-
.
: .
: .
, 2008
-
.
: .
: .
2008.
, 2008
............................ .
............................ .
............................ .
144
-
0
................................... .
...
Copyright . , 2008. . All rights reserved. , , , . , , , . .
.
-
1
,
,
.
MATLAB(Simulink) PSCAD/EMTDC.
,
,
.
150kV,
.
(R),
.
.
MATLAB.
. ,
,
.
, PSCAD/EMTDC
.
.
, , , , ,
, , , ,
Simulink, PSCAD
-
2
ABSTRACT
The purpose of this diploma thesis, which was written by Christos Apostolakis and
Anastasia Mitropoulou, is the study of the application of surge arresters in high voltage
installations. The progress of the research was helped by the use of appropriate computer
programs, like MATLAB(Simulink) and PSCAD/EMTDC. Before the final simulations, is
presented the theoretical base, on which the thesis is based, and a brief review of the
relevant studies that have been conducted about these issues.
The first simulation concerns transmission lines of 150kV, where is estimated the
probability of the surge arresters destruction. The factors which influence the results are the
grounding resistance (Rg), the energy tolerance of the surge arresters and their location step.
These probabilities will be used later as data for the training of a neural network.
The second simulation concerns the protection of a substation by surge arresters and
was done also in MATLAB. An easy program to handle with was designed to receive data
from the user. In this way probabilities of surge arresters failures can be estimated by
converting different parameters.
Finally, with the use of PSCAD program, a wind farm was simulated. Especially,
was studied the phenomena of back flow surge of surge arresters and how this phenomena
influence the wind generators of the wind farm that were not stroken by the lightning and
the rest of its electrical parts.
KEY WORDS
lightning, transmission lines, surge arrester, substation, wind farm, wind generators, back
flow surge of surge arresters, neural network, simulation, Simulink, PSCAD
-
3
. ,
(MATLAB, Simulink, PSCAD)
150kV,
. :
, .
.
.
, ,
.
,
.
MATLAB
. ,
.
.
MATLAB
. ,
,
. ,
(interface),
.
-
4
Q.
,
Simulink.
PSCAD .
.
.
:
. . ,
,
.
. . ,
... ..., ,
,
.
. ,
...
PSCAD.
. ,
.
. ,
... .
-
5
. ,
Riverside
MATLAB.
,
..,
.
.
.
2008
-
6
.. 1
Abstract Key Words... 2
3
... 6
1 - .. 11
1.1. - ..................... 11
1.1.1. ... 11
1.1.2. 12
1.1.3. .. 13
1.1.4. . 15
1.1.5. . 17
1.1.6. .. 18
1.1.7. .. 19
1.1.8. ... 19
1.1.9. . 20
1.2. ... 21
1.3.... 22
2 - 23
2.1.. 23
2.2. 23
2.2.1. 24
2.2.2. ... 29
2.3.... 35
-
7
3 - . 37
3.1. ... 37
3.1.1... 37
3.1.2. . 38
3.2. ... 39
3.3. . 41
3.3.1. (R).... 42
3.3.2. (L)... 43
3.3.3. (C) 44
3.3.4. (G).. 44
3.4. .... 45
3.4.1. ... 45
3.4.2. .... 48
3.5. (Basic Insulation Level)... 48
3.5.1. ... 49
3.5.2. ... 49
3.5.3. ... 51
3.5.4. . 52
3.6.... 53
4 - ... 54
4.1. .. 54
4.1.1. ... 54
4.1.2. .. 55
4.1.3. . 56
4.2. .... 57
4.3.
.. 60
4.4.... 63
-
8
5 -
. 64
5.1.. 64
5.1.1. 64
5.2. ... 66
5.3. . 67
5.4. . 69
5.5. . 69
5.6.
70
5.6.1. 71
5.6.2. .. 78
5.6.3. .... 89
5.7. ... 91
5.8.... 92
6 -
... 94
6.1.. 94
6.2.
.... 95
6.3. . 98
6.4. (interface)
... 101
6.4.1. . 101
6.4.2. .. 102
6.5.. 102
7 - .. 103
7.1. . 103
7.1.1. 104
7.2. 109
7.2.1.. 109
-
9
7.2.2. ... 110
7.2.3. (
).. 111
7.3. ... 114
7.3.1.. 114
7.3.2. 115
7.3.3. Hebb 116
7.3.4. . 117
7.3.5. Boltzmann... 119
7.3.6. ... 120
7.3.7. . 121
7.3.8. 122
7.3.8.1.. 122
7.3.8.2. ... 123
7.3.9. Q.. 124
7.3.9.1. Q. 124
7.3.9.2. .. 126
7.3.9.3. .. 127
7.4. 130
7.5. . 132
7.6.. 132
8
. 133
8.1. ... 133
8.1.1. ... 133
8.1.2. 134
8.2. ...... 136
8.3. .. 138
8.4. .. 140
8.5. .. 144
8.5.1. 145
8.5.2. 146
8.5.3. ... 150
-
10
8.5.4. 153
8.6. 158
8.6.1..... 158
8.6.2. . 158
8.6.3.
. 160
8.6.4.
. 160
8.7. ... 162
8.8. ... 163
8.9.
.. 164
8.10. ... 165
8.10.1. .. 165
8.10.2. .. 167
8.11. PSCAD. 167
8.11.1. 167
8.11.2. . 173
8.12. .. 179
8.13.... 180
.. 181
183
-
11
1
1.1. -
1.1.1.
,
, .
,
.
, ,
, ,
-
12
, ,
.
1.1.2.
. :
,
[1].
,
[2].
:
)
.
.
,
Cb
. ,
,
, ( 1.1).
1.1: -.
-
13
)
, ,
.
)
( ).
1.1.3.
( 1.2):
1.2:
.
-
14
) :
, , ,
.
, .
. ,
.
. ,
.
.
.
) :
.
,
.
1000 Amperes.
.
-
15
) :
1 km
12 km. , 40 km.
1.1.4.
( 1.3):
1.3: .
-
16
) :
,
5kV/m. ,
.
,
,
.
.
,
.
.
,
[1].
, V/m.
(),
. , ,
. , , ,
,
.
( , , ,
,
).
) :
. ,
.
,
( 30kV/cm).
, Corona (
), .
-
17
. ,
. , Corona,
,
, ,
.
.
) :
, ,
.
.
10-100kA,
20-100kA/s,
s.
,
,
. ,
.
,
, , .
.
1.1.5.
.
:
) , 0.1 2
ms. 20 50 ms,
100 kA,
2 kA/s.
-
18
) ,
. , 0.2 1 ms.
( 10 15 s).
,
0.5 1 s.
20 kA/s,
( 40 kA/s).
