Post on 04-Apr-2018
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 1 -
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 2 -
The Harmonic Case: Standing Waves
Each electromagnetic wave (in the free space/on a line)
has a certain velocity of propagation.
Reflections at the end of the line result in
standing waves on the line.
Dependence on time and location
from:
H.- G. Unger
Elektromagnetische Wellen auf Leitungen
Hthig- Verlag, Heidelberg, 1980
ISBN 3- 7785- 0601- 3
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 3 -
The Harmonic Case: Standing Waves
Advancing wave
Advancing wave
Regressing wave
Regressing wave
Resultingstanding wave
Resultingstanding wave
1,0
0,7
- 1,0
- 0,7
z
z
z
t
t
t
1,0
0,7
1,0
0,7
1,0
0,7
- 0,7
- 1,0
- 0,7
- 1,0
- 0,7
- 1,0
a)
a) b)
b) c)
c)
a)
a)
b)
b)
c)
c)
As a function of location:
As a function of location: As a function of time:
As a function of time:
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 4 -
The Transient Case (Surges):Traveling Waves
Each electromagnetic wave (in the free space/on a line)
has a certain velocity of propagation.
Changes of voltage and current result in
traveling waves on the line.
Dependence on time and location
u
t
0 1 s 2 s 3 s
u
x
0 300 m 600 m 900 m 1200 m
Example: lightning overvoltage on an OHL
Dependence on time
at a certain location
Dependence on location
at a certain time instant
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 5 -
Traveling Waves Example: Surge Starts at t= 0 and z= 0
t
0 1 s 2 s 3 s
z
0 300 m 600 m 900 m
u
t= 1 st= 1 s
t= 2 st= 2 s
t= 3 st= 3 s
t= 4 st= 4 s
u
4 s
z= 0 mz= 0 m
z= 300 mz= 300 m
z= 600 mz= 600 m
z= 900 mz= 900 m
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 6 -
Traveling Waves Example: Lightning Overvoltage on an OH Line
300 m/s
Span length (typ.): 300 mTime to crest (typ.): 1 s
Time to half value (typ.): (10100) s
0 20 40 60 80 100
In the (theoretical) case of a standard lightning impulse voltage 1.2/50:
time / s
voltage
/kV
location / km
0 6 12 18 24 30
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 7 -
Traveling Waves
Traveling waves to be taken into account whenever the change
in voltage or current takes place in a time duration of the same
order of magnitude as the propagation time electrically long line
Velocity of propagation in air: v= c0 = 300 m/s
Time for traveling along one span of a HV-OHL (300 m): 1 s
Time for traveling along an OHL of 300 km length: 1 ms
Spatial length of a lightning overvoltage surge (100 s): 30 km
Spatial length of the front of a lightning overvoltage surge (1s): 300 m
Spatial length of a switching overvoltage surge (5 ms): 1500 km
Spatial length of the front of switching overvolage surge (250 s): 75 km
Spatial length of one half-period of 50-Hz voltage (10 ms): 3000 km
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 8 -
Traveling Waves
Velocity of propagation in air: v= c0 = 300 m/sVelocity of propagation in a measuring cable: v= 150 m/s
Impact on measurement of changes in sub-microsecond range
Example: fast voltage change voltage breakdown/flashover
t= 100 ns t= 10 ns
in the test circuit (air)
along the cable
Spatial length of voltage ramp (-du/dt)
30 m 3 m
15 m 1,5 m
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 9 -
Traveling Waves
Occurrence of traveling waves / Making use of traveling wave effects
energization of a unloaded line
propagation of lightning overvoltages on lines
propagation of very fast transients in GIS
separation effects / protective zone of surge arresters
generating and measuring of LI voltages generating rectangular current impulses (energy tests on surge arresters)
