Part 1 Distance Protection for transmission lines Gustav Steynberg © Siemens AG AG 2008 Energy Sector
Basic principle of impedance protection Localization of short-circuits by means of an impedance measurement:
fault on the protected line Z1 relay A
fault outside the protected line
Z2
relay A
selectivity Page 2
November 09
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© Siemens AG 2008 Energy Sector
Distance measurement (principle) IL1 ZL
Z L
=
R L +
j XL
Z E
= R E +j X E
IL2 IL3 IE ZE L1
L2
6 loops: loops:
L3
3 phasephase- phase phase loops and 3 phase phase-- ground ground loop loops s
phasepha se- pha phase se -loop -loop::
U L1-L2
= Z L ( I L1 - I L2)
Measured current measured voltage
The same applies to the remaining loops Page 3
November 09
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© Siemens AG 2008 06.08.97 dtgerdis3 Energy Sector
Distance measurement (principle) IL1 ZL IL2
Z L
=
R L +
j XL
Z E
= R E +j X E
IL3 IE ZE UL1 UL2 UL3 phase-ground-loop:
U L1
= Ι L1 · ( R L + j XL )- Ι E · ( R E +j X E)
Ι L1, Ι E measured current U L1
measured voltage
The same applies to the remaining loops Page 4
November 09
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© Siemens AG 2008 06.08.97 dtgerdis3 Energy Sector
Load and short-circuit impedances ZL
distance relay operating characteristic
ZLF1 ZLF2
Fault area
X
ZL D
Z
RR
ZLF1
ZF1 j
Fault in reverse direction
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j
j SC1
November 09
SC2
RF F2
ZLoad
Phase - Phase Fault
F2
ZLoad RR
RF F1
RR ≈ RF / 2 Phase - Earth Earth Fault Fault
L
RR ≈ RF /(1 + RE /RL)
R Load area
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Minimum Load Impedance: Minimum voltage 0,9 Un Un Maximum current 1,1 In ± 30° Maximum angle © Siemens AG 2008 Energy Sector
Principle of (analog) distance relaying ZS A
ISC
ZL
B
ZSC
E
U = k ⋅ U = k ⋅ I ⋅Z
.
Relay design: operation if U1< U2 i.e. ZSC< ZReplica
comparator
X Z Replica ZReplica (line replica impedance) (corresponds to the set zone reach)
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November 09
U2=k2 ⋅ ISC⋅ZReplica
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Ext. fault
Internal fault R
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Fourier analysis of measured values
Sampled signal i(t)
Processing with two orthogonal filters
I (k) = I S(k) + j ⋅ I C(k)
10,000 8,000 6,000 4,000 2,000 0,000
1 Ø I S = I (ωt) ⋅ sin ωt dt 2π Ø -∫360° I C =
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1
0
20
40
60
80
100
-2,000 -4,000 -6,000
Ø
2π Ø ∫- 360°
I (ω t) ⋅ cos ω t dt
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Fourier analysis: Filtering characteristics
Half cycle (10 ms at 50 Hz)
Full cycle (20 ms at 50 Hz) 1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
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50
100
200
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300
400
500Hz
0
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50 100
200
300
400
500Hz
© Siemens AG 2008 Energy Sector
Discrete Fourier transform (window = 1 cycle) i0
i1 i2
iN
∆t
n 0 1 2 3 ....
0 1 2 3 ...
