Transmission Line Parameters

1
????????????????? Transmission Line Parameters
??????? ??????????
2
???????

• ????????????????? (Overhead Transmission Line)

• ???????????????? (Line Resistance)

• ?????????????????? (Line Inductance)

• ?????????????????? (Line Capacitance)

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
3
?????? (Transmission Line)

• ????????????????????????????????????????????

• ?????????? ??????????, ???? ??????????? (Shield
  wires)

• ??????????????????????????? ???????
  ??????????????????? (???????? 1 )

• ???????????????????? ????????????????????????????
  ??????????? (69 kV, 115 kV, 138 kV, 161 kV, 230
  kV, 345 kV, 500 kV ??? 765 kV)

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
4
Overhead Transmission Line
Single Circuit
5
Overhead Transmission Line
220 kV
Double Circuit
6
Underground Transmission Line
7
????????????????????????
???????????????????? ????? ???????????
?????????????? ????????????????????????
?????????????????
????????????????? ????????

1. AAC All Aluminum Conductor
2. AAAC All Aluminum Alloy Conductor
3. ACSR Aluminum Conductor, Steel Reinforced
4. ACAR Aluminum Conductor, Alloy Reinforced

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
8
AAC All Aluminum Conductor

• ???????????????????????? ????????

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
9
AAA All Alulminum Alloy Conductor

• ??????????????????????? ????????? ????????

• ?????????????????? ??? AAC

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
10
ACSR Aluminum Conductor, Steel Reinforced

• ??????? (Steel) ??????????? ?????????????????????
  ????

steel
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
11
ACAR Aluminum Conductor, Alloy Reinforced

• ????????????????????????????????? ???????????
  ?????????????????????????

• ??????? 7 ????
• ?????? 30 ???
• 2 ???? (2 layers)

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
12
??????????????????????
???????????????????
????????????????????????? ? Circular mils (cmil)
?????????????????? ? ??? (foot, ft)
???? SI
????????????????????????? ? ????????? (m2)
?????????????????? ? ???? (meter, m)
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
13
1 circular mil (cmil ???? CM)
- ????????????????????????????????????? (d) 1 mil
(1/1000 ????)
?????????????????????
d
???????
1 MCM 1,000 cmil
14
??????????? 1
???????????????? AAC ??? Hawkweed?????????????????
???????????????????????????? ?????????????????????
0.1644 ???? ????? 37 ???? ???????????????????????
???????????????????????????????? 1,000,000 cmil
????
1. ????????????????????????? ?????????????????????
2. ???????????????????????????????????
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
15
???
1 mil 1/1000 ????
1 ???? 1,000 mil
??????????????????????????????? (mils)
d
164.4 mils / ??? 1 ????
?????????????????????? (A) ????? cmil
16

• ??????????????????????? mm2

???
1 ???? ? 2.54 cm ? 25.4 mm
?????????????????????????????????????????? ????
???????????????????????????????? ?????????
17
???????????????????
???????? ?????????????????????????? 4 ??? ???

1. ?????????????? (Resistance)
2. ???????????????? (Inductance)
3. ?????????????? (Capacitance)
4. ????????? (Conductance)

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
18
??????????????????? Line Resistance
19
??????????????????????? ????????
??????????????????? ??????????????????????
?????????????????????? ???
??? ??? Resistivity ????????
??? ??????????????????
??? ??????????????????????
??????????????? ???????????????????????? 2
20
????????????????????????????????????
Skin Effect, Skin dept
1. ???????
2. ?????????????
??????????
3. ????????
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
21
???????????????????????????????????????

• ?????????????????????????????????
  ????????????????????

R1,R2 ??? ?????????????????????????????? t1 ???
t2 (OC)
T ??? ???????????????? ???????????????? ???? Al
?? T 228
Cu ?? T 234.5
22
??????????? 2
?????????????????????????????????? 20oC ?????
21.72 Ohm ????????????????????????????????????????
20oC
???
??????
Cu ?? T 234.5
?????
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
23
??????????????????????? ?????????

• ??????????????????????????????????????

• ??????????????????????????????????? ????? Skin
  Effect

• ?????????????????????? ????????????????????????
  ??????????????????????????????? ?????? 2

????????? ??????????????????????
?????????????????????????
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
24
(No Transcript)
25
http//www.allaboutcircuits.com/vol_2/chpt_3/6.htm
l
Gage size k factor Gage size k factor
4/0 124.5 8 34.8
2/0 99.0 10 27.6
1/0 88.0 14 17.6
2 69.8 18 10.9
4 55.5 22 6.86
6 47.9
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
????????????????????? Line Inductance
30
?????????????????????????
?????????????????????????? ???????????????????????
??????? ????????? ???????????????????????????????
???????????????????
Flux Linkage
Piyadanai Pachanapan, 303327 Power System
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31
????????????????????????? ??????????????

