Short transmission line modeling

1. Short transmission line model

2. 2
Introduction
Short line model
Medium line model
Long line model
Voltage and current waves
Surge impedance loading
Complex power flow through TLs
Power Transmission Capability
Line Compensation
Line Model and Performance

3. 3
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 considered.
• The performance of transmission line is
measured based on the voltage regulation and
line load ability.

4. 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. 5
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.

6. 6
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
R
R
S
R
R
S
I
V
D
C
B
A
I
V
DI
CV
I
BI
AV
V

7. 7
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.

8. 8
Short Line Model
l
VR
VS
IR
IS
R XL
Z

9. 9
Short Line Model
 
length
line
inductance
phase
-
per
resistance
phase
-
per
:
where











L
r
jX
R
L
j
r
z
Z
L


10. 10
Short Line Model
• Thus, the ABCD parameters are easily
obtained from KVL and KCL equations as
below:
S
C
Z
B
pu
D
A
I
V
Z
I
V
I
I
ZI
V
V
R
R
S
S
R
S
R
R
S
0
;
;
1
1
0
1




























11. 11
Complex Power
 Sending end power
 Receiving end power
     
     
line
R
line
R
R
phase
R
phase
R
R
I
V
S
or
I
V
S
*
3
*
3
3
3




     
     
line
S
line
S
S
phase
S
phase
S
S
I
V
S
or
I
V
S
*
3
*
3
3
3




phase
line V
V 3
Remember!


12. 12
Transmission Line Efficiency
• Total Full–Load Line Losses
• Transmission Line Efficiency
– Note that only Real Power are taken into account!
     


 3
3
3 R
S
L P
P
P 

 
 
 
 
100
%
3
3
3
3









S
R
S
R
P
P
P
P

13. 13
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.

14. 14
Voltage Regulation
R
FL
R
S
NL
R V
V
A
V
V 
 )
(
)
(
100
%
)
(
)
(
)
(



FL
R
FL
R
NL
R
V
V
V
VR
No–load
receiving–end voltage
Full–load
receiving–end voltage

15. 15
??
2
1
V
V
V
V
V
;
0
:
AV
V
S
RNL
S
RNL
RNL
RNL
S
Line
Long
ZY
Line
Medium
Line
Short
A
V
Thus
I
Condition
Load
No
BI
s
R
R














16. 16
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. 18
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.

18. Home task
• Draw the phasor diagram of short
transmission line connected to inductive load
• Draw the phasor diagram of short
transmission line connected to capacitive load