1. For D > 10r, and height above ground > 10D
Two current-carrying wires, each having radius r I D
<
>
For D > 10r, and height above ground > 10D
Magnetic flux
Henries per meter
µo is the permeability of free space (e.g., air) = 4π•10-7

2. Same two wires, energized by V
<
> V
Farads per meter
εo is the permittivity of free space (e.g., air) = 8.854•10-12

4. D
<
>
Velocity of propagation of disturbances down a lossless overhead transmission line

5. A If Each Conductor is Actually a Bundle
Double Bundle, Each Conductor Has Radius r A
Equivalent Radius of the Bundled Conductors

6. China

10. Bus 2 DFW Bus 5 VAL Bus 3 UT Bus 1 HOU Bus 7 WIND Bus 4 SA Bus 6 COAL
300 km
250 km
150 km
400 km
500 km
Bus 3 UT
Bus 1
HOU
Bus 7
WIND
Bus 4 SA
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 6
COAL
BUS
LOAD % OF TOTAL
GEN
% OF TOTAL
1, HOU
30%
45%
2, DFW
25%
15% ( 10%)
3, UT 5%
4, SA
20%
10%
5, VAL
6, COAL
15% ( 5%)
7, WIND
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

11. Bus 2 DFW Bus 5 VAL Bus 3 UT Bus 1 HOU Bus 7 WIND Bus 4 SA Bus 6 COAL
300 km
250 km
150 km
400 km
500 km
Bus 3 UT
Bus 1
HOU
Bus 7
WIND
Bus 4 SA
Bus 6
COAL
No wind in West Texas in summer
(HOU makes up WIND gen. in summer)
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
4, SA
12 GW
6 GW
5, VAL 3
6, COAL
7, WIND
0 GW
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
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

12. 6 3 ??? ??? ??? ??? 3 Bus 2 DFW Bus 6 COAL Bus 7 WIND Bus 3 UT Bus 1
HOU
???
Bus 4 SA
??? 3
Bus 5
VAL

13. Ohms for 1 phase of a 100km three-phase circuit
Bus 2
DFW
Bus 6
COAL 6
500km 3
Bus 7
WIND
300km
40 / 5 Ω
40 Ω 2
40 Ω
400km 6
Bus 3 UT 2
Bus 1
HOU
40 Ω
150km
Bus 4 SA
300km 6
40 / 6 Ω (on each a-b-c phase)
3.0
j37.7
-j2210
Ohms for 1 phase of a 100km three-phase circuit
40 / 4 Ω
400km
3 GW load corresponds to 40Ω on each a-b-c phase 3
Bus 5
VAL
40 / 2 Ω