iso v 15

Prévia do material em texto

Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 1 -
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 µs 2 µs 3 µs
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
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 2 -
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/µs
• Time for traveling along one span of a HV-OHL (300 m): 1 µs
• Time for traveling along an OHL of 300 km length: 1 ms
• Spatial length of a lightning overvoltage surge (100 µs): 30 km
• Spatial length of the front of a lightning overvoltage surge (1µs): 300 m
• Spatial length of a switching overvoltage surge (5 ms): 1500 km
• Spatial length of the front of switching overvolage surge (250 µs): 75 km
• Spatial length of one half-period of 50-Hz voltage (10 ms): 3000 km
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 3 -
Traveling Waves
Velocity of propagation in air: v = c0 = 300 m/µs
Velocity of propagation in a measuring cable: v = 150 m/µs
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
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 4 -
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
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 5 -
Traveling Waves - Laws of Propagation
General electrical equivalent circuit of a line element
R‘ ... Resistance
L‘ ... Inductance
G‘ ... Parallel conductance
C‘ ... Capacitance
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 6 -
Traveling Waves - Laws of Propagation
Electrical equivalent circuit of a loss-less line element
( d ) ' du iu u x L x
x t
∂ ∂
− + = ⋅
∂ ∂
'
u iL
x t
∂ ∂
− = ⋅
∂ ∂
( d ) ' di ui i x C x
x t
∂ ∂
− + = ⋅
∂ ∂
'
i uC
x t
∂ ∂
− = ⋅
∂ ∂
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 7 -
Traveling Waves - Laws of Propagation
'
u iL
x t
∂ ∂
− = ⋅
∂ ∂
'
i uC
x t
∂ ∂
− = ⋅
∂ ∂
Partial derivative with respect to x:
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
∂ ∂
= ⋅
∂ ∂
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 8 -
Traveling Waves - Laws of Propagation
'
u iL
x t
∂ ∂
− = ⋅
∂ ∂
'
i uC
x t
∂ ∂
− = ⋅
∂ ∂
Partial derivative with respect to t:
Partial derivative with respect to x:
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
∂ ∂
= ⋅
∂ ∂
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 9 -
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 d‘Alembert (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 iZ Z= − − + = +
uv ur
iv ir
1
' '
v
L C
=
'
'
LZ
C
=
Velocity of propagation
Surge impedance
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 10 -
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 a
positive forward current wave:
A positive backward voltage wave is linked to
negative backward current wave:
uv
iv
x
ur
ir
x
1 2( , ) ( ) ( ) v ru x t f x vt f x vt u u= − + + = +
uv ur
1 2
1 1( , ) ( ) ( ) v ri x t f x vt f x vt i iZ Z= − − + = +
iv ir
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 11 -
Traveling Waves - Laws of Propagation
Wanderwellenausbreitung beim plötzlichen Abfließen einer freigewordenen Influenzladung auf einer 
Freileitung; linke Bildhälfte: zeitliche Entwicklung der Felder; rechte Bildhälfte: 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: ur and ir have the same traveling direction, but the measured current is negative.)
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 12 -
Velocity of propagation
Traveling Waves - Laws of Propagation
d
r r
0
' lnr dL
r
µ µ
pi
=
0
'
ln
rC d
r
ε ε pi
=
with µ0 = 1.256·10-6 Vs/Am Permeability of vacuum
ε0 = 8.854·10-12 As/Vm Permittivity of vacuum
c0 ≈ 300 m/µs Velocity of light
0
0 0
1 1 1
r r r r
c
µ ε µ ε µ ε
= ⋅ = ⋅
1
' '
v
L C
=Velocity of propagation
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 13 -
Traveling Waves - Laws of Propagation
As µr = 1: 0
1
r
v c
ε
= ⋅
Air: εr = 1.0006 ≈ 1 vair = c0 = 300 m/µs
Cable: εr = 2.5 ... 4 vcable = 190 m/µs ... 150 m/µs
• exclusively dependent on dielectrics!
