1 BEE 3133 ELECTRICAL POWER SYSTEMS Chapter 4 Line Model and Performance Rahmatul Hidayah Salimin
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1
BEE 3133 ELECTRICAL POWER
SYSTEMS
Chapter 4Line Model and Performance
Rahmatul Hidayah Salimin
2
Introduction Analyze the performance of single-phase
and balanced three-phase transmission lines under normal steady-state operating conditions.
Expression of voltage and current at any point along the line are developed, where the nature of the series impedance and shunt admittance is taken into account.
The performance of transmission line is measured based on the voltage regulation and line loadability.
3
Transmission Line Representation
ABCD
+
VR
-
+
Vs
-
Is IR
A line is treated as two-port network which the ABCD parameters and an equivalent π circuit are derived.
4
Transmission Line Representation To facilitate the performance calculations
relating to a transmission line, the line is approximated as a series–parallel interconnection of the relevant parameters.
Consider a transmission line to have: A sending end and a receiving end; A series resistance and inductance; and A shunt capacitance and conductance
5
Transmission Line Representation The relation between sending–end and
receiving–end quantities of the two–port network can be written as:
R
R
S
S
RRS
RRS
I
V
DC
BA
I
V
DICVI
BIAVV
6
Transmission Line Representation Short Line Model < 80 km in length Shunt effects are neglected.
Medium Line Model Range from 80–240 km in length Shunt capacitances are lumped at a few
predetermined points along the line. Long Line Model >240 km in length. Uniformly distributed parameters. Shunt branch consists of both capacitance and
conductance.
7
Short Line Model
l
VRVS
IRIS R XL
Z
8
Short Line Model
length line
inductance phase-per
resistance phase-per
:where
L
r
jXR
LjrzZ
L
9
Short Line Model Thus, the ABCD parameters are easily
obtained from KVL and KCL equations as below:
SCZBpuDA
I
VZ
I
V
II
ZIVV
R
R
S
S
RS
RRS
0;;1
10
1
10
Complex Power Sending end power
Receiving end power
lineRlineRR
phaseRphaseRR
IVS
or
IVS
*3
*3
3
3
lineSlineSS
phaseSphaseSS
IVS
or
IVS
*3
*3
3
3
phaseline VV 3
Remember!
11
Transmission Line Efficiency Total Full–Load Line Losses
Transmission Line Efficiency
Note that only Real Power are taken into account!
333 RSL SSS
100%
3
3
3
3
S
R
S
R
P
P
P
P
12
Voltage Regulation ABCD parameters can be used to describe
the variation of line voltage with line loading.
Voltage regulation is the change in voltage at the receiving end of the line when the load varies from no–load to a specified full–load at a specified power factor, while the sending end is held constant.
13
Voltage Regulation
RFLRS
NLR VVA
VV )()(
100%)(
)()(
FLR
FLRNLR
V
VVVR
No–load receiving–end voltage
Full–load receiving–end voltage
14
??
21
VV
VV
V
;
0:
AVV
SRNL
SRNL
RNL
RNLS
LineLong
ZYLineMedium
LineShortA
V
Thus
IConditionLoadNo
BI
s
R
R
15
Voltage Regulation The effect of load power factor on voltage
regulation is illustrated in phasor diagram. The phasor diagrams are graphical
representation of lagging, unity and leading power factor.
17
Voltage Regulation In practice, transmission line voltages
decrease when heavily loaded and increase when lightly loaded.
EHV lines are maintained within ±5% of rated voltage, corresponding to about 10% voltage regulation.
10% voltage regulation for lower voltage lines also considered good operating practice.
19
Example 1 :Short TL A 220-kV, 50 Hz, three-phase transmission line
is 40 km long. The resistance per phase is 0.15 Ω/km and the inductance per phase is 1.5915 mH/km. The shunt capacitance is negligible. Use the line model to find the voltage and power at the sending end and the voltage regulation and efficiency when the line is supplying a three-phase load of
a) 381 MVA at 0.8 pf lagging at 220 kVb) 381 MVA at 0.8 pf leading at 220 kV
20
Example 2 :Short TL A 220-kV, 50 Hz, three-phase transmission line
is 40 km long. The resistance per phase is 0.15 Ω/km and the inductance per phase is 1.5915 mH/km. The shunt capacitance is negligible. Use the line model to find the voltage and power at the sending end and the voltage regulation and efficiency when the line is supplying a three-phase load of
a) 381 MVA at 0.8 pf lagging at 220 kVb) 381 MVA at 0.8 pf leading at 220 kV
21
Solution (a) Given
R = 0.15 Ω/km , L = 1.5915 mH/kmS =381 MVA with pf 0.8 lagVR(line)=220 kV
+
Vs
_
+
VR
_
Is IR
R jXL
Z=R+jωL Ω
22
206
405915.150215.0
Z
phase;per impedance series The
40km
j
mj
lLjr
kV
kV
VV
o
o
LineRphaseR
0127
3
0220
3
RR
RRS
I and Z,,V find Therefore,
ZIVV voltage,end sending Find
23
A
kV
MVA
MjMWMVAS
Thus
o
o
o
oR
o
87.361000
01273
87.36381
3V
S I
3V
S I
I3VS
var6.2288.30487.36381
,
87.368.0cos MVA, 381S
*R(Phase)
*R
R
R(Phase)
R*R
*RR(Phase)R
-1
24
250V
144.33
3
93.4144.3
87.3610002060127
VV
Therefore,
PhaseRS(Phase)
PhaseSLineS
o
oo
R
VV
kV
AjkV
ZI
25
SISS 3V S Power, end-Sending Find
MVA
MjMW
AV
AII
o
o
oRS
8.41433
var6.2888.322
87.3610004.93144.33 3
I3VS
87.361000
o
*SS(Phase)S
26
%6.13
100220
220250
100 %VR
RFL
RFLRNL
V
VV
Voltage Regulation,
%4.94
1008.322
8.304
100 %
S
R
P
P
Effiency,η
27
Medium Line Model – Nominal π Circuit
l
VR
IRIS R XL
Z
VS Y/2 Y/2
28
Medium Line Model Shunt capacitor is considered. ½ of shunt capacitor considered to be
lumped at each end of the line – π circuit Total shunt admittance, Y
length line
kmper econductanc line
kmper ecapacitanc neutral toline
:where
g
C
CjgY
29
Medium Line ModelUnder normal condition, shunt conductance per unit length (the
leakage current) over the insulators and due to corona is negligible
Thus, g = 0
30
Medium Line Model To obtain ABCD parameters, the current in
the series branch is denoted as IL.
