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CALCULATION OF ELECTRICALCALCULATION OF ELECTRICALINDUCTION NEAR POWER LINESINDUCTION NEAR POWER LINES
Direction Expertise et Support Technique de TransportLignes, Cbles et environnement
Prepared by : Richard Lehoux, [email protected]
May 2008May 2008
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Scope of the presentationScope of the presentation
1. Calculation of Electric Field
2. Electric field induction in a human body1. IEEE Std80-2000 (Guide for Safety in AC Substation Grounding)2. EPRI (Electric Power Research Institute)3. CSA (Canadian Standard Association)
3. Design criteria
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1. CSA2. HQT (Hydro-Qubec Transnergie)
4. Methods of determining induced current1. Empirical2. Boundary Element Method (BEM)
5. Comparison results: Empirical versus BEM
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Electric field induction in a human bodyElectric field induction in a human body
Range of tolerable current in a human body IEEE Std 80-2000, Article 5.2 "Effect of magnitude and duration"
1mA: threshold of perception 1-6 mA: unpleasant to sustain 10.5 mA: threshold for women let-go currents 16 mA: threshold for men let-go currents Note: the duration of the fault is infinite
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Range of tolerable current in a human body EPRI "TRANSMISSION LINE REFERENCE BOOK",
Chapter 8, "Field effect of overhead transmission lines and stations",
Article 8.10 "Electric-field induction in people", paragraph "Response tosteady-State Currents" 5 mA: let-go values for children for a probability of 0.5% have been
conservatively estimated as equal to 5 mA threshold of perception
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Electric field induction in a human bodyElectric field induction in a human body
CSAC22.3 No.1-06, Article A.5.3.1 "Vertical desing clearances of wiresand conductors above ground or rails and Tables 2 and 4"
5 mA: let-go currents
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Design criteriaDesign criteria Height of conductorsHeight of conductors
CSA calculation criteria Article : A5.3.1 Based on the worst-case condition :
Vehicle is insulated from the ground by rubber tires Person contacting the vehicle is touching or standing on a well-grounded surface Induced current in all cases is below 5 mA (Let-go currents) Maximum line to ground voltage
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HQT Use CSA design criteria
4,15 m
5 mA
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Methods of determining induced currentMethods of determining induced current
Two methods are available at HQT to determine theinduced current (5 mA let-go) in a human body
Empirical method (EPRI) Eas , fast, chea , a roximate
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Boundary Element Method (Maxwell's Equations) Expensive, accurate
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Empirical methodEmpirical method
Method of approximating induced current in objects closeto ground EPRI "TRANSMISSION LINE REFERENCE BOOK"
Chapter 8, "Field effects of overhead transmission lines and stations" Method of approximating calculation of current induced on objects
close to the ground
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Figure 8.8.2 "Shape for a rectangular solids"
(The shape is collecting electrical charge)
Many others shape available Horizontal / Vertical cylinder Flat plate House Horse Etc.
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Empirical methodEmpirical method
Sizes of vehicles(m)
Length Width Height
ArticleC22.3-01-06
2003 2006 HQ 2003 2006 HQ 2003 2006 HQ
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Truck A5.3.1 15.2 23.0 23.0 2.4 2.6 2,6 4.15 4.15 4,15
Large
farm
A5.3.1 7.6 7.6 7.6 2.4 2.4 2.4 4.15 4.15 4.5 *
TrainA5.3.1
(example 4)4000.0 6.706
* : Height used by HQT
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Calculation with EPRI method to get 5 mA induced in a human body
Size of the truck :Length (A): 23 m
Width (B) : 2.6mHeight (H) : 4.15mCenter : 4.15/2 = 2.08
Ratio :A/B : 23/2.6=9.62
H/B
Empirical methodEmpirical method -- Exemple : TruckExemple : Truck
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H/B : 4.15/2.6=1.6
With abacus :S/(A*B)=S/(23*2.6)=5.1
S=304.9
5mA=S*E/300 (E: Electric field)E=(5mA*300)/304.9=4.9kV/m
at 2.08m (center of vehicle) See slide 14 to determine
height of conductors
9.62
1.6
S/(AB
)
A/B
5.1
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Calculation with EPRI to get 5 mA induced in a human body
Size of the Large Farm Vehicle :Length (A) : 7.6 mWidth (B) : 2.4m
Height (H) : 4.5m (HQT - Study)Center : 4.5/2=2.25m
H/B
B)
Ratio :A/B : 7.6/2.4=3.2
Empirical methodEmpirical method -- Exemple : Large FarmExemple : Large Farmvehiclevehicle -- HQTHQT
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1.9
S/(
A/B
8.0
. . = .
With abacus :S/(A*B)= 8S=8(7.6*2.4)=146
5mA = S*E/300 (E: Electric field)E=(5mA*300)/146=10.3kV/m
at 2.25m (center of vehicle) See slide 14 to determine
height of conductors
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Calculation with EPRI to get 5 mA induced in a human body
Size of the Large Farm Vehicle :Length (A) : 7.6 mWidth (B) : 2.4m
Height (H) : 4.15m (CSA)Center : 4.15/2=2.08m
H/B
B)
Ratio :A/B : 7.6/2.4=3.2
Empirical methodEmpirical method -- Exemple : Large FarmExemple : Large Farmvehiclevehicle -- CSACSA
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1.9
S/(
A/B
7.0
. . = .