Velocity of propagation
with µ0 = 1.256·10-6 Vs/Am Permeability of vacuum
ε0 = 8.854·10-12 As/Vm Permittivity of vacuum
c0 ≈ 300 m/µs Velocity of light
0
0 0
1 1 1
r r r r
c
µ ε µ ε µ ε
= ⋅ = ⋅
1
' '
v
L C
=Velocity of propagation
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 14 -
Surge impedance
Traveling Waves - Laws of Propagation
d
r r
0
' lnr dL
r
µ µ
pi
=
0
'
ln
rC d
r
ε ε pi
=
Surge impedance 0
0
1 lnr
r
d
r
µ µ
pi ε ε
=
• depends on dielectrics!
• depends on geometry!
• does not depend on location!
'
'
LZ
C
=
with µ0 = 1.256·10-6 Vs/Am Permeability of vacuum
ε0 = 8.854·10-12 As/Vm Permittivity of vacuum
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 15 -
Surge impedance
Traveling Waves - Laws of Propagation
0
0
1 lnr
r
dZ
r
µ µ
pi ε ε
=
Figures:
OHL 420 kV, quadruple bundle: Z ≈ 250 Ω
OHL 123 kV, single conductor: Z ≈ 400 Ω
GIS, GIL: Z ≈ 60 Ω
polymeric (XLPE) hv-cable: Z ≈ 40 Ω
polymeric (XLPE) mv-cable: Z < 40 Ω
measuring (coaxial) cable (RG-58): Z ≈ 50 Ω
transformerwinding: Z ≈ 102 Ω ... 104 Ω
with µ0 = 1.256·10-6 Vs/Am Permeability of vacuum
ε0 = 8.854·10-12 As/Vm Permittivity of vacuum
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 16 -
Traveling Waves - Reflection and Refraction
uv
iv
Leitung 1 Leitung 2
Z1 Z2
uv
iv
Leitung 1 Leitung 2
Z1 Z2
uv = Z1·iv
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
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 17 -
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 = u2
i1 = i2
u1 = u1v + u1r
i1 = i1v + i1r
u2 = u2v + u2r = u2v
i2 = i2v + i2r = i2v
u1v + u1r = u2v
i1v + i1r = i2v
line 1 line 2
=
=
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 18 -
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 = u2
i1 = i2
u1 = u1v + u1r
i1 = i1v + i1r
u2 = u2v + u2r = u2v
i2 = i2v + i2r = i2v
u1v + u1r = u2v
i1v + i1r = i2v 1v 2v1r
1 1 2
u uu
Z Z Z
− =
1
1v 1r 2v
2
Z
u u u
Z
− = ⋅
2v 2
u
1v 1 2
2u Z b
u Z Z
⋅
= =
+
line 1 line 2
=
=
1.
2.
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 19 -
Traveling Waves - Reflection and Refraction
2v 2
u
1v 1 2
2u Z b
u Z Z
⋅
= =
+ voltage refraction factorvoltage refraction factor
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 20 -
Traveling Waves - Reflection and Refraction
2v u 1
2v 1v 1v u
2 2 2
u b Zi u i b
Z Z Z
= = ⋅ = ⋅ ⋅ 2v 2
u
1v 1 2
2u Z b
u Z Z
⋅
= =
+
2v 1 1
u i
1v 2 1 2
2i Z Zb b
i Z Z Z
⋅
= ⋅ = =
+
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 21 -
Traveling Waves - Reflection and Refraction
2v 1
i
1v 1 2
2i Z b
i Z Z
⋅
= =
+
current refraction factorcurrent refraction factor
2v 2
u
1v 1 2
2u Z b
u Z Z
⋅
= =
+ voltage refraction factorvoltage refraction factor
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 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 = u2
i1 = i2
u1 = u1v + u1r
i1 = i1v + i1r
u2 = u2v + u2r = u2v
i2 = i2v + i2r = i2v
u1v + u1r = u2v
i1v + i1r = i2v
line 1 line 2
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 23 -
Traveling Waves - Reflection and Refraction
1r 2v 1v u 1v 1v 1v u 1v u( 1)u u u b u u u b u r= − = ⋅ − = ⋅ − = ⋅
