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Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 1 -
Fast-front overvoltages may be:
– lightning overvoltages affecting overhead lines;
– lightning overvoltages affecting substations;
– overvoltages due to switching operations and faults.
Fast-front overvoltages may be:
– lightning overvoltages affecting overhead lines;
– lightning overvoltages affecting substations;
– overvoltages due to switching operations and faults.
Fast-Front Overvoltages
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 2 -
Reasons for lightning overvoltages affecting OHL:
– direct lightning strikes to the phase conductor Æ see later;
– lightning strikes to tower/ground wire and subsequent back flashover;
– induced by lightning strikes to ground nearby the OHL.
Reasons for lightning overvoltages affecting OHL:
– direct lightning strikes to the phase conductor Æ see later;
– lightning strikes to tower/ground wire and subsequent back flashover;
– induced by lightning strikes to ground nearby the OHL.
Lightning Overvoltages affecting Overhead Lines (OHL)
Amplitudes of induced overvoltages usually below 400 kV
Æ problem for distribution systems, but not an issue for high-voltage
(LIW(Um = 72.5 kV) = 325 kV, LIW(Um = 123 kV) ≥ 450 kV)
Back flashovers
• less probable in range II than in range I
• rare in systems of Us = 550 kV and above
The representative voltage stress is characterized by:
– a representative voltage shapeÆ 1.2/50 µs;
– a representative amplitude which can be either
• an assumed maximum overvoltage or
• a probability distribution of the overvoltage amplitudes.
The representative voltage stress is characterized by:
– a representative voltage shapeÆ 1.2/50 µs;
– a representative amplitude which can be either
• an assumed maximum overvoltage or
• a probability distribution of the overvoltage amplitudes.
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 3 -
Amplitudes and rates of occurrence depend on:
– lightning performance of the OHLs connected to it;
– substation layout, size and in particular number of OHLs connected to it;
– instantaneous value of the operating voltage (at the moment of strike).
Amplitudes and rates of occurrence depend on:
– lightning performance of the OHLs connected to it;
– substation layout, size and in particular number of OHLs connected to it;
– instantaneous value of the operating voltage (at the moment of strike).
Lightning Overvoltages affecting Substations
Reduction of overvoltages phase-to-ground by
• cables (due to their low surge impedance)
• many lines connected in parallel (Æ reduction of effective surge impedance)
see 
lecture on 
traveling 
waves
Phase-to-phase:
Effects of power-frequency voltage and coupling between 
conductors roughly cancel each other.
Æ The neighbored phase may be considered as earthed.
L1
L2
LI by direct 
strike to L1
induced LI voltage 
by coupling L1↔ L2
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 4 -
For back flashovers:
Back flashovers most likely occur on the phase
that has the highest instantaneous power-frequency
voltage at opposite polarity.
Æ Representative overvoltage composed of the
representative LI voltage phase-to-earth at one terminal
and 1 p.u. power-frequency voltage of opposite polarity at the other
Terminal 2
Terminal 1
Terminal 2
Terminal 1
Longitudinal:
Power-frequency voltage of opposite terminal to be taken into account!
For direct strikes:
Representative overvoltage composed of the representative
LI voltage phase-to-earth at one terminal and 0.7 p.u.
power-frequency voltage of opposite polarity at the other
(empirical finding)
Lightning Overvoltages affecting Substations
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 5 -
Fast Front Overvoltages due to Switching Operations
Occur when
– equipment is (dis-)connected from the system via short connections, 
mainly in substations;
– external insulation flashes over.
Occur when
– equipment is (dis-)connected from the system via short connections, 
mainly in substations;
– external insulation flashes over.
Representative voltage = Standard Lightning Impulse Voltage 1.2/50 µs
(though the real voltages are usually oscillatory)
Representative voltage = Standard Lightning Impulse Voltage 1.2/50 µs
(though the real voltages are usually oscillatory)
Amplitudes usually lower than those caused by lightning strikes.
Maximum values:
• circuit breaker switching without restrike Æ 2 p.u.
• circuit breaker switching with restrike Æ 3 p.u.
(exception: with vacuum breakers up to 6 p.u. Æ voltage limiters required!)
• disconnector switching Æ 3 p.u.
It may be assumed that phase-to ground overvoltages constitute the decisive 
stress for insulation coordination purposes.
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 6 -
Direct Lightning Strikes to OHL
21 ln( )
21 e for 0( ) 2
0 for 0
x M
xf x x
x
β
π β
⎡ ⎤− ⎢ ⎥⎣ ⎦
⎧⎪ >= ⎨⎪ ≤⎩
Statistical distribution of parameters of the flash to be approximated
by a lognormal distribution (Berger, Anderson, Eriksson, CIGRÉ)
Probability density function:
M ... Median = 0.5 probability – not to be mixed
up with the mean or average value!
β .... log standard deviation
Calculation of the mean or average value:
2
2eµ M
β
=
Calculation of the standard deviation:
2
2
2e e 1M
β
βσ = ⋅ −
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 7 -
Direct Lightning Strikes to OHL – Berger's Data
Lightning research station of Prof. Berger
in a radio transmission station on top of 
Monte San Salvatore (912 m; Lake of 
Lugano, Switzerland)
Installed 1942 on behalf of SEV
Lightning studies up to ≈ 1970
Æ „Berger‘s Data“
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 8 -
Direct Lightning Strikes to OHL – Berger's Data
t10/30
t30/90
I10
I30
I90
I100
F
m
m
It
S
=
I
m
m
It
S
′ =
The strike 
current's front 
typically has a 
concave shape.
The strike 
current's front 
typically has a 
concave shape.
2 2
F
F F
0.484
2 2e 31.1 e 35 kA
I
I Iµ M
β
= ⋅ = ⋅ =
Difference Median – Mean value:
Mean value of first strike's final crest current
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 9 -
Extract of the table – values of primary importance
Direct Lightning Strikes to OHL – Berger's Data
F
m
m
It
S
=
91.5 µs
29 kA/µs
4.46 µs
1.54 µs
µ, mean value
2
2eµ M
β
=
Sm
S30/90
Sm
S30/90
57.4 kA/µs
32.1 kA/µs
29 kA/µs
8.7 kA/µs
35 kA
14.2 kA
µ, mean value
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 10 -
CIGRÉ and IEEE strike current 
probability curves, first strike, negative 
downward flash [CIG-91]
Direct Lightning Strikes to OHL – CIGRÉ Model
CIGRÉ curve:
P
(
I
<
 
I
F
)
The CIGRÉ distribution is based on the latest 
data available and better represents the 
actual data.
Æ CIGRÉ curve should preferably be used!
The CIGRÉ distribution is based on the latest 
data available and better represents the 
actual data.
Æ CIGRÉ curve should preferably be used!
IF, median = 33.3 kA
IF, median = 61.1 kA
Note: M = 61.1 kA for IF < 20 kA does not mean that this 
current really occurs. It is just a parameter that 
characterizes the curve, which is actually valid onlyin the 
range < 20 kA, however!
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 11 -
Derived parameters of conditional lognormal distributions, derived from 
Berger's data
Direct Lightning Strikes to OHL – Berger's Data
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 12 -
Direct Lightning Strikes to OHL – CIGRÉ Model
Average wave shape of the first and subsequent negative strike currents 
as developed by CIGRÉ [CIG-91]
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 13 -
Direct Lightning Strikes to OHL – CIGRÉ Model
Models of lightning strike acc. to IEC 60071-4
Double ramp shape
Æ easy to use
Double ramp shape
Æ easy to use
CIGRÉ concave shape, parameters from [CIG-91]
Æ higher accuracy
CIGRÉ concave shape, parameters from [CIG-91]
Æ higher accuracy
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 14 -
> 90%> 90%
from exposed 
points such 
as aerials, tv
towers
no subsequent 
strikes, highest 
reported 
current peak 
values and 
charges
Seldom!
downward flash
upward flash
cloud-to-cloud flash
negative cloud-to-ground positive cloud-to-ground
negative ground-to-cloud positive ground-to-cloud
Direct Lightning Strikes to OHL – strike Multiplicity
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 15 -
Only 45% of negative downward flashes consist of one strike per flash. In all other 
cases: multiple strikes in time intervals of 10 ms to 100 ms (see HVT II, Chapter 11).
Subsequent strikes have
• higher front steepness
• lower amplitude
• up to 54 follow strikes reported
• often: dc component
(in ca. 50% of all cases)11 current impulses of 7 kA up to 63 kA peak value
dc component
scale of dc 
component
Direct Lightning Strikes to OHL – strike Multiplicity
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 16 -
Direct Lightning Strikes to OHL – strike Multiplicity
Number of strikes per flash, negative downward flash 1)
=∑
Probability of 4 strikes or more
=∑ Probability of 8 strikes or more
1) R. B. Anderson, A. J. Eriksson
Lightning Parameters for Engineering Application
ELECTRA 69, Mar. 1980, pp. 65-102
• based on 6000 flash records from different regions of the world
• median of the distribution: 2
• mean or average value: 3
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 17 -
TD = 20 ... 80
TD = 80 ... 180
Keraunic levels worldwide
Middle Europe: TD = 10 ... 25
in equator regions: TD = 100 ... 180
Middle Europe: TD = 10 ... 25
in equator regions: TD = 100 ... 180
Lightning ground flash density Ng = number of lightning ground flashes per km2 and year
= ⋅N T 1.25g d0.04 Ng in (km2·a)-1Empirical relation:
TD = number of
thunderstorm days per year
• reported by Eriksson1) from observations in South Africa
• generally accepted both by CIGRÉ and IEEE
1) A. J. Eriksson
The Incidence of Lightning Strikes to Transmission Lines
IEEE Trans. on Power Delivery, Jul. 1987, pp. 859-870
Direct Lightning Strikes to OHL – Lightning Activity
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 18 -
Direct Lightning Strikes to OHL – Geometric Model
For a specific current I, calculate 
the striking distance rg and rc.
Draw a line parallel to the ground 
at a distance rg from the ground.
With compasses centered at the 
tower top, draw an arc of radius rc
until it intersects the parallel lines 
drawn in 2, above.
Any strike that arrives between A and B will terminate on the ground wire, and any strike that arrives to 
the left of A or to the right of B will terminate to ground.
Any strike that arrives between A and B will terminate on the ground wire, and any strike that arrives to 
the left of A or to the right of B will terminate to ground.
Basic idea (see also HVT II, Chapter 11)
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 19 -
Basic idea (see also HVT II, Chapter 11) g g( ) 2IN G N LD′=
N(G)|I ... number of strikes to 
ground wire for current I
L ... length of line
( )g g
3 kA
( ) 2 dN G N L D f I I
∞
′= ∫
f(I) ... probability that current I occurs
3 kA = lowest observed lightning 
flash current amplitude
D'g may be expressed in terms of striking 
distances and tower height:
( )22g c g c cosD r r h r Θ′ ′= − − =
Direct Lightning Strikes to OHL – Geometric Model
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 20 -
Practical approach (by empirical observations) (Eriksson)
b
( )0.6g 28( )
10
N b h
N G
+ ⋅′ =
N'(G) ... number of strikes to the line in (100 km · a)-1
Ng ... ground flash density in (km2 · a)-1
b … distance of outer conductors in m
h … average ground wire height (htower – 2/3·sag) in m
(assuming an 
approximate median 
current of 35 kA)
N'(G)
h
TD = 35 d
TD = 20 d
[BAL-04]
Note: in case of 
good shielding most 
of these strikes will 
hit the shield wire!
Note: in case of 
good shielding most 
of these strikes will 
hit the shield wire!
Direct Lightning Strikes to OHL – Geometric Model
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 21 -
Striking distance
Basic dependence: br A I= ⋅
for references, see [HIL-99]
Adopted by CIGRÉ Working Group
0.75
c 7.1r I= ⋅
[I] = kA, [rc] = m
= striking distance to an OHL
conductor or ground wire
Æ many different factors A, b published:
Direct Lightning Strikes to OHL – Geometric Model
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 22 -
Direct Lightning Strikes to OHL – Shielding Failure
strikes between A and B Æ phase conductor
strikes between B and C Æ ground wire
strikes beyond A Æ ground
strikes between A and B Æ phase conductor
strikes between B and C Æ ground wire
strikes beyond A Æ ground
Shielding effect of ground wire
Shielding failure rate:
m
g c
g c
3 kA
2
2 ( )d
I
I
SFR N LD
N L D f I I
=
= ∫
Im is the maximum current at and 
above which no strikes will 
terminate on the phase conductor
Æ see next slide
α = shielding angleα = shielding angle
L ... length of line
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 23 -
Shielding effect of ground wire
Æ Dc = 0Æ Currents I ≥ Im will hit
ground wire or ground
Æ Dc = 0Æ Currents I ≥ Im will hit
ground wire or ground
Point where all three striking 
distances rc,GW, rc,PhC, rg meet 
each other.
