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8/3/2019 Power System Engineering Lecture 11
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Review of Last Lecture
Lossless transmission line Surge impedance loading
Power flow through the transmission line
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Lossless Transmission Line
In loss less line, resistance is assumed to be zero
RRx
RCRx
IxVZc
xI
IxZVxV
coshsinh
sinhcosh
C
LZ
C ljl
RRx
RCRx
IxVZc
xjI
IxjZVxV
cossin
sincos
=0
and
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Surge Impedance Loading
RRCx
RCRx
IxVxZjI
IxjZVxV
cossin1
sincos
R
RCRCR
I
VZIZV
lj
RS
lj
RS
eII
eVV
xRCRxRCR eIZV
eIZV
V
22
If the line is terminated with surge impedanceZc , the
power transferred to load is called surge impedance
loading
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Power Transfer Through Transmission
Line
SV 0
RV
RRR jQPS SSS jQPS
Gen Load
B
AV
B
VIBIAVV RSRRRS
BBAA andLet
B
VA
B
VI
RS
R
ABCD
B
VA
B
VI
RS
R
0
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Power Flow Through Transmission Line
Complex power VRIR* at receiving end:
BVA
BVI RSR
*
BVA
B
VVjQPIV
RRS
RRRR
2
*
Real Part:
Imaginary Part:
coscos
2
B
VA
B
VV
P
RRS
R
sinsin2
B
VA
B
VVQ
RRS
R
Separating real and imaginary parts
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Power Flow Through Transmission Line
Maximum power will get transferred, if=
cos2
max_
B
VA
B
VVP
RRS
R
sin2
max_B
VAQ
R
R
Real Part:
Imaginary Part
coscos2
B
VA
B
VVPRRS
R
sinsin2
B
VA
B
VVQ
RRS
R
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Receiving End Circle Diagram
B
VV RSB
VAR
2
RR IV
R
BVA
B
VVIV
RRS
RRR
2
W
Var
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Maximum Power in Short Line
Approximation
For Short lineA=1,B=Z, C=0,D=1
ZRCZBDA /cos,0,,01
RZ
V
Z
VV
Z
V
Z
VVP
RRSRRS
R 2
22
max_ cos
cos2
max_BVA
BVVP RRSR
sin2
max_B
VAQ
R
R
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With large X/R Ratio
jXZXR thenGenerally,
sinXVVP RSR
,0,90,01 CXBDA
X
VVP
RS
R max_
X
V
X
VVQ
RRS
R
2
cos VX
VVV
X
VQ
R
RS
R
R
Real Part:
Imaginary Part
coscos2
BVA
BVVP RRSR
sinsin2
B
VA
B
VVQ
RRS
R
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Steady State Stability Limit
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Power Transfer Capability
Thermal Limit Voltage drop limit Stability limit
lSIL
lZ
V
B
VVP
c
RRS
R
sin
sinsin
sinsin
2
Actual Design
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Sending End Power
RRS DICVI
B
V
B
DVI
B
BCADVVB
D
VB
DAV
B
DCVI
RS
S
RS
RSRS
BAV
BVI RSR but
Complex power VSIS* at receiving end:
BBADA andLet
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Sending End Power
B
VV
B
VAjQPIV
RSS
SSSS
2
*
Real Part:
Imaginary Part
coscos2
B
VV
B
VAP
RSS
S
sinsin2
B
VV
B
VAQ
RSS
S
Separating real and imaginary parts
B
V
B
VA
B
V
B
VD
IRSRS
S
0
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Overhead Transmission Lines
Mechanical Design, Insulators, Electrical Design
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Main Objectives
Choice of voltage, choice of conductor, spacing between
conductors
Calculation line constants, regulation and efficiency
Calculation of Corona Loss
Choosing number and type of insulators Choice of method of grounding
Calculation of radio interference
Stability considerations
Electrostatic and electromagnetic effect
Insulation coordination
Protective system
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Main Components of Overhead Line
Conductors Copper
Aluminum: ACSR, AAAR, AAC, Expanded ACSR
Support Structure (Towers)
Galvanized steel (for high voltage) Wood, concrete, steel (for low voltage)
Insulators
Porcelain
Glass
Polymer insulation
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Mechanical Design
Main Factors Selection of line route
Types of tower or pole
Right of way
Ground and conductor clearance Tower spacing, span length
Mechanical loadings
Weight of conductor per unit length
Load due to wind, ice, snow, etc. Temperature
Conductor tension
Distance between the supports (Span length)
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Sag and Tension:
Maximum sag so thatclearance to ground
and other conductors
can be maintained.
Maximum tension sothat structures can be
designed to withstand
it.
Minimum sag to
control structure uplift
problems.
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Calculation of Sag and Tension
L =Span length
O is the lowest point on the wire
ws =weight per unit length
H= tension at point O
T= tension at point P
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Calculation of Sag and Tension
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Calculation of Sag and Tension
Integrating
Atx=0, s=0, therefore c1=0
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Calculation of Sag and Tension
Also
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Calculation of Sag and Tension
Integrating
Aty=0,x=0, therefore
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Calculation of Sag and Tension
For tension at point P,
We know
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Support at Same Heights
If the towers at same height and span is 2l, i.e. half span is l
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Supports at Different Heights
ya
yb
2l
2l-x1
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Supports at Different Heights
For towerB
For towerA
Therefore, difference in tower heights
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Approximate Formulae for Sag and Tension
and
and