transmission lines parametersscholar.cu.edu.eg/?q=mostafa_elshahed/files/lec_6.pdf ·...
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TRANSMISSION LINESPARAMETERS
To develop models of transmission lines, we first need to determine the TL parameters.
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CAPACITANCE OF A SINGLE PHASE
TWO-WIRE LINE
The capacitance between conductors is:
If r1 = r2 = r
2
• k ≡ Permittivity in farads/m (())
• k ≡ kr ko
• ko≡ Permittivity of free space (8.85410-12 F/m)
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CAPACITANCE OF A SINGLE PHASE
TWO-WIRE LINE
Capacitance to neutral:
3
Charging Current:
Vab ≡ the applied voltage of single phase supply
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CAPACITANCE OF A THREE-PHASE LINE WITH EQUILATERAL SPACING
Capacitance to neutral:
The charging current in each phase:
Van ≡ Phase Voltage
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CAPACITANCE OF A THREE-PHASE LINE WITH UNSYMMETRICAL SPACING
TRANSPOSED
Capacitance to neutral:
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CAPACITANCE FOR BUNDLED CONDUCTORS
Capacitance to neutral:
GMD
GMR
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ACSR TABLES Because ACSR conductors are stranded, actual resistance,
inductance, and capacitance needs to be determined from tables.
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Inductance and Capacitance assume a geometric mean distance Deq of 1 ft.
GMR is equivalent toeffective radius r’
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ACSR TABLES
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Term independent of conductor, but with spacing Dm in feet.
Term from table, depending on conductor type,but assuming a one foot spacing
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TRANSMISSION LINESREPRESENTATION
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After determining the TL parameters, we can develop models of transmission lines
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TL MODEL
= r + j wL
= j wC
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r wL r wL r wL r wL
C C C C
Sending End Receiving End
Is Ir
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Short TL
Neglect the Shunt Capacitance
Medium TL
Lumped-parameter representation
TL MODEL
Lumped-parameter representation
Π model T model
Long TL
Distributed-parameters is required to get high degree of accuracy
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SHORT TL
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%100
R
RS
V
VVVR
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SHORT TL
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0 1 CZBDAThese ABCD constants are sometimes called the generalized circuit constants of the TL. A and D are dimensionless and equal each other if the line is the same when viewed from either end. The dimensions of B and C are ohms and mhos, respectively.
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MEDIUM TL (NOMINAL Π)Lumped Parameters
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MEDIUM TL (NOMINAL Π)
Check:
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Check:
%100
R
RS
V
VAVVR
To get voltage Regulation, IR = Zero. Hence, no load
receiving end voltage VR0 = VS / A
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MEDIUM TL (NOMINAL T)
Report:
Find the ABCD matrix model for a T-modeledmedium transmission line. In a T-modeledmedium transmission line, the line capacitancesare lumped together and placed in the middle of
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are lumped together and placed in the middle ofthe line as one capacitor. The line seriesimpedance is divided into two equal parts placedbefore and after the line capacitance so that theline’s equivalent circuit looks like letter “T”.
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LONG TL
Self Study
17Characteristic Impedance
Propagation Constant