Point where all three striking 
distances rc,GW, rc,PhC, rg meet 
each other.
Direct Lightning Strikes to OHL – Shielding Failure
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 24 -
Situation for I = Im
α
ϕ x
ϕ = 180° - α – 90°
x = 180° - ϕ - 90° = 180° - 180° + α + 90° - 90° = α
c
a
c
Direct Lightning Strikes to OHL – Shielding Failure
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 25 -
Situation for I = Im
c
α
2
2
cm 4
cr −
gm
2
2
cm
2sin
4
h yr
cr
α
+−
=
−
2
2
cm 4
cr ⇒�As gm
cm
2sin
h yr
r
α
+−
=
Simplification: gm cm mr r r≈ =
m
m
2sin
h yr
r
α
+−
≈
m
2
1 sin
h y
r α
+
≈ −
Direct Lightning Strikes to OHL – Shielding Failure
Fachgebiet
Hochspannungstechnik OvervoltageProtection and Insulation Coordination / Chapter 4 - 26 -
Situation for I = Im
Direct Lightning Strikes to OHL – Shielding Angle
m
2
1 sin
h y
r α
+
≈ −
With 0.75m m7.1r I= ⋅ (see slide 20) ⇒ 0.75m m2 7.11 sin
h y
r Iα
+
≈ ≈ ⋅−
( )
1
0.75
m
2
7.1 1 sin
h y
I α
+⎡ ⎤⎢ ⎥≈ ⎢ ⎥⋅ −⎢ ⎥⎣ ⎦
Examples:
h = 60 m, y = 45 m, α = 30 °⇒ Im ≈ 36.3 kA
h = 30 m, y = 25 m, α = 15 °⇒ Im ≈ 9.1 kA
The higher the structure and the larger the shielding angle, the higher 
is the maximum current of a direct lightning strike to the OHL conductor.
The higher the structure and the larger the shielding angle, the higher 
is the maximum current of a direct lightning strike to the OHL conductor.
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 27 -
Situation for I = Im
deg
h = 60 m, y = 45 m
h = 45 m, y = 35 m
h = 30 m, y = 25 m
[BAL-04]
Direct Lightning Strikes to OHL – Shielding Angle
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 28 -
iBlitz
i
uu
i = iBlitz/2
u = Z·i
i
iBlitz
i
uu
i = iBlitz/2
u = Z·i
i
Strom- und Spannungswellen nach Blitzeinschlag in ein Leiterseil 
i = istroke /2
u = Z·i
istroke
Current and voltage surges after lightning stroke into a line conductor
iBlitz
i
uu
i = iBlitz/2
u = Z·i
i
iBlitz
i
uu
i = iBlitz/2
u = Z·i
i
Strom- und Spannungswellen nach Blitzeinschlag in ein Leiterseil 
i = istroke /2
u = Z·i
istroke
Current and voltage surges after lightning stroke into a line conductor
Choice of Im
Direct Lightning Strikes to OHL – Shielding Angle
If flashovers of the insulators shall be avoided, following requirement has to be fulfilled:
50 neg
m
2
Z
U
I
⋅< Example:Um = 420 kV Æ U50 neg = 2 100 kV, Z = 350 Ω
⇒ Im < 12 kA
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 29 -
Direct Lightning Strikes to OHL – Corona Damping
When the corona inception voltage is exceeded Æ corona
Corona inception voltage of a single conductor:
0 0
i 60
r Z EU ⋅ ⋅= Z0 ... natural (non-corona) surge impedance in ΩE0 ... critical voltage gradient in kV/cm
r ... conductor radius in cm
Critical voltage gradient (CIGRÉ):
0 0.37
1.2223 1 kV/cmE
d
⎛ ⎞= +⎜ ⎟⎝ ⎠
d ... conductor diameter in cm
0
10
20
30
40
50
60
0 2 4 6 8 10 12
conductor diameter (cm)
c
r
i
t
i
c
a
l
 
v
o
l
t
a
g
e
 
g
r
a
d
i
e
n
t
 
(
k
V
/
c
m
)
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 30 -
Direct Lightning Strikes to OHL – Corona Damping
When the corona inception voltage is exceeded Æ corona
Corona inception voltage of a single conductor:
0 0
i 60
