day 2 part 1 dist principle
TRANSCRIPT
HV Power Seminar Nov 2009 1
Part 1
Energy Sector© Siemens AG 2008
Distance Protectionfor transmission lines
Gustav Steynberg
HV Power Seminar Nov 2009 2
Localization of short-circuits by means of an impedance measurement:
� fault on the protected lineZ1
relay A
Basic principle of impedance protection
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Page 2 November 09
� fault outside the protected line
selectivity
relay A
Z2
HV Power Seminar Nov 2009 3
Distance measurement (principle)
ZL = RL + j XL
ZE = RE +j XE
IL1
IL2
IL3
IE
ZL
ZE
U U U
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6 loops: 3 phase- phase loops and3 phase- ground loops
phase- phase -loop:
The same applies to the remaining loops
UL1-L2 = ZL ( IL1 - IL2)
Measured currentmeasured voltage
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UL1UL2UL3
HV Power Seminar Nov 2009 4
IL1
IL2
IL3
IE
ZL
ZE
ZL = RL + j XL
ZE = RE +j XE
Distance measurement (principle)
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Page 4 November 09
phase-ground-loop: UL1 = ΙL1 · ( RL + j XL )- ΙE · ( RE +j XE)
ΙL1, ΙE measured currentUL1 measured voltage
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The same applies to the remaining loops
UL1UL2UL3
HV Power Seminar Nov 2009 5
ZL
ZLF1
ZLF2
RF RF
ZLoadDF1 F2
X
ZL
ZLF2R ZF2
Fault area
distance relayoperating characteristic
Phase - Phase Fault
Load and short-circuit impedances
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Page 5 November 09
R
ZLF2
j SC1
j SC2
j L
RR
ZF1
ZF2
RR
ZLoad
ZLF1
Fault in reverse
direction Load area
Minimum Load Impedance:Minimum voltage 0,9 UnMaximum current 1,1 InMaximum angle ± 30°
Phase - Phase Fault
RR ≈ RF / 2
Phase - Earth Fault
RR ≈ RF /(1 + RE/RL)
HV Power Seminar Nov 2009 6
ISC
E
ZL
ZSC
U1= k1⋅ USC= k1⋅ ISC⋅ZSC.
ZS A B
Principle of (analog) distance relaying
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Page 6 November 09
comparator
ZReplica (line replica impedance)(corresponds to the set zone reach)
U1= k1⋅ USC= k1⋅ ISC⋅ZSC.
U2=k2 ⋅ISC⋅ZReplica
Relay design:operation if
U1< U2
i.e. ZSC< ZReplica
ZReplicaX
R
Ext. fault
Internal fault
HV Power Seminar Nov 2009 7
Fourier analysis of measured values
C(k)S(k)(k) j III ⋅+=Sampled signal i(t) Processing with two
orthogonal filters
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Page 7 November 09
-6,000
-4,000
-2,000
0,000
2,000
4,000
6,000
8,000
10,000
0 20 40 60 80 100
dt t sin t)( 21
360 - Ø
Ø
S ω⋅ωπ
=°
∫ II
dt t cos t)( 1
360 - Ø
Ø
ωωπ
⋅=°
∫ II2C
HV Power Seminar Nov 2009 8
Fourier analysis: Filtering characteristics
0.6
0.8
1
0.6
0.8
1
Full cycle (20 ms at 50 Hz) Half cycle (10 ms at 50 Hz)
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Page 8 November 09
0 100 200 300 400 500Hz
0.2
0.4
50 0 100 200 300 400 500Hz
0.2
0.4
50
HV Power Seminar Nov 2009 9
Discrete Fourier transform (window = 1 cycle)
)(
∑ ⋅⋅⋅=
−
=
1N
1n
nS i∆nωsin2 tN
I
∆∆∆∆t
i0i1 i2
iN
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Page 9 November 09
=1nN
)(
∑ ⋅⋅⋅++=
−
=
1N
1n
nNO
C i∆tnωcos2i
2i2
NI
n0 1 2 N
0 1 2 N
3 . . . .
3 . . .
