1
EXPERIMENT 12
Transmission Line Parameters
Series Impedance and Shunt Capacitance Calculations using
MATLAB
Objectives
Calculate the inductance and capacitance of a modern transmission line.
Statement of the problem:
Complete the work required in each part of Problems 1 2 and 3.
Describe how you intend to solve the problem. What tools will you use What input
data is required Carefully read the following examples first.
The function GMD GMRL GMRC gmd is developed for the computation of
GMD GMR
L
and GMR
C
for single-circuit double-circuit vertical and horizontal
transposed lines with up to four bundled conductors. A menu is displayed for the
selection of any of the above three circuits. The user is prompted to input the phase
spacing number of bundled conductors and their spacing conductor diameter and the
GMR of the individual conductor. The specifications for some common ACSR
conductors are contained in a file named ascr.m. The command acsr will display the
characteristics of ACSR conductors. Also the function L C gmd21c in addition to
the geometric mean values returns the inductance in mH per km and the capacitance in
F µ per km.
Example 1
A 735-k V three-phase transposed line is composed of four ACSR 954000-cmil 45/7
Rail conductors per phase with horizontal conductor configuration as shows in Figure
E.1. Bundle spacing is 46 cm. Use acsr in MATLAB to obtain the conductor size and the
electrical characteristics for the Rail conductor. Find the inductance and capacitance per
phase per kilometer of the line.
FIGURE E.1
Conductor layout for Example 1.
The command acsr displays the conductor code name and the area in cmils for the ACSR
conductors. The user is then prompted to enter the conductor code name within single
quotes.
23
44.5 D
12
44.5 D
18"
a b c
13
89 D

slide 2:

2
Enter ACSR code name within single quotes -› ‘rail’
Al Area Strand Diameter GMR Resistance Ohm/km Ampacity
Cmil Alt/St cm cm 60Hz 25C 60Hz 50C Ampere
954000 45/7 2.959 1.173 0.0624 0.0683 1000
The following commands
GMD GMRL GMRC gmd
L0.2logGMD/GMRL mH/km
C 0.0556/logGMD/GMRC micro F/km
result in
Number of three-phase circuits Enter
Single-circuit 1
Double-circuit vertical configuration 2
Double-circuit horizontal configuration 3
To quit 0
Select number of menu -› 1
Enter spacing unit within quotes ‘m’ or ‘ft’ -› ‘ft’
Enter row vector D12 D23 D13 44.5 44.5 89
Cond. size bundle spacing unit: ‘cm’ or ‘in’ -› ‘cm’
Conductor diameter in cm 2.959
Geometric Mean Radius in cm 1.173
No. of bundled cond. enter 1 for single cond. 4
Bundle spacing in cm 46
GMD 56.06649 ft
GMRL 0.65767 ft GMRC 0.69696 ft
L 0.8891
C 0.0127
Example 2
A 345-kV double-circuit three-phase transposed line is composed of two ACSR
1431000-cmil 45/7 Bobolink conductors per phase with vertical conductor
configuration as shows in Figure E.2. The conductors have a diameter of 1.427 in and a
GMR of 0.564 in. The bundle spacing is 18 in. Find the inductance and capacitance per
phase per kilometer of the line. The following commands
FIGURE E.2
Conductor layout for Example 2.
11
11 Sm
12
7 H m
22
16.5 Sm
23
6.5 H m
33
12.5 Sm

slide 3:

3
GMD GMRL GMRC gmd
L0.2logGMD/GMRL mh/KM
C 0.0556/logGMD/GMRC micro F/km
result in
Number of three-phase circuits Enter
Single-circuit 1
Double-circuit vertical configuration 2
Double-circuit horizontal configuration 3
To quit 0
Select number of menu -› 2
Circuit Arrangements
1 abc-c’b’a’
2 abc-a’b’c’
Enter 1 or 2 -› 1
Enter spacing unit within quotes ‘m’ or ‘ft’ -› ‘m’
Enter row vector S11 S22 S33 11 16.5 12.5
Enter row vector H12 H23 7 6.5
Cond. size bundle spacing unit: ‘cm’ or ‘in’ -› ‘in’
Conductor diameter in inch 1.427
Geometric Mean Radius in inch 0.564
No. of bundled cond. enter 1 for single cond. 2
Bundle spacing in inch 18
GMD 11.21352 m
GMRL 1.18731 m GMRC 1.25920 m
L 0.4491
C 0.0254
Example 3
A 345-kV double-circuit three-phase transposed line is composed of one ACSR 556500-
cmil 26/7 Dove conductor per phase with horizontal conductor configuration as shown in
Figure E.3. The conductors have a diameter of 0.927 in and a GMR of 0.3768 in
Example 3. Find the inductance and capacitance per phase per kilometer of the line. The
following commands
FIGURE E.3
Conductor layout for Example 3.
GMD GMRL GMRC gmd
L0.2logGMD/GMRL mH/km
C 0.0556/logGMD/GMRC micro F/km
11
9 Sm

slide 4:

4
Result in
Number of three-phase circuits Enter
Single-circuit 1
Double-circuit vertical configuration 2
Double-circuit horizontal configuration 3
To quit 0
Select number of menu - 3
Circuit Arrangements
1 abc-a’b’c’
2 abc-c’b’a’
Enter 1 or 2 - 1
Enter spacing unit within quotes ‘m’ or ‘ft’ - ‘m’
Enter row vector D12 D23 D13 8 8 16
Enter distance between two circuits S11 9
Cond. size bundle spacing unit: ‘cm’ or ‘in’ - ‘in’
Conductor diameter in inch 0.927
No. of bundled cond. enter 1 for single cond. 1
GMD 14.92093 m
GMRL 0.48915 m GMRC 0.54251 m
L 0.6836
C 0.0168

slide 5:

5
Prob. 1 A three-phase transposed line is composed of one ACSR 1.431000-cmil
45/7 Bobolink conductor per phase with flat horizontal spacing of 11 m as
shown in Figure 1. The conductors have a diameter of 3.625 cm and a
GMR of 1.439 cm. The line is to be replaced by a three-conductor bundle
of ACSR 477000-cmil 26/7 Hawk conductors having the same cross-
sectional area of aluminum as the single-conductor line. The conductors
have a diameter of 2.1793 cm and a GMR of 0.8839 cm. The new line
will also have a flat horizontal configuration but it is to be operated at a
higher voltage and therefore the phase spacing is increased to 14 m as
measured from the center of the bundles as shown in Figure 2. The
spacing between the conductors in the bundle is 45 cm. Determine
a The percentage change in the inductance.
b The percentage change in the capacitance.
FIGURE 1
Conductor layout for Problem 1 a.
FIGURE 2
Conductor layout for Problem 1 b.
13
28 D m
12
14 Dm
23
14 Dm
13
22 Dm
12
11 D m
23
11 D m

slide 6:

6
Prob. 2 A single-circuit three-phase transposed transmission line is composed of
four ACSR 1272000-cmil conductor per phase with horizontal
configuration as shown in Figure 3. The bundle spacing is 45 cm. The
conductor code name is pheasant. In MATLAB use command acsr to find
the conductor diameter and its GMR. Determine the inductance and
capacitance per phase per kilometer of the line. Use function GMD
GMRL GMRC gmd in MATLAB to verify your results.
FIGURE 3
Conductor layout for Problem 2.
Prob 3. A double circuit three-phase transposed line is composed of two ACSR
2167000-cmil 72/7 Kiwi conductor per phase with vertical configuration
as shown in Figure 4. The conductors have a diameter of 4.4069 cm and a
GMR of 1.7374 cm. The bundle spacing is 45 cm. The circuit
arrangement is
11 1 2 2 2
abc c b a . Find the inductance and capacitance per
phase per kilometer of the line. Find these values when the circuit
arrangement is
11 1 2 2 2
abc a b c . Use function GMD GMRL GMRC
gmd in MATLAB to verify your results.
FIGURE 4
Conductor layout for Problem 3.
13
28 D m
12
14 Dm
23
14 D m
12
16
aa
Sm
12
10 Hm
12
24
bb
Sm
23
9 Hm
12
17
cc
Sm

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