DIGITAL DIFFERENTIAL RELAYS FOR TRANSFORMER PROTECTION USING WALSH SERIES AND LEAST SQUARES...
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Transcript of DIGITAL DIFFERENTIAL RELAYS FOR TRANSFORMER PROTECTION USING WALSH SERIES AND LEAST SQUARES...
DIGITAL DIFFERENTIAL RELAYS DIGITAL DIFFERENTIAL RELAYS FOR TRANSFORMER PROTECTIONFOR TRANSFORMER PROTECTION USING WALSH SERIES AND LEAST USING WALSH SERIES AND LEAST
SQUARES ESTIMATORSSQUARES ESTIMATORS
Ali Reza FEREIDUNIAN*,Ali Reza FEREIDUNIAN*,
Mansooreh ZANGIