Transient Recovery Voltages (TRVs)
for High-Voltage Circuit Breakers
Part 1
Denis Dufournet
Chair CIGRE WG A3.28 & IEEE WG C37.011, Fellow IEEE
San Antonio (USA), 19/09/2013
GRID
Content
(1/3)
Page
•
•
•
•
•
•
•
Introduction & General Considerations
Capacitive Current Switching TRV
Types of Fault TRVs
TRV Modification
Terminal Fault TRV
4 &13
29
45
63
72
− First-pole-to-clear factor
− TRV rating & testing
− TRV & arcing times
73
88
120
− TRV for generator circuit breakers
138
Short-Line Fault TRV
ITRV (Initial TRV)
TRV HV Circuit Breakers P 2
148
187
Content
(2/3)
Page
•
Out-of-Phase TRV
194
•
Three-Phase Line Faults TRV
199
•
Shunt Reactor Switching TRV
217
•
Transformer Limited Fault TRV
229
•
Series Reactor Limited Fault TRV
264
•
Influence of Series Capacitors on TRV
271
•
Harmonization of TRVs in IEC & IEEE
282
TRV HV Circuit Breakers P 3
Content
(3/3)
Page
• Annexes
306
− A: First-pole-to-clear factor
307
− B: Second-pole-to-clear factor
316
− C: Complement on line faults
321
− D: Equivalent circuit for 3-phase to ground fault
326
− E: Test circuit for kpp = 1.3
329
− F: Bibliography
333
TRV HV Circuit Breakers P 4
Introduction
GRID
Importance of TRV
•
The TRV is a decisive parameter that limits the interrupting capability
of a circuit breaker.
•
The interrupting capability of a circuit breaker was found to be strongly
dependent on TRV in the 1950’s.
•
When developing interrupting chambers, manufacturers must verify
and prove the TRV withstand specified in the standards for different
test duties.
•
Users must specify TRVs in accordance with their applications.
•
Type tests in high-power laboratories must be performed in
accordance with international standards, in particular with rated values
of TRVs.
TRV HV Circuit Breakers P 6
“Recent” TRV Studies in International Bodies
• TRV Studies by International Working Groups
1993-1996: CIGRE-CIRED WG CC03 “Medium Voltages TRVs“
1994-1998: IEC SC17A WG21 “Revision Circuit Breaker Standard”
1997-2002: IEC SC17A WG23 “Harmonization TRVs Circuit Breakers ≥ 100kV”
2002-2006: IEC SC17A WG35 “”Revision TRVs Circuit Breakers < 100kV”
2001-2009: IEEE C37-04 & 06 ”Harmonization TRVs Circuit Breakers”
2002-2005: IEEE C37-011 “Revision Application Guide HV Circuit Breakers”
2004-2008: CIGRE WG A3-19 ”Implications of Three-phase Line Faults”
2007-2009: CIGRE WG A3-22 ”Technical Requirements for UHV Equipment”
2009-2011: IEC SC17A MT36 TF ”Introduction UHV TRVs in IEC 62271-100”
2008-2011: IEEE C37-011 ”Revision Application Guide HV Circuit Breakers”
2011-2013: CIGRE WG A3-28 ”Switching Phenomena for UHV & EHV Equipment”
TRV HV Circuit Breakers P 7
Main References
•
A.Greenwood, Electrical Transients in Power Systems. (book) 2nd
edition, John Wiley & Sons (1991).
•
R.Alexander, D.Dufournet, IEEE Tutorial on TRVs (2003-05)
http://www.ewh.ieee.org/soc/pes/switchgear/presentations/trvtutorial/T
utorialTRVAlexander-Dufournet.pdf
•
D.Dufournet, TRVs for High-Voltage Circuit Breakers, Presentation at
IEEE Switchgear Committee meeting in Calgary (2008-10)
http://www.ewh.ieee.org/soc/pes/switchgear/presentations/2008cbtutor
ial/Part4_IEEETutorialonTRVHVCircuitBreakers-Dufournet.pdf
•
CIGRE Technical Brochure N°134, Transient Recovery Voltages in
Medium Voltage Networks (1998-12)
•
CIGRE Technical Brochure N°408, Line fault phenomena and their
implications for 3-phase short and long-line fault clearing, (2010-02)
TRV HV Circuit Breakers P 8
Main References
•
A.Janssen, D.Dufournet, “Travelling Waves at Line Fault Clearing and
Other Transient Phenomena”, CIGRE Session 2010, Paper A3-102.
•
CIGRE Technical Brochure 456, “Background of Technical
Specifications for Substation Equipment Exceeding 800kV AC”, by
CIGRE WG A3-22 (2011-04).
•
D.Dufournet, A.Janssen, “Transformer Limited fault TRV”, Tutorial at
IEEE Switchgear Committee Meeting in San Diego (2012-10)
• Denis Dufournet, Joanne (Jingxuan) Hu, High-Voltage Circuit
Breakers Seminar Part 2 Transient Recovery Voltages, University of
Manitoba, Winnipeg (2012-06)
TRV HV Circuit Breakers P 9
Standards & Guides
•
•
•
•
•
•
•
•
•
IEC 62271-100, High-Voltage Circuit-Breakers (2012-09)
IEC 62271-101, Synthetic testing (2012-10)
IEC 62271-110, Inductive load switching (2012-09)
IEC 62271-306, Guide to IEC 62271-100, 62271-1 .. (2012-12)
ANSI/IEEE C37.04, 04a, 04b, IEEE Standard Rating Structure for AC
High-Voltage Circuit Breakers.
IEEE Std C37.06-2009, Draft AC High-Voltage Circuit Breakers Rated on
a Symmetrical Current Basis-Preferred Ratings and Related Required
Capabilities
IEEE Std C37.09, 09b-2010, IEEE Standard Test Procedure for AC HighVoltage Circuit Breakers Rated on a Symmetrical Current Basis.
IEEE C37.011, Application Guide for TRV for AC High-Voltage Circuit
Breakers” (2011).
IEEE C37.013, IEEE Standard for AC High-Voltage Generator Circuit
Breakers Rated on a Symmetrical Current Basis.
TRV HV Circuit Breakers P 10
Historical Perspective
•
In the second edition of IEC 56 published in 1954, the TRV, defined as
"restriking voltage”, was of single frequency.
The amplitude factor (or crest value) and the TRV frequency (related to
the rate-of-rise) were not specified but had to be evaluated during the
tests.
•
In the third edition of IEC 56, published in 1971, IEC introduced for the
first time the term “TRV” and its representation by two or four
parameters. The short-line-fault tests were also introduced in this
edition.
•
TRVs requirements were also introduced in 1971 in ANSI C37.0721971 (IEEE Std. 327), with TRV ratings in C37.0722-1971 and TRV
Application Guide C37.0721-1971 (IEEE Std. 328).
TRV HV Circuit Breakers P 11
Historical Perspective
•
In the fourth edition of IEC 56, published in 1987, a first-pole-to-clear
factor of 1.3 is the only factor specified for rated voltages ≥ 245 kV.
− the rate of rise of recovery voltage (RRRV) is doubled to 2.0 kV/µs
for terminal fault test duty T100.
− ITRV is introduced for rated voltages ≥ 100 kV.
•
ITRV is introduced in ANSI C37.04 and C37.09 in 1991 (amendments
04i and 09g).
•
ANSI C37-06 (1997) harmonize partly TRV parameters with those in
IEC (e.g. RRRV = 2.0 kV/µs for T100).
•
As in IEC, line surge impedance is 450 Ω for all rated voltages in
ANSI/IEEE C37.04-1999 (instead of 450 Ω for Ur ≤ 242 kV and 360 Ω
for Ur ≥ 362 kV).
TRV HV Circuit Breakers P 12
Historical Perspective
• Further Harmonization of TRVs between IEC and IEEE lead
to
− Amendments 1 and 2 of IEC 62271-100 (respectively in 2002 and
2006)
− Amendments of IEEE C37.04b (2008), IEEE C37.06 (2009) and
IEEE C37.09b (2010).
Harmonization of IEC and IEEE standards for high-voltage circuit
breakers is presented in detail in a specific chapter.
TRV HV Circuit Breakers P 13
General considerations on
Transient Recovery Voltages
GRID
General Considerations
• The recovery voltage is the voltage which appears across the
terminals of a pole of circuit breaker after current interruption.
Xs
U
A
B
CURRENT
Recovery
voltage
TRANSIENT RECOVERY
VOLTAGE
TRV HV Circuit Breakers P 15
RECOVERY
VOLTAGE
General Considerations
• Current Interruption Process in SF6 Circuit Breakers
Two
contacts
are
separated
in
each
interrupting chamber.
An arc is generated, it is
cooled and extinguished
when current passes
through zero.
Simulation arc interruption
TRV HV Circuit Breakers P 16
General Considerations
•
During the interruption process, the arc loses rapidly its conductivity as
the instantaneous current approaches zero.
TRV (kV)
I (A)
TRV
Gas
circuit
breakers:
Within a few microseconds
after current zero, arc
resistance (RARC) rises to
one million ohm in a few
microseconds and current
stops flowing in the circuit.
Interruption when current passes through zero
•
During the first microseconds after current zero, the TRV withstand is
function of the energy balance in the arc: it is the thermal phase of
interruption.
TRV HV Circuit Breakers P 17
General Considerations
•
Later, the voltage withstand is function of the dielectric withstand
between contacts: it is the dielectric phase of interruption.
The breaking operation is successful if the circuit breaker is able to
withstand the TRV and the power frequency recovery voltage.
The TRV is the difference between the voltages on the source side
and on the load side of the circuit breaker.
•
During type tests, standards require that the recovery voltage is
applied during 300 ms after current interruption.
TRV HV Circuit Breakers P 18
General Considerations
•
The nature of the TRV is dependent on the circuit being interrupted,
whether primarily resistive, capacitive or inductive, (or some
combination).
•
When interrupting a fault at the circuit breaker terminal (terminal fault)
in an inductive circuit, the supply voltage at current zero is maximum.
The circuit breaker interrupts at current zero (at a time when the power
input is minimum) the voltage on the supply side terminal meets the
supply voltage in a transient process called the TRV.
TRV frequency is
1
2
LC
with L = short-circuit inductance
C = supply capacitance.
TRV HV Circuit Breakers P 19
Fault
General Considerations
TRV during inductive current breaking
CURRENT
Supply voltage
TRANSIENT RECOVERY
Current and TRV waveforms during interruption of inductive current
VOLTAGE
Note: voltage polarity not respected on Figure
TRV HV Circuit Breakers P 20
General Considerations
TRV and recovery voltage in resistive, inductive
and capacitive circuits
2,5
2
1,5
CAPACITIVE
CIRCUIT
1
0,5
0
0
0,005
0,01
0,015
0,02
-0,5
-1
-1,5
RESISTIVE
CIRCUIT
-2
TRV HV Circuit Breakers P 21
INDUCTIVE CIRCUIT
(with stray capacitance)
0,025
0,03
0,035
General Considerations
•
Combination of the former basic cases are possible, for example the
TRV for mainly active load current breaking is a combination of TRVs
associated with inductive and resistive circuits.
•
They are specified for high-voltage switches only as circuit-breakers
are able to interrupt with more severe TRVs (in inductive circuits).
TRV HV Circuit Breakers P 22
General Considerations
•
Fault interruptions are often considered to produce the most onerous
TRVs. Shunt reactor switching is one of the exceptions.
•
TRVs can be oscillatory, triangular, or exponential and can occur as a
combination of these forms.
•
The highest peak TRVs are met during capacitive current and out-ofphase current interruption,
•
TRVs associated with the highest short-circuit current are obtained
during terminal fault and short-line-fault interruption.
•
In general, a network can be reduced to a simple parallel RLC circuit
for TRV calculations.
This representation is valid for a short-time period until voltage
reflections return from remote buses (see IEEE C37.011-2011)
TRV HV Circuit Breakers P 23
General Considerations
Equivalent circuit
Real network
(Vcb)
L
C
R
N Lines, each with surge
impedance
TRV HV Circuit Breakers P 24
Z
l
c
R
Z
N
L: source inductance, lines excepted
C: source capacitance, lines excepted
General Considerations
(Vcb)
L
R
C
− The TRV in the parallel RLC circuit is oscillatory (under-damped) if
1
R 
L/C
2
− The TRV in the parallel RLC circuit is exponential (over-damped) if
1
R 
L/C
2
TRV HV Circuit Breakers P 25
General Considerations
TRV (p.u.)
2
0.5
R / (L / C)
1,8
= 10
4
1,6
2
1,4
1
1,2
0.75
1
0,8
0,6
0,5
0,4
0,3
0,2
0
0
1
2
3
4
5
6
7
8
9
t/RC
t / RC
Damping of the oscillatory TRV is provided by R, as R is in parallel
to L and C
(parallel damping) the damping increases when the resistance decreases (the
TRV peak increases when R increases).
TRV HV Circuit Breakers P 26
General Considerations
• Reflection from end of lines
When longer time frames are
considered, typically several hundreds
of micro-seconds, reflections on lines
must be considered.
VOLTAGE (kV)
900
800
SYSTEM TRV
TRV CAPABILITY FOR A
STANDARD BREAKER
700
600
500
400
300
200
REFLECTED WAVE
100
0
0
100
200
300
400
500
600
700
800
900
1000
TIME (µs)
TRV HV Circuit Breakers P 27
Lines or cables must then be
treated as components with
distributed elements on
which voltage waves travel
after current interruption.
These traveling waves are
reflected and refracted when
reaching an open circuit or a
discontinuity.
General Considerations
•
The most severe TRV occurs across the first pole to clear of a circuit
breaker when it interrupts a three-phase terminal fault with a
symmetrical current and when the system voltage is maximum (see
section on Terminal fault).
•
By definition, all TRV values defined in the standards are inherent,
i.e. the values that would be obtained during interruption by an ideal
circuit breaker without arc voltage.
(arc resistance changes from zero to an infinite value at current
zero).
TRV HV Circuit Breakers P 28
Capacitive Current Switching
TRV & Recovery Voltage
GRID
Capacitive Current Switching
U (p.u.)
2,5
2
Recovery voltage
1,5
1
0,5
current
interruption
Supply voltage
0
-0,5
Example of a single
phase interruption at
50 Hz
Load voltage
-1
-1,5
0,005
0,01
0,015
0,02
0,025
0,03
0,035
Time (s)
Capacitive current interruption: recovery voltage has a (1 – cos) waveshape
TRV HV Circuit Breakers P 30
Capacitive Current Switching
Supply-side voltage
Load-side voltage
Recovery voltage
Current
Contact separation
Current interruption
TRV HV Circuit Breakers P 31
Final current interruption
Restrike
Capacitive Current Switching
U (p.u.)
Overvoltage 3 p.u.
3,5
3
2,5
2 p.u.
2
1,5
1
Recovery voltage
instant of current
interruption
0,5
2 p.u.
0
-0,5
-1
-1,5
0,005
Restrike
Reignition
0,01
no overvoltage
0,015
overvoltage
0,02
0,025
Time (s)
TRV HV Circuit Breakers P 32
Capacitive Current Switching
•
Two cases can be distinguished, depending on when the restrike
happens:
− When it is less than 1/4 of a cycle after current interruption: it is
called a reignition,
no overvoltage is produced on the circuit during the transient
period when the load voltage tend to reach the supply voltage.
− When it is more than 1/4 of a cycle after current interruption, it is
called a restrike,
there is an overvoltage on the circuit during the transient period
following the restrike.
TRV HV Circuit Breakers P 33
"1-Cos" Waveshape
• Special case of series capacitor switching by by-pass switches
− By-pass switches must be able to withstand the reinsertion voltage
without restrike during the transfer of reinsertion current.
TRV HV Circuit Breakers P 34
"1-Cos" Waveshape
• Special case of series capacitor switching
by by-pass switches
− Several transient reinsertion voltage
waveshapes can be obtained in service.
− The reinsertion voltage waveshape should be determined by
systems studies.
− For standardization purposes, and in order to cover the greatest
number of practical cases, IEC 62271-109 recommends a "1-cos"
waveshape having a preferred first time-to-peak of 5,6 ms.
− A restrike happens if there is a resumption of current 2.8 ms or
later after the initial current interruption.
TRV HV Circuit Breakers P 35
Capacitive Current Switching
Voltage Jump
Circuit with capacitive and inductive
components.
•
The recovery voltage is the sum a 1– cos
wave-shape and a high-frequency voltage
oscillation on the supply side due to a
transient
across
the
short-circuit
(inductive) reactance at the time of
interruption (explanation on next slide).
•
There is an initial voltage jump.
•
It tends to increase the minimum arcing
time and therefore to increase the shortest
duration between contact separation and
the instant of peak recovery voltage.
•
Interruption is easier when the voltage
jump is higher
TRV HV Circuit Breakers P 36
A
E
Capacitive Current Switching
Voltage Jump
1
0
1- Supply-side voltage after
current interruption, with
voltage jump
2- Load-side voltage after
current interruption
Voltage before
current interruption
UA 
TRV HV Circuit Breakers P 37
3- Recovery voltage across
circuit-breaker terminals
I
1
E
E



1
C C
1  Ls C  2
 Ls 
C
Three-Phase Capacitive Current Breaking
Capacitor Bank with Isolated Neutral
ER
ES
A
B
CR
CS
CT
ET
TRV HV Circuit Breakers P 38
EN
N
Three-Phase Capacitive Current Breaking
Capacitor Bank with Isolated Neutral
Recovery voltage for the first pole to interrupt
2,0
VB
1,5
1,0
2.5 p.u.
0,5
VN
0,0
-0 ,0 05
-0,003
-0,00 1
0,00 1
0 ,0 03
0,00 5
0,0 07
0 ,0 09
0,01 1
0,0 13
0 ,0 15
-0,5
-1,0
VA
-1,5
Due to neutral voltage shift (VN) after interruption by the first pole, the peak
recovery voltage is 2.5 p.u. instead of 2 p.u. for single-phase interruption.
TRV HV Circuit Breakers P 39
Three-Phase Capacitive Current Breaking
Capacitor Bank with Isolated Neutral
Recovery voltage (RV) on each pole
uc= 2.5 p.u.
kc= 1.25
RV on firstpole-to-clear
The recovery voltage is higher on the first pole to clear
TRV HV Circuit Breakers P 40
Three-Phase Capacitive Current Breaking
Capacitor Bank with Isolated Neutral
TRV 3-PHASE CAPACITIVE CURRENT SWITCHING (50Hz)
Capacitor bank with isolated neutral
Single-phase test with kc= 1,4
2,5
2
TRV (p.u.)
The
three-phase
recovery voltage is
considered to be
covered during a
single phase test
with
a
supply
voltage equal to the
phase to ground
voltage multiplied
by 1.4
3
Three-phase test
1,5
1
Single-phase test with kc= 1,25
0,5
0
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10
TRV HV Circuit Breakers P 41
T (ms)
Three-Phase Line-Charging Current Breaking
In the case of line switching
The recovery voltage is
influenced by phase-toground and phase-to-phase
capacitances
Equivalence during singlephase test is obtained with a
supply voltage equal to the
phase-to-ground
voltage
multiplied by a factor = 1.2
(U is 2.4 p.u.).
TRV HV Circuit Breakers P 42
Three-Phase Cable-Charging Current Breaking
• Types of cables & equivalent circuits
Similar case as
overhead lines
Same case as
capacitor bank
with grounded
neutral
C1/C0=3 Ur ≤ 52kV
C1/C0=2 Ur > 52kV
Screened cable
TRV HV Circuit Breakers P 43
Belted cable
Three-Phase Capacitive Current Breaking
Single-phase tests to simulate three-phase conditions
• Test voltage for single-phase tests: U test  k c
Ur
3
•
Voltage factors in case of effectively grounded neutral systems
− Line-charging current
kc = 1.2
− Cable-charging current kc = 1.0 (screened cable)
= 1.4/ 1.2 (belted cable ≤52kV / >52kV)
− Capacitor-bank current kc = 1.0/1.4 grounded/isolated neutral
•
Voltage factors in case of non-effectively grounded neutral systems
− Line-charging current
kc = 1.4
− Cable-charging current kc = 1.4
− Capacitor-bank current kc = 1.4
•
Voltage factors in the case of fault on another line(s)
− Effectively grounded neutral systems
kc = 1.4
− Non-effectively grounded neutral systems kc = 1.7
TRV HV Circuit Breakers P 44
Types of Fault TRVs
GRID
Types of Fault TRVs / Reminder
Equivalent circuit
Real network
(Vcb)
L
C
R
N Lines, each with surge
impedance
TRV HV Circuit Breakers P 46
Z
l
c
R
Z
N
L: source inductance, lines excepted
C: source capacitance, lines excepted
Types of Fault TRVs / Overdamped TRV
Exponential (overdamped) TRV
• The exponential part of a TRV occurs when the equivalent resistance
of the circuit with N connected lines in parallel
Z
R = Zeq =  1 is lower or equal to 0.5 Leq / Ceq
N
where Z1 = positive sequence surge impedance of a line
Z0 = zero sequence surge impedance of a line
3 Z0