r Z EU ⋅ ⋅= Z0 ... natural (non-corona) surge impedance in ΩE0 ... critical voltage gradient in kV/cm
r ... conductor radius in cm
Critical voltage gradient (CIGRÉ):
0 0.37
1.2223 1 kV/cmE
d
⎛ ⎞= +⎜ ⎟⎝ ⎠ d ... conductor diameter in cm
Example: 123-kV OHL (d = 1.9 cm, r = 0.95 cm, Z0 = 450 Ω)
0 0.37
1.2223 1 = 42 kV/cm
1.9
E ⎛ ⎞= +⎜ ⎟⎝ ⎠ i
0.95 450 42 299 kV
60
U ⋅ ⋅= =
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 31 -
Direct Lightning Strikes to OHL – Corona Damping
Effect of corona
• Apparent increase of radius from non-corona conductor radius r to corona 
conductor radius Rc
• Æ Increase of conductor capacitance (whereas inductance remains unchanged)
• Æ Decrease of surge impedance for surge front:
• Æ Decrease of velocity for parts of surge voltage u > Ui:
0 c
L LZ Z
C C C∆
′ ′= ⇒ =′ ′ ′+
0 c
1 1
( )
v v
L C L C C∆= ⇒ =′ ′ ′ ′ ′+
t = t0t > t0
Decrease of steepness!Decrease of steepness!
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 32 -
Direct Lightning Strikes to OHL – Corona Damping
Effect of corona
Steepness of the surge depending on traveling distance:
C0
0
1
1S K
S
=
⋅ +A A
Sℓ ... steepness of surge after traveling distance ℓ in kV/µs
KC0 ... corona damping constant in µs/(kV·m)
ℓ ... traveling distance in m
S0 ... initial steepness of surge in kV/µs
Distribution 5 x 10-6 [IEC 60071-2], [BAL-04]
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 33 -
Direct Lightning Strikes to OHL – Corona Damping
[BAL-04]
(for S0Æ ∞)
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 34 -
Direct Lightning Strikes to OHL – Corona Damping
Time
V
o
l
t
a
g
e
ca. 2200 kV/µs
ca. 370 kV/µs
Measured overvoltage surges on a single-line conductor
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 35 -
Back Flashover
iB = 2·iE + iM
uM = iM·RM
RM ... tower surge impedanceRM ... tower surge impedance
uinsul. = uM - uL
At unfavorable phase relation:
uinsul. = uM + |uL|
If
uinsul. > ud, LI
Shield wire
Line conductor
See HVT II, Chapter 11 and [BAL-04]
Problem: extreme du/dt-values!Problem: extreme du/dt-values!
For tower footing resistances < 10 Ω:
Flashovers at IB > 190 kA
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 36 -
Protection by Surge Arresters and Representative Overvoltage
• Due to separation effects, surge arresters have a limited protection distance.
• The larger the distance between arrester and the equipment to be protected and the higher the 
steepness, the higher the fast front overvoltage at its terminals.
Representative overvoltage when surge arresters are applied (simplified equation):
rp pl pl
rp pl pl
2 for 2
 (!) 2 for 2
U U ST U ST
U U U ST
= + ≥
= <
S ... steepness of surge in kV/µs
T ... travel time along distance L in µs
0
LT
c
=
L ... distances a1 + a2 + a3 + a4 in m Æ next slide
c0 ... velocity of light: 300 m/µs
Example: Um = 420 kV Æ Upl = 825 kV; S = 1000 kV/µs; L = 30 m
rp pl
30 m2 825 kV 2 1000 kV/µs 1025 kV
300 m/µs
U U ST= + = + ⋅ ⋅ =
Note: Urp depends exclusively on steepness and distance arrester ↔ equipment,
but not on the overvoltage amplitude!
Note: Urp depends exclusively on steepness and distance arrester ↔ equipment,
but not on the overvoltage amplitude!
