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