N = number of lines,
Z1  2 Z 0
Leq = equivalent inductance, Ceq = equivalent capacitance.
• It typically occurs when one or several lines are on the unfaulted side
of the circuit breaker and when the fault is cleared at the circuit
breaker terminals.
• The rate of rise of recovery voltage is RRRV = Zeq x (di/dt)
TRV HV Circuit Breakers P 47
Types of Fault TRVs / Overdamped TRV
Three-phase to ground fault
(Vcb)
• Equivalent inductance
L eq
when
3 L 0 L1

L1  2 L 0
LLeq
L0  3 L1
ZReq
Ceq
C
9 L1
Leq 
 1.3 L1
7
see Annex D: 3-phase
network representation
• Equivalent capacitance
Ceq
2 (C1  C0 )
 C0 
3
TRV HV Circuit Breakers P 48
C0  2 C1

3
Types of Fault TRVs / Overdamped TRV
Three-phase to ground fault
• Equivalent surge impedance (first pole to clear)
Z eq 
Z 0Z1
3

N
Z1  2Z 0
Z0  ZS  2 ZM
Z1  Z S  Z M
ZM 
Z 0  Z1
3
ZS: self value
ZM: mutual value
TRV HV Circuit Breakers P 49
3 Z0

Z1  2 Z 0
see Annex D: 3-phase network
representation
See section on SLF for the calculation of line
surge impedance
Types of Fault TRVs / Overdamped TRV
• TRV for parallel RLC circuit
ucb  u1 (1  e
with
 t

(cosh  t  sinh  t ))

ucb
is the voltage across the open circuit-breaker
u1
=

= 2  f = 377 rad/s at 60 Hz and 314 rad/s at 50 Hz
I
is the short-circuit current (rms)

=

=
2 I ω Leq
TRV HV Circuit Breakers P 50
1
2 Z eq Ceq
 2  1 /( Leq Ceq )
Types of Fault TRVs / Overdamped TRV
• TRV when Ceq can be neglected
ucb  u1 (1  e t /  )
where

Leq
Z eq
• RRRV
ducb

dt
TRV HV Circuit Breakers P 51
dI
2 I ω Z eq  Z eq 
dt
Types of Fault TRVs / Overdamped TRV
• Special case of three-phase ungrounded faults
− Equivalent inductance
− Equivalent capacitance
Ceq 
2 C1
3
with C1= C0
TRV HV Circuit Breakers P 52

C1
1.5
L eq 
3 L1
 1 . 5 L1
2
Types of Fault TRVs / Overdamped TRV
•
This exponential part of TRV is transmitted as traveling waves on
each of the transmission lines. Reflected wave(s) returning from open
lines or discontinuities contribute also to the TRV.
TRV HV Circuit Breakers P 53
Types of Fault TRVs / Overdamped TRV
•
As an example, the following figure shows the one line diagram of a
550 kV substation. The TRV seen by circuit breaker (A) when clearing
the three-phase fault is shown in the next slide. Circuit breaker (B) is
open.
TRV HV Circuit Breakers P 54
Types of Fault TRVs / Overdamped TRV
System TRV with reflected wave
VOLTAGE (kV)
900
800
SYSTEM TRV
TRV CAPABILITY FOR A
STANDARD BREAKER
700
600
500
400
300
200
REFLECTED WAVE
100
0
0
100
200
300
400
500
600
700
800
900
1000
TIME (µs)
A reflection occurs from the end of the shortest
line after 2 x 81 / 0.3 = 540 µs
TRV HV Circuit Breakers P 55
Types of Fault TRVs / Reflected Waves
•
•
•
•
The exponential part of TRV is transmitted as traveling waves on each
of the transmission lines.
When a wave reaches a discontinuity on the line (another bus or a
transformer termination) a reflected wave is produced, which travels
back towards the faulted bus.
It takes 6.67 µs for a wave to go out and back to a discontinuity 1km
away as the wave travels at 300 000 km/s (speed of light).
At a discontinuity transmitted and reflected waves can be described by
the following equations:
2 Zb
et  ei
Za  Zb
Za
TRV HV Circuit Breakers P 56
Zb
Zb  Za
er  ei
Za  Zb
Types of Fault TRVs / Reflected Waves
Zb
Za
•
•
A wave that reaches a shortcircuit point (Zb= 0) is reflected
with an opposite sign
A wave that reaches an open
point (Zb is infinite) is reflected
with the same sign.
The voltage at this point is then
doubled.
TRV HV Circuit Breakers P 57
2 Zb
et  ei
Za  Zb
er  ei
Zb  Za
Za  Zb
Types of Fault TRVs / Reflected Waves
• Example of TRV resulting from several traveling waves
From CIGRE WG A322/28 tutorial in Rio
de Janeiro (2012-02)
Times in µs and not in
ms
TRV HV Circuit Breakers P 58
Types of Fault TRVs / Underdamped TRV
Oscillatory (underdamped) TRV
•
An oscillatory TRV occurs generally when a fault is limited by a
transformer or a series reactor and no transmission line (or cable) surge
impedance is present to provide damping.
TRV HV Circuit Breakers P 59
Types of Fault TRVs / Underdamped TRV
•
To be oscillatory, the equivalent resistance of the source side has to
be such that
Leq
Z
Req  
 0.5
N
Ceq
Leq = equivalent source inductance
Ceq = equivalent source capacitance.
•
To meet this requirement, only a low number of lines (N) must be
connected on the source side.
Therefore oscillatory TRVs are specified for
− terminal fault test duties T10 and T30 for circuit breakers in
transmission systems (Ur  100 kV),
− all terminal fault test duties in the case of circuit breakers in
distribution or sub-transmission systems (Ur < 100 kV).
TRV HV Circuit Breakers P 60
Types of Fault TRVs / Underdamped TRV
• Transmission systems (Ur  100 kV)
In the large majority of cases, TRV characteristics (peak value and
rate-of-rise) for faults with 10% or 30% of rated short-circuit current
are covered by the rated values defined in the standards for test
duties T10 and T30.
TRV HV Circuit Breakers P 61
Types of Fault TRVs / Triangular wave-shape
•
Triangular-shaped TRVs are associated with short-line faults (see
separate chapter on SLF).
•
After current interruption, the line-side voltage exhibits a characteristic
triangular waveshape.
•
The rate-of-rise of the saw-tooth shaped TRV is function of the line
surge impedance and current. The rate-of rise is usually higher than
that experienced with exponential or oscillatory TRVs (with the same
current), however the TRV peak is generally low.
line
Circuit breaker
TRV HV Circuit Breakers P 62
TRV Modification
GRID
Current Asymmetry and Circuit
Breaker Influence on TRV
TRV HV Circuit Breakers P 64
TRV Modification / Current Asymmetry
•
When interrupting asymmetrical currents, TRV is less severe (lower
RRRV and TRV peak) than when interrupting the related
symmetrical current because the instantaneous value of the supply
voltage at the time of interruption is less than the peak value.
SUPPLY VOLTAGE
CURRENT
TIME
TRV HV Circuit Breakers P 65
TRV Modification / Current Asymmetry
•
Correction factors of the TRV peak and rate of rise of recovery voltage
(RRRV) when interrupting asymmetrical currents are given in
− IEEE C37.081 “IEEE Guide for Synthetic Fault Testing of AC HighVoltage Circuit Breakers Rated on a Symmetrical Current Basis”.
− IEEE C37.081a “Supplement to IEEE Guide for Synthetic Fault
Testing 8.3.2: Recovery Voltage for Terminal Faults; Asymmetrical
Short-Circuit Current”.
− IEC 62271-100 “High-Voltage Circuit-Breakers” (2012-09).
− IEC 62271-101 “Synthetic testing” (2012-10): Annex I
TRV HV Circuit Breakers P 66
TRV Modification / Current Asymmetry
• The RRRV is proportional to the slope of current before interruption
(di/dt). Factor F1 gives the correction due to current asymmetry:
D
F1  1  D 
X /R
2
with
D
degree of asymmetry (p.u.)
-D
interruption after a major loop of current
+D
interruption after a minor loop of current
X/R
short-circuit reactance divided by resistance
• When time to peak TRV is relatively short (< 500 µs), the correction
factor for the TRV peak is also F1.
TRV HV Circuit Breakers P 67
TRV Modification / Current Asymmetry
• Correction factor for the TRV peak in case of long time to peak TRV
(> 500 µs) :
TRV HV Circuit Breakers P 68
TRV Modification / Circuit Breaker Influence
•
During current interruption, the circuit TRV can be modified by a
circuit breaker:
− by arc resistance,
− by the circuit breaker capacitance or opening resistor (if any).
•
The TRV measured across the terminals of two different types of
circuit breakers under identical conditions can be different.
•
To simplify both rating and application, the power system TRV is
calculated ignoring the influence of the circuit breaker.
The circuit breaker is considered to be ideal i.e. without modifying
effects on the electrical characteristics of a system,
− when conducting its impedance is zero,
− at current zero its impedance changes from zero to infinity.
TRV HV Circuit Breakers P 69
TRV Modification / Circuit Breaker Influence
•
When a circuit breaker is fitted with grading capacitors or with line-toground capacitors, these capacitors can reduce significantly the rateof-rise of TRV during short-line faults.
•
Opening resistors (R) are used to assist interruption by air blast circuit
breakers, they are used on some SF6 circuit breakers (Japanese
550kV 1 break & 1100 kV 2 breaks).
The RRRV (rate of rise of
recovery voltage) is reduced
as follows
du Z  R di Z  R


I 2
dt Z  R dt Z  R
The resistor (R) is in parallel
with the surge impedance of
the system (Z).
TRV HV Circuit Breakers P 70
Air blast Generator Circuit Breaker
with opening resistor
TRV Modification / Circuit Breaker Influence
Interruption with Opening Resistance
R
Arc extinction is facilitated by reducing the voltage stress (RRRV) after
current interruption, a parallel resistance is used for this purpose
TRV HV Circuit Breakers P 71
Terminal Fault TRV
GRID
Terminal fault TRV
First pole to clear factor
TRV HV Circuit Breakers P 73
Terminal Fault TRV
CURRENT
TRANSIENT RECOVERY
VOLTAGE
Current - TRV - Recovery Voltage
TRV HV Circuit Breakers P 74
RECOVERY
VOLTAGE
Terminal Fault TRV
• First Pole to Clear Factor (kpp)
− During 3-phase faults interruption, the recovery voltage is higher on
the first pole to clear.
− The first-pole-to clear factor is the ratio of the power frequency
voltage across the first interrupting pole, before current interruption
in the other poles, to the power frequency voltage occurring across
the pole after interruption in all three poles.
− It is the ratio between the recovery voltage (RV) across the first
pole to clear and the phase to ground voltage of the system.
kpp
TRV HV Circuit Breakers P 75
Recovery Voltage

Ur
3
Terminal Fault TRV
• First Pole to Clear Factor (kpp)
kpp 
Ur
3
ER
ES
ET
TRV HV Circuit Breakers P 76
A
Ur
3
B
Terminal Fault TRV
•
When tests are performed on one pole (single-phase tests), the supply
voltage must be multiplied by kpp in order to have the recovery voltage
that would be met on the first pole during a three-phase interruption.
•
The first–pole–to-clear factor (kpp) is a function of the grounding
arrangements of the system and of the type of fault.
For systems with non-effectively grounded neutral, kpp is 1.5.
For three-phase to ground faults in systems with effectively grounded
neutral, kpp is 1.3 (see Annex A).
Note: for UHV systems (rated voltages 1100 & 1200kV) the ratio X0/X1
is close to 2 and the standardized value of kpp is 1.2.
•
For three-phase ungrounded faults, kpp is 1.5.
TRV HV Circuit Breakers P 77
Terminal Fault TRV
Three-phase faults in non-effectively grounded systems
or three-phase ungrounded faults
In these cases, kpp is 1.5
TRV HV Circuit Breakers P 78
Terminal Fault TRV
Example of First-Pole-To-Clear Factor (kpp)
3-phase
ungrounded fault
in effectivelygrounded neutral
L
i
L
i
When pole A
interrupts.
voltage eA is
maximum = 1 p.u.
eB = eC = - 0.5 p.u.
TRV HV Circuit Breakers P 79
di
 eC  0
dt
di e  eC
L  B
2
dt
e  eC
di
eP  eB  L  eB  B
dt
2
e  eC
eP  B
  0.5
2
e A  eP   1  (0.5)  1.5
eB  2 L
L
First-pole-to-clear
factor is 1.5
Terminal Fault TRV
Example of First-Pole-To-Clear Factor (kpp)
3-phase to ground fault in non-effectively grounded system
When the first pole interrupts:
Voltage at neutral point N:
EN + ES = Xsc I
EN + ET = - Xsc I
N
ES
ES = Emax cos (120°) = -0.5 p.u.
ET
ET = Emax cos (240°) = -0.5 p.u.
then EN = 0.5 p.u.
Voltage EA = EN + ER = 1.5 p.u.
First-pole-to-clear factor is 1.5
TRV HV Circuit Breakers P 80
B
1 p.u. Xsc kpp= 1.5
Xsc
EN = – (ES + ET)/2
ER is maximum = Emax cos(0°) = 1 p.u.
A
ER
Xsc
Terminal Fault TRV
First-Pole-To-Clear Factor (kpp)
Single-phase fault in an effectively grounded system
•
In this case, kpp is 1.0 as the circuit breaker interrupts under the phaseto-ground voltage.
E
I3
V3
I2
V2
I1
TRV HV Circuit Breakers P 81
V1
Terminal Fault TRV
First-Pole-To-Clear Factor (kpp)
Three-phase to ground fault in effectively
grounded neutral systems
•
The value of kpp is dependent upon the sequence impedances from the
location of the fault to the various system neutral points (ratio X0/X1).
3X 0
k pp 
X1  2X 0
where
X0 is the zero sequence reactance of the system,
X1 the positive sequence reactance of the system.
For systems up to 800 kV, the ratio X0/X1 is taken to be  3.0.
Hence, for systems with effectively grounded systems kpp is 1.3.
TRV HV Circuit Breakers P 82
Terminal Fault TRV
Pole-To-Clear Factor
Equations for the other clearing poles
•
In systems with non-effectively grounded neutral, after interruption of
the first phase (R), the current is interrupted by the last two poles in
series under the phase-to-phase voltage (ES – ET) equal to 3 times
the phase voltage
ER
ES
ES - ET
ET
TRV HV Circuit Breakers P 83
I
I
Terminal Fault TRV
Pole-To-Clear Factor
It follows that, in systems with non-effectively grounded neutrals,
for the second and third pole to clear:
k pp 
Current in each phase
TRV HV Circuit Breakers P 84
3
 0.87
2
After interruption of the
3 poles, the recovery
voltage is 1 p.u.
TRV in each phase
Terminal Fault TRV
Pole-To-Clear Factor
In systems with effectively grounded neutrals, the second pole clears
a three-phase to ground fault
with a factor
k pp 
3 X 02  X 0 X 1  X 12
X 0  2X1
See Annex B
If X0 / X1 = 3.0 the second pole to clear factor is 1.25.
Currents
TRV HV Circuit Breakers P 85
TRVs
Terminal Fault TRV
Pole-To-Clear Factor
In systems with effectively grounded neutral, for the third pole-toclear:
k pp  1
E
I3
V3
I2
V2
I1
TRV HV Circuit Breakers P 86
V1
Terminal Fault TRV
Pole-To-Clear Factor
Pole-to-clear factors (kp) for each clearing pole
3-phase to ground case
Neutral
Pole to clear factor
X0/X1
first pole
2nd pole
3rd pole
isolated
infinite
1.5
0.87
0.87
effectively
grounded
3.0
1.3
1.27
1.0
see note
1.0
1.0
1.0
1.0
Note: values of the pole-to-clear factor are given for X0/X1 = 1.0 to
indicate the trend in the special case of networks with a ratio X0/X1 of
less than 3.0.
kpp= 1.5 is taken for all systems that are not effectively grounded, it
includes (but is not limited to) systems with isolated neutral (it is also
taken for three-phase ungrounded faults).
TRV HV Circuit Breakers P 87
Terminal fault TRV
Rating & Testing
TRV HV Circuit Breakers P 88
Terminal Fault TRV Rating
Current
CURRENT
SupplySupply
voltage
voltage
Transient recovery
TRANSIENT
RECOVERY
voltage
VOLTAGE
TRV HV Circuit Breakers P 89
Terminal Fault TRV Rating
•
The TRV ratings for circuit breakers are applicable for interruption
of three-phase faults with
− a rated symmetrical short circuit current
− at the rated voltage of the circuit breaker.
• In IEC
− While three-phase ungrounded faults produce the highest TRV
peaks, the probability of their occurrence is very low.
Therefore, in IEC 62271-100 the TRV ratings are based on
three-phase to ground faults.
− TRV parameters are given in subclause 4.102 of IEC 62271100.
− For values of fault current other than rated and for line faults,
related TRV capabilities are given in subclause 6.104.5 of IEC
62271-100.
TRV HV Circuit Breakers P 90
Terminal Fault TRV Rating
• In ANSI/IEEE
− TRV withstand capabilities are given in ANSI/IEEE C37.04 and
IEEE C37.06.
− In the case of terminal faults, for circuit-breakers of rated
voltages equal or higher than 100 kV, separate Tables give
TRVs for three-phase to ground and three-phase ungrounded
faults.
TRV HV Circuit Breakers P 91
Terminal Fault TRV Rating
• ANSI/IEEE C37.06 – Table 10
TRV HV Circuit Breakers P 92
Terminal Fault TRV Rating
• ANSI/IEEE C37.06 – Table 11
TRV HV Circuit Breakers P 93
Terminal Fault TRV Rating
•
For circuit breakers applied on systems 72.5 kV and below, the TRV
ratings assume that the system neutrals can be non-effectively
grounded.
•
For circuit breakers applied on systems 245 kV and above, the TRV
ratings assume that the system neutrals are effectively grounded.
•
Standard TRV are defined by two-parameter and four-parameter
envelopes.
•
These envelopes are used to compare
− System TRVs
− Standard TRVs
− Test TRVs
TRV HV Circuit Breakers P 94
Terminal Fault TRV Rating
• A two-parameter envelope is used for oscillatory (underdamped)
TRVs specified in standards for:
− circuit breakers rated less than 100 kV, at all values of breaking
current,
− circuit breakers rated 100 kV and above if the short-circuit
current is equal or less than 30% of the rated breaking current.
Ur
 2  k pp  k af
3
u '  uc / 3
uc 
t d  0.15 t3
(Class S1, cable  systems)
t d  0.05 t3
(Class S 2, line  systems)
The test TRV must not cross the
delay segment defined by (td , 0)
and (t’, u’)
TRV HV Circuit Breakers P 95
Terminal Fault TRV Rating
•
A four-parameter envelope is specified for circuit breakers rated 100 kV
and above if the short-circuit current is more than 30% of the rated
breaking current (cases with over-damped TRVs).
u1 
Ur
 2  k pp  0.75
3
TRV HV Circuit Breakers P 96
uc 
Ur
 2  k pp  k af
3
u '  u1 / 2
t 2  4 t1
Terminal Fault TRV Rating
The peak value of TRV is defined as follows:
U c  k af  k pp  2 
Ur
3
where
kpp
is the first pole to clear factor
kaf is the amplitude factor (ratio between the peak value of TRV and
the peak value of the recovery voltage at power frequency).
In IEC 62271-100 and IEEE C37.04, kaf is 1.4 at 100% rated breaking
current.
TRV HV Circuit Breakers P 97
Terminal Fault TRV Rating - Ur < 100 kV
TRV envelopes for terminal fault (Ur < 100 kV)
VOLTAGE
0.1 I
0.3 I
0.6 I
I is the rated short-circuit current
TRV HV Circuit Breakers P 98
1.0 I
TIME
Terminal Fault TRV Rating - Ur < 100 kV
• Cable systems and line systems
In order to cover all types of networks (distribution, industrial and subtransmission) and for standardization purposes, two types of systems
are introduced:
− Cable systems
Cable systems have a TRV during breaking of terminal fault at
100% of short-circuit breaking current that does not exceed the
envelope derived from Table 24 in Edition 1.2 of IEC 62271-100.
TRV values are those defined in the former editions of IEC
standard for high-voltage circuit breakers.
− Line systems
Line systems have a TRV during breaking of terminal fault at 100%
of short-circuit breaking current defined by the envelope derived
from Table 25 in Edition 1.2 of IEC 62271-100. Standard values of
TRVs for line systems are those defined in ANSI/IEEE C37.06 for
outdoor circuit-breakers.
TRV HV Circuit Breakers P 99
Terminal Fault TRV Rating - Ur < 100 kV
• Comparison of TRVs for cable systems and line-systems
Envelope of
Line system TRV
Envelope of
Cable system TRV
Uc
t3
The rate of rise of recovery voltage (RRRV) for line
systems is approximately twice the value for cable systems
TRV HV Circuit Breakers P 100
Terminal Fault TRV Rating - Ur < 100 kV
• Classes of Circuit breakers
Circuit breaker Ur < 100 kV
ClassCS
S1
Class
SLF ?
Cable-system
No
Class
Class S2
LS Direct connection
to OH line
Yes
Direct connection
to OH line
Yes
Line-system
Cable-system
Class S2
LS
Class
Short-line fault breaking performance is required only for class S2
TRV HV Circuit Breakers P 101
Terminal Fault TRV Rating - Ur < 100 kV
Amplitude factor for terminal fault (Ur < 100 kV)
Class S2 circuit breakers
1,9
Amplitude factor (p.u.)
1,8
1,7
1,6
1,5
1,4
1,3
1,2
T10
10% I
TRV HV Circuit Breakers P 102
T30
30% I
T60
60% I
T100
100% I
Terminal Fault TRV Rating - Ur < 100 kV
RRRV for terminal fault T100 (Ur < 100 kV)
Class S2 circuit breakers
1,6
RRRV
(kV/µs)
72.5kV
1.47
1,4
1,2
1.33
52kV
1.21
38kV
1.05
1
0,8
0.91
24kV
15kV
0,6
0,4
12,5
TRV HV Circuit Breakers P 103
22,5
32,5
42,5
52,5
62,5
72,5
Ur
(kV)
Terminal Fault TRV Rating - Ur < 100 kV
• Calculation of standard RRRV: circuit breaker 72.5 kV class S2
− Time to peak TRV was taken from ANSI C37.06: T2  106 µs
− Time t3 is 88% of T2 (1-COS waveshape):
t3 = 93 µs
− TRV peak uc is calculated from Ur, kpp and kaf
72.5 2
uc  1.5  1.54 
 137 kV
3
137
VATR 
 1.47 kV / µs
− RRRV is the ratio of uc and t3 :
93
it is the present value in IEC and IEEE standards.
TRV HV Circuit Breakers P 104
Terminal Fault TRV Rating - Ur < 100 kV
RRRV for terminal fault T100 (Ur < 100 kV)
Class S2 circuit breakers
1,6
RRRV
(kV/µs)
72.5kV
1.47
1,4
1,2
1.33
52kV
1.21
38kV
1.05
1kV/µs 1
0,8
0.91
24kV
15kV
RRRV  0.4  U r0.305
0,6
20kV
0,4
12,5
TRV HV Circuit Breakers P 105
22,5
32,5
42,5
52,5
62,5
72,5
Ur
(kV)
Terminal Fault TRV Rating - Ur < 100 kV
• RRRV
at reduced short-circuit current (Class S2)
− Time t3 for T100 is multiplied by the following factors
0.67
for T60
0.40
for T30 and T10
− Compared with the standard value for T100, the RRRV at
reduced short-circuit current is divided by the multiplier for time
t3 and multiplied by the increase of amplitude factor.
− Example: T60 72.5 kV
RRRV 
TRV HV Circuit Breakers P 106
1.47 1.65