HV Power Seminar Nov 2009 10
UU tjj eUeUU ωϕ ⋅=⋅=
II tjj eIeII ωϕ ⋅=⋅=UU t⋅= ωϕ
Impedance calculation using U- and I-phasors
IUZ ϕϕϕ −=
( ) XjRjZeZZ j ⋅+=⋅+⋅=⋅= ϕϕϕ sincos
R
X
Z
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Page 10 November 09
II t⋅=ωϕ0=t
( ) ( ) ( )IUIUj
j
j
I
Uj
I
Ue
I
U
eI
eU
I
UZ IU
I
U
ϕϕϕϕϕϕϕ
ϕ
−+−⋅=⋅=⋅⋅== − sincos
R X
( ) XjRjZeZZ ZZj Z ⋅+=⋅+⋅=⋅= ϕϕϕ sincos
HV Power Seminar Nov 2009 11
Distance protectionImpedance calculation using U- und I-phasors (princi ple)
{ } ( )dttuUR ∫+
−
⋅⋅⋅=T/2
T/20LL ωcos(t)
T1
e
{ } ( )dttuUI ∫+
−
⋅⋅⋅=T/2
T/20L ωsin(t)
T1
m L
{ } { }LL me UjIURU +=L
{ } ( )dttiR ∫+
−
⋅⋅⋅=T/2
T/20L ωcos(t)
T1
e LI
{ } ( )dttiI ∫+
−
⋅⋅⋅=T/2
T/20LL ωsin(t)
T1
m I
{ } { }LLL me III jIR +=
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Page 11 November 09
( ) ( ) ( )[ ]UUL
)tj(ω
LL ωsinωcosU ϕϕϕ +⋅++⋅⋅=⋅= +⋅ tjtUeUtu ( ) ( ) ( )[ ]IIL)tj(ω
LL ωsinωcosI ϕϕϕ +⋅++⋅⋅=⋅= +⋅ tjte IIti
LLLLL II ⋅+⋅= jXRU
{ } { } ( ) { } { }( )LLLLLL meme II jIRjXRUjIUR +⋅+=+
{ } { } { }LLLLL mee II IXRRUR ⋅−⋅=
{ } { } { }LLLLL mem II IRRXUI ⋅+⋅=
{ } { } { } { }{ } { }2
L2
L
LLLLL
me
meem
II
II
IR
IURRUIX
+⋅−⋅=
{ } { } { } { }{ } { }2
L2
L
LLLLL
Ime
ImImee
II
II
+⋅+⋅=
R
URURR
Note: This calculation does not consider the a-periodic DC component in the measured signals
HV Power Seminar Nov 2009 12
Distance protectionFast impedance estimation using Kalman Filters
)ωt)t)ωt)t(
i cos( C
t
e - cos( B sin( A ⋅+τ−
ω⋅+⋅=
Task: Estimation of the coefficients A, B, C on ba sis of measured currents and voltages
Method: Gauß‘s Minimization of error squares:
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Method: Gauß‘s Minimization of error squares:
2
(i)(i)
k
N-ki
f - u Delta
∑=
=MIN
Delta = quality valuek = sampling numberN = length of data windowi = variable
0 dC dBdA
Delta =
HV Power Seminar Nov 2009 13
10 ms 20 ms 30 ms 40 ms
i
t
Estimator 1 (Gauss) (5 samples)
X
R
X
Z = 50%
Estimator 2 (Gauss)
Jump detector
Fault inception
0 ms
Distance protection: Adaptive measuring method
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Page 13 November 09
X
R
X
R
X
R
Normal measuring step 1 (Fourier)(2x16 samples, 5 ms shifted)
Z = 80%
Z = 90%
Z = 100%
Estimator 2 (Gauss) (7 samples)
Estimatorr 3 (Gauss)(9 samples)
Estimator 4 (Gauss) (11 samples)
Estimator 5 (Gauss) (13 samples)
Normal measuring step 2 (Fourier)(2x21samples, 5 ms shifted)
As previous measurement
HV Power Seminar Nov 2009 14
Distance protection,Typical operating time characteristic
Operating time (ms)
10
15
20
25
30
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Page 14 November 09
Fault location in % zone reachShort-circuit data:SIR = 26f = 50 HzFault: L1-E5 shots per fault caseFault inception: 0°... 90°
010 20 30 40 50 60 70 80 90 100
5
HV Power Seminar Nov 2009 15
RL + j XLIL1
RE + j XE
VL1 VL2 VL3
IL2
IL3
IE
Distance measurement Fault loop formulas
Relay location
Ph-Ph Ph-E
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Page 15 November 09
Phase-to-Earth loop:
Phase-to-Phase loop:
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( ) ( )
⋅−+
⋅−⋅=
+⋅−+⋅=
E
L
ELLE
L
ELLL
EEELLLL
IX
XIjXI
R
RIRV
jXRIjXRIV
111
11
( ) ( )2121 LLLLLL IIjXRV −⋅+=−
HV Power Seminar Nov 2009 16
time
t1
t2
t3
Z1
Z2
Z3
∆t = grading time
A CB D
Graded distance zones
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Page 16 November 09
D1 D2 D3
distance
A CB D
Z1 = 0,85 ZAB
Z2 = 0,85 (ZAB + 0,85 ZBC)Z3 = 0,85 (ZAB + 0,85 (ZBC + 0,85 ZCD))
Safety margin is 15 %:� line error� CT, VT error� measuring error
Grading rules:
HV Power Seminar Nov 2009 17
2nd Zone: It must initially allow the 1st zone on the neighbouring feeder(s) to clear the fault.The grading time therefore results from the addition of the following times:
� operating time of the neighbouring feeder mechanical 25 - 80 msstatic: 15 - 40digital: 15 - 30
+ circuit breaker operating time HV / EHV: 60 ms (3 cycles) / 40 ms (2 cycles) MV up to about 80 ms (4 cycles)
+ distance relay reset time mechanical: approx. 60-100 ms static: approx. 30 ms
Determination of grading times(With numerical relays 250 ms is possible)
Energy SectorEnergy Automation© Siemens AG 2008
static: approx. 30 ms digital: approx. 20 ms.