fault location on cables
fault location on light wave guides / optical fibers
location of partial discharges in GIS
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 10 -
Traveling Waves - Laws of Propagation
General electrical equivalent circuit of a line element
R ... Resistance
L ... Inductance
G ... Parallel conductance
C ... Capacitance
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 11 -
Traveling Waves - Laws of Propagation
Electrical equivalent circuit of a loss-less line element
( d ) ' du i
u u x L xx t
+ = '
u i
Lx t
=
( d ) ' di u
i i x C xx t
+ =
'
i uC
x t
=
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 12 -
Traveling Waves - Laws of Propagation
'u i
Lx t
=
'i u
C
x t
=
Partial derivative with respect tox:2 2
2'
u iL
x t x
=
2 2
2'
i uC
t x t
=
Partial derivative with respect to t:
2 2
2 2' 'u uL C
x t =
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 13 -
Traveling Waves - Laws of Propagation
'u i
Lx t
=
'i u
C
x t
=
Partial derivative with respect to t:
Partial derivative with respect tox:
2 2
2'
u iL
x t t
=
2 2
2'
i uC
x x t
=
2 2
2 2' '
i iL C
x t
=
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 14 -
Traveling Waves - Laws of Propagation
2 2
2 2' '
i iL C
x t
=
2 2
2 2' '
u uL C
x t
=
General wave equations of the loss-less line
General solution acc. to dAlembert (1717-1783):
1 2( , ) ( ) ( ) v ru x t f x vt f x vt u u= + + = +
1 2
1 1( , ) ( ) ( ) v ri x t f x vt f x vt i i
Z Z= + = +
uv ur
iv ir
1' '
vL C
=
'
'
LZ
C=
Velocity of propagation
Surge impedance
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 15 -
Traveling Waves - Laws of Propagation
Both voltage and current are composed of a forward and a backward wave.
A positive forward voltage wave is linked to apositive forward current wave:
A positive backward voltage wave is linked tonegative backward current wave:
uv
ivx
ur
ir
x
1 2( , ) ( ) ( ) v ru x t f x vt f x vt u u= + + = +
uv ur
1 21 1( , ) ( ) ( ) v ri x t f x vt f x vt i i
Z Z= + = +
iv ir
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 16 -
Traveling Waves - Laws of Propagation
Wanderwellenausbreitung beim pltzlichen Abflieen einer freigewordenen Influenzladung auf einer
Freileitung; linke Bildhlfte: zeitliche Entwicklung der Felder; rechte Bildhlfte: Wanderwellen auf der Leitung
Traveling waves after sudden release of influenced charges on an OHL - left: development with time of fields
right: traveling waves on the line (Note: urand irhave the same traveling direction, but the measured current is negative.)
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 17 -
Velocity of propagation
Traveling Waves - Laws of Propagation
d
r r
0' lnrd
Lr
=
0'
ln
rC
dr
=
with 0 = 1.25610-6 Vs/Am Permeability of vacuum
0 = 8.85410-12As/Vm Permittivity of vacuum
c0 300 m/s Velocity of light
0
0 0
1 1 1
r r r r
c
= = 1
' '
v
L C
=Velocity of propagation
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 18 -
Traveling Waves - Laws of Propagation
As r= 1: 01
r
v c
=
Air: r= 1.0006 1 vair= c0 = 300 m/s
Cable: r= 2.5 ... 4 vcable = 190 m/s ... 150 m/s
exclusively dependent on dielectrics!
Velocity of propagation
with 0 = 1.25610-6 Vs/Am Permeability of vacuum
0 = 8.85410-12As/Vm Permittivity of vacuum
c0 300 m/s Velocity of light
0
0 0
1 1 1
r r r r
c
= = 1
' 'v
L C=Velocity of propagation
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 19 -
Surge impedance
Traveling Waves - Laws of Propagation
d
r r
0' lnrd
Lr
=
0'
ln
rC
dr
=
Surge impedance0
0
1
lnr
r
d
r
=
depends on dielectrics!
depends on geometry! does not depend on location!
