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

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

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

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

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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

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

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

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