 2.35 kV / µs
0.67 1.54
Terminal Fault TRV Rating - Ur ≥ 100 kV
TRV envelopes for terminal fault (Ur  100 kV)
I is the rated short-circuit current
Note: time to peak for T60 is shown here according to IEEE, it is half the IEC value
TRV HV Circuit Breakers P 107
Terminal Fault TRV Rating - Ur ≥ 100 kV
Amplitude factor for terminal fault (Ur  100 kV)
according to IEC and IEEE C37.06
kaf (p.u.)
1,8
IEC & IEEE k pp=1.3
1,7
1,6
1,5
IEEE k pp=1.5
1,4
1,3
1,2
1,1
1
10
20
30
40
50
60
70
80
90
100
% Isc
Case 10 % Isc: kpp x kaf = 2.46 (IEEE kpp=1.5) and 2.29 (IEC & IEEE kpp=1.3)
TRV HV Circuit Breakers P 108
Terminal Fault TRV Rating - Ur ≥ 100 kV
Rate-of-rise-of-recovery-voltage for terminal fault
(Ur  100 kV)
8
7
RRRV (kV/µs)
6
5
4
3
2
1
T10
TRV HV Circuit Breakers P 109
T30
T60
T100
Terminal Fault TRV
Application
•
A circuit breaker TRV capability is considered to be sufficient if the two
or four parameter envelope drawn with rated parameters is equal or
higher than the two or four parameter envelope of the system TRV.
Voltage
System TRV envelope
Circuit breaker rated TRV envelope
time
TRV HV Circuit Breakers P 110
Terminal Fault TRV
Application
•
The parameters that define the circuit breaker TRV capabilities vary
with the circuit breaker voltage rating and short-circuit current
interrupting level.
•
The circuit breaker TRV capabilities at 10%, 30%, 60% and 100% of
rated short-circuit interrupting current (Isc), corresponding to terminal
fault test duties T10, T30, T60 and T100, are given in IEEE Std
C37.06.
•
The circuit breaker TRV withstand capability envelope at any other
short-circuit interrupting current below rated can be derived using the
multipliers given in Table 1 of IEEE C37.011-011.
•
TRV studies are sometimes carried out to determine if a system TRV
is covered by the circuit breaker TRV capability demonstrated by type
tests, either when new circuit breakers are to be installed or following
a system change.
TRV HV Circuit Breakers P 111
Terminal Fault TRV
Application
•
It is not uncommon that the maximum short-circuit current falls in
between 30% and 60% of the circuit breaker rated short-circuit current.
•
To allow comparison of system TRV and circuit breaker TRV withstand
capability and to avoid additional testing, a method of interpolation of
TRV capabilities demonstrated by type tests was introduced in the
former editions of IEEE C37.011.
•
Following the introduction of the two-parameter and four-parameter
description of TRVs, this method of interpolation in the current range
between T30 and T60 (terminal faults with respectively 30% and 60%
of Isc) was not clearly stated in the 2005 edition of IEEE C37.011.
•
Thus, the method of interpolation has been further developed in IEEE
C37.011-2011 to define the circuit breaker TRV withstand capability for
short-circuit currents in this range between T30 and T60.
TRV HV Circuit Breakers P 112
Terminal Fault TRV
Application
•
In standards, it is considered that 30 % of Isc is the maximum shortcircuit current for which a two parameter TRV is applicable for circuit
breakers rated 100 kV and above.
•
The related TRV capability for short-circuit currents between 30 % of Isc
and 60 % of Isc is then necessarily a four parameter TRV.
•
The Working Group in charge of IEEE Guide C37.011 has defined that
the TRV capability between T30 and T60 can be considered to have a
rate-of-rise (u1/t1) and a first reference voltage (u1) that have
intermediate values between those of T30 and T60.
TRV HV Circuit Breakers P 113
Terminal Fault TRV
Application
•
TRV parameters (u1, t1, uc, t2) for any terminal fault current between
30 % and 60 % of Isc can be obtained as follows:
− u1 and t1 are linearly interpolated between u1 and t1 of T60 and uc
and t3 of T30
− uc and t2 are linearly interpolated between uc and t2 of T60 and uc
and t3 of T30
•
The method of interpolation is illustrated by the Figure shown on the
next slide.
TRV HV Circuit Breakers P 114
Terminal Fault TRV
Application
245kV Breaker TRV Envelope
500
450
T100
T75
400
T60
350
T55
T50
300
kV
T45
250
T40
T35
200
T30
150
T10
u1,t1
100
50
0
0
50
100
150
200
250
Time (µs)
Example of TRV interpolation for a 245kV circuit breaker
TRV HV Circuit Breakers P 115
Terminal Fault TRV
Application
* When the system TRV has an initial slope that is higher than the value
specified for terminal fault type tests, Guide IEEE C37.011 authorizes
to combine the TRV withstands demonstrated during terminal fault and
short-line-fault (same range of currents).
Voltage withstand by a 550kV circuit breaker at 75% rated breaking capability
TRV HV Circuit Breakers P 116
Terminal Fault TRV
Testing
•
Tests are required at 100% (T100), 60% (T60), 30% (T30) and 10%
(T10) of rated short-circuit current with the corresponding rated TRVs
and recovery voltages.
•
In IEC 62271-100, 3 tests are required with a symmetrical current for
each test duty, except T100 that is performed as follows
− 3 tests with symmetrical current and
− 3 tests with asymmetrical current (when interrupting asymmetrical
currents, the rate-of-rise and peak value of TRV are reduced but the
energy in the arc is higher).
•
In IEEE Std C37.09
− for each test duty T10, T30, T60: 2 tests are required with
symmetrical current and 1 test with asymmetrical current.
− test duty T100 is performed as in IEC
TRV HV Circuit Breakers P 117
Terminal Fault TRV
Testing
•
During testing, the envelope of the test TRV (in red) must be equal or
higher than the specified TRV envelope (in blue).
U
(kV)
Envelope of prospective test TRV
uc
A
C
Prospective test TRV
B
u1
Reference line of specified TRV
u'
Delay line of specified TRV
0
td
t'
t1
t2
t (µs)
This procedure is justified as it allows to compare TRVs in the two
regions where a restrike is likely: during the initial part of the TRV where
the RRRV is maximum and in the vicinity of the peak voltage (uc).
TRV HV Circuit Breakers P 118
Terminal Fault TRV
Initial TRV
•
In a network, the initial part of the TRV may have a high-frequency
oscillation of small amplitude.
•
This ITRV (Initial Transient Recovery Voltage) is due to reflections
from the first major discontinuity along the busbar.
•
It may influence the thermal phase of interruption.
•
In most cases the ITRV withstand capability is proven during short-linefault tests.
More information is given in the chapter dedicated to ITRV
TRV HV Circuit Breakers P 119
Terminal fault
TRV & Arcing Times
TRV HV Circuit Breakers P 120
Terminal Fault TRV & Arcing Time
Arcing time
1,5
Contacts separation
1
Interruption at 2nd
passage through zero
Current
0,5
Arcing time = 13 ms
0
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
0,04
0,045
Time
-0,5
1st passage
through zero
-1
-1,5
TRV HV Circuit Breakers P 121
0,05
Terminal Fault TRV & Arcing Times
In the case of periodic
phenomena,
durations
can be expressed in
milliseconds
or
in
electrical degrees.
For a system frequency
of 50 Hz, the duration of
one half loop is 10 ms, it
corresponds to 180° el., it
follows that 18° el. = 1ms
For a system frequency
of 60 Hz the duration of
one half loop is 8.33 ms
so 18° el. = 0.83 ms
TRV HV Circuit Breakers P 122
1,5
1
0,5
10 ms
0
0
0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 0,018 0,02
-0,5
-1
-1,5
One period at 50 Hz
Terminal Fault TRV & Arcing Times
Current
Arcing time
1st pole
Arcing time
last poles
One period (360°) at 60Hz is 16.7 ms
One period (360°) at 50Hz is 20 ms
TRV HV Circuit Breakers P 123
Contacts
separation
1st pole
clears
last poles
clear
Minimum & Maximum Arcing Times
• Case 1: Reference case with contact separation at 29.67ms
Example
three-phase
fault
interruption
Fr = 50 Hz
Pole 3
interrupts first
Arcing time
pole 3 = 8.4ms
(minimum arcing
time)
System with non-effectively grounded neutral
TRV HV Circuit Breakers P 124
Minimum & Maximum Arcing Times
• Case 2: Contact separation advanced by 3.33ms (60°) = 26.34ms
Arcing time
pole 1 = 8.4ms
Pole 1 interrupts
first with the same
arcing time as in
Case 1 by pole 3
i.e. same breaking
conditions in
terms of arcing
times
TRV HV Circuit Breakers P 125
Minimum & Maximum Arcing Times
• Case 3: Contact separation advanced by 2.33ms (42°) = 27.34ms
Arcing time pole 1
= 15.7ms
= 8.4ms + 7.3ms
= 8.4ms + 132°
maximum arcing
time
Pole 3 interrupts
first with the
longest arcing
time for a first
pole to clear
Arcing time
pole 3 = 10.7ms
= 8.4ms + 42°
The range of arcing times for the first pole to clear is 42°
TRV HV Circuit Breakers P 126
Minimum & Maximum Arcing Times
Three-phase
faults
grounded
systems
ungrounded faults
in
non-effectively
or
three-phase
20000
Example with fr = 50 Hz
tarc min = 12 ms
10000
Iarc
Current (A)
0
Contact separation
-10000
18°
-20000
Iarc
-30000
Contact separation
-40000
tarc max = 19,33 ms
-50000
0
5
10
15
20
Time (ms)
TRV HV Circuit Breakers P 127
25
30
35
40
Minimum & Maximum Arcing Times (50Hz)
Three-phase faults in noneffectively grounded systems or
three-phase ungrounded faults
time [ms]
0
5
10
15
20000
20
25
30
35
40
Tmin = 12 ms
15000
Minimum arcing time (blue
phase) Tmin = 12 ms
10000
Iarc
current [A]
5000
0
Contact separation delayed
by 18° el.
(or 1 ms)
Contact
separation
-5000
-10000
18° el.
-15000
-20000
time [ms]
0
5
10
15
20
25
30
20000
15000
current [A]
10000
5000
Iarc
0
-5000
-10000
Contact
separation
-15000
-20000
TRV HV Circuit Breakers P 128
T max = 19.33 ms
35
40
Arcing time 1st phase (red
phase) = 14.33 ms
(Tmin + 60° - 18°
= Tmin + 42°)
Maximum arcing time (blue
phase) = 19.33 ms
(14.33 ms + 90°
= Tmin + 132°)
Minimum & Maximum Arcing Times (60Hz)
Three-phase faults in noneffectively grounded systems or
three-phase ungrounded faults
time [ms]
0
5
10
15
20
25
30
35
40
20000
Tmin = 12 ms
15000
current [A]
10000
5000
Minimum arcing time (blue
phase) Tmin = 12 ms
Iarc
0
Contact
separation
-5000
Contact separation delayed
by 18° el.
(or 0.83 ms)
-10000
18° el.
-15000
-20000
time [ms]
0
5
10
15
20
25
30
20000
15000
current [A]
10000
5000
Iarc
0
-5000
-10000
Contact
separation
-15000
-20000
TRV HV Circuit Breakers P 129
T max = 18.1 ms
35
40
Arcing time 1st phase (red
phase) = 13.94 ms
(Tmin + 60° - 18°
= Tmin + 42°)
Maximum arcing time
(blue phase) = 18.1 ms
(13.94 ms + 90°
= Tmin + 132°)
Terminal Fault Arcing times
Three-Phase Short-Circuit Current Interruption
Three-phase fault in network with isolated neutral (Ur < 245kV)
Current
ER
A
B
ES
ET
Contact
separation
Time
Interruption of current in a first pole, followed ¼ cycle later by
interruption of the two other poles in series
Breaking Tests HV Circuit-Breakers – Denis Dufournet
Terminal Fault Arcing Times
Three-Phase Short-Circuit Current Interruption
Three-phase fault in network with effectively grounded
neutral (Ur ≥ 245kV)
Voltages
Currents
ER
A
B
ES
ET
Contact
separation
The three poles interrupt at separate current zeros with
different arcing times
Breaking Tests HV Circuit-Breakers – Denis Dufournet
Arcing Times and TRVs / Fr = 60 Hz
Three-phase faults in
non-effectively grounded
systems or three-phase
ungrounded faults
0.87
90°
Maximum arcing time
0.87
1.5
Currents
= Tmin + 132°
= Tmin + 6.1 ms
TRVs (pole factor)
Three-phase faults in
effectively grounded
systems
1.27
120°
Maximum arcing time
= Tmin + 162°
= Tmin + 7.5 ms
1.3
TRV HV Circuit Breakers P 132
1.0
Arcing Times and TRVs / Fr = 50 Hz
Three-phase faults in
non-effectively grounded
systems or three-phase
ungrounded faults
0.87
90°
Maximum arcing time
0.87
1.5
Currents
= Tmin + 132°
= Tmin + 7.3 ms
TRVs (pole factor)
Three-phase faults in
effectively grounded
systems
1.27
120°
Maximum arcing time
= Tmin + 162°
= Tmin + 9 ms
1.3
TRV HV Circuit Breakers P 133
1.0
Terminal Fault TRV & Arcing Times
Pole to clear factor
Arcing time
° el.
Reference = Minimum arcing time first pole
TRV HV Circuit Breakers P 134
Minimum arcing time + 180° -18°
Terminal Fault TRV & Arcing Times at 60Hz
Pole to clear factor
Arcing times in ms FR = 60 Hz
Arcing time
° el.
0
1.95
3.55 4.15
5.5
5.55
Reference = Minimum arcing time first pole to clear
TRV HV Circuit Breakers P 135
6.1
7.5
ms
Terminal Fault TRV & Arcing Times
Pole to clear factor
Single-phase "umbrella" test with
kpp=1.3
Increased
stress
° el.
Reference = Minimum arcing time first pole Minimum arcing time + 180° -18°
TRV HV Circuit Breakers P 136
Terminal Fault TRV & Arcing Times
1,5
Contacts separation
1
Current
Single-phase tests
with minimum &
maximum arcing time
0,5
Minimum arcing time
= 13 ms
0
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
0,04
0,045
0,05
Time
-0,5
-1
-1,5
1,5
Contacts separation
1
Current
Mximum arcing time = 22 ms
= 13 ms + 10 ms - 1 ms
= 13ms + 180° el. - 18° el.
0,5
0
0
Example with F=50Hz
0,005
0,01
0,015
0,02
0,025
0,03
0,04
0,045
Time
-0,5
restrike with arcing
time 12 ms
-1
-1,5
TRV HV Circuit Breakers P 137
0,035
0,05
Terminal Fault TRV
Generator Circuit Breakers
TRV HV Circuit Breakers P 138
Generator Circuit Breakers TRV
•
Special TRV requirements are applicable for generator circuit breakers
installed between a generator and a transformer.
•
Two types of faults need to be considered
A1
TRV HV Circuit Breakers P 139
System-source fault
B1 Generator-source fault
Generator Circuit Breakers TRV
•
For the two types of fault, the TRV has an oscillatory waveshape and
the first-pole-to-clear factor is 1.5 in order to cover three-phase
ungrounded faults.
•
TRV parameters, i.e. peak voltage uc, rate-of-rise (RRRV) and time
delay, are listed in ANSI/IEEE C37.013.
TRV for system-source faults
•
RRRV for system-source faults is 3 to 5 times higher than the value
specified for distribution or sub-transmission circuit breakers ANSI/IEEE
C37.04.
This is due to the fact that the TRV frequency is dominated by the
natural frequency of the step-up transformer.
•
IEEE has defined TRV parameters in several ranges of transformer
rated power.
TRV HV Circuit Breakers P 140
Generator Circuit Breakers TRV
• TRV parameters for System-Source Faults
Table 5a– TRV parameters for system - source faults
Inherent TRV
Transformer
Rating
T2 -Time to - Peak
E2 -Peak Voltage
TRV Rate
(MVA)
(µs)
(kV)
(kV / µs)
Line
Column 1
Column 2
Column 3
Column 4
1
10 - 50
0.68 V
1.84 V
3.2
2
51 - 100
0.62 V
1.84 V
3.5
3
101 - 200
0.54 V
1.84 V
4.0
4
201 - 400
0.48 V
1.84 V
4.5
5
401 - 600
0.43 V
1.84 V
5.0
6
601 - 1000
0.39 V
1.84 V
5.5
7
1001 or more
0.36 V
1.84 V
6.0
TRV HV Circuit Breakers P 141
Generator Circuit Breakers TRV
• TRV
for system-source faults (Cont’d)
In IEEE C37.013-1993, the WG introduced time t3 (coming from IEC) to
define precisely the determination of the TRV rate.
E2 is equal to 1.84 V where V is
the rms value of the rated
maximum voltage and the value
1.84 is equal to
2 x 1.5 (= first-pole-to-clear3
factor) x 1.5 (= amplitude factor)
T2 
t3
E2

0.85 0.85  TRV rate
TRV HV Circuit Breakers P 142
Generator Circuit Breakers TRV
TRV for system-source faults (Cont’d)
•
The RRRV can be significantly reduced if a capacitor is installed
between the circuit breaker and the transformer. It is also reduced in
the special cases where the connection between the circuit breaker
and the transformer(s) is made by cable(s) [29].
TRV RATE FOR SYSTEM FED FAULTS TRANSFORMER 50MVA<<=100MVA
3,6
3,4
TRV RATE (kV/µs)
3,2
3
81MVA
100MVA
2,8
2,6
65,5MVA
2,4
2,2
2
0
2000
4000
6000
CABLE CAPACITANCE (pF)
TRV HV Circuit Breakers P 143
8000
10000
12000
Generator Circuit Breakers TRV
TRV for system-source faults (Cont’d)
•
When a capacitance is added between the circuit breaker and the
step-up transformer, the TRV peak is increased (explanation: see
general considerations).
E2 MULTIPLIER FOR SYSTEM FED FAULTS TRANSFORMER 50MVA<<=100MVA
TRV peak
increase (p.u.)
1,3
1,25
E2 MULTIPLIER (p.u.)
65.5 MVA
1,2
81 MVA
1,15
100 MVA
1,1
1,05
Capacitance
(pF)
1
0
2000
4000
6000
8000
CABLE CAPACITANCE (pF)
TRV HV Circuit Breakers P 144
10000
12000
Generator Circuit Breakers TRV
• TRV for generator-source faults
RRRV for generator-source faults is roughly 2 times the values
specified for distribution or sub-transmission circuit breakers.
“Table 6a – TRV parameters for generator - source faults
Inherent TRV
Generator
Rating
T2 -Time - to – Peak
E2 -Peak Voltage
TRV Rate
(MVA)
(µs)
(kV)
(kV / µs)
Line
Column 1
Column 2
Column 3
Column 4
1
10 - 50
1.44 V
1.84 V
1.5
2
51 - 100
1.35 V
1.84 V
1.6
3
101 - 400
1.20 V
1.84 V
1.8
4
401 - 800
1.08 V
1.84 V
2.0
5
801 or more
0.98 V
1.84 V
2.2
TRV HV Circuit Breakers P 145
Generator Circuit Breakers TRV
• TRV in case of asymmetrical currents
− Due to the large time constants of generators and transformers
(high X/R), generator circuit breakers are required to interrupt
currents with a high percentage of dc component (high asymmetry).
− The rate-of rise and peak value of TRV during interruption of
currents with large asymmetry are significantly reduced.
− In this case, the stress is mainly due to the current amplitude and
the energy in the arc (mechanical and thermal stresses), and to a
lesser extent to the TRV.
− The more severe TRV stress is obtained during interruption of
symmetrical currents.
TRV HV Circuit Breakers P 146
Terminal Fault TRV / Summary
• First-pole-to-clear factor
− Effectively earthed systems
kpp = 1.3 (1.2 for UHV)
− Non-effectively earthed systems kpp = 1.5
• Rating
− TRV with 2 or 4 parameters
− Classes S1 and S2 for rated voltages < 100 kV
• Testing circuit breakers ≥ 100 kV
− RRRV:
7 – 5 – 3 – 2 kV/µs for resp. T10, T30, T60, T100s
− Interrupting window: 162° (kpp = 1.3) or 132° (kpp = 1.5)
• Generator circuit breakers
TRV HV Circuit Breakers P 147
higher RRRV for T100s
Short-Line-Fault (SLF)
TRV HV Circuit Breakers P 148
Introduction
•
The severity of SLF with its associated very fast rate-of-rise-ofrecovery-voltage (RRRV) was identified at the end of the 1950’s.
•
First SLF tests were performed in 1956-1958 in the USA (G.E.), also
at Mettlen substation (CH), Fontenay (EDF High Power Laboratories)
and CESI. The aim was to compare theoretical studies and
experiments.
•
The first published paper on SLF is considered to be by W.F. Skeats,
C.H. Titus, W.R. Wilson (G.E.) in Transactions AIEE, submitted in
April 1957 and published in February 1958.
•
In Europe, a paper by Michel Pouard (EDF) was published in the
Bulletin de la Société Française des Electriciens in Nov. 1958.
TRV HV Circuit Breakers P 149
Introduction
Paper in Power Apparatus and
Systems, Part III, Transactions of
the
American
Institute
of
Electrical Engineers. Publication
in February 1958
TRV HV Circuit Breakers P 150
Test laboratory line used by General
Electric in 1957 to test air-blast
circuit-breakers. It was 1.6km long,
short-circuit power of the source was
50kA under 31kV.
Introduction
•
During the general meetings of CIGRE, SLF was first mentioned
during the session of 1958.
Two reports were presented during the CIGRE session of 1960 (by
France and Switzerland).
•
IEC introduced for the first time short-line-fault (SLF) requirements
in 1971.
•
SLF TRVs were introduced also in ANSI/IEEE C37.072 in 1971.
TRV HV Circuit Breakers P 151
Introduction
•
The requirement of a SLF interrupting capability had and still has a
great influence on the design of high-voltage circuit breakers.
It was already the case with air blast type that had to be fitted with
opening resistors for SLF interruption.
•
SLF is also a critical test duty for SF6 type circuit breakers.
Sufficient pressure build-up and mass flow rate are necessary for SF6
circuit breakers to interrupt at current zero.
TRV HV Circuit Breakers P 152
Short-Line-Fault (SLF)
•
•
Short-line faults occur from a few hundred meters up to several
kilometers down the line.
− L90: short-line fault with 90% of rated short-circuit current
− L75: short-line fault with 75% of rated short-circuit current
After current interruption, the line-side voltage exhibits a characteristic
triangular waveshape.
U
line
Circuit breaker
TRV, neglecting the contribution from
the supply-side
TRV HV Circuit Breakers P 153
Short-Line-Fault (SLF)
•
The circuit-breaker interrupts the current, at a passage through zero,
the supply voltage and the di/dt are both maximum (in amplitude). The
voltage on the circuit-breaker terminals (U0) is a fraction of the supply
voltage Us0.
LS
Us0
Supply side
Voltage (point B)
LL
line
U0
At the time of interruption
Us0 = (LS + LL ) di/dt
U0 = LL di/dt
where di/dt is the current
derivative at current zero
Example Ur = 245kV
U s0 
U0
Line side
Voltage (point C)
TRV HV Circuit Breakers P 154
2
Ur
3
 200 kV
90 