'
'
L
Z C=
with 0 = 1.25610-6 Vs/Am Permeability of vacuum
0 = 8.85410-12As/Vm Permittivity of vacuum
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 20 -
Surge impedance
Traveling Waves - Laws of Propagation
0
0
1lnr
r
dZ
r
=
Figures:
OHL 420 kV, quadruple bundle: Z 250
OHL 123 kV, single conductor: Z 400
GIS, GIL: Z 60
polymeric (XLPE) hv-cable: Z 40
polymeric (XLPE) mv-cable: Z< 40 measuring (coaxial) cable (RG-58): Z 50
power transformer winding: Z 102 ... 104
with 0
= 1.25610-6 Vs/Am Permeability of vacuum
0 = 8.85410-12As/Vm Permittivity of vacuum
FM antenna cable: Z 75
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 21 -
Traveling Waves - Reflection and Refraction
uv
iv
Leitung 1 Leitung 2
Z1 Z2
uv
iv
Leitung 1 Leitung 2
Z1 Z2
uv = Z1iv
uv and iv suffer changes at the location of discontinuity
Refraction (forward waves proceed at increased or reduced amplitudes)
Reflection (waves travel back from the location of discontinuity)
line 1 line 2
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 22 -
Traveling Waves - Reflection and Refraction
u1v, i1v
i1
Leitung 1 Leitung 2
Z1 Z2
i2
u1 u2
u1v, i1v
i1
Leitung 2
i2
u1 u2
u1 = u2i1 = i2
u1 = u1v + u1ri1 = i1v + i1r
u2 = u2v + u2r= u2vi2 = i2v + i2r= i2v
u1v + u1r= u2v
i1v + i1r= i2v
line 1 line 2
=
=
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 23 -
Traveling Waves - Reflection and Refraction
u1v, i1v
i1
Leitung 1 Leitung 2
Z1 Z2
i2
u1 u2
u1v, i1v
i1
Leitung 2
i2
u1 u2
u1 = u2i1 = i2
u1 = u1v + u1ri1 = i1v + i1r
u2 = u2v + u2r= u2vi2 = i2v + i2r= i2v
u1v + u1r= u2v
i1v + i1r= i2v1v 2 v1r
1 1 2
u uuZ Z Z
= 11v 1r 2 v2
Zu u uZ
=
2v 2u
1v 1 2
2u Zb
u Z Z
= =
+
line 1 line 2
=
=
1.
2.
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 24 -
Traveling Waves - Reflection and Refraction
2v 2u
1v 1 2
2u Zb
u Z Z
= =
+voltage refraction factorvoltage refraction factor
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 25 -
Traveling Waves - Reflection and Refraction
2 v u 12 v 1v 1v u
2 2 2
u b Zi u i b
Z Z Z= = = 2v 2
u
1v 1 2
2u Zb
u Z Z
= =
+
2 v 1 1u i
1v 2 1 2
2i Z Zb b
i Z Z Z
= = =
+
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 26 -
Traveling Waves - Reflection and Refraction
2 v 1i
1v 1 2
2i Zb
i Z Z
= =
+current refraction factorcurrent refraction factor
2v 2u
1v 1 2
2u Zb
u Z Z
= =
+voltage refraction factorvoltage refraction factor
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 27 -
Traveling Waves - Reflection and Refraction
u1v, i1v
i1
Leitung 1 Leitung 2
Z1 Z2
i2
u1 u2
u1v, i1v
i1
Leitung 2
i2
u1 u2
u1 = u2i1 = i2
u1 = u1v + u1ri1 = i1v + i1r
u2 = u2v + u2r= u2vi2 = i2v + i2r= i2v
u1v + u1r= u2v
i1v + i1r= i2v
line 1 line 2
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 28 -
Traveling Waves - Reflection and Refraction
1r 2 v 1v u 1v 1v 1v u 1v u( 1)u u u b u u u b u r = = = =
1r 2 1u u
1v 2 1
1u Z Zr bu Z Z
= = =+
u1v + u1r= u2v
2vu
1v
ub
u=
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 29 -
Traveling Waves - Reflection and Refraction
voltage reflection factorvoltage reflection factor1r 2 1
u u
1v 2 1
1u Z Z
r bu Z Z
= = =
+
2 v 1i
1v 1 2
2i Zb
i Z Z
= =
+current refraction factorcurrent refraction factor
2v 2u
1v 1 2
2u Zb
u Z Z
= =
+voltage refraction factorvoltage refraction factor
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 30 -
Traveling Waves - Reflection and Refraction
u1v, i1v
i1
Leitung 1 Leitung 2
Z1 Z2
i2
u1 u2
u1v, i1v
i1
Leitung 2
i2
u1 u2
u1 = u2i1 = i2
u1 = u1v + u1ri1 = i1v + i1r
u2 = u2v + u2r= u2vi2 = i2v + i2r= i2v
u1v + u1r= u2v
i1v + i1r= i2v
line 1 line 2
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 31 -
Traveling Waves - Reflection and Refraction
1r 2v 1v i 1v 1v 1v i 1v i( 1)i i i b i i i b i r = = = =
1r 1 2i i
1v 1 2
1i Z Z
r bi Z Z
= = =+
i1v + i1r= i2v
2 vi
1v
ib
i
=
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 32 -
Traveling Waves - Reflection and Refraction
current reflection factorcurrent reflection factor1r 1 2i i1v 1 2
1i Z Z
r bi Z Z
= = =
+
voltage reflection factorvoltage reflection factor1r 2 1
u u
1v 2 1
1u Z Z
r bu Z Z
= = =
+
2 v 1i
1v 1 2
2i Zb
i Z Z
= =
+current refraction factorcurrent refraction factor
2v 2u
1v 1 2
2u Zb
u Z Z
= =
+voltage refraction factorvoltage refraction factor
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 33 -
Traveling Waves - Reflection and Refraction at End of Line
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri uline 1
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 34 -
a) end = open circuit R