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I S =
2 N−1 sin(ω ⋅n ⋅ ∆t )⋅in ∑ =
I C =
2 iO iN N−1 + + ∑ cos(ω ⋅n ⋅ ∆t )⋅in N 2 2 n=1
N
N
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Impedance Impedance calculatio calculation n using U- and I-phasors I-phasors
U = U ⋅ e
jϕ U
= U ⋅ e
R
jω t U
Z X
I = I ⋅ e
ϕ U = ω ⋅ t U
Z =
I
=
U ⋅ e I ⋅ e
ϕ Z = ϕ U − ϕ I
=
U I
⋅e
j (ϕ U −ϕ I )
=
U
November 09
= Z ⋅ cos ϕ Z + j ⋅ sin ϕ Z = R + j ⋅ X
I
⋅ cos(ϕ U − ϕ I ) + j R
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Z
t = 0
jϕ U
jϕ I
= I ⋅ e
jω t I
Z = Z ⋅ e
ϕ I = ⋅ t I
U
jϕ I
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U I
sin (ϕ U − ϕ I ) X
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Distance protection Impedance calculation using U- und I-phasors (principle)
+ T/2
R e{U L } =
1 ⋅ ∫ u L (t)⋅ cos(ω0 ⋅ t )dt T −T/2
I m{U L } =
1 ⋅ ∫ u L (t)⋅ sin(ω0 ⋅ t )dt T −T/2
+ T/2
R e{ I L } =
1 ⋅ ∫ i L (t)⋅ cos(ω0 ⋅ t )dt T −T/2
I m{ I L } =
1 ⋅ ∫ i L (t)⋅ sin(ω0 ⋅ t )dt T −T/2
+ T/2
+ T/2
I L = R e{ I L }+ jI m{I L }
U L = R e{U L }+ jI m{U L }
uL (t ) = U L ⋅ e
j(ω⋅t +ϕ U )
= U L ⋅ [cos(ω ⋅ t + ϕ U ) + j sin(ω ⋅ t + ϕ U )]
iL (t ) = I L ⋅ e
j(ω⋅t +ϕ I )
U L = R L ⋅ I L + jX L ⋅ I L
R e{U L } + jI m{U L } = (R L + jX L )⋅ (R e{ I L } + jI m{I L })
X L =
= I L ⋅ [cos(ω ⋅ t + ϕ I ) + j sin(ω ⋅ t + ϕ I )]
I m{U L }⋅ R e{ I L } − R e{U L }⋅ I m{ I L } 2
2
R e{ I L } + I m{ I L }
R e{U L } = R L ⋅ R e{ I L } − X L ⋅ I m{I L}
R L =
I m{U L } = X L ⋅ R e{ I L } + R L ⋅ I m{I L }
R e{U L}⋅ R e{ I L } + Im{U L} ⋅ Im{ I L} 2
2
R e{ I L } + Im{ I L}
Note: This calculation does not consider the a-periodic DC component in the measured signals
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Distance protection Fast impedance estimation using Kalman Filters t − = A ⋅ sin(ωt) + B ⋅ cos(ωt) - e τ + C ⋅ cos(ωt ) i (t )
Task:
Estimation Estimati on of the coefficients coeffic ients A, B, C on basis of measured currents and voltages
e o :
Delta =
au s k
∑ i = k - N
u - f (i) (i)
n m za on o error squares: 2
MIN
Delta =0 dA dB dC
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Delta = quality value k = sampling number N = length of data window i = variable
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Distance protection: Adaptive measuring method Jump detector Fault inception
i
0 ms
10 m s
20 m s
30 m s
40 ms
t
X Z = 50% R
Z = 80%
Estimator 2 (Gauss) (7 samples) Estimatorr 3 (Gauss) (9 samples)
R X Z = 90% R X Z = 100% R
Estimator 1 (Gauss) (5 samples)
Estimator 4 (Gauss) (11 (11 samples) s amples) Estimator 5 (Gauss) (13 samples) Normal measuring step 1 (Fourier) (2x16 samples, 5 ms shifted) Normal measuring step 2 (Fourier)
Distance protection, Typical operating time characteristic 30 25 Operating Operating time time (ms)
20 15 10 5 0 10
20
30
40
Short-circuit data: SIR = 26 f = 50 Hz Fault: L1-E 5 shots per fault case Fault inception: 0°... 90°
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November 09
50
60
70
80
90
10 0
Fault location in % zone reach
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Distance measurement Fault loop formulas Relay location
I L1
RL + j XL
I L2 I L3
Ph-Ph
VL1 VL2 VL3 I E
Phase-to-Phase Phase-to-Phase loop: Phase-to-Earth Phase-to-Earth loop:
RE + j XE
V L1− L 2 = ( R L + jX L ) ⋅ ( I L1 − I L 2 ) V L1 = I L1 ⋅ ( R L + jX L ) − I E ⋅ ( R E + jX E )
R E
R L
V L1 = R L ⋅ I L1 −
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November 09
Ph-E
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X E
X L
⋅ I E + jX L I L1 −
⋅ I E
© Siemens AG 2008 15.10.97 engerdis3 Energy Sector
Graded distance zones Z3 ∆t = grading time
time
Z2
Z1
t3 t2
t1
C D1
D2
D D3 distance
Grading rules:
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
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Determination of grading times (With numerical relays 250 ms is possible) 2nd 2nd Zone: Zone: It must must init initia iall lly y allo allow w the the 1st 1st zone one on the the neig neighb hbou ouri ring ng feed feeder er(s (s)) to clea clearr the the faul fault. t. The grading time therefore results from the addition of the following times:
operating time of the neighbouring feeder
mechanical mechanical 25 - 80 ms static: 15 - 4 40 0 digital: 15 - 30
+ circuit breaker operating time
HV / EHV: EHV: MV
+ distance relay reset time
mechanical: approx. 60-100 ms s a c: appr approx ox.. ms digital: approx. 20 ms.
