Department of Electrical and Computer Engineering
Ground Resistance Computations Using theNumerical Electromagnetics Code (NEC)
J. Patrick Donohoe, Ph.D., P.E.Professor
Dept. of Electrical and Computer EngineeringMississippi State University
Steel Distribution Pole ForumReston, Virginia
May 17, 2002
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Objectives:
(1) Use the Numerical Electromagnetics Code(NEC-4) to accurately determine the ground resistance of steel poles.
(2) Compare the computed ground resistanceof a steel distribution pole to that ofcommonly used grounding electrodes(ground rods, concrete piles).
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Numerical Electromagnetics Code (NEC-4)
l Code Description!Designed for analyzing antennas and scatterers!Method of moments solution!Electric field integral equation (frequency domain)
l Code Features!Versatile geometry input
(straight segments for wires, flat patches for surfaces)!Solution algorithm applicable to electrically small
structures (low frequency) !Allows for perfect conductors and/or conductors of
finite conductivity!Allows for lossy ground planes and conductors that
penetrate the ground plane
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DefinitionsANSI / IEEE Std 81-1983 IEEE Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Ground System
Ground Resistance (of a grounding electrode) – the ohmic resistance between the grounding electrode and a remote grounding electrode of zero resistance.
A remote grounding electrode is sufficiently distant that the mutual resistance between the two electrodes is zero.
Mutual Resistance (of grounding electrodes) – the voltage change in one electrode produced by a change of one ampere of direct current in the other, expressed in ohms.
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Components of the Electrode Ground ResistanceIEEE Std 142-1982 IEEE Recommended Practice for Grounding of Industrial and Commercial Power Systems
1. Resistance of the electrode
2. Contact resistance between the electrode and the soil
3. Resistance of the soil from the electrode surface outward
• Resistance components (1) and (2) are very small in comparison to component (3).
• Resistance components (1) and (3) are included in NEC-4 analysis.
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Components of the Electrode Ground Resistance(Equivalent Current Carrying Capability)
Steel Pole
Wall Thickness
Cross Sectional
Area*
Resistance per unit length
Equivalent copper
conductor 40 ft. Class 5
(40G5) 0.10 in. 12.127 cm2 107.20 µµΩΩ/m 350 MCM
(19 strand) 45 ft. Class 3
(45SX3) 0.12 in. 142.127 cm2 87.63 µµΩΩ/m
400 MCM (19 strand)
65 ft. Class 2 (65EP2) 0.162 in. 19.414 cm2 66.96 µµΩΩ/m
500 MCM (37 strand)
0.507 V
* Cross sectional area is determined 5 ft. from the pole top
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Methods of Measuring Ground ImpedanceANSI / IEEE Std 81-1983
1. Two-Point Method2. Three-Point Method3. Ratio Method4. Staged Fault Tests5. Fall-of-Potential Method
Modeled with NEC- 4
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Fall-of-Potential Method
+
VoI
+
Groundelectrode
z
x
s
Currentelectrode
Voltageprobe
V(x) IV(x)
R(x) =
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Code Validation
• NEC-4 is used to determine the ground resistance of a 10 ft. steel ground rod (5/8 in. diameter) for different soil types. The computed ground resistances are compared with results obtained using the analytical formula.
• 62% Rule - Using the fall-of-potential method under ideal conditions, the measured resistance should match the theoretical ground resistance at a distance of 0.618s.