• ?????????????????? ??????????????????????????????
  ???????

• ???????????????? ? ??????????????? (
  )??????????????? (in phase)

?????
??? ????????????????
??????????????????????????????????????????????????
??????????????
32
???????????????? (Faradays Law) ?????

• ???????????????????????????????????
• ???????????????

????????????????????????????
???
?????
??? ????????????? ????????? Henry, H
??? ???????????????????????? (Flux Leakage)
(waber turns)
33
???????????????????????????? ?????????????????????
????? (flux linkage) ????????????????????
??????
??? ????????? ??? ?????????????
???????????????????? (????????) ????????? flux
linkage ??????????
-
V
V
????????

V
34
????????????????????????? ???????????
????????? 2 ?????????? ??????????????????????????
?? ????????????????????????????????? ?????
????????????????? (mutual inductance) ????

• ??? I2 ??????? 2 ????????? flux linkage ?????? 1
  ?????

• ??????????????? flux linkage ?????? 1
  ???????????? 2 ????

Piyadanai Pachanapan, 303327 Power System
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35
2
1
??????????????????????????? 2 ????????????????????
???????????????? 1
36
???????????????????????????

• Amperes Circuital Law

At
????? H - ???????????????????? At/m
S - ???????????????????? ???????????? m
I - ????? A
At Ampare - turn
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
37
?????????????????????????? ??????? x ??? Hx
??????????????????
?????

• ????????????????????????????????????? ?????????
  skin effect

?????
At/m
38
??????????????????????? ?????????
- Permeability
?????? Hx ?????
Wb/m2
????????? ??????????????????? dx
????????????
Wb/m
39
???
???
????? flux linkage ( ) ??????????????? m
????????? ????
?????? ?????
Wb.t / m
40
Flux linkage ?????????? ??????? ???
Wbt / m
(??????????????????)
??????
???
Cu, Al
41
?????
???
??????????????????????????????????????? ????
Henry / m
?????????????????????????? ????????????????????
??
42
??????????????????????????????????????????????????
?

• ???? x gt r

• ??????????????? Ix I ???????

• ???????????????????????? P1 ??? P2
  ??????????????????????????????????????????????????
  ????

r

• ??????? x ?????????????????????????? Hx

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
43
??? Amperes law
???
Wb/m2
?????? ??????????????????? dx ???
Wb/m
44

• Flux linkage ??? ??????
  ???????????? ?????????????????????????????????????
  ???? ??????????????? (Ix I ????)

• ????? Flux Linkage ?????????? P1 ??? P2 ????

P1
P2
45
??????
??????
(??????????????????)
???
Cu, Al
?????
???
?????
Henry / m
46
?????????????????????? 2 ??????????????????
???? 1 ??? 2 ???
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
47
?????? 2 ??????????? r1 ??? r2 ???????????????????
?? D ????????????????????????????????????????? ?
I2 - I1

-
48
???????????????????????? ???? 4 ???? ??????

• ?????????????????????

• ?????????????????????????????????

• ????????????????????????????????????????????????

• ?????????????????????????????

49
??????????????????????????????????? 1 ?????
??????? ??????????????????????? 1
???? lt D r2
?????????????????????????????? 0 (????? 1)
???? gt D r2
???????? ???????????
??????? D r2 ??? D r2
50
?????????
? ????????????????????????????????
?????
???
(????????? r2)
??????????????????????????????????? 1
H/m
?????
H/m
??????
??????????????????????????? 1 ???
H/m
51
???????????????????????????????? ????
52
?????
?????
??? ???????????????????????? (geometric mean
distance) ????????????? r (GMR)
???? ??????????????????? (Geometric mean
radius) ???????????? Ds
53
????????????????????????????????????????? ?????
???
??????????????????????????????????? ???????????
???????????????????????????????????????
???????????
54
??????????????????????????????????????????????????
?? (Flux Linkage of One Conductor in a Group)

• ??????????????????? n ???

• ??????????????????????????????????