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 37 -
Protection by Surge Arresters and Representative Overvoltage
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 38 -
Steepness is reduced inversely proportional to number n of connected lines:
C0
C0
0
1 1
1S KK
S
= ≈ ⋅⋅ +A AA
(for S0Æ ∞)
C0
1S
n K
= ⋅ ⋅A A
Considerations on steepness S – Impact of number of connected lines
Sℓ ... steepness of surge after traveling distance ℓ in kV/µs
KC0 ... corona damping constant in µs/(kV·m)
ℓ ... traveling distance in m
S0 ... initial steepness of surge in kV/µs
(Explanation see next slide)
Protection by Surge Arresters and Representative Overvoltage
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 39 -
Considerations on steepness S – Impact of number of connected lines
n = 1:n = 1: 2U0
Z
UTr= → ∞−1
ZZ
n =Tr 02U U
n = 2:n = 2: 2U0
Z
UTr= =−1
ZZ Z
n
= ⇒ = ⋅Tr Tr 0
0
1 2
2 2 2
U Z U U
U Z
n = 3:n = 3: 2U0
Z
UTr= =−1 2
Z ZZ
n
= ⇒ = ⋅Tr Tr 0
0
1 2
2 3 3
U Z U U
U Z
… and when thevoltage amplitude is reduced, the steepness is reduced proportionally.
Protection by Surge Arresters and Representative Overvoltage
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 40 -
Practical observations on the relevant traveling distance ℓ :
1) Shielding failures do not occur in the first span adjacent to the substation.
Reason: shielding is intentionally improved by lower shielding angles or double ground wires.
2) Back flashovers do not occur at the first tower(s) adjacent to the substation.
Reason: low footing impedance due to connection to substation earthing.
C0
1S
n K
= ⋅ ⋅A A
Considerations on steepness S – Impact of number of connected lines 
Sℓ ... steepness of surge after traveling distance ℓ in kV/µs
KC0 ... corona damping constant in µs/(kV·m)
ℓ ... traveling distance in m
n ... number of connected lines
Protection by Surge Arresters and Representative Overvoltage
The minimum value of ℓ is one span length Lsp.The minimum value of ℓ is one span length Lsp.
( )rp C0 sp t
1S
n K L L
= ⋅ ⋅ +
Srp ... representative steepness of surge in kV/µs
Lsp ... span length in m
Lt ... overhead line length with the adopted return rate; in m
⋅t
adopted return rate 1/a = 
shielding failure rate + back flashover rate 1/a m
L
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 41 -
Protection by Surge Arresters and Representative Overvoltage
rp pl 2U U ST= + (from slide 35)S ... steepness of surge in kV/µsT ... travel time along distance L in µs
( )rp pl C0 sp t
12U U T
n K L L
= + ⋅ ⋅ +
Introduction of a factor A describing the lightning performance of the OHL:
C0 0
2A
K c
= ⋅
[IEC 60071-2]
compare with slide 31, e.g.:
6
C0
µs0.6 10 
kV m
K −= ⋅ ⋅
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 42 -
Protection by Surge Arresters and Representative Overvoltage
( ) ( )0rp pl plsp t sp t
cA A LU U T U
n nL L L L
= + = ++ + L ... distances a1 + a2 + a3 + a4 in m
Assumed maximum value (worst case) by assuming the return rate equal 
to zero, i.e. Lt = 0: 
rp pl
sp
A LU U
n L
= +
(To be used for convenience if the result gives satisfyingly low Urp)
Note: n should reasonably be set to n = 1 (if only one line is connected) or n = 2 (if two 
or more lines are connected). Assuming n > 2 could yield too optimistic results that are 
not valid in a real failure scenario (e.g. possible loss of lines).
Note: n should reasonably be set to n = 1 (if only one line is connected) or n = 2 (if two 
or more lines are connected). Assuming n > 2 could yield too optimistic results that are 
not valid in a real failure scenario (e.g. possible loss of lines).
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 43 -
Protection by Surge Arresters and Representative Overvoltage
rp pl
sp
11000 kV 30 m825 kV 1238 kV
2 400 m
A LU U
n L
= + = + ⋅ =
Example: Um = 420 kV
Æ Upl = 825 kV; A = 11000 kV (quadruple bundle); L = 30 m; Lsp = 400 m; ≥ 2 lines connected;
shielding failure rate (typ. for Germany; one OHGW): 2.5 per 100 km and year = 2.5·10-5 (a·m)-1
adopted failure rate: 1·10-3 a-1
rp pl
sp t
11000 kV 30 m825 kV 1200 kV
2 (400+40) m
A LU U
n L L
= + = + ⋅ =+
LIWV = 1425 kV; 15% safety factor Æ allowed umax = 1211 kV
5
3
t 5
1 10 40 m
2.5 10
L
−
−
⋅= =⋅
a) using the "worst case" equation:
4
b) using the "realistic" equation: Note again:
No effect of the lightning 
overvoltage amplitude!!
