This document discusses transmission line models of different lengths and their voltage and current characteristics. It introduces short, medium, and long line models. The short line model approximates lines less than 80 km by neglecting shunt effects. It derives the ABCD parameters for the short line model using series resistance, inductance and impedance. The document also covers voltage regulation with changes in load and power factor.

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