?????
??? ?????????????????? 1,2,...,n
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
55
??????????????????????????
??????????????? P ???? External Flux Linkage
56
?????????????????? 1

• Flux Linkage ??????????????? 1 ?????????????? I1

• Flux Linkage ??????????????? 1 ?????????????? I2

?????
??? ????????????? P ?????????? n
DnP
57
????????????????????? n ??? ????? Flux linkage
???????? 1 ???????????????????????????????????????
? ?????????????? P ?????????
???
58
????????
?????? P ??????????? ?
0
59
??????????????????????????? 1 ?????????
?????????????????????? ???????
?????
??????
??? ????????????????????????? i ???????? j
60
???????????????????????????? 3 ???
?????????????????????????????????? ??? 3 ???? ???
1. ?????????????????????
2. ????????????????????????
3. ?????????????
Piyadanai Pachanapan, 303327 Power System
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61
???????????? 3 ?????????????????? (Symmetrical
Spacing)

• ????? 3 ???? ????????????????????? D ???????

• ???????????????????? r ??????????????????

• ????????????????????????????? ??????? ?????

62
????????? ???????????????
???
?????????? n 3 ????? Flux Linkage ??????????? a
????
???
Wbt/m
63
?????????????????? ?
H/m
????
mH/km
?????
??? Geometric mean radius, GMR, ?????????? Ds
??????? ????????????????????? ?
??????? ????????????????? ?
?????????.?????????
64
???????????? 3 ?????????????????????
(Asymmetrical Spacing)

• ???????????????? ????????????????????????????????
  ???????

• ??????????????????? ? ???????????????????????????
  ????????????

Piyadanai Pachanapan, 303327 Power System
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65
Flux Linkage ???????????????? ?????????
66
???????????????????????? ???????
???????? L ????
??????????????????????? (Couple Flux)
67
?????????????????? a ????????????????
?????????????????? ????
???????????????????????????????????????
??? a
68
???
??????????????????????
????????????? ???????????????????????????? ????
?????????????
69
???????????????????????????????????????????
(Transpose Line)

• ?????????????????? ? ????????????????????????????
  ?????

• ????????????????????? 3 ??? ?????????????????????
  (per phase) ???????????????????????????????

• ??????????????????????????????????????????
  ????????????????????? (Transposition) ?
  ?????????????????????????????

???????????????????????? 3 ??? ????????? !!!
Piyadanai Pachanapan, 303327 Power System
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??????????????????????????????
?????????????????????? ????????
????????????????????????????????????
71
?????? La, Lb, Lc ?????????? 3 ??????????????????
???
?????
72
???????????????
H/m
mH/km
????
(Geometric mean distance)
?????
????????????????????????????
73
?????????????????????????????????????????????????
(Inductance of Composite Conductors)

• ????????????? ???????????????????????????????????
  ????????? (Stranded Conductor) ???????????????????
  ??????????????

• ???????????????????? ????????????? (Bundled
  Conductor) ???????????????????????????????????????
  ?

2 ???? !!
??????
74
???????????? 1 ??? ?????????????????? 2 ???
X

• ????? x ??????????? n ??? ???????????????????????
  ?????? ??????????????? rx

• ????? y ??????????? m ??? ???????????????????????
  ?????? ??????????????? ry

75
??????????????????????????????????????????????????
?????????????

• ????????????????????????? x ???

• ????????????????????????? y ???

Total Flux Linkage ???????????? a (???? x )
?????????
??????? Flux linkage ?????????? 1 ??? 2 ???
76
?????????? ???? ???????
???????????????????????????? a ???????
????????????? ????????? n ?????? x ??????? L
???????
77
?????????????????????? ???????????????
????????????????? x ???????
?????????????????????????? ??????????
?????????????????????????????????? x ????
?????? La, Lb, Lc,, Ln ?????
78
?????

?????
??????
GMD
??????????? mn ??????????????????????????????? n
??????????? x ?????????????? m ??? ???????? y
GMRx
?????????????????? x ??????????? n2
????????????????????????????????? n ?????? x
?????? r ????????????????????
79

• ?????????????????????????? y ????????????????????

• ?????????????????????????????????? ???????

80
??????????? 3
Stranded Conductor ??????????????? 7 ????
????????? ??????????????? r ????? GMR ????????
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
81
???????????????? 1 ??????????????????? ????
?? GMR ???
??????
82
???????????????? ????? 1 ??? 6 ???????????????????
??????
????? 1
(????? 2 6 ??????????)
????? 7
83
?????????????????????? ? ??????????????????????
??? GMR ????????? (???????) ???????????????
84
??????????? 4
?????????? 1 ??? ?????????????????????????? 3 ???
????????? 0.25 cm ??????????????????????????????
2 ??? ????????? 0.5 cm ???? 1.
??????????????????????????????????????????????????
2. ???????????????????????????
85
?????????????????
86
?????????????? x
???
?????
?? GMD ????????????
87
?????
88
?? GMR ??????? x
??????
89
?????????????? y
????? GMDy GMDx
?? GMR ??????? y
??????
90
???????????????????????????????????????????
???????
?????????????????????????????
??????????
91
???????? GMR ??? L ????????