Note again:
No effect of the lightning 
overvoltage amplitude!!
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 44 -
Protection by Surge Arresters and Representative Overvoltage
Example: Um = 420 kV
Æ Upl = 825 kV; A = 11000 kV (quadruple bundle); L = 30 m; Lsp = 400 m; ≥ lines connected
shielding failure rate (typ. for Germany; one OHGW): 2.5 per 100 km and year = 2.5·10-5 (a·m)-1
adopted failure rate: 1·10-3 a-1
rp pl
sp t
11000 kV 30 m825 kV 1031 kV
2 (400+400) m
A LU U
n L L
= + = + ⋅ =+
LIWV = 1425 kV; 15% safety factor Æ allowed umax = 1211 kV
3
t 6
1 10 400 m
2.5 10
L
−
−
⋅= =⋅
Effect of double OHGW in span field adjacent to substation:
shielding failure rate reduced by factor of 10, i.e. to 2.5·10-6 (a·m)-1
Note: these equations yield the representative overvoltages, which are not implicitly the real
overvoltages (see next two slides)!
Note: these equations yield the representative overvoltages, which are not implicitly the real
overvoltages (see next two slides)!
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 45 -
Protection by Surge Arresters and Representative Overvoltage
Making use of breakdown voltage-time-characteristic of the insulation
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
t [µs]
U
 
[
k
V
]
V-t air
V-t SF6
1.5 MV/µs 1.0 MV/µs
0.7 MV/µs
0.5 MV/µs
3.0 MV/µs
Steepness of overvoltage
0.3 MV/µs
V-t-curves of 245 kV
AIS and GIS equipment
(LIWV = 1050 kV)
The V-t-curve of GIS is flatter 
due to more homogeneous 
field distribution.
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 46 -
Protection by Surge Arresters and Representative Overvoltage
Making use of breakdown voltage-time-characteristic of the insulation
Example: Um = 300 kV
LIWV = 950 kV
Upl = 550 kV
Case 1: the representative 
overvoltage Urp is the real 
overvoltage as there is no time 
dependance of the V-t-curve.
Case 2: the representative 
overvoltage Urp is lower than the 
real overvoltage, e.g. 650 kV. 
(The first voltage peak will not 
cause a dielectric breakdown.) 
The real overvoltage at the 
equipment's terminals, limited by 
the surge arrester, has oscillations 
due to traveling wave effects.
0
200
400
600
800
1000
0 5 10 15
Time in µs
A
m
p
l
i
t
u
d
e
 
i
n
 
k
V
1
2
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 47 -
Very-Fast-Front Overvoltages
• VFFO originate from disconnector operations or 
faults within GIS due to the fast breakdown of the 
gas gap and the nearly undamped surge 
propagation within the GIS.
• Amplitudes are rapidly damped and front times 
increased when leaving the GIS through the 
bushing.
• VFFO are usually not a concern or a 
dimensioning parameter for the hv insulation. 
Therefore no standardized test has yet been 
defined (and is not under consideration, either).
• Mainly an EMI problem, as external electric fields 
may appear between the metal enclosure and 
ground Æ problem for secondary control circuits. 
Countermeasures: usual means of EMC.
OHL
VFFO measured in a GIS [ETG-93]
(LS…circuit breaker; TR…disconnector, operated; D…bushing; OHL…overhead line
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 48 -
Very-Fast-Front Overvoltages
Occurrence of VFFO depends on type of disconnector:
SF6 disconnecor, type A SF6 disconnector, type B
Fachgebiet
Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter 4 - 49 -
Very-Fast-Front Overvoltages
10 -7 10-6 10 -4 10 -2 10 0 102 10 4 10 6
cont. service voltage DC-voltage
temporary overvoltage
slow-front overvoltage
VFTO
fast-front overvoltage
7
6
5
4
3
2
Û
p.u.
second
1
0
very-fast-front-overvoltage