula in comparison to FEA presented and error of 27% using Visacro formula. • No alternative method was used because in a mesh the mutual resistance is not negligible. • Conclusion: • More simulations must be done in order to determine if this formula can be used within the same range of error.
  • 31. Final Conclusion  For simple electrodes, all the expressions presented agree with FEA.  For complex electrodes, none of the expressions presented, agree with FEA, with exception of Mesh without rods, and Mesh with rods using Visacros expression, that has an error of 27%.  Subsequent studies will determine the precise expression to take account the mutual resistance between complex electrodes, using FEA as tool to model this equations.
  • 32. Thank you for your time  Please, let me know if you have any other expressions for the grounding electrodes configurations. I will test them and insert them in another presentation  Any errors you found, incorrect expressions you find, wrong calculations, suggestions that you want to share, please, leave a comment on my post.  https://de.linkedin.com/pub/camilo-chaves/11/323/a72