ru = 1 u1r= u1v u = 2u1v
ri = 1 i1r= i1v i= 0
Doubling of voltage at lines end, current = zero
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri uline 1
Traveling Waves - Reflection and Refraction at End of Line
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entranceu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entrance u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of lineu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of line
l fl d f E d f
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 35 -
b) end = short-circuit R= 0
ru = 1 u1r= u1v u = 0
ri= 1 i1r= i1v i= 2i1v
Doubling of current at lines end, voltage = zero
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri uline 1
Traveling Waves - Reflection and Refraction at End of Line
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entranceu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entrance u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of lineu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of line
T li W R fl i d R f i E d f Li
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 36 -
c) matched end R= Z
ru = 0 u1r= 0 u = u1v
ri= 0 i1r= 0 i= i1v
Neither refraction nor reflection
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri uline 1
Traveling Waves - Reflection and Refraction at End of Line
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entranceu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entrance u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of lineu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of line
T li W R fl ti d R f ti t E d f Li
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 37 -
d) end = any real-valued resistance Z1 R
ru = 0 1 u1r= 0 u1v u = (12)u1v
ri= 0 -1 i1r= 0 -i1v i= 0 i1v
Increase of voltage and decrease of current at lines end
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri uline 1
Traveling Waves - Reflection and Refraction at End of Line
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entranceu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entrance u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of lineu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of line
T li W R fl ti d R f ti t E d f Li
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 38 -
e) end = any real-valued resistance 0 R Z1
ru = 0 -1 u1r= 0 -u1v u = 0 u1v
ri= 0 1 i1r= 0 i1v i= (12)i1v
Decrease of voltage and increase of current at lines end
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri uline 1
Traveling Waves - Reflection and Refraction at End of Line
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entranceu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entrance u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of lineu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of line
T lin W s R fl ti n nd R f ti n t End f Lin
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 39 -
f) capacitor at line's end Z from 0 to
Exponential functions of voltage and current at lines end
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri uline 1
Traveling Waves - Reflection and Refraction at End of Line
C
( )11( ) 2 1 e t Z Cvu t u = 11( ) 2 et Z C
vi t i
=
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entranceu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entrance u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of lineu
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11
21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of line
Traveling Waves Reflection and Refraction at End of Line
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 40 -
g) inductor at line's end Z from to 0
Exponential functions of voltage and current at lines end
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri uline 1
Traveling Waves - Reflection and Refraction at End of Line
L
( )11( ) 2 1 e tL Zvi t i = 11( ) 2 e tL Zvu t u =
u
t11 21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entranceu
t11 21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11 21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
line entrance u
t11 21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of lineu
t11 21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
u
t11 21
1u1v
2u1v
t11 21
1i1v
2i1v
i
0
0
end of line
Traveling Waves Reflection and Refraction at End of Line
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 41 -
Traveling Waves - Reflection and Refraction at End of Line