With abacus :S/(A*B)= 7S=8(7.6*2.4)=129
5mA = S*E/300 (E: Electric field)E=(5mA*300)/129=11.6kV/m
at 2.25m (center of vehicle) See slide 14 to determine
height of conductors
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Calculation of Electric FieldCalculation of Electric Field
The electric field is determined by these parameters :1. Voltage2. Distance between phases3. Diameter of conductors4. Number of conductors per bundle5. Presence of overhead ground wire6. Distance of conductors from the ground
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Software available to calculate the electric field : CDEGS of SES (Package : MultiField - 38 k$ - Available on market) Coulomb (3D Electric Field Solver Used by IREQ - Available on
market) Expomag (In house software HQ)
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Calculation of Electric FieldCalculation of Electric Field
FAA TOWER - 735 kV /
Electro-mechanicals specifications 1 circuit Conductors
4 per bundles : 3.556 cm
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s ances e ween
Voltage max 765 kV
Overhead ground wire Quantity : 2 : 1.27cm
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735 kV Electric Field
8
10
12
kV/m
Calculation of Electric FieldCalculation of Electric Field
Electric field 735 kV (FAA Tower) Conductors at rest
Heightof
Max. Elec. field: 10.3 kV/m Large Farm Vehicle
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0
2
4
6
0 4 8 12 16 20 24 28 32 36
m
21.0 m
13.4 m
conductors
HQT ROW (80 m)< 2 kV/m
Max. Elec. field: 4.9 kV/m - Truck
Center of the ROW
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Boundary Element Method (BEM)Boundary Element Method (BEM)
Equivalent circuit of a truck near a power linesEquivalent circuit of a truck near a power lines
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Human body
Represented by a 1 k
Isc = 5 mA
Modelizationdone by IREQ(Alain Turgeon)
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BEM ExampleBEM Example Truck parallel to the lineTruck parallel to the line
Capacitive induction simulation for a truck located at 17 metersof the center line and parallel to conductors
735 kV with FAA towers
4
4.5
5kV/m
17 m
Height of conductors simulation :21 - 22 - 23 - 24 Height of conductors
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0
0.5
1
1.5
2
2.5
3
3.5
-50 -40 -30 -20 -10 0 10 20 30 40 50
m
Example of an electric profile field
ROW
2,6 m
4,15 m
15,7 18,3
5 mA
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BEM ExampleBEM Example Truck parallelTruck parallel
Height of
conductorsCapacitances
Currentin a human
body
(m)Ca-t(pF)
Cb-t(pF)
Cc-t(pF)
Ct-g(pF)
ISC(ma)
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21 3,03 15,8 43,4 1,46 5,9622 3,19 15,4 40,6 1,46 5,51
23 3,33 15,0 38,0 1,46 5,09
24 3,45 14,6 35,6 1,46 4,71
o m t t e
current in ahuman body
at 5 mAthe height ofconductors
must behigher than
23.2 m
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BEM ExempleBEM Exemple Truck perpendicular to lineTruck perpendicular to line
Capacitive induction simulation for a truck located perpendicular to conductors735 kV with FAA towers
5
6 kV/m
Height of conductors simulation :17 - 18 - 19 - 20 Height of conductors
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0
1
2
3
4
-50 -40 -30 -20 -10 0 10 20 30 40 50
m
4,15 m
Example of an electric profile field
ROW
23 m
5,5 28,5
5 mA
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BEM ExampleBEM Example Truck perpendicularTruck perpendicular
Heightof conductors
CapacitancesCurrent
in a humanbody
(m)Ca-t(pF)
Cb-t(pF)
Cc-t(pF)
Ct-g(pF)
ISC(mA)
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17 4,19 21,2 49,1 1,44 6,54
18 4,36 20,3 45,9 1,45 6,05
19 4,52 19,5 42,9 1,45 5,58
20 4,65 18,7 40,3 1,45 5,18
To limit thecurrent in ahuman bodyat 5 mA theheight of
conductorsmust be
higher than20.5 m
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Comparison results: Empirical versus BEMComparison results: Empirical versus BEM
Height of conductors
735 kV FAA towerEmpiricalMethod
(m)
BEMMethod
(m)
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21 20.5 perpendicular23.2 parallel
HQT chose empirical method for it's in house standard
BEM method permitted HQT to check the accuracy of empiricalmethod
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Empirical methodEmpirical method HQT resultsHQT results
NominalVoltage
(kV)TOWER
MINIMUM HEIGHT OF CONDUCTORS(m)
TRUCK(Electric Field : 4.9 kV/m)
LARGE FARM VEHICULE(Electric Field : 10.3 kV/m)
735 FAA Single circuit 21 13.8
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ou e c rcu t . < .
315 EFK Single circuit 10.6 7
230 DPD Double circuit 6.7
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ACKNOWLEDGEMENTSACKNOWLEDGEMENTS
Daniel Goulet, Ph. D.
Alain Turgeon, P. Eng. M. Sc. A.
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