60 ms (3 cycles) / 40 ms (2 cycles) up to about 80 ms (4 cycles)
+ errors of the distance relay internal timers mechanical: 5% of the set time, minimum 60-100 60-100 ms static: 3% of of the s se et time, minimum 10 ms digital: 1% of the set time, minimum 10 ms + distance protection starting time *)
mechanical: mechanical: O/C starter: starter: 10 ms, impedance impedance starter: starter: 25 ms static: O/C st stater: 5 ms, ms, impe mpedance starter: 25 ms ms digital: generally 15 ms
+ safety margin (ca.)
grading;
mec mechanical-mec mechanical: static/digital-mechanical or vice versa: digital-digital or static-static
100 ms 75 ms 50 ms
*) only relevant if the set relay times relate to the instant of f ault 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 c ase the starting time has to be dropped.
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Determination of fault direction
Fault location
Where is the fault ?
Current area for forward faults
USC ϕSC
X
Impedance area for forward faults
Ι SC
ZSC SC R
Z'SC
Ι SC Current area for reverse faults
Impedance area for reverse faults
current / voltage diagram
impedance diagram
The impedance also shows the direction, but .... Page 18
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Impedance measurement and directional determination Why impedance measurement and directional determination separately? separately? A
B
X
line characteristic au t w t arc res stance in forward direction fault in forward direction
close-in fault R fault in reverse direction
direction may be determined together with the impedance measurement but: problems may arise in certain cases (e.g. close-in faults) separate directional determination required! Page 19
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Alternatives Alternatives for the directional measurement ~
~
~
~
~
~
~
~
~
Z grid
relay
fault L1-E
Z line
Method 1 V L1 V f
V L1
Method 2
V f
V L1
I f
V L3
V f
V L2
I f
V L3
V L2-L3
faulty phase voltage I f
V L3
V L2
healthy-phase voltage (phase to phase voltage) voltage) Page 20
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V L2
voltage memory (pre-fault voltage) voltage) © Siemens AG 2008 Energy Sector
Directional measurement Summery of all 3 methods u RI
= u L2-
L3
u f
= u L1
i f(t) uL1
Measuring window
uL1
if if uL2-L3 if
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Distance measurement Direction measurement with voltage memory Direction measurement with unfaulted voltage
06.08.97 dtgerdis9
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Impedance zones of digital relays (7SA6 and 7SA52)
X
Distance zones Line
Inclined with line angle ϕ Angle α prevents overreach of Z1 on faults with fault resistance that are fed from both line ends
Z5 Z4 Z2 Z1B α
Z1
ϕ
Load
Load
R
no fault detection polygon: the largest zone determines the fault detection characteristic simple setting of load encroachment area with Rmin and ϕLoad
Z3
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Fault detection
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Ring feeder: with grading against against opposite end
grading time (s) (s) 0.6 0.3
The same grading from both sides
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Grading in a branched radial system Z3
L2
Z1
L1
L3
Z2
L4 The impedances of the Z2 and Z3 must be grading with the shortest impedance Page 24
November 09
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