1 Psych 5510/6510 Chapter Nine: Outliers and Data Having Undue Influence Spring, 2009.
Two current-carrying wires, each having radius r
description
Transcript of Two current-carrying wires, each having radius r
Two current-carrying wires, each having radius r
Henries per meter
I I
D< >
For D > 10r, and height above ground > 10D
Magnetic flux
r
DL o ln
µo is the permeability of free space (e.g., air) = 4π•10-7
rD
C o
ln
Farads per meter
εo is the permittivity of free space (e.g., air) = 8.854•10-12
D< >
V
Same two wires, energized by V
61.4)100ln( ,30.2)10ln(
mHtotor
DL o /8.1 9.0)61.4 30.2(104.0ln 6
mpFtoto
rD
C o /12 61061.4 30.2
8.27
ln
12
D< >
oooo
rDr
DLC
ln
ln
sec/10311 8metersc
LC oo
Velocity of propagation of disturbances down a lossless overhead transmission line
rAreq 2
Equivalent Radius of the Bundled Conductors
If Each Conductor is Actually a Bundle
Double Bundle, Each Conductor Has Radius r
A
China
5.7 m
4.4 m 7.6 m
8.5 m
22.9 m at tower, and sags down
10 m at mid-span to 12.9 m.
7.6 m
7.8 m
Tower Base
345kV Double-Circuit Transmission Line Scale: 1 cm = 2 m
Double conductor phase bundles, bundle radius = 22.9 cm, conductor radius = 1.41 cm, conductor resistance = 0.0728 Ω/km
Single-conductor ground wires, conductor radius = 0.56 cm, conductor resistance = 2.87 Ω/km
5 m
10 m
33 m
Tower Base
500kV Single-Circuit Transmission Line Scale: 1 cm = 2 m
Triple conductor phase bundles, bundle radius = 20 cm, conductor radius = 1.5 cm, conductor resistance = 0.05 Ω/km
Single-conductor ground wires, conductor radius = 0.6 cm, conductor resistance = 3.0 Ω/km
10 m
5 m
39 m
Conductors sag down 10 m at
mid-span
30 m
Earth resistivity ρ = 100 Ω-m
Bus 2DFW
Bus 5VAL
300 km
250 km
150 km
300 km
400 km
500 km
400 km
Bus 3UT
Bus 1HOU
Bus 7WIND
Bus 4SA
• Summer Peak, 3 kW per person, 20 million people, 60 GW
• Winter Peak, 80% of Summer Peak
• Spring/Fall Peak, 50% of Summer Peak
• Nightime, 50% of Daily Peak
• Approx 5% losses
No Wind(Good Wind)
Bus 6COAL
BUS
LOAD % OF
TOTAL
GEN
% OF TOTAL
1, HOU 30% 45%
2, DFW 25% 15% ( 10%)
3, UT 5% 5%
4, SA 20% 10%
5, VAL 10% 5%
6, COAL 5% 15% ( 5%)
7, WIND 5% 5% ( 20%)Positive-sequence line constants for each 345kV a-b-c circuit:
• R = 0.06 Ω/km per conductor
• L = 1 µH/m
• C = 12 pF/m
• Rating = 800 A per conductor
• Two conductors per phase
• Three phases per circuit
• 200kV line-to-ground
• Approx. 1 GW per circuit
Bus 2DFW
Bus 5VAL
300 km
250 km
150 km
300 km
400 km
500 km
400 km
Bus 3UT
Bus 1HOU
Bus 7WIND
Bus 4SA
• Summer Peak, 3 kW per person, 20 million people, 60 GW
• Winter Peak, 80% of Summer Peak
• Spring/Fall Peak, 50% of Summer Peak
• Nightime, 50% of Daily Peak
• Approx 5% losses
No wind in West Texas in summer
(HOU makes up WIND gen. in summer)
Bus 6COAL
BUS
Summer Peak Load
GEN
Minimum Circuits Needed
1, HOU 18 GW 30 GW 12
2, DFW 15 GW 9 GW 6
3, UT 3 GW 3 GW 0
4, SA 12 GW 6 GW 6
5, VAL 6 GW 3 GW 3
6, COAL 3 GW 9 GW 6
7, WIND 3 GW 0 GW 3
Positive-sequence line constants for each 345kV a-b-c circuit:
• R = 0.06 Ω/km per conductor
• L = 1 µH/m
• C = 12 pF/m
• Rating = 800 A per conductor
• Two conductors per phase
• Three phases per circuit
• Each conductor is 200kV line-to-ground
• Approx. 1 GW per circuit
Each 100 km of circuit has
• R = 3 Ω
• ZL = j37.7 Ω
• ZC = -j2210 Ω
3 GW load corresponds to 40Ω on each a-b-c phase
Bus 2DFW
Bus 5VAL
6
3
3
???
Bus 3UT
Bus 1HOU
Bus 7WIND
Bus 4SA
Bus 6COAL
???
???
???
Bus 2DFW
Bus 5VAL
6
3
3
6Bus 3
UTBus 1HOU
Bus 7WIND
Bus 4SA
Bus 6COAL
6
2
2
40 / 6 Ω (on each a-b-c phase)
40 / 2 Ω
40 / 4 Ω
40 / 5 Ω 40 Ω
40 Ω
40 Ω
3.0 j37.7
-j2210-j2210
Ohms for 1 phase of a 100km three-phase
circuit
500km
250km
400km
400km
300km
300km
150km
3 GW load corresponds to 40Ω on each a-b-c phase