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Transmission Line Example

# Transmission Line Example - Transmission Line Parameters...

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Transmission Line Parameters - Example 5-10 Dr. M. Giesselmann, Mar 07, 2008 ORIGIN 1 := N 2 := Bundle 4 := 2 neutrals and 3 phases with bundles of 4: μ o 4 π 10 7 henry m := Permeability of Free Space: ε o 8.854187817 10 12 farad m := Permittivity of Free Space: R N 0.489 cm := GMR N 0.0636 cm := ρ N 1.52 Ω km := Radius, GMR, and Resistivity of Neutrals: R P 1.519 cm := GMR P 1.229 cm := ρ P 0.0701 Bundle Ω km := Radius, GMR, and Resistivity of Phases: ρ Earth 100 Ω m := Resistivity of Earth along the line: freq 60 Hz := ω 2 π freq := ω 376.991 Hz = Power Frequency and Omega: d 45.7 cm := MW 1000 kW Bundle Spacing: Geometric Mean Radius (GMR) of bundled Conductors; left column is for Inductance, right column is for Capacitance, Rows are for the number of conductors in a bundle: GMR GMR P GMR P d 3 GMR P d 2 4 2 GMR P d 3 R P R P d 3 R P d 2 4 2 R P d 3 :=

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D Er 658.5 coul kg m ρ Earth freq := D Er 850.12 m = Distance of Earth Return Conductors: 5.7.2 ρ Er 9.869 10 7 kg m coul 2 freq := ρ Er 0.059 Ω km = Resistance of Earth Return Conductors: 5.7.3 Defining x-y Coordinate system for Conductor positions: x=0 is the center of the tower, y=0 is the ground level: X 13.7 0 13.7 11 11 m := Y 23 23 23 33.5 33.5 m := GMR L GMR Bundle 1 , GMR Bundle 1 , GMR Bundle 1 , GMR N GMR N := ρ c ρ P ρ P ρ P ρ N ρ N := X - Pos. of Conductors: Y - Pos. of Conductors: GMR of Conductors for Ind. calc: Resistivity of Conductors: Calculating Series Impedance: Total Flux linking conductor k in an array of M conductors carrying currents I m , whose sum is zero. i13N + () .. := Defining Index i: λ k 210 7 1 M m I m ln 1 D km = = j13N + .. := Defining Index j: If i=j then distance is geometric mean radius GMR of conductor: Calculating distance from overhead conductor i to overhead conductor j: Dist ij , X i X j 2 Y i Y j 2 + if GMR L i otherwise := Note that X(Overhead) = X(Return) Calculating distance from overhead conductor i to earth return conductor j: Dist_g , X i X j 2 Y i Y j D Er 2 + := λ i μ o 2 π 1 3N + j I j ln Dist_g , Dist , = = Total flux Linkage of over- head conductor i: Defining Elements of Impedance Matrix: Z , ρ Er j μ o freq ln Dist_g , Dist , + if ρ c i ρ Er + j μ o freq ln Dist_g ii , Dist , + otherwise := The following equation system is used for series impedance calculation: E P Z A I P Z B I N + = Or in short form: 0Z C I P Z D I N + = E Aa , E Bb , E Cc , 0 0
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Transmission Line Example - Transmission Line Parameters...

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