Transmission Line Parameters  Example 510
Dr. M. Giesselmann, Mar 07, 2008
ORIGIN
1
:=
N
2
:=
Bundle
4
:=
2 neutrals and 3 phases with bundles of 4:
μ
o
4
π
⋅
10
7
−
⋅
henry
m
⋅
:=
Permeability of Free Space:
ε
o
8.854187817 10
12
−
⋅
farad
m
⋅
:=
Permittivity of Free Space:
R
N
0.489 cm
⋅
:=
GMR
N
0.0636 cm
⋅
:=
ρ
N
1.52
Ω
km
⋅
:=
Radius, GMR, and Resistivity of Neutrals:
R
P
1.519 cm
⋅
:=
GMR
P
1.229 cm
⋅
:=
ρ
P
0.0701
Bundle
Ω
km
⋅
:=
Radius, GMR, and Resistivity of Phases:
ρ
Earth
100
Ω
⋅
m
⋅
:=
Resistivity of Earth along the line:
freq
60 Hz
⋅
:=
ω
2
π
⋅
freq
⋅
:=
ω
376.991 Hz
=
Power Frequency and Omega:
d
45.7 cm
⋅
:=
MW
1000 kW
⋅
≡
Bundle Spacing:
Geometric Mean Radius (GMR) of bundled
Conductors; left column is for Inductance,
right column is for Capacitance, Rows are
for the number of conductors in a bundle:
GMR
GMR
P
GMR
P
d
⋅
3
GMR
P
d
2
⋅
4
2
GMR
P
⋅
d
3
⋅
R
P
R
P
d
⋅
3
R
P
d
2
⋅
4
2
R
P
⋅
d
3
⋅
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
:=
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Er
658.5
coul
kg m
⋅
⋅
ρ
Earth
freq
⋅
:=
D
Er
850.12 m
=
Distance of Earth Return Conductors: 5.7.2
ρ
Er
9.869 10
7
−
⋅
kg m
⋅
coul
2
⋅
freq
⋅
:=
ρ
Er
0.059
Ω
km
=
Resistance of Earth Return Conductors: 5.7.3
Defining xy Coordinate system for Conductor positions: x=0 is the center of the tower, y=0 is the ground level:
X
13.7
−
0
13.7
11
−
11
⎛
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎠
m
⋅
:=
Y
23
23
23
33.5
33.5
⎛
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎠
m
⋅
:=
GMR
L
GMR
Bundle 1
,
GMR
Bundle 1
,
GMR
Bundle 1
,
GMR
N
GMR
N
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
:=
ρ
c
ρ
P
ρ
P
ρ
P
ρ
N
ρ
N
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
:=
X  Pos. of
Conductors:
Y  Pos. of
Conductors:
GMR
of
Conductors
for Ind. calc:
Resistivity of
Conductors:
Calculating Series Impedance:
Total Flux linking conductor k
in an array of M conductors
carrying currents I
m
, whose
sum is zero.
i13N
+
()
..
:=
Defining Index i:
λ
k
210
7
−
⋅
1
M
m
I
m
ln
1
D
km
⎛
⎜
⎝
⎞
⎟
⎠
⋅
⎛
⎜
⎝
⎞
⎟
⎠
∑
=
⋅
=
j13N
+
..
:=
Defining Index j:
If i=j then distance is geometric mean radius GMR of conductor:
Calculating distance from
overhead conductor i
to
overhead conductor j:
Dist
ij
,
X
i
X
j
−
2
Y
i
Y
j
−
2
+
≠
if
GMR
L
i
otherwise
:=
Note that X(Overhead) = X(Return)
Calculating distance from
overhead conductor i
to
earth return conductor j:
Dist_g
,
X
i
X
j
−
2
Y
i
Y
j
D
Er
−
−
⎣
⎦
2
+
:=
λ
i
μ
o
2
π
⋅
1
3N
+
j
I
j
ln
Dist_g
,
Dist
,
⎛
⎜
⎝
⎞
⎟
⎠
⋅
⎛
⎜
⎝
⎞
⎟
⎠
∑
=
⎡
⎢
⎢
⎣
⎤
⎥
⎥
⎦
⋅
=
Total flux Linkage of over
head conductor i:
Defining Elements of
Impedance Matrix:
Z
,
ρ
Er
j
μ
o
⋅
freq
⋅
ln
Dist_g
,
Dist
,
⎛
⎜
⎝
⎞
⎟
⎠
⋅
+
≠
if
ρ
c
i
ρ
Er
+
j
μ
o
⋅
freq
⋅
ln
Dist_g
ii
,
Dist
,
⎛
⎜
⎝
⎞
⎟
⎠
⋅
+
otherwise
:=
The following equation system is used for series impedance calculation:
E
P
Z
A
I
P
⋅
Z
B
I
N
⋅
+
=
Or in short form:
0Z
C
I
P
⋅
Z
D
I
N
⋅
+
=
E
Aa
,
E
Bb
,
E
Cc
,
0
0
⎛
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 Spring '08
 GIESSELMANN
 Orders of magnitude, Electrical impedance, Konrad Zuse, GMR, GMR Bundle

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