1r 2 1
u u
1v 2 1
1u Z Zr b
u Z Z
−
= = − =
+
u1v + u1r = u2v
2v
u
1v
u b
u
=
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 24 -
Traveling Waves - Reflection and Refraction
voltage reflection factorvoltage reflection factor1r 2 1u u
1v 2 1
1u Z Zr b
u Z Z
−
= = − =
+
2v 1
i
1v 1 2
2i Z b
i Z Z
⋅
= =
+
current refraction factorcurrent refraction factor
2v 2
u
1v 1 2
2u Z b
u Z Z
⋅
= =
+ voltage refraction factorvoltage refraction factor
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 25 -
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 = u2
i1 = i2
u1 = u1v + u1r
i1 = i1v + i1r
u2 = u2v + u2r = u2v
i2 = i2v + i2r = i2v
u1v + u1r = u2v
i1v + i1r = i2v
line 1 line 2
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 26 -
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 2
i i
1v 1 2
1i Z Zr b
i Z Z
−
= = − =
+
i1v + i1r = i2v
2v
i
1v
i b
i
=
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 27 -
Traveling Waves - Reflection and Refraction
current reflection factorcurrent reflection factor1r 1 2i i
1v 1 2
1i Z Zr b
i Z Z
−
= = − =
+
voltage reflection factorvoltage reflection factor1r 2 1u u
1v 2 1
1u Z Zr b
u Z Z
−
= = − =
+
2v 1
i
1v 1 2
2i Z b
i Z Z
⋅
= =
+
current refraction factorcurrent refraction factor
2v 2
u
1v 1 2
2u Z b
u Z Z
⋅
= =
+ voltage refraction factorvoltage refraction factor
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 28 -
Traveling Waves - Reflection and Refraction at End of Line
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri u
line 1
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 29 -
a) end = open circuit ⇒⇒⇒⇒ R→→→→ ∞∞∞∞
ru = 1 ⇒ u1r = u1v ⇒ u = 2·u1v
ri = –1 ⇒ i1r = – i1v ⇒ i = 0
⇒⇒⇒⇒ doubling of voltage at line‘s end, current = zero
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri u
line 1
Traveling Waves - Reflection and Refraction at End of Line
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 30 -
b) end = short-circuit ⇒⇒⇒⇒ R = 0
ru = – 1 ⇒ u1r = – u1v ⇒ u = 0
ri = 1 ⇒ i1r = i1v ⇒ i = 2·i1v
⇒⇒⇒⇒ doubling of current at line‘s end, voltage = zero
u1v, i1v
Leitung 1
Z1
Ri u
u1v, i1v
Leitung 1
Z1
Ri u
line 1
Traveling Waves - Reflection and Refraction at End of Line
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 31 -
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 u
line 1
Traveling Waves - Reflection and Refraction at End of Line
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 32 -
Traveling Waves - Reflection and Refraction at End of Line
open circuit
short-circuit
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 33 -
matched: R = Z
open circuit
short-circuit
Traveling Waves - Reflection and Refraction at End of Line
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 34 -
Traveling wave equivalent electrical circuit
2·uv
Z1
R L C2·uv
Z1
R L C
ik = 2·uv/Z1 = 2·iv2·uv
2·iv
u
i
Z1
Traveling Waves - Reflection and Refraction at End of Line
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 35 -
Protective Distance of Surge Arresters – Model Calculation
Overvoltage surge
of s = 800 kV/ µs
upl = 800 kV = const.
