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Series Inductance of Transmission Lines

# Series Inductance of Transmission Lines - Series Inductance...

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Now considering a completely transposed line with bundeled conductors: L 1 L 2 = 2 10 7 ln D GMR = L a λ a I a = 2 10 7 ln D GMR = λ a 2 10 7 I a ln D GMR = λ a 2 10 7 I a ln 1 GMR I a ln 1 D = Using the Fact, that all currents add to zero: I a I b I c + ( ) = λ a 2 10 7 I a ln 1 GMR I b I c + ( ) ln 1 D + = λ a 2 10 7 I a ln 1 GMR I b ln 1 D + I c ln 1 D + = 2 10 7 ln 1 GMR ln 1 D ln 1 D I a I b I c = Assume positive sequence currents whose sum is zero: Three-Phase, Three-Wire Line with equal Phase Spacing D: Symmetrical Arrangement of Conductors without Ground Return: λ k 2 10 7 1 M m I m ln 1 D km = = Total Flux linking conductor k in an array of M conductors carrying currents Im, whose sum is zero. Starting from Equation (4.4.30) on Page 180 Glover, Sarma 4 th edition: Dr. M. Giesselmann, Mar-03-2008: Series Inductance of Transmission Lines:

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L a λ a I a = 2 10 7 ln D GMR = L a L 1 = L 2 = λ a I a = 2 10 7 ln D eq GMR Bundle = D eq D 12 D 23 D 31 ( ) 1 3 = λ a 2 10 7 I a ln D 12 D 23 D 31 ( ) 1 3 GMR Bundle = λ a 2 10 7 3 3 I a ln 1 GMR Bundle I a ln 1 D 12 D 23 D 31 = Using Boundary condition for positive Sequence: I a I b I c + ( ) = λ a 2 10 7 3 3 I a ln 1 GMR Bundle
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Series Inductance of Transmission Lines - Series Inductance...

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