• ???????????? ?????????????????? GMR ???????????
  ?????????????????? Inductive Reactance (XL)

• Inductive Reactance ???????? 1 ??? 2 ??? ????

????
92

• GMD - ????????????????????

• GMR ????????????? (DS) ?????????????????????
  60 Hz

• ?????????????????? XL ?????? GMR ??????

??????
Xa Inductive Reactance at 1 ft spacing
Xd Inductive Reactance spacing factor
93
(No Transcript)
94
(No Transcript)
95
??????????? 5
??????? Inductive Reactance ??????? ??????? 1 ???
??? 60 Hz ???????? ??? Partridge
?????????????????? 20 ft (????????????????????????
?????)
??????
????? A.1 ????? GMR (DS) ??????????
????? 1 ???
???
Piyadanai Pachanapan, 303327 Power System
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96

• ????? A.1 ????? GMR (DS) ??? ? ?? Xa ???

• ??????????? Xd ??????????? A.2 ????????????????
  (20 ft)

• ????? XL ???????? 1 ??? ??????

97
?????????????????????? 2 ???? ??????? Inductive
Reactance ?????????????
98
??????????? 6
?????????? 3 ??? 60 Hz ?????? ?????????????? ACSR
Drake ??????? Inductive Reactance ??? ???? ??? ???
???????????? ?????????????????????????????????????
??
Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
99
???????? A.1 ?? GMR ???????
?????? 3 ???????????????????? ???????????????
?????
??????????????????
100

• ????? Inductive Reactance

• ???????? XL ??????????? A3 ??? A4

101
?????? GMD (Deq) 24.8 ft
????????? interpolation
???? 24 ft ??? Xd 0.3856
????? A4
???? 25 ft ??? Xd 0.3906
?????
???????? Inductive Reactance gt
102
GMR ???????????????????? (GMR of Bundled
Conductor)
????????????????????????

• ???????????????????

• ???????????????????????????????????????????????

• ?????? Surface Voltage Gradient ?????? ?????
  Corona loss ??? Radio interference ????

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
103
Spacer Damper
104
2-conductor bundle "wire" spacer
4-conductor bundle with unique spacer. NYS Thruway
105

• Spacer Damper ????????????????????

106
???????????????
??? GMR ????????????????????? ????????
107
????????
DS
??? GMR ????????????????????
d
??? ????????????????????????????? (Bundled
Spacing)
?????????? 2 ????
108
?????????? 3 ????
?????????? 4 ????
109
??????????? 7
?????????? 3 ??? 60 Hz ?????? ??????????????
ACSR, 1,272,000 cmil Pheasant ??????? Inductive
Reactance (Ohm/km) ????? d 45 cm
Piyadanai Pachanapan, 303327 Power System
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110
???????????? 2 ??????????
GMR
??????????
?? Ds ???????? A.1 ?
0.080 m
111
??????? ????????????????????????
??????????? XL ??????????
112
?????????????????????????????? (Inductance of
Three Phase Double Circuit Lines)

• ?????????? 2 ??????????? ??????????

- ???????????????????????????
- ??????????????????????????????

• ?????????????????????????????????????????????????
  ????????????????????????????????????????

• ????????????????????????????????? ??????????????
  ????????????????????????????

Piyadanai Pachanapan, 303327 Power System
Engineering, EECPE, NU
113

??????????????????????????????????
114
?????????????????????????????????????? (?????????)
Phase A
Phase B
Phase C
115
????????????????????? GMD ??? GMR
????? GMD ??????????????????????
??? GMD ?????? (Equivalent GMD) ??????????? ????
GMDL
116
????? GMR ??????????????????????
?????
Geometric mean radius of the bundled conductors
(??????????????? )
117
???????? GMR ?????? (Equivalent GMR) ???????????
?????????????????????????? ????
?????????????????????????????????? ??????
mH/km
118
??????????? 8
?????? 3 ??? 60 Hz 2 ???? ??????????? 300,000
cmil 26/7 ACSC Ostrich ?????????????????? ???????
Inductive Reactance (Ohms / mi / phase)
119

• ?? GMD ??????????

??????? a b
??????? a b
??????? a a
120
????? GMD ??????????????????????
??? GMD ?????? (Equivalent GMD) ??????????? ????
121
0.0229 ???

• ???????? A.1 ??? Ostrich ????? Ds

• ????? GMR ??????????? (??????????????)

• a-a

• b-b

• c-c

• ???????? GMR ?????? (Equivalent GMR) ???????????
  ?????????????????????????? ????

122

• ?????????????????????????????????? ??????

H/m

• ??????????? Inductive Reactance ???????? ??????