6. Transmission Line Models Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 1 Volts per meter for h r. Wire over Earth capacitance 2π 8.854 pF per meter length 55.6 pF meter ln(10000) 9.2, C 6.0 pfm
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6. Transmission Line Models Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 1 Volts per meter for h >> r. Wire over Earth capacitance 2π • 8.854 pF per meter length = 55.6 pF / meter ln(10000) = 9.2, C = 6.0 pf/m
ln(1000) = 6.9, C = 8.1 pf/m
ln(100) = 4.6, C = 12.1 pf/m Reasonable estimate is 10 pF/m Electric Field<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 2 Wire over Earth inductance for h >> r. (4π •10-7) / 2π Henries per meter length = 0.2 μH/m ln(10000) = 9.2, L = 1.8 μH/m
ln(1000) = 6.9, L = 1.4 μH/m
ln(100) = 4.6, L = 0.92 μH/m Reasonable estimate is 1 μH/m<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 3 Figure 8. Equivalent Radius for Three Common Types of Bundled Phase Conductors Symmetric bundles have an equivalent radius<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 4 Three phases If the transmission line is symmetric, then the “P matrix” has the equal diagonal, equal off-diagonal property that permits 0-1-2 analysis rather than a-b-c analysis<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 5 If the transmission line is symmetric, then the “L matrix” has the equal diagonal, equal off-diagonal property that permits 0-1-2 analysis rather than a-b-c analysis<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 6 Summary of Positive/Negative Sequence Capacitance and Inductance Calculations<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 7 Summary of Positive/Negative Sequence Capacitance and Inductance Calculations<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 8 Summary of Zero Sequence Capacitance and Inductance Calculations meters<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 9 Summary of Zero Sequence Capacitance and Inductance Calculations<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 10 Summary of Zero Sequence Capacitance and Inductance Calculations<br>
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6. Transmission Line Models, cont. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 11 Ready for Use!<br>
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Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 6, March 31, 2015 12 345kV Double-Circuit Transmission Line 22.9 m at tower, sags down 10 m at mid-span to 12.9 m. 6. Transmission Line Models, cont. Double conductor phase bundles, bundle radius = 22.9 cm, conductor radius = 1.41 cm, conductor resistance = 0.0728 Ω/km