Using KCL and KVL, the sending–end voltage is:
3..2
1
2
2 and 1 From
2..2
1..
RR
RRRS
RRL
LRS
ZIVZY
VY
IZVV
VY
II
ZIVV
31
Medium Line Model
32
Medium Line Model
33
Medium Line Model Using KCL to obtain equation for sending–
end current:
5..2
14
1
221
2
4 into 3 and 2 Substitute
4..2
RR
RRR
RS
SLS
IYZ
VYZ
Y
YZIV
YZYVII
VY
II
34
Medium Line Model Thus, the ABCD parameters can be
obtained from equation [3] and [5];
SZY
YCZBpuZY
DA
I
V
ZYZYY
ZZY
I
V
R
R
S
S
41;;
21
21
41
21
35
Medium Line Model ABCD constant are complex since π model
is a symmetrical two-port networkA = D
The determinant of the transmission matrix is unity(1)
AD – BC = 1 (Prove this!)
36
Medium Line Model The receiving and quantities can be
expressed in terms of the sending end quantities
If, ignore the shunt capacitance of the TL, the shunt admittance, Y=0, it become the short transmission line constant.
S
S
R
R
I
V
AC
BD
I
V
37
Example 2 : Medium TL A 345-kV, 60 Hz, three-phase transmission line
is 130 km long. The resistance per phase is 0.036 Ω/km and the inductance per phase is 0.8 mH/km. The shunt capacitance is 0.0112 μF/km. Use the medium line model to find the voltage and power at the sending end and the voltage regulation and efficiency when the line is supplying a three-phase load of
a) 325 MVA at 0.8 pf lagging at 325 kVb) 381 MVA at 0.8 pf leading at 325 kV
38
Medium Line Model – Nominal
T Circuit
l
VR
IRIS
VS Y
Z/2 Z/2
Find the ABCD Parameters for this circuit using KVL and KCL
39
Long Line Model
l
VR
IRISZ’
VS Y’/2 Y’/2
40
Long Line Model The shunt capacitance and series
impedance must be treated as distributed quantities
The ‘V’ and ‘I’ on the line must be found by solving the differential equation of the transmission line.
41
Long Line Model
2tanh
1
2
2tanh
22
'
sinhsinh
'
c
c
c
Z
YY
ZZZ
y
zZzy
CjgyLjRz
γ = propagation constant
Zc = characteristic impedance
42
Long Line Model If γl <<0 sinh (γl )/( γl ) & tanh (γl /2)/ (γl /2) ≈ 1.0The ABCD parameters:
12
'' D 1
4
'''
' 12
''
YZYZYC
ZBYZ
A
I
V
DC
BA
I
V
R
R
S
S
43
ABCD Parameters
ABCD Parameters
A B
C D
Short Line
1 Z
0 1
Mediumπ
MediumT
LongLine
44
Surge Impedance Loading When the line is loaded by being
terminated with an impedance equal to its characteristic impedance, the receiving end current is
For a lossless line, Zc is purely resistive. The load corresponding to the surge impedance at rated voltage is known as the surge impedance loading (SIL).
C
RR Z
VI impedanceSurge
C
LZC ;
45
Surge Impedance Loading
Since VR = VLrated/√3, SIL in MVA becomes
3
32
C
RRR Z
VIVSIL
MW
2
C
Lrated
Z
kVSIL
46
Surge Impedance Loading SIL is useful measure of transmission line
capacity as it indicates a loading where the line’s reactive requirement are small.
For loads significantly above SIL, shunt capacitor may be needed to minimize voltage drop along the line.
While for light loads significantly below SIL, shunt inductors may be needed.
47
Power Transmission Capability Power handling ability of a line is limited
by: Thermal loading limit Stability limit
Thermal loading limit:
3 thermalratedthermal IVS
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