Traveling Waves Reflection and Refraction at End of Line
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 42 -
matched: R= Z
open circuit
short-circuit
Traveling Waves - Reflection and Refraction at End of Line
Traveling Waves - Reflection and Refraction at End of Line
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 43 -
Traveling wave equivalent electrical circuit
2uv
Z1
R L C2uv
Z1
R L C
ik = 2uv/Z1 = 2iv2uv
2iv
u
i
Z1
Traveling Waves - Reflection and Refraction at End of Line
Traveling Waves Bewley Diagram
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 44 -
Traveling Waves Bewley Diagram
2
3
4
2
3
4
local axislocal axis
time axis at location "A"time axis at location "A"
Factors of reflectionand refractionFactors of reflectionand refraction
Incoming
voltage surge
Incoming
voltage surge
11 22 33loc
al-timeaxes
local-timeaxes
local-tim
e axes
local-tim
e axes
time axis at location "B"time axis at location "B"
z
Traveling Waves Bewley Diagram
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 45 -
Traveling Waves Bewley Diagram
Traveling Waves Bewley Diagram
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 46 -
Traveling Waves Bewley Diagram
Traveling Waves Bewley Diagram
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 47 -
Traveling Waves Bewley Diagram
Traveling Waves Bewley Diagram
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 48 -
Traveling Waves Bewley Diagram
Traveling Waves Bewley Diagram
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 49 -
g y g m
Traveling Waves Application Example: Oscillations
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 50 -
g pp p
line with surge impedance Z2and propagation time
u1 u2Ri
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 51 -
line with surge impedance Z2and propagation time
u1 u2Ri
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 52 -
line with surge impedance Z2and propagation time
g pp p
u1 u2Ri
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 53 -
line with surge impedance Z
and propagation time u1 u2Ri
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 54 -
Occurrence of traveling waves / Making use of traveling wave effects
energization of a unloaded line
propagation of lightning overvoltages on lines propagation of very fast transients in GIS
separation effects / protective zone of surge arresters
generating and measuring of LI voltages
generating rectangular current impulses (energy tests on surge arresters)
fault location on cables
fault location on light wave guides / optical fibers
location of partial discharges in GIS
Making Use of Traveling Waves Effects
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 55 -
Long duration current impulse generator with LC distributed network
t [ms]
U[
kV]
-4-3-2
-1012345
6
0 0,5 1 1,5 2 2,5 3 3,5 4
-0,200,2
0,40,60,811,21,41,6
1,8
I[kA]
Long duration current impulse(2,4 ms, 1200 A)
=
Making Use of Traveling Waves Effects
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 56 -
Rdut = ZZ,
Rdut = ZZ,
t= 0
U
I
Long duration current impulse generator with LC distributed network
Ucharge
Ucharge
Making Use of Traveling Waves Effects
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 57 -
t> 0
Uv = U0/2
Iv = I0/2Z
Rdut = ZZ,
Rdut = ZZ,
U
I
Long duration current impulse generator with LC distributed network
Ucharge
Ucharge
Making Use of Traveling Waves Effects
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 58 -
t=
Uv = U0/2
Iv = I0/2Z
Rdut = ZZ,
Rdut = ZZ,
U
I
Long duration current impulse generator with LC distributed network
Ucharge
Ucharge
Making Use of Traveling Waves Effects
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 59 -
t>
Uv = U0/2
Iv = I0/2Z
Rdut = ZZ,
Rdut = ZZ,
U
I
Long duration current impulse generator with LC distributed network
Ucharge
Ucharge
Making Use of Traveling Waves Effects
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 60 -
t= 2
Uv = U0/2
Iv = I0/2Z
Ucharge Rdut = ZZ,
Rdut = ZZ,
U
I
Long duration current impulse generator with LC distributed network
Ucharge
Making Use of Traveling Waves Effects
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 61 -
t [ms]
U[
kV]
-4-3
-2-1012
3456
0 0,5 1 1,5 2 2,5 3 3,5 4
-0,20
0,20,40,60,81
1,21,41,61,8
I[kA]
Long duration current impulse(2.4 ms, 1200 A)
Long duration current impulse generator with LC distributed network
Traveling Waves Line Discharge
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Fachgebiet
HochspannungstechnikOvervoltage Protection and Insulation Coordination / Chapter 5 a - 62 -