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-5 0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x (m)
V(x
) (V
olt
s)
0.618s=18.84m (61.8 ft)
V(0.618s)
Current electrodelocation
s=30.48m (100 ft)
Ground rodlocation
Voltage probelocation
Fall-of-Potential Method 10ft. (5/8 in. diameter) Ground Rod
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Alternative Fall-of-Potential Method
+
VoI
+
Groundelectrode
z
x
s
Currentelectrode
Voltageprobe
V(x) IV(x)
R(x) =
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-125 -100 -75 -50 -25 0 25 500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x (m)
V(x
) (V
olt
s)
Voltage probelocation
Current electrodelocation
Ground rodlocation
Alternative Fall-of-Potential Method 10ft. (5/8 in. diameter) Ground Rod
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Length Radius Soil Type
V I Rcomputed Ranalytical
10 ft 5/8 in sand 0.443 V 1.46 mA 304 ΩΩ 311 ΩΩ
10 ft 5/8 in clay 0.443 V 33.7 mA 13.1 ΩΩ 13.4 ΩΩ
8 ft 5/8 in sand 0.489 V 1.33 mA 368 ΩΩ 375 ΩΩ
8 ft 5/8 in clay 0.489 V 30.9 mA 15.8 ΩΩ 16.2 ΩΩ
8 ft 1/2 in sand 0.500 V 1.31 mA 382 ΩΩ 389 ΩΩ
8 ft 1/2 in clay 0.500 V 30.4 mA 16.4 ΩΩ 16.8 ΩΩ 0.507 V
Grounding Resistances of Typical Ground Rods
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Current Density Surrounding a 10ft. (5/8 in. diameter)Steel Ground Rod in Sand (total current = 1A)
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10.4 m (34 ft)
1.83 m (6 ft)
Outside diameter at groundline0.303 m (11.93 in)
Outside diameter at pole base0.333m (13.11 in)
Outside diameter at pole top0.133 m (5.25 in)
Steel thickness3.05 mm (0.12 in)
40 ft. Class 3 Steel Pole
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NEC-4 Steel Pole Modeling Issues
l Pole Taper! NEC allows for tapered conductors.! The conductor radius must be constant for conductors
that penetrate the air/soil interface.
The steel pole is modeled as a straight conductor with radius equal to the mean radius of the tapered pole below ground[6.26 in. (0.159m) for the 40 ft. class 3 steel pole].
l Below Grade Protection (Insulation)! NEC allows for insulated conductors. ! NEC does not allow for insulated conductors below
the air/soil interface.
An upper limit on the grounding resistance of the coated steelpole is determined by modeling only the bare portion of polebelow ground.
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Grounding Resistance of a Coated Steel Pole
I
Coated pole(Rcoated)
Rcoated < Rbare
I
Bare pole(Rbare)
Coated portion
Bare portion
db
db
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Length of bare
portion (db)
Soil Type Rbare
Length of bare
portion (db)
Soil Type Rbare
6 ft sand 213 ΩΩ 6 ft clay 9.20 ΩΩ
5 ft sand 239 ΩΩ 5 ft clay 10.3 ΩΩ
4 ft sand 269 ΩΩ 4 ft clay 11.7 ΩΩ
3 ft sand 310 ΩΩ 3 ft clay 13.4 ΩΩ
2 ft sand 366 ΩΩ 2 ft clay 15.8 ΩΩ
1 ft sand 465 ΩΩ 1 ft clay 20.3 ΩΩ 0.507 V
Computed Grounding Resistances (Upper Bounds) for Partially Coated Steel Poles
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NEC-4 Concrete Pile Modeling Issues
l Inhomogeneous Ground (Concrete/soil)! NEC does not allow for an inhomogeneous ground.! The conductivity of concrete is lower than the average
conductivities of sand or clay. The conductivity of concrete is comparable to dry sand.
A lower limit on the grounding resistance of the concretepile is determined by computing the grounding resistanceof the bare conductors in homogeneous soil.
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Grounding Resistance of a Concrete Pile
I
Concrete pile(Rpile)
Rbare < Rpile
I
Steelconductors in
concrete
Steelconductors in
soil
Bare Conductors(Rbare)
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Soil Type Rbare
sand 243 ΩΩ
clay 10.6 ΩΩ 0.507 V
Computed Grounding Resistances (Lower Bounds) for the Concrete Pile
Concrete Pile DetailsAll conductors – ½ in. diameter steelVertical conductors – 6 ft. in lengthHorizontal conductors – 1 ft. diameter circles
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Sand Clay
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Conclusions
l A 40 ft. class 3 steel pole with between 3 and 4 feet of buried bare length offers equivalent groundingcapability to a 10 ft. (5/8 in. diameter) ground rod.
l A 40 ft. class 3 steel pole with approximately 2 feet of buried bare length offers equivalent groundingcapability to an 8 ft. (5/8 in. diameter) ground rod.
l A 40 ft. class 3 steel pole with between 1 and 2 feet of buried bare length offers equivalent groundingcapability to a 8 ft. (1/2 in. diameter) ground rod.
l A 40 ft. class 3 steel pole with between 4 and 5 feet of buried bare length offers equivalent groundingcapability to the concrete pile.
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Conclusions
lThe steel pole grounding equivalencies computed here are very conservative given the assumptions made in the steelpole and concrete pile modeling.
lMore precise numbers for the steel pole grounding equivalencies could be computed using a custom code developed especially for this purpose.