L90 : U 0  U s 0 1 
  20 kV
100


Short-Line-Fault (SLF)
•
•
As the TRV is at high frequency, the line must be treated as a
transmission line with distributed elements.
The line side voltage oscillates as travelling waves are transmitted with
positive and negative reflections at the open breaker and at the fault,
respectively.
After current interruption
The supply voltage varies
much more slowly than the
line-side voltage
The TRV is mainly due to the
voltage variation on the line
side.
Line-side
voltage (point C)
TRV HV Circuit Breakers P 155
Supply side
voltage (point B)
Short-Line-Fault (SLF)
• Supply-side and line-side voltages
Current
t
Supply-side voltage
Um
U=0
t
Uo
UL
Line-side voltage
Um: supply voltage at the time of interruption
Uo: voltage on circuit breaker terminals at the time of interruption
Example L75: Ur = 245kV : Um= 200 kV, Uo= 50 kV, UL= 80 kV
TRV HV Circuit Breakers P 156
SLF / Evolution of Line Voltage
Voltage profile at current zero (t=0),
Voltage decreases linearly towards 0 at the fault point
It is considered to be sum of two voltage waves moving in opposite directions.
TL = Travel time for wave to travel from one end of line to the other and back.
TRV HV Circuit Breakers P 157
SLF / Evolution of Line Voltage
Traveling waves that
reach the fault point are
reflected with an opposite
polarity.
Traveling waves that
reach the open point, at
the
circuit
breaker
terminal, are reflected
with the same polarity.
Voltage at any location
on the line is the sum of
each component.
TRV HV Circuit Breakers P 158
SLF / Evolution of Line Voltage
TRV HV Circuit Breakers P 159
SLF / Evolution of Line Voltage
Voltage on the line after current interruption
VOLTAGE (p.u.)
2
tL/4
0.5 tL
3 tL/4
tL
1.5 tL
0
TIME
Voltage at x = 0.75 L
-2
TRV HV Circuit Breakers P 160
Voltage half-way
to the fault x = 0.5 L
Voltage at circuit-breaker
Terminal x = 0
SLF / Evolution of Line Voltage
Voltage on Circuit Breaker line-side terminal
Line side Voltage
(p.u.)
1,5
1
0,5
0
0
0,25
0,5
0,75
1
1,25
1,5
1,75
2
-0,5
-1
-1,5
Time / TL
Damping is neglected, in practice at time TL voltage is -0.6 to -0.8 p.u.
TRV HV Circuit Breakers P 161
SLF TRV
Voltage (kV)
TRV
Supply voltage
Line voltage
Time (µs)
TRV HV Circuit Breakers P 162
SLF / RRRV
•
The rate-of-rise of recovery voltage (RRRV) on the line side is function
of the slope of current before interruption and of the surge impedance
of the line:
du
di
RRRV 
Z
ZI 2sI
dt
dt
Z
L
C
Z is the surge impedance of the line (450 ohm)
L and C are respectively the self inductance and the capacitance of the
line per unit length
I
fault current (kA)
ω
pulsation
s
multiplier = 0.20 (f = 50Hz) or 0.24 (f = 60 Hz), du/dt in kV/µs
TRV HV Circuit Breakers P 163
at 50 Hz
Z  2  0.2 10 6
SLF / Line Surge Impedance
•
Assumptions: conductors of infinite length, the electrical field and magnetic field
do not penetrate the ground.
•
Self surge impedance
D = 2 h with h = height of line
r = radius of conductor
Ln = natural logarithm µ0 = magnetic constant = 4π×10−7 H/m
= electric constant = 8.854×10−12 F/m
with
Z
L
D
 2h
 60 Ln    60 Ln 