Transformer
LIW = 1425 kV
?= 300 m
x = 0 x = 
Arrester
upl = 800 kV = const. LIW = 1425 kV
ℓ = 300 m
x = 0 x = ℓ
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 36 -
-1200
-800
-400
0
400
800
1200
1600
2000
x = 0 x = ℓ
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
400
8001200
1600
0
0 0,5 1,51 2 2,5µs
kV
uArr (x = 0)
uTr (x = ℓ)
x = 0: uArr = 0 kVx = 0: uArr = 0 kV
x = ℓ: uTr = 0 kVx = ℓ: uTr = 0 kV
t = 0 µst = 0 µs
Protective Distance of Surge Arresters – Model Calculation
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 37 -
-1200
-800
-400
0
400
800
1200
1600
2000
u1v
x = 0 x = ℓ
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
uArr (x = 0)
uTr (x = ℓ)
x = 0: uArr = u1v = 400 kVx = 0: uArr = u1v = 400 kV
x = ℓ: uTr = u1v = 0 kVx = ℓ: uTr = u1v = 0 kV
t = 0,5 µst = 0,5 µs
Protective Distance of Surge Arresters – Model Calculation
-1200
-800
-400
0
400
800
1200
1600
2000
u1v
x = 0 x = ℓ
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
uArr (x = 0)
uTr (x = ℓ)
x = 0: uArr = u1v = 800 kVx = 0: uArr = u1v = 800 kV
x = ℓ: uTr = u1v = 0 kVx = ℓ: uTr = u1v = 0 kV
t = 1 µst = 1 µs
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 38 -
Protective Distance of Surge Arresters – Model Calculation
-1200
-800
-400
0
400
800
1200
1600
2000
u1v
u1r
u2v
x = 0 x = ℓ
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
uArr (x = 0)
uTr (x = ℓ)
x = 0: uArr = u1v + u2v =(1200 – 400) kV = 800 kV
x = 0: uArr = u1v + u2v =(1200 – 400) kV = 800 kV
x = ℓ: uTr = u1v + u1r =(400 + 400) kV = 800 kV
x = ℓ: uTr = u1v + u1r =(400 + 400) kV = 800 kV
t = 1,5 µst = 1,5 µs
Increase at
double steepness!
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 39 -
Protective Distance of Surge Arresters – Model Calculation
-1200
-800
-400
0
400
800
1200
1600
2000
u1v
u1r
u2v
x = 0 x = ℓ
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
uArr (x = 0)
uTr (x = ℓ)
x = 0: uArr = u1v + u2v =(1600 – 800) kV = 800 kV
x = 0: uArr = u1v + u2v =(1600 – 800) kV = 800 kV
x = ℓ: uTr = u1v + u1r =(800 + 800) kV = 1600 kV
x = ℓ: uTr = u1v + u1r =(800 + 800) kV = 1600 kV
t = 2 µst = 2 µs
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 40 -
Protective Distance of Surge Arresters – Model Calculation
-1200
-800
-400
0
400
800
1200
1600
2000
u1v
u1r
u3v
u2v
u2r
x = 0 x = ℓ
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
400
800
1200
1600
0
0 0,5 1,51 2 2,5µs
kV
uArr (x = 0)
uTr (x = ℓ)
x = 0: uArr = u1v + u1r + u2v + u3v =(2000 + 400 – 1200 – 400) kV = 800 kV
x = 0: uArr = u1v + u1r + u2v + u3v =(2000 + 400 – 1200 – 400) kV = 800 kV
x = ℓ: uTr = u1v + u1r + u2v + u2r =(1200 + 1200 – 400 – 400) kV = 1600 kV
x = ℓ: uTr = u1v + u1r + u2v + u2r =(1200 + 1200 – 400 – 400) kV = 1600 kV
t = 2,5 µst = 2,5 µs
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 41 -
Protective Distance of Surge Arresters – Model Calculation
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 42 -
Due to traveling wave effects on the line the protection of the equipment by an arrester
can be guaranteed only for short distances between arrester and equipment.