+ errors of the distance relay internal timers mechanical: 5% of the set time, minimum 60-100 msstatic: 3% of the set time, minimum 10 msdigital: 1% of the set time, minimum 10 ms
+ distance protection starting time *) mechanical: O/C starter: 10 ms, impedance starter: 25 msstatic: O/C stater: 5 ms, impedance starter: 25 msdigital: generally 15 ms
+ safety margin (ca.) grading; mechanical-mechanical: 100 msstatic/digital-mechanical or vice versa: 75 msdigital-digital or static-static 50 ms
*) only relevant if the set relay times relate to the instant of fault detection / zone pick-up. This is the case with all Siemens relays. There are other relays where the
time is adapted by software to relate to the instant of fault inception. In the latter case the starting time has to be dropped.
HV Power Seminar Nov 2009 18
ZSC
Impedance area for forward faultsX
ϕ
Fault location Where is the fault ?
Determination of fault direction
ϕSC
Current area forforward faults
ΙSC
USC
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Page 18 November 09
R
Z'SC
Impedance area forreverse faults
ϕSC
current / voltage diagram impedance diagram
The impedance also shows the direction, but ....
ΙSC
Current area for reverse faults
HV Power Seminar Nov 2009 19
Why impedance measurement and directional determination separately?
line characteristic
fault with arc resistanceX
A B
Impedance measurement and directional determination
Energy SectorEnergy Automation© Siemens AG 2008
Page 19 November 09
direction may be determined together with the impedance measurementbut: problems may arise in certain cases (e.g. close-in faults)
separate directional determination required!
fault with arc resistancein forward direction
fault in forward direction
fault in reverse direction
close-in fault
R
HV Power Seminar Nov 2009 20
Alternatives for the directional measurement
Vf
~
~
~
~
~
~
~
~
~
ZlineZgrid relay
fault L1-E
Method 1 Method 2VL1
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Page 20 November 09
faulty phase voltage
If
VL2
VL3
voltage memory(pre-fault voltage)
If
VL2VL3
VL1
healthy-phase voltage(phase to phase voltage)
If
Vf
VL2-L3 VL2VL3
VL1 Vf
HV Power Seminar Nov 2009 21
Directional measurementSummery of all 3 methods
uRI = uL2-L3
uf = uL1
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Distance measurement
Direction measurementwith voltage memoryDirection measurementwith unfaulted voltage
if(t)uL1
if
if
if
uL2-L3
uL1
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Measuringwindow
HV Power Seminar Nov 2009 22
X
Z1
Z2
Z4
Z1B
Z5
Line
αααα
Distance zones
Inclined with line angle ϕAngle α prevents overreach of
Z1 on faults with fault resistance that are fed from both line ends
Impedance zones of digital relays (7SA6 and 7SA52)
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Page 22 November 09
R
ϕϕϕϕ LoadLoad
Z3
Fault detection
no fault detection polygon: the largest zone determines the fault detection characteristic
simple setting of load encroachment area with Rmin and ϕLoad
HV Power Seminar Nov 2009 23
0.6
0.3
grading time(s)
Ring feeder: with grading against opposite end
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Page 23 November 09
The same grading from both sides