EEE471Ch4

EEE471Ch4 - Transmission Line Parameters Chapter 4 1...

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1 Transmission Line Parameters Chapter 4
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2 Transmission Line Parameters Four parameters which determine the electrical characteristics of a line: Series inductance Series resistance Shunt capacitance Shunt conductance Will review how parameters are determined for positive sequence (Z 1 and Y 1 ) and negative sequence ( Z 2 and Y 2 ) Will go into depth on determination of zero sequence parameters ( Z 0 and Y 0 )
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3 Positive and Negative Sequence Resistance DC resistance can be calculated by: Where ρ T is at standard temperature usually 20 o C ( See Table 4.2, Page 173) At other temperatures: A R T dc ρ = T T T T R R dc dc + + = 1 2 2 1
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4 Positive and Negative Sequence Resistance We are usually dealing with AC circuits with a f = 50 or 60 Hz. Due to “ skin effect ” when AC current is flowing, the current is forced toward the outside of the conductor so the effective resistance is increased. Even greater effect for conductors with steel core. (See Page 736) 2 I P R R loss eff ac = = R ac is obtained from tables on Pages 735 and 736
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5 Inductance Inductance is a function of: Conductor size Material Stranding (See Fig. 4.1, Page 167) Spacing between conductors
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6 Inductance (for solid, round, non-ferrous conductor) Inductance can be characterized by 2 relationships: dt d e λ = and i L = or LI = So that dt di L e = For ) ( φ ϖ+ = t Cos I i m or / 2 m I I = ) 90 ( ) ( o m m t Cos LI t Sin LI e - + - = + - = ϖ ) 90 ( o m t Cos LI e + + = I jX I L j E L = = In phasor form
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7 Flux Linkages with Conductor Due to Current in Conductor I dx x r D I distributed uniformly over cross section of conductor Want to find L = λ / I λ is flux that links the current inside radius x, I x There are 2 types of flux linkages: Internal to the conductor x<r External to conductor x>r
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8 I dx x r D I distributed uniformly over cross section of conductor First we will find general relationship for λ from At distance x from center: MMF = F x = I x amps Magnetic field intensity = x x F H = Where is length of closed path for constant H Flux density = x x x F H B μ = = Webers / m 2 ) 1 ( dx F dA B d x x φ = = Webers / m for 1 meter of conductor dx F n d n d x x x λ = = dx F n r r x x = 2 1 12 Weber-turns / m for flux between r 2 and r 1
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9 For internal flux linkages: 0 < x < r 2 2 2 2 r x I r x I I F x x = = = π 2 2 2 2 r x r x n x = = x 2 = and 7 10 4 - = = μ o and Henries / m for non ferrous material 4 10 2 ) 10 2 ( 2 10 4 4 4 7 0 3 7 4 2 2 2 2 0 7 int r r dx x I r Idx r x r x x r r - - - = = = λ I 2 10 7 int - = 2 10 7 int int - = = I L dx F n r r x x = 2 1 12 I dx x r D I distributed uniformly over cross section of conductor
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10 dx F n r r x x = 2 1 12 μ λ x π 2 = D r D r ext x I dx I x ln 10 2 ) 1 ( 2 10 4 7 7 - - = = For External flux linkages: r < x < D µ = µ 0 , n x = 1 , F x = I , and r D I ext ln 10 2 7 - = r D I L ext ext ln 10 2 7 - = = (2) External flux linkages. To be used elsewhere I dx x r D I distributed uniformly over cross section of conductor
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11 Self Inductance of A Conductor 7 7 7 int 10 ) ln 2 2 1 ( ln 10 2 2 10 - - - + = + = + = r D r D L L L ext self r D e r D e r D L self 4 1 7 4 1 7 7 ln 10 2 ) ln (ln 10 2 ) ln 4 1 ( 10 2 - - - = + = + = r D re D L self 7788 .
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EEE471Ch4 - Transmission Line Parameters Chapter 4 1...

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