Simplified estimation of the protective zone *):
xs protective zone [m]
LIWV standard rated lightning impulse withstand voltage [kV]
Upl LI protection level of the arrester [kV]
s front steepness of the overvoltage [kV/µs]
(in the range of 1000 kV/µs)
vtw propagation speed of travelling wave:
- 300 m/µs (overhead line) (equals c0)
- 200 m/µs (cable)
(LIWV / 1.15) - Upl
2·s
· vtwxs =
Example 1: Distribution network, Um = 24 kV, insulated neutral, arrester of Ur = 30 kV:
(125 / 1.15) - 80
2·1000
· 300 = 4.3 mxs =
Example 2: Transmission network, Um = 420 kV, effectively earthed, arrester of Ur = 336 kV:
(1425 / 1.15) - 823
2·1000
· 300 = 62.4 mxs =
*) For more detailed information see IEC 60099-5, IEC 60071-1 and IEC 60071-2
Protective Distance of Surge Arresters – Model Calculation
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 43 -
Traveling Waves – Bewley Diagram
ττττ
2ττττ
3ττττ
4ττττ
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 44 -
Traveling Waves – Bewley Diagram
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 45 -
Traveling Waves – Bewley Diagram
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 46 -
Traveling Waves – Bewley Diagram
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 47 -
Traveling Waves – Bewley Diagram
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 48 -
Traveling Waves – Bewley Diagram
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 49 -
Traveling Waves – Application Example: Oscillations
line with surge impedance Z2
and propagation time τu1
u2Ri<<Z
1 2 3
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 50 -
line with surge impedance Z2
and propagation time τu1
u2Ri<<Z
Traveling Waves – Application Example: Oscillations
1 2 3
1 2 i 2
21
1 2 i 2
1Z Z R Zr
Z Z R Z
− −
= = ≈ −
+ +
3 2 2
23
3 2 2
1Z Z Zr
Z Z Z
− ∞−
= = ≈ +
+ ∞+
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 51 -
line with surge impedance Z2
and propagation time τ
u1 u2Ri<<Z
Traveling Waves – Application Example: Oscillations
1 2 321 1r = − 23 1r =
1ττττ
3ττττ
5ττττ
7ττττ
9ττττ
2ττττ
4ττττ
6ττττ
8ττττ
10ττττ
0
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 52 -
line with surge impedance Z
and propagation time τu1
u2Ri<<Z
0
0,5
1
1,5
2
0 2 4 6 8 10
t/τ
u
/
u
0
u1
u2
0
0,5
1
1,5
2
0 2 4 6 8 10
t/τ
u
/
u
0
u1
u2
Traveling Waves – Application Example: Oscillations
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 53 -
Traveling Waves – Exercise
cable
ZL1 = 50 Ω
OHL
ℓL2 = 600 m
ZL2 = 500 Ω
vL2 = 300 m/µs
cable
ZL3 = 50 Ω
Problem: an overvoltage surge (simplified by a triangular shape as shown above)
(upeak = 100 kV, front ramp duration 1 µs, total duration 6 µs) is arriving from left
Task: calculate the voltages at points A and B
overhead line
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 54 -
Traveling Waves – Exercise
overhead line
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 55 -
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 locationon light wave guides / optical fibers
• location of partial discharges in GIS
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 56 -
Making Use of Traveling Waves Effects
Long duration current impulse generator with LC distributed network
t [ms]
U
 
[
k
V
]
-4
-3
-2
-1
0
1
2
3
4
5
6
0 0,5 1 1,5 2 2,5 3 3,5 4
-0,2
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
I
 
[
k
A
]
Long duration current impulse
(2,4 ms, 1200 A)
=
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 57 -
Rdut = ZZ, τ
Rdut = ZZ, τ
t = 0
U
I
Making Use of Traveling Waves Effects
Long duration current impulse generator with LC distributed network
Ucharge
Ucharge
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 58 -
t > 0
Uv = U0/2
Iv = I0/2Z
Making Use of Traveling Waves Effects
Rdut = ZZ, τ
Rdut = ZZ, τ
U
I
Long duration current impulse generator with LC distributed network
Ucharge
Ucharge
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 59 -
t = τ
Uv = U0/2
Iv = I0/2Z
Making Use of Traveling Waves Effects
Rdut = ZZ, τ
Rdut = ZZ, τ
U
I
Long duration current impulse generator with LC distributed network
Ucharge
Ucharge
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 60 -
t > τ
Uv = U0/2
Iv = I0/2Z
Making Use of Traveling Waves Effects
Rdut = ZZ, τ
Rdut = ZZ, τ
U
I
Long duration current impulse generator with LC distributed network
Ucharge
Ucharge
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 61 -
t = 2τ
Uv = U0/2
Iv = I0/2Z
Making Use of Traveling Waves Effects
Ucharge Rdut = ZZ, τ
Rdut = ZZ, τ
U
I
Long duration current impulse generator with LC distributed network
Ucharge
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 62 -
t [ms]
U
 
[
k
V
]
-4
-3
-2
-1
0
1
2
3
4
5
6
0 0,5 1 1,5 2 2,5 3 3,5 4
-0,2
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
I
 
[
k
A
]
Long duration current impulse
(2.4 ms, 1200 A)
Making Use of Traveling Waves Effects
Long duration current impulse generator with LC distributed network
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 5 - 63 -
Traveling Waves – Line Discharge