C
r
r
 


(1)
•
Mutual surge impedance (ZM) between 2 conductors is given by (1) where D is
the distance between one conductor and the image of the other conductor, and r
represents the distance between the two conductors (see next slide).
•
A matrix equation is done in case of multi-conductors circuits with self and
mutual couplings. Modal analysis done by digital calculations gives the relevant
modes of travelling waves (see Annex C in [39] and [47]).
TRV HV Circuit Breakers P 164
SLF / Line Surge Impedance
•
Distances to consider for mutual surge impedance calculation
d12
Bundle 1
Bundle 2
Bundle 3
D12
Ground
D 
Z M 12  60 Ln  12 
 d12 
Image of bundle of conductors 2
TRV HV Circuit Breakers P 165
SLF / Line Surge Impedance
•
Factors that influence the surge impedance
− Geometry of a conductor
− Arrangement of the conductors in relation to the towers and the ground
(single or double circuits..)
− Frequency of the TRV: Z decreases by 4% when the frequency increases
from 1 to 100 kHz.
− In case of bundled conductors, they can clash if the current is high enough.
The surge impedance is higher after conductor clashing and reach the
value for a single conductor: 450 Ω.
− Line height: the surge impedance of lines increases with the conductor
height above ground.
− Earth resistivity: the surge impedance increases by 5.7% at 1kHz and
3.2% at 100 kHz when earth resistivity changes from 10 to 1000 Ω-m.
− Tower footing resistance: if it rises from 0 to 10 Ω the surge impedance
increases by about 2%.
TRV HV Circuit Breakers P 166
Short-line-fault
• Percentage of SLF (or M)
V
I S  LG
XS
TRV HV Circuit Breakers P 167
IL 
VLG
XS  XL
Short-line-fault
•
The transmission line parameters are given in terms of the effective
surge impedance ( Zeff) of the faulted line and a peak factor (d)
d
uL
uO
uL
u L  Z eff  di / dt  2  / v
uo    X L  I L
2
uO
d  2
Z eff
XL v
XL is the line reactance per unit length
v is the velocity of light (0.3 km/µs),  is the line length
 is 2   system power frequency (314 or 377 rad/s for 50 or 60 Hz)
TRV HV Circuit Breakers P 168
SLF / Voltage at Current Zero
U0  X L  IL
US  X S  IS
U0
US
IL  M  IS
M
XS
XS  XL
or M  X L  X S  M  X S
U0  X L  M  IS
U0  X S  M  X S   IS
U 0  1  M   X S  I S  1  M   U S
U 0  1  M   U S
TRV HV Circuit Breakers P 169
SLF / Line-side Contribution to TRV
•
The rated values for the line surge impedance Z and the peak factor
d are defined in standards as follows:
Z  450  d  U L / U 0  1.6
•
The line side voltage contribution to TRV is defined as a triangular
wave as follows (where IS is the rated short-circuit current) :
U L  1.6 (1  M )
2
Ur
3
du
di
Z
 Z  M IS
dt
dt
2
the first peak UL decreases when M increases
the rate-of-rise of recovery voltage increases with M
•
•
There is a critical value of the short-line-fault current for which the
circuit breaker has more difficulty to interrupt.
The critical value of M is close to 90% for SF6 circuit breakers
(generally in the range 90%-95%). it is between 75% and 80% for
air blast circuit breakers.
TRV HV Circuit Breakers P 170
Short-line-fault
•
The following Table gives the comparison of current and voltage
stresses during test duties L90 and L75, respectively at 90% and 75%
of rated short-circuit current, for a circuit-breaker 245kV 40kA 50Hz.
•
The current and RRRV are higher during L90, but the (first) peak
voltage is higher during L75.
•
In practice, L90 is usually the most severe test duty.
L90
L75
Current (kA)
36
30
RRRV (kV/µs)
7.2
6
UL (kV)
32
80
RRRV: rate of rise of recovery voltage
Voltage on the line side only is considered
TRV HV Circuit Breakers P 171
UL= first peak voltage
SLF / Comparison of Test Duties
140
120
4.8 kV/µs
100
U (kV)
Ur = 245kV
L60
80
Isc = 40kA
fr = 50Hz
L75
6 kV/µs
60
40
L90
7.2 kV/µs
20
0
0
5
10
15
20
25
30
35
T (µs)
When current decreases (longer line), the slope decreases but the peak
value increases. It is generally considered that for SF6 circuit breakers
interruption is more influenced by the voltage slope (RRRV).
TRV HV Circuit Breakers P 172
Short-line-fault
•
The TRV seen by the circuit breaker is the sum of a contribution
from the line side (eL) and a contribution from the supply side (eS):
e  e L  eS
with (in a first approximation)
eS  2 M (TL  t d )
where
2M
= RRRV (T100) x M = 2 kV/µs x M
TL
is the time to peak of the line side TRV
td
is the time delay of TRV on the source side
TRV HV Circuit Breakers P 173
Short-line-fault
•
Example of calculation of SLF TRV : L90 245 kV 50 kA 50 Hz
Fault current = 0.9 x 50 = 45 kA (assuming time delay tdL= 0 µs)
TRV HV Circuit Breakers P 174
Short-line-fault
•
This rate-of-rise of TRV during SLF is much higher than the values
that are met during terminal fault interruption:
Test duty
RRRV
(kV/µs)
I
(kA)
F
(Hz)
SLF
L90 50 kA
10.8
45
60
SLF
L90 50 kA
9
45
50
SLF
L90 40 kA
8.64
36
60
Terminal fault
T60
3
30
50/60
Terminal fault
T100
2
50
50/60
For SLF, this table gives the RRRV of the line side voltage
TRV HV Circuit Breakers P 175
SLF / Line Characteristics
• Standard values of lines characteristics for SLF
IEC values are shown, ANSI/IEEE values cover rated voltages up to 800kV
TRV HV Circuit Breakers P 176
Short-Line-Fault
Influence of an Additional Capacitor
TRV HV Circuit Breakers P 177
SLF / Influence of an Additional Capacitor
•
The SLF performance can be increased by adding a capacitor, either
between terminals or phase to ground (see figure).
•
A capacitor has two effects:
− it decreases the oscillation frequency and the RRRV of the line
side contribution to TRV;
− it increases the time delay of the line side contribution to TRV.
XS
VLG
TRV HV Circuit Breakers P 178
C.B.
XL
SLF / Influence of an Additional Capacitor
60
[ kV ]
50
40
30
1 2
3
20
10
0
0
4
(file t r v 2 .pl4 ; x - v ar t ) v :P 0 0
8
v :P 1
v :P 4
16
[ u s]
20
v :P 1 0
TRV without
capacitor
TRV HV Circuit Breakers P 179
12
TRV with capacitor
(capacitance increase from 1 to 3)
SLF / Influence of an Additional Capacitor
− Equation of the line-side contribution to TRV up to the first peak:

e(t )  Z (di / dt ) t  Z C  Z C e  t / Z C

− If the capacitor is connected phase to ground on the line side, the
reduction of the line side RRRV can be estimated by a simple
calculation, as detailed in the next slide, with
Cadd
additional line-to-ground capacitance;
L
line inductance;
Z
line surge impedance;
CL
total line capacitance = L/Z2;
Ce
equivalent line capacitance: capacitance which, together
with the inductance L, gives the line frequency of oscillation
TRV HV Circuit Breakers P 180
SLF / Influence of an Additional Capacitor
− By definition of Ce
fL 
1
2 LCe
2u *L
− The period of oscillation is equal to
 du 
 
 du 
and    Z    I L 2
 dt  L
 dt  L
Z 
fL 
− It follows that
4X L
and
with u *L  2 X L  I L 2
4L
4 CL
Ce  2
 2  0.4 CL
2
 Z

If an additional capacitance is added at the line entrance, the RRRV on
the line side is reduced in the same manner as the line frequency of
oscillation.
TRV HV Circuit Breakers P 181
SLF / Influence of an Additional Capacitor
− The RRRV on the line side is then
2 LCe
du
 Z   IL
dt
2 L(Ce  Cadd )
Ce
du
 Z   IL
dt
Ce  Cadd
CL
du
 Z   IL 2
dt
C L  2.5 Cadd
TRV HV Circuit Breakers P 182
Short-Line-Fault
Influence of an Opening Resistor
TRV HV Circuit Breakers P 183
SLF / Breaking with Opening Resistor
• Some circuit breakers, mainly air-blast, have an opening resistor to
assist a short-circuit interruption.
• It was introduced to improve the SLF breaking capability of air-blast
circuit breakers, but it has been used also to facilitate the interruption
of fast TRVs by some SF6 circuit breakers.
TRV HV Circuit Breakers P 184
SLF / Breaking with Opening Resistor
• In case of SLF, the RRRV (or du/dt) is modified as follows:
du Z  R di Z  R


I
dt Z  R dt Z  R
where R = value of opening resistor
Z = line surge impedance
I = short-circuit current
TRV HV Circuit Breakers P 185
2
Short-Line--Fault TRV / Summary
• Very fast RRRV (rate-of-rise of recovery voltage)
− Product of fault current derivative by surge impedance
− Standard value of surge impedance = 450 Ω
• Triangular waveshape due to travelling waves
• Test duties L90 and L75 (+ L60 is some cases)
− Single-phase tests that cover all SLF conditions
• SLF performance improved by
− additional capacitor (or opening resistor)
TRV HV Circuit Breakers P 186