, , 80 90%
.
,
:
) ,
) , .
, ,
.
(.. ).
1.1.6.
. ,
, , .
-
.
. , -
, .
,
- .
.
-
19
,
.
.
.
1.1.7.
:
,
.
,
ms. :
) ,
, .
) ,
.
) ,
.
) ,
,
( , ).
1.1.8.
,
.
.
km2 .
-
20
,
A.J.Eriksson :
25.104.0 TNg
g km2
.
1.1.9.
[3]:
) :
Joule,
R, :
.
.
, ,
. ,
,
. ,
,
.
) :
, .
) :
(),
, , .
2-3 .
-
21
,
.
) :
, ,
.
,
. ,
,
(, ,
). ,
, ,
.
1.2.
,
. ,
,
. ,
[4].
, .
:
,
.
,
-
22
, .
:
,
,
,
,
.
1.3.
[1] R.H. Golde, Lightning Physics of lightning, vol.1, pp.85-89, Academic Press,
London, 1977.
[2] .. , ,
, , 1989.
[3] . , , 1994
[4] . , , E
H, 1985
-
23
2
2.1.
. ,
,
.
,
,
. , , [1,2]:
(
1mA),
.
2.2.
( ),
: ,
,
. ,
, , ,
-
24
,
(ZnO).
2.2.1.
, .
- ,
, ,
. ,
.
(SiC),
, ,
, :
aUkI
k .
2.1 ,
. ,
,
[1-4].
2.1:
-
25
[5]:
. : (rms)
,
. , ,
.
.
: ,
( ).
IEC 100kV/sec 12kV
, 1200kV/sec (.. 21kV,
21/12100 = 175kV/sec).
100%:
( IEC 1.2/50sec), ,
.
50% ():
(1.2/50sec) , ,
50% .
- (
2.4),
.
. :
,
( 8/20sec).
. .. (50 Hz): ..
, .
. :
.
-
26
. : (8/20sec),
,
().
.
, () ,
.
. : ()
4/10sec, .
. : 50Hz
.
:
.
.
, , ,
( )
. (grading resistors)
.
(grading capacitors)
. ,
,
[1-6].
, .
,
, 100 .
-
27
. ,
:
,
.
200kV,
[1-6].
( , )
SiC. , , .
, ,
10-15%. , ,
. ,
[1-6].
,
,
[1-6].
(pressure
relief arrangement),
. ,
,
.
[1].
-
28
2.2:
(1. , 2. , 3. , 4.
, 5. , 6, 7. , 8. )
(SiC) 25
,
1970-80 (ZnO),
SiC ,
2.3. ZnO
SiC.
2.3: -
-
29
2.2.2.
,
,
(ZnO), SiC,
-
8 ( 2.4).
[4].
2.4 [8]
mA,
kA.
Vl( ),
,
Vm>Vl, ,
Vm [4,7-8].
,
,
,
.
.
-
30
ZnO
, Bi2O3, MnO, Cr3O3 Sb2O3.
,
. , ,
. 80
( ).
,
, ,
[4].
[9]:
. (Maximum Continuous Operating Voltage-
Uc):
.
(Uc = 1.05-1.1U).
. (Rated Voltage-Ur):
,
(10-100sec). 1.25
: Ur = 1.25Uc.
. (Ures):
.
. (Lightnning Impulse Protective Level):
,
.
. (Thermal energy absorption capability):
,
.
-
31
2.5 2.6 ,
() ,
,
.
(
) ,
150kV 400kV, ( 2.7).
2.5: [10]
2.6: [7]
-
32
2.7: 400kV 150kV [7]
, ,
. ( 2.8,2.9),
.
2.8: [7]
-
33
2.9: [8]
, .
( 2.10)
- .
2.10: [7]
-
34
. ,
.
2.11: [8]
( 2.12)
.
, .
.
2.12: [8]
-
35
,
, , .
[11]:
,
- .
,
.
.
2.3.
[1] . , , , 1985
[2] . . , , ,
..., 1996
[3] . . , ,
[4] . , , . , 2005
[5] 23 .
, , .01/06/1988
[6] . , , : , .
,
-
36
[7] Buyers Guide, High Voltage Surge Arresters, Edition 5.1, 2004-2007
[8] V. Hinrichsen, Metal-Oxide Surge Arresters, Siemens, 1st Edition, 2001
[9] IEC 60099-4, Surge Arresters: Part 4: Metal-Oxide surge arresters without gaps for a.c.
systems, second edition, 2004-2005
[10] Tyco Electronics
[11] R.E. James, Q.Su, Condition Assessment of high Voltage Insulation in Power System
Equipment, IET Power and Energy Series 53, 1st Edition 2008
-
37
3
3.1.
3.1.1.
.
,
, [1].
:
1. , ,
.
2.
.
3. ,
.
4. ,
, , ,
,
-
38
, ,
.
,
,
(, .)
3.1.2.
--, o
, 150kV
66kV, 400kV. ,
,
. ,
, , , ,
,
. 150kV
400kV .
,
, 15 20kV, 220/330V.
, .
,
330-400m.
... 150kV
750kV,
400kV 1550kV [2].
... 150kV
:
-
39
3.1: ...
...
, 3.2.
, ,
,
.
3.2:
3.2.
,
. ,
. ,
-
40
, ,
[3]:
1. ,
,
2. ,
,
3. .
,
, .
,
, , ,
.
.
,
. ,
, ,
.
,
.
,
.
.
, ,
,
, ,
. , ,
.
,
, ( )
. ,
,
.
-
41
.
,
, , .
, .
,
,
.
.
,
. :
1. , 40km.
2. , 40km
150km ,
3. , 150km.
3.3.
,
, .
[3]:
1. (R), ohm ,
2. (L), henry ,
3. (C), farad
4. (G), mho .
,
, .
-
42
3.3.1. (R)
, ,
. ,
R, , :
: ,
l:
q: .
100% 20C
0.017241 microhm-meters,
1.7241 microhm-centimeters.
, ,
100%. , ,
2.5% ,
0.017683 microhm-meters 1.7683 microhm-centimeters 20C.
61%,
62%,
2.8080 microhm-centimeters 20C.
, ,
( ) ,
, . , ,
,
.
,
20C . 10C 100C,
,
, ,
, :
R2: 2,
R1: 1
: 1.
-
43
3.3.2. (L)
, .
:
:
,
, r, I, :
weber-turn . ,
:
henry .
,
D
r=1, :
:
, , ,
D :
r=0.7788r, (
).
,
:
-
44
,
.
3.3.3. (C)
.
, ,
,
. , ,
.
300 500kV 300 ,
.
,
, ,
30 50 , .
:
,
. , :
,
:
D:
r: .
3.3.4. (G)
, ,
-
45
,
,
.
,
, .
.
3.4.
, ,
.
,
. , ,
, ,
. , , , ,
,
.
3.4.1.
p
,
. x y
. P , P, S,
,
P. , P,
, P,
y x, ps P,
P.
-
46
3.3:
, ,
, :
xTH (3.1)
psT y (3.2)
, x,
. , , :
x
y
T (3.3)
, ,
dx
dy (3.4)
,
H
ps
T
T
dx
dy
x
y (3.5)
P
22 dydxds (3.6)
,
2
222
11H
sp
dx
dy
dx
ds
(3.7)
-
47
2
22
1H
sp
dsdx
(3.8)
H
ps
p
HCx 1sinh (3.9)
C . , , s=0, x=0, C=0,
, s, :
H
px
p
Hs sinh (3.10)
(3.5) s (3.10)
:
H
px
dx
dysinh
dxH
pxy sinh
,
DH
px
p
Hy
cosh
(3.11)
D . x=0 y=0,
(3.11) :
p
HD
, :
1coshH
px
p
Hy (3.12)
.
P , (3.1),(3.2)
(3.10),
H
pxH
H
pxHHTyx 2222222 coshsinh
H
pxHT cosh (3.13)
-
48
,
2l, , lx :
H
plHT cosh (3.14)
,
, .
y (3.12) x=l:
1coshH
pl
p
Hd (3.15)
(3.10) :
H
pl
p
Hs sinh2 (3.16)
3.4.2.
, 0 oC,
,
. ,
,
, .
.
3.5. (Basic Insulation Level)
, (
),
[4].
,
(.. ) (, ),
.
,
-
49
,
.
(
)
.
. , ,
.
. ,
, ,
,
,
.
.
[5]:
1) ,
2)
3) .
3.5.1.
Us ,
(.. 25%)
Uw. ,
, ,
. ,
, , ,
,
.
3.5.2.
.
-
50
( )
, ,
, ,
.
,
,
,
.
(
, Po(V)) .
. :
1^
U ,
^
2U , 3^
U ,, ^
U 1n , ^
nU ,
^
U ,
^
2U - 1^
U = 3^
U -^
2U =.=^
nU -^
U 1n =^
U
, (..
)
^
iU . Ki ,
N
K ii
^
iU .
i , ^
iU
. (^
iU ,i)
Pw(U). Pw(U), ,
. ,
,
(Vi,Pw(Vi)) :
-
51
- - Vi ,
Pw(Vi) ( )
, Vi Pw(Vi).
Po( U) Pw(U),
(risk of failure) :
dUUPUPR ow )()( ,
,
( Pw). ,
(
) ,
, .
3.5.3.
,
, .
, ,
,
. ,
U2%,
2%,
Uw90%, , , , 90%
. , ()
() :
%2
%90
w
U
U
1%2
%2%90
w
U
UU
3.4
.
-
52
3.4: R
3.5.4.
(IEC .),
, ,
.
BIL (Basic Insulation Level)
. , Um=420kV,
1050 1175 1300
1175 1300 1425 .
,
,
(
).
-
53
3.6.
[1] . . , , ,
1994
[2] . ,
,
, , 2006
[3] . , , ,
1999
[4] . . , ,
[5] . , , , 1985
-
54
4
4.1.
[1]:
, ,
.
4.1.1.
,
i(t),
. ,
.
, .
, ,
)(tiZ .
, i(t)
, )2/)(( tiZ [2].
,
(
) . ,
-
55
1
, .
,
,
.
4.1:
4.1.2.
:
,
, ,
, , , ,
, [3].
.
R, L
-
56
. Ki(t)
, :
][)(dt
diLRiKtU
4.2:
,
.
. , ,
, .
4.1.3.
,
,
( ).
,
, , ,
. ,
xx ,
-
57
,
.
,
V=ZI.
,
. , ,
[4].
4.3:
4.2.
:
)
( ) ,
.
)
().
[ 5]
-
58
, ,
, .
,
[1].
, , ,
, , ,
.
,
. , , ,
, .
, ,
,
.
,
. ,
,
.
,
.
4.4). , ,
, . 30
, 40 .
-
59
4.4:
,
,
. ,
, Rg (
),
IRV g
200kV
,
,
,
, 66kV.
.
-
60
4.3.
,
,
, , ,
.
, ,
, ,
,
[4].
, ,
:
, ,
.
,
, ,
, ,
, .
,
, .
,
.
(striking distance)
Whitehead [5].
.
( ) .
,
, .
-
61
,
3-6kV/cm.
(rs)
, , 4.5,
, .
, ,
, (rsg), , ,
(rs).
rsg rs
sgsg
s
kr
r 1
. ksg
0.65 1
. 4.5 ksg=1.
4.5, rs ,
, ,
, rs,
, .
4.5: (striking
distance)
-
62
I0,
rs I0. Whitehead
)(7.6 08.0
0 kAIrIr ss
Love
)(8 065.0
0 kAIrIr ss
4.6
. 3
.
4.6:
I0=20 kA, 3 rs=68m,
Whitehead Love rs=73.6 56 m .
I0
, , ,
. , I0=I
V )(21
0
V 0 ,
, . rsc I
.
-
63
, , , I0
.
4.4.
[1] . ,
, , 1997
[2] . , , 2005
[3] . , , 1994
[4] . . , ,
[5] , ,
, 2008
-
64
5
5.1.
,
. ,
, ,
,
. ,
.
5.1.1.
(
, , ,
), , ,
. [1]
MTP/ATP
5.1
,
, . , ,
, .
-
65
5.1:
, .
Carlos . Mata [2]
20kV, 829m,
,
.
,
.
5.2:
-
66
Short Ammon [3] 13kV
.
, ,
,
13kV, 40m, 200m
400m.
5.2.
,
[4]:
(5.1)
1 sec,
2 sec,
0
n 7 [5]
10sec,
20 1000sec.
, ,
10 300kA.
[5]
(5.2)
(5.3)
50 50 24kA 30sec ,
nc nt
-
67
5.3.
Montanes Garcia [6]
. akada [7]
.
.
, ,
.
, .
c, ,
.
, IEEE Working Group[8]
c
(5.4)
.
5.3,
:
(5.5)
(5.6)
, , Ip,
:
:
(5.7)
(5.8)
-
68
Xc Xr
Ip.
5.3:
,
, :
tt
T TI
pPApA dTTgdIIhIfPr tA
)()()()(
(5.9)
tt
T TI
pPBpB dTTgdIIhIfPr tB
)()()()(
(5.10)
PA ,
,
PB ,
,
IA(Tt)
, ,
IB(Tt)
, ,
f(IP)
g(Tt) .
-
69
,
(5.11)
5.4.
H :
t
to
dttituE )()(
(5.12)
: u(t) kV
i(t) kA
5.5.
, ,
:
-
70
T=TminIp=Iinitial
SimulinkIp
Tr=2secTt=Tsec
a =
Ea > Emax
Isg = Ip
Ip>=Isg
sgn II
NgNtBi IhIfTTP )()()(
T < Tmax
max
min
)()(T
TBiB TPTgP
O
= +
p = Ip + I
O
5.4: Block
,
.
5.6.
Matlab/Simulink,
Matlab.
-
71
5.6.1.
,
. , ,
,
. , 400kJ
700kJ.
, ,
, .
, 21m ( 3.1), Pi Section Lines
200, Pi Section
Lines 400 700
[6].
.
:
5.5:
-
72
5.6:
5.7:
-
73
,
, :
400kJ 700kJ
R P0 P1 P2 P0 P1 P2
1 2,010% 2,280% 2,280% 0,810% 0,980% 0,980%
5 1,040% 1,720% 1,800% 0,340% 0,600% 0,720%
10 0,660% 1,200% 1,480% 0,190% 0,400% 0,530%
15 0,440% 0,890% 1,170% 0,127% 0,275% 0,463%
20 0,350% 0,720% 1,000% 0,100% 0,220% 0,402%
25 0,295% 0,600% 0,880% 0,085% 0,185% 0,344%
30 0,255% 0,500% 0,775% 0,073% 0,160% 0,287%
35 0,220% 0,440% 0,675% 0,063% 0,135% 0,235%
40 0,190% 0,370% 0,580% 0,055% 0,115% 0,190%
45 0,163% 0,330% 0,500% 0,047% 0,092% 0,150%
50 0,140% 0,300% 0,430% 0,040% 0,082% 0,120%
55 0,120% 0,260% 0,374% 0,034% 0,070% 0,098%
60 0,108% 0,238% 0,328% 0,030% 0,060% 0,085%
65 0,100% 0,217% 0,294% 0,026% 0,055% 0,075%
70 0,092% 0,198% 0,265% 0,024% 0,050% 0,067%
75 0,086% 0,178% 0,238% 0,022% 0,048% 0,061%
80 0,080% 0,160% 0,210% 0,020% 0,042% 0,056%
85 0,071% 0,145% 0,186% 0,017% 0,038% 0,052%
90 0,067% 0,132% 0,170% 0,016% 0,035% 0,047%
95 0,063% 0,120% 0,162% 0,016% 0,031% 0,045%
100 0,060% 0,110% 0,150% 0,015% 0,030% 0,038%
105 0,050% 0,100% 0,138% 0,012% 0,023% 0,030%
110 0,039% 0,096% 0,129% 0,010% 0,015% 0,020%
115 0,029% 0,090% 0,120% 0,005% 0,007% 0,010%
120 0,020% 0,085% 0,110% 0,004% 0,002% 0,003%
125 0,018% 0,080% 0,103% 0,003% 0,002% 0,002%
130 0,018% 0,076% 0,097% 0,003% 0,001% 0,001%
5.8:
(0), (1) (2)
-
74
:
0 20 40 60 80 100 120 1400
0.5
1
1.5
2
2.5
Rg ()
Pro
babi
lity
(%)
5.9: 400kJ
0 20 40 60 80 100 120 1400
0.5
1
1.5
2
2.5
Rg ()
Pro
babi
lity
(%)
5.10: 400kJ
-
75
0 20 40 60 80 100 120 1400
0.5
1
1.5
2
2.5
Rg ()
Pro
babi
lity
(%)
5.11: 400kJ
0 20 40 60 80 100 120 1400
0.5
1
1.5
2
2.5
Rg ()
Pro
babi
lity
(%)
5.12:
400kJ
(: , : , : )
-
76
0 20 40 60 80 100 120 1400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Rg ()
Pro
babi
lity
(%)
5.13: 700kJ
0 20 40 60 80 100 120 1400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Rg ()
Pro
babi
lity
(%)
5.14: 700kJ
-
77
0 20 40 60 80 100 120 1400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Rg ()
Pro
babi
lity
(%)
5.15: 700kJ
0 20 40 60 80 100 120 1400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pro
babi
lity
(%)
Rg ()
5.16:
700kJ
(: , : , : )
-
78
:
) ,
. , ,
.
) ,
, .
, ,
, .
) , ,
,
.
5.6.2.
,
, .
(
,
).
,
. ,
.
, , , .
,
.
,
.
,
,
750kV.
400kJ 700kJ.
-
79
:
5.17: ( )
5.18: ( )
-
80
5.19: ( )
,
, :
400kJ 700kJ
R P0 P1 P2 P0 P1 P2
1 0,016% 0,036% 0,037% 0,003% 0,008% 0,009% 5 0,380% 0,683% 0,750% 0,004% 0,015% 0,014%
10 0,820% 1,400% 1,480% 0,012% 0,067% 0,082% 15 1,300% 2,100% 2,320% 0,045% 0,103% 0,117% 20 1,720% 2,680% 2,710% 0,083% 0,158% 0,186% 25 2,200% 2,730% 2,800% 0,104% 0,180% 0,200% 30 2,600% 2,900% 2,930% 0,127% 0,214% 0,235% 35 3,000% 3,220% 3,300% 0,189% 0,275% 0,280% 40 3,420% 3,650% 3,760% 0,216% 0,306% 0,310% 45 3,810% 4,010% 4,190% 0,250% 0,362% 0,379% 50 4,100% 4,420% 4,490% 0,275% 0,390% 0,402% 55 4,300% 4,500% 4,560% 0,302% 0,422% 0,450% 60 4,480% 4,570% 4,620% 0,327% 0,461% 0,478% 65 4,630% 4,810% 4,980% 0,362% 0,489% 0,507% 70 4,800% 4,930% 5,060% 0,384% 0,500% 0,532% 75 4,960% 5,030% 5,200% 0,415% 0,540% 0,588% 80 5,100% 5,170% 5,370% 0,467% 0,587% 0,605% 85 5,300% 5,420% 5,540% 0,520% 0,610% 0,620% 90 5,550% 5,600% 5,780% 0,603% 0,643% 0,657%
-
81
95 5,800% 5,860% 5,920% 0,652% 0,688% 0,715% 100 6,000% 6,100% 6,230% 0,698% 0,724% 0,738% 105 6,200% 6,300% 6,470% 0,722% 0,745% 0,767% 110 6,390% 6,450% 6,540% 0,734% 0,783% 0,810% 115 6,560% 6,620% 6,700% 0,815% 0,850% 0,878% 120 6,680% 6,780% 6,850% 0,847% 0,900% 0,932% 125 6,870% 7,010% 7,120% 0,878% 0,967% 0,980% 130 7,030% 7,320% 7,410% 0,907% 1,100% 1,107%
5.20:
(0), (1) (2)
:
0 20 40 60 80 100 120 1400
1
2
3
4
5
6
7
8
Rg ()
Pro
babi
lity
(%)
5.21: 400kJ
-
82
0 20 40 60 80 100 120 1400
1
2
3
4
5
6
7
8
Rg ()
Pro
babi
lity
(%)
5.22: 400kJ
0 20 40 60 80 100 120 1400
1
2
3
4
5
6
7
8
Rg ()
Pro
babi
lity
(%)
5.23: 400kJ
-
83
0 20 40 60 80 100 120 1400
1
2
3
4
5
6
7
8
Rg ()
Pro
babi
lity
(%)
5.24:
400kJ
(: , : , : )
0 20 40 60 80 100 120 1400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Rg ()
Pro
babi
lity
(%)
5.25: 700kJ
-
84
0 20 40 60 80 100 120 1400
0.2
0.4
0.6
0.8
1
1.2
1.4
Rg ()
Pro
babi
lity
(%)
5.26: 700kJ
0 20 40 60 80 100 120 1400
0.2
0.4
0.6
0.8
1
1.2
1.4
Rg ()
Pro
babi
lity
(%)
5.27: 700kJ
-
85
0 20 40 60 80 100 120 1400
0.2
0.4
0.6
0.8
1
1.2
1.4
Rg ()
Pro
babi
lity
(%)
5.28:
700kJ
(: , : , : )
:
) ,
. , ,
.
) ,
, .
, ,
, .
) , ,
,
.
-
86
,
.
0 20 40 60 80 100 120 1400
1
2
3
4
5
6
7
8
Rg ()
Pro
babi
lity
(%)
5.29: 400kJ
[ () ()]
0 20 40 60 80 100 120 1400
1
2
3
4
5
6
7
8
Rg ()
Pro
babi
lity
(%)
5.30: 400kJ
[ () ()]
-
87
0 20 40 60 80 100 120 1400
1
2
3
4
5
6
7
8
Rg ()
Pro
babi
lity
(%)
5.31: 400kJ
[ () ()]
0 20 40 60 80 100 120 1400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Rg ()
Pro
babi
lity
(%)
5.32: 700kJ
[ () ()]
-
88
0 20 40 60 80 100 120 1400
0.2
0.4
0.6
0.8
1
1.2
1.4
Rg ()
Pro
babi
lity
(%)
5.33: 700kJ
[ () ()]
0 20 40 60 80 100 120 1400
0.2
0.4
0.6
0.8
1
1.2
1.4
Rg ()
Pro
babi
lity
(%)
5.34: 700kJ
[ () ()]
-
89
, , ,
,
,
. , ,
.
5.6.3.
,
,
.
400kJ 700kJ
R P0 P1 P2 P0 P1 P2
1 2,026% 2,316% 2,317% 0,813% 0,988% 0,989% 5 1,420% 2,403% 2,550% 0,344% 0,615% 0,734%
10 1,480% 2,600% 2,960% 0,202% 0,467% 0,612% 15 1,740% 2,990% 3,490% 0,172% 0,378% 0,580% 20 2,070% 3,400% 3,710% 0,183% 0,378% 0,588% 25 2,495% 3,330% 3,680% 0,189% 0,365% 0,544% 30 2,855% 3,400% 3,705% 0,200% 0,374% 0,522% 35 3,220% 3,660% 3,975% 0,252% 0,410% 0,515% 40 3,610% 4,020% 4,340% 0,271% 0,421% 0,500% 45 3,973% 4,340% 4,690% 0,297% 0,454% 0,529% 50 4,240% 4,720% 4,920% 0,315% 0,472% 0,522% 55 4,420% 4,760% 4,934% 0,336% 0,492% 0,548% 60 4,588% 4,808% 4,948% 0,357% 0,521% 0,563% 65 4,730% 5,027% 5,274% 0,388% 0,544% 0,582% 70 4,892% 5,128% 5,325% 0,408% 0,550% 0,599% 75 5,046% 5,208% 5,438% 0,437% 0,588% 0,649% 80 5,180% 5,330% 5,580% 0,487% 0,629% 0,661% 85 5,371% 5,565% 5,726% 0,537% 0,648% 0,672% 90 5,617% 5,732% 5,950% 0,619% 0,678% 0,704% 95 5,863% 5,980% 6,082% 0,668% 0,719% 0,760%
100 6,060% 6,210% 6,380% 0,713% 0,754% 0,776% 105 6,250% 6,400% 6,608% 0,734% 0,768% 0,797% 110 6,429% 6,546% 6,669% 0,744% 0,798% 0,830% 115 6,589% 6,710% 6,820% 0,820% 0,857% 0,888% 120 6,700% 6,865% 6,960% 0,851% 0,902% 0,935% 125 6,888% 7,090% 7,223% 0,881% 0,969% 0,982% 130 7,048% 7,396% 7,507% 0,910% 1,101% 1,108%
5.35:
(0), (1) (2)
-
90
:
0 20 40 60 80 100 120 1401
2
3
4
5
6
7
8
Rg ()
Pro
babi
lity
(%)
5.36:
400kJ
(: , : , : )
0 20 40 60 80 100 120 1400
0.2
0.4
0.6
0.8
1
1.2
1.4
Rg ()
Pro
babi
lity
(%)
5.37:
700kJ
(: , : , : )
-
91
.
5.38:
,
, .
, ,
xx,
.
5.7.
, ,
. ,
, .
-
92
,
400kV, ,
,
.
,
,
, .
5.8.
[1] Luis Cera Zanetta, Carlos Eduardo de Morais Pereira, Application Studies of Line
Arresters in Partially Shielded 138kV Transmission Lines, IEEE Transactions on Power
Delivery, Vol. 18, No.1, January 2003
[2] Carlos T. Mata, Vladimir A. Rakov, Keith J. Rambo, Pepe Diaz, Raimundo Rey, and
Martin A. Uman, Measurement of the Division of Lightning Return Stroke Current Among
the Multiple Arresters and Grounds of a Power Distribution Line, IEEE Transactions on
Power Delivery, Vol. 18, No. 4, October 2003
[3] T. A. Short, R. H. Ammon, Monitoring Results of the Effectiveness of Surge Arrester
Spacings on Distribution Line Protection, IEEE Transactions on Power Delivery, Vol. 14,
No. 3, July 1999
[4] Cveti J., Heidler, F. and Stani B., Calculation of Lightning Current Parameters,
IEEE Transactions on Power Delivery, Vol. 14, No. 2, pp. 399-404, 1999
[5] David John Browne, Development of an Assessment Tool to Study the Effects of
Transient Over Voltages in Medium Voltage Distributions, Curtin University of
Technology, November 2005
[6] Luis Montanes, Miguel Garcia-Gracia, Mariano Sanz, and Miguel Angel Garcia, An
Improvement for the Selection of Surge Arresters Based on the Evaluation of the Failure
Probability, IEEE Transactions on Power Delivery, Vol. 17, No. 1, January 2002
[7] K. Nakada, S. Yokoyama, T. Yokota, A. Asakawa, T. Kawabata, Analytical Study on
Prevention Methods for Distribution Arrester Outages Caused by Winter Lightning, IEEE
Transactions on Power Delivery, Vol. 13, No. 4, October 1998
-
93
[8] IEEE Working Group on Lightning Performance of Transmission Lines, A Simplified
Method for Estimating Lightning Performance of Transmission Lines, IEEE Trans. Power
App. Syst., Vol. PAS-104, pp. 919932, April 1985
[9] Minoo Mobedjina and Lennart Stenstrom, ABB Switchgear, Ludvika, Sweden, An
Improved Transmission Line Performance Using Polymer-Housed Surge Arresters, for
presentation at CEPSI seminar, Manila, Philippines, October 2000
-
94
6
6.1.
, , ,
.
,
, .
[1].
,
. , ,
, ,
,
,
[2].
, ,
. ,
.
-
95
L ,
.
6.2.
. ( U)
. L -
'U . 'U
L
m , s kV/s, c m/s
[2,3].
t=0. t=L/c
( 2s,
6.1).
6.1:
-
96
t=2L/c .
t=2L/c
2LU s
c . :
,
U , U
2LU U s
c .
U U
2LU U s
c .
(U>U) t1 ,
6.2
1 1
2
2 2
U U UL Lt t
c s c s
(6.1)
6.2:
'1
22
LsU s t U
c (6.2)
-
97
(U
-
98
'
' ' 1 12BIL U BIL BIL
LsU U Uc
(6.8)
, 25%,
1.252
BILLs
Uc
(6.9)
max ( )2 1.25
c BILL U
s (6.10)
:
max
300 1425865 41.2
2 1000 1.25L m
, ,
25%
41.2m .
(.. s=1200kV/s)
Lmax 34m. 400kV
30m.
6.3.
, ,
.
:
-
99
6.1:
6.2:
,
. , Pi Section Lines
: Pi Section Line
-
100
( 240m), Pi Section Line
( 30m).
750kJ
. , ,
Pi Section Line .
Line Transformer 100.
.
[4].
,
, .
:
R ()
10 4.31% 1.77% 6.08% 20 4.30% 0.89% 5.19% 30 4.29% 0.61% 4.90% 40 4.29% 0.44% 4.73%
6.1:
,
,
.
-
101
6.4. (interface)
6.4.1.
GUI, (interface),
:
6.3:
,
:
) Pi Section Line 1,
,
) Pi Section Line 2,
,
) Rg ,
) ,
,
) .
-
102
6.4.2.
,
:
6.4:
, :
) ,
) ,
)
6.5.
[1] , ,
, 2008
[2] . , , E
H, 1985
[3] .. , ,
, , 1989.
[4] V. Hinrichsen, Metal-Oxide Surge Arresters, Siemens, 1st Edition, 2001
-
103
7
7.1.
,
(black box),
, .
,
.
,
, .
, , .. .
,
[1].
,
,
. ,
,
.
, ,
,
.
. ,
, .. , ,
-
104
, , ,
, , , .
7.1.1.
,
.
, Mc Culloch Pitts.
, ,
.
( )
. .
1.5x1010 .
104 . , ,
, : ,
, 7.1.
7.1: ( )
, , , ,
. 10-80m.
.
.
. , ,
-
105
,
. m.
,
. ,
,
. ,
,
.
5000 /sec,
100V,
+30mV.
0.1msec 1msec.
.
,
Mc Culloch-Pitts,
,
. 7.2.
7.2: Mc Culloch-Pitts
( )
( ).
:
. ,
,
-
106
.
.
.
. Mc
Culloch-Pitts ,
.
,
Mc Culloch-Pitts 7.3.
7.3:
, :
(),
( )
( )
(weight, strength),
(excitatory)
(inhibitory).
. ,
. ,
( , , /squashing function)
-
107
()
( [0,1] , , [-1,1]).
, ,
. ,
,
b, (b= - ).
7.3
:
1
n
i ii
u w x
(7.1)
)( ufy , >0
ix (i=1,2,,n) , wi (i=1,2,n)
, u , , f
y .
7.3 ,
(u) () f.
u H(s),
s Laplace,
.
.
,
( 7.4):
,
7.4:
-
108
7.4 :
1, 0( )
0, 0
uf u
u
(7.2)
n
iii xwu
1
(7.3)
1, 0
0, 0
uy
u
(7.4)
Mc Culloch-Pitts .
0, 1/ 2
( ) , 1/ 2 1/ 2
1, 1/ 2
u
f x u u
u
(7.5)
, ()
( ).
. ,
:
1( )
1 uf u
e
(7.6)
.
. (u=0) /4.
7.4 0 1,
0 ( ) 1f u .
, [-1,+1],
7.5.
-
109
7.5: [-1,+1]
7.5 :
( )
1, 0
( ) 0, 0
1, 0
u
f u u
u
(7.7)
1, 1
( ) , 1 1
1, 1
u
f u u u
u
(7.8)
( )
1( ) tanh
2 1
u
u
u ef u
e
(7.9)
7.2.
7.2.1.
.
(layers) .
,
,
.
-
110
7.2.2.
, ,
,
, ,
.
(feedforward) ( 7.6)
,
( ) .
() , .
7.6:
()
,
.
,
,
.
,
. ,
, ...
.
-
111
(h=4), (p=8)
(q=2) 7.7.
8-4-2.
7.7: 8-4-2 (
)
,
. ,
,
.
7.2.3. ( )
,
,
(recurrent)
.
,
, ,
.
-
112
. , ,
. ,
.
7.8, ,
.
, z-1 z-1y(k)=y(k-1) k
. z-1 .
7.8:
Hopfield.
8-4-2 7.7,
, 7.9.
,
.
.
-
113
7.9: ()
, ()
7.10
.
7.10:
-
114
7.3.
7.3.1.
,
.
.
,
. ,
[2].
. ,
,
.
.
.
,
, :
()
(-)
:
Hebb
Boltzmann
-
115
7.3.2.
,
[3].
, :
dk(t): k t
x(t):
yk(t): k
, (x(t),dk(t))
t. dk(t)
yk(t) :
ek(t)= dk(t)- yk(t)
:
21 ( )2 kk
I E e t
(7.10)
.
,
.
.
:
21 ( )2 kk
J e t (7.11)
wkj , wkj
j k.
, :
wkj(t)=ek(t)xj(t) (7.12)
wkj(t) t wkj
, .
-
116
,
,
ek(t)=dk(t)-yk(t) (7.13)
xj(t) j.
wkj(t+1)
:
Wkj(t+1)= wkj(t)+ wkj(t) (7.14)
t=0.
, J ,
. , ,
, ,
.
7.3.3. Hebb
( )
Hebb ,
,
,
[4].
:
) () , , ,
, .
) () , , ,
, .
Hebb ( )
. ,
.
. wkj k
xj yk. ,
Hebb, wkj t :
-
117
wkj(t)=H(yk(t),xj(t)) (7.15)
.
7.3.4.
. , ,
,
.
. -
.
,
.
.
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-
118
k , uj
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7.12.
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-
119
,
.
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.
.
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OFF. si i wji
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2 ji j ii ji j
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Boltzmann :
-
120
( ),ji ji jiw r r i j
(7.18)
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-
121
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-
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-
125
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r=r(s,)
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Q(s,) .
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's s
s
-
126
(s),
(1), .
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k
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To a
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-
127
7 ,
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-
128
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-
129
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-
130
7.4.
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Simulink
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300 .
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.
-
131
Simulink,
,
:
R ()
(KJ)
x
Simulink
32 400 0 3,00% 2,97% 2,81% 1,000% 6,333% 57 400 2 4,90% 4,93% 4,93% 0,612% 0,612% 71 700 1 0,55% 0,48% 0,54% 12,727% 1,818% 92 400 2 6,00% 6,02% 5,99% 0,333% 0,167%
106 700 0 0,73% 0,69% 0,71% 5,479% 2,740% 48 700 2 0,53% 0,64% 0,59% 21,905% 12,381% 17 400 1 3,20% 3,02% 3,00% 5,625% 6,250% 28 370 0 2,70% 3,02% 2,83% 11,852% 4,815%
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,
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5),
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.
-
132
7.5.
,
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.
,
.
. ,
.
7.6.
[1] . , , :,
2002
[2] . ,
,
, 2006
[3] . , . , . , . , . ,
, , 2005
[4] S. Haykin, Neural Networks A Comprehensive Foundation, Prentice Hall, 1999
[5] C. J. C. H. Watkins and P. Dayan, Machine Learning, 8, 279-292
[6] N. J. Nilsson, Introduction to Machine Learning, 1996
[7] T. Mitchell, Machine Learning, McGraw Hill, 1997
[8] Mr. Herrmann, R. Der, Efficient Q-learning by division of labor, 1998
[9] R. S. Sutton, A. G. Barto, Reinforcement Learning: An introduction, The MIT Press,
2005
[10] L. Kaebling, M. L. Littman, A. W. Moore, Reinforcement Learning: A survey, Journal
of Artificial Intelligence, Research 4, pp 237-285, 1996
-
133
8
8.1. -
8.1.1.
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-
139
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140
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3. (Pitch)
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6. (Gear box)
7. (Generator)
8. (Controller)
9. (Anemometer)
10. (Wind vane)
11. (Nacelle)
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8.4.
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-
141
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-
142
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-
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-
144
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-
145
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-
146
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147
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-
148
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149
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-
152
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-
153
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-
160
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-
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-
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-
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-
166
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-
167
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8.11.1.
PSCAD/EMTDC
.
(case1) ( 8.16),
(case2) ( 8.17).
-
168
[8]. A
B
C
A
B
C20.0 [kV]
#2#1
230.0 [V]
1.0 [MVA]
A
B
C
Ia1
Ia2
Ia3
50 [ohm
]
50 [ohm
]
Ia*500000000000000000TIME
TIME
* *X2
AeBx
Ia4
Ia5
Ia6
50 [ohm
]
Tline
1
Tline
1
Tline
1
TLineT
Tline
1
A
B
C
A
B
C20.0 [kV]
#2#1
230.0 [V]
1.0 [MVA]
Ia7
Ia8
Ia9
50 [ohm
]
50 [ohm
]
Ia10
Ia11
Ia12
50 [ohm
]
A
B
C
A
B
C
A
B
C150.0 [kV]
#2#1
20.0 [kV]
100.0 [MVA]
Ia13
Ia14
Ia15
50 [ohm
]
TLineT
Tow erT
Ia16
Ia17
Ia18
50 [ohm
]
50 [ohm
]
Ia1
Ia5
Ia8Ia7
Ia9 Ia10
Ia2
Ia3 Ia4
Ia6
Ia11 Ia12
Ia13 Ia14
Ia15 Ia16
Ia17 Ia18
Ia
Ea
1 Ea
4
Ea7
Ea1
0
Ea13
Ea16
Ea1
Ea4Ea7
Ea10Ea13
Ea6
*Ia1
Ea1
Power1 *Ia4
Ea4
Power4
*Ia7
Ea7
Power7 *Ia10
Ea10
Power10
*Ia13
Ea13
Power13
P+j
QP
+jQ
P+j
Q
8.16:
A
B
C
A
B
C20.0 [kV]
#2#1
230.0 [V]
1.0 [MVA]
A
B
C
Ia1
Ia2
Ia3
50 [ohm]
50 [ohm]
Ia*500000000000000000TIME
TIME
* *X2
AeBx
Ia4
Ia5
Ia6
50 [ohm]
Tline
1
Tline
1
Tline
1
TLineT
Tline
1
A
B
C
A
B
C20.0 [kV]
#2#1
230.0 [V]
1.0 [MVA]
Ia7
Ia8
Ia9
50 [ohm]
50 [ohm]
Ia10
Ia11
Ia1250 [ohm]
A
B
C
A
B
C
A
B
C150.0 [kV]
#2#1
20.0 [kV]
100.0 [MVA]
Ia13
Ia14
Ia15
50 [ohm]
TLineT
Tow erT
Ia16
Ia17
Ia18
50 [ohm]
50 [ohm]
Ia1
Ia5
Ia8Ia7
Ia9 Ia10
Ia2
Ia3 Ia4
Ia6
Ia11 Ia12
Ia13 Ia14
Ia15 Ia16
Ia17 Ia18
Ia
Ea1 E
a4
Ea7
Ea10
Ea13
Ea16
Ea1
Ea4Ea7
Ea10Ea13
Ea6
*Ia1
Ea1
Power1 *Ia4
Ea4
Power4
*Ia7
Ea7
Power7 *Ia10
Ea10
Power10
*Ia13
Ea13
Power13
P+j
QP
+jQ
P+j
Q
8.17:
(case1).
-
169
(/1) ,
10 .
Arrester Current WT#1 (case 1)
0.00 0.01m 0.02m 0.03m 0.04m 0.05m 0.06m 0.07m 0.08m 0.09m 0.10m ... ... ...
-10.0
-5.0
0.0
kA
Arrester Current
Arrester Voltage WT#1 (Case 1)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
-20
-10
0
kV
Arrester Voltage
8.18: /1
10
Arrester Current WT#2 (case 1)
0.00 0.01m 0.02m 0.03m 0.04m 0.05m 0.06m 0.07m 0.08m 0.09m 0.10m ... ... ...
0.0
5.0
kA
Arrester Current
-
170
Arrester Voltage WT#2 (Case 1)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0
10
20
kV
Arrester Voltage
8.19: /2
10
Arrester Current Transformer (case 1)
0.00 0.01m 0.02m 0.03m 0.04m 0.05m 0.06m 0.07m 0.08m 0.09m 0.10m ... ... ...
0.0
1.0
2.0
kA
Arrester Current
Arrester Voltage Transformer (Case 1)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0
10
20
kV
Arrester Voltage
8.20:
10
-
171
(case2).
Arrester WT#1 (case 2)
0.00 0.01m 0.02m 0.03m 0.04m 0.05m 0.06m 0.07m 0.08m 0.09m 0.10m ... ... ...
-5.0
0.0
kA
Arrester Current
Arrester Voltage WT#1 (Case 2)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
-20
-10
0
kV
Arrester Voltage
8.21: /1
10
Arrester WT#2 (case 2)
0.00 0.01m 0.02m 0.03m 0.04m 0.05m 0.06m 0.07m 0.08m 0.09m 0.10m ... ... ...
0.0
5.0
kA
Arrester Current
-
172
Arrester Voltage WT#2 (Case 2)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0
10
20
kV
Arrester Voltage
8.22: /2
10
Arrester WT#2 (case 2)
0.00 0.01m 0.02m 0.03m 0.04m 0.05m 0.06m 0.07m 0.08m 0.09m 0.10m ... ... ...
0.0
5.0
kA
Arrester Current
Arrester Voltage Transformer (Case 2)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0
10
20
kV
Arrester Voltage
8.23:
10
-
173
/1
.
.
(/1) (/2) ,
1/3 .
8.11.2.
[9]. ,
, , 10.
( 8.24,8.25 8.26)
(case1) (case2)
20.
Arrester Current WT#1(case 1)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
kA
Arrester Current
-
174
Arrester Voltage WT#1 (Case 1)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
-20.0
-15.0
-10.0
-5.0
0.0
kV
Arrester Voltage
8.24: /1
20
Arrester Current WT#2 (case 1)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0.0
2.0
4.0
6.0
8.0
10.0
kA
Arrester Current
Arrester Voltage WT#2 (Case 1)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0.0
5.0
10.0
15.0
20.0
kV
Arrester Voltage
8.25: /2
20
-
175
Arrester Current Transformer (case 1)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0.00
0.50
1.00
1.50
2.00
2.50
kA
Arrester Current
Arrester Voltage Transformer (Case 1)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0.0
5.0
10.0
15.0
20.0
kV
Arrester Voltage
8.26:
20
(case2).
Arrester Current WT#1 (case 2)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
-6.0
-4.0
-2.0
0.0
kA
Arrester Current
-
176
Arrester Voltage WT#1 (Case 2)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
-20.0
-15.0
-10.0
-5.0
0.0
kV
Arrester Voltage
8.27: /1
20
Arrester Current WT#2 (case 2)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0.0
1.0
2.0
3.0
4.0
kA
Arrester Current
Arrester Voltage WT#2 (Case 2)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0.0
5.0
10.0
15.0
20.0
kV
Arrester Voltage
8.28: /2
20
-
177
Arrester Current Transformer (case 2)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0.0
1.0
2.0
kA
Arrester Current
Arrester Voltage Transformer (Case 2)
0.000 0.010m 0.020m 0.030m 0.040m 0.050m 0.060m 0.070m 0.080m 0.090m 0.100m ... ... ...
0.0
5.0
10.0
15.0
20.0
kV
Arrester Voltage
8.29:
20
,
, ,
.
/1. /2. 10 Case 1 23 kJ 14 kJ 2,5 kJ 10 Case 2 6 kJ 3,2 kJ 1,4 kJ 20 Case 1 30 kJ 18 kJ 3,9 kJ 20 Case 2 7,8 kJ 4,5 kJ 2,1 kJ
8.1:
-
178
10.
8.30: /1 10
8.31: /2 10
8.32: 10
, ,
20.
8.33: /1 20
-
179
8.34: /2 20
8.35: 20
,
.
. ,
,
. ,
. , ,
,
.
8.12.
,
.
,
.
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.
-
180
,
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,
,
.
8.13.
[1] www.eletaen.gr
[2] www.cres.gr
[3] www.ewea.org
[4] . ,
, , 2003
[5] . , . , ,
, , 1997
[6] Y. Yasuda and T. Funabashi, Analysis on Back-Flow Surge in Wind Farms,
2007
[7] Y. Yasuda and T. Funabashi, Surge Analysis on Wind Farm at Winter Lightning
Stroke, 28th International Conference on Lightning Protection
[8] N. Umo, H. Kobayashi, Y. Yasuda and T. Funabashi, Surge Analysis on Wind Farm
When Winter Lightning Strikes, IEEE Transactions on Energy Conversion, 2008
[9] Lightning Protection Guide, Lightning and Surge Protection of Multi-megawatt Wind
Turbines, DEHN
-
181
close all;clear all;clc; Emax = 400e3 ; Iin = 10e3 ; Tmin = 20e-6 ; Tmax = 1000e-6 ; dI = 10e3 ; dT = 20e-6 ; Ip = Iin ;
d = 2.2 ; yg = 23.75 ; yt = 21.14 ; b = 0.36+0.168*log10(43-yg) ; Io = Iin ; Ta = Tmin ; Imax = 300e3 ; I50 = 24e3; T50 = 30e-6; nc = 1.89; nt = 1.82; Pbx = 0; Pby = 0; for T = Tmin:Tmax for Ip = Ip:Imax T = Ta ; Ip = Io SurgeEqn='(Ip*(u/10e-6)^7*exp(-u/T))/((1+u/T)*
exp(-2e-6/(T*(7*2e-6/T)^(1/8))))'; set_param([bdroot,'/Fcn'],'Expression',SurgeEqn); sim('C:\Users\Anastasia\Desktop\runsim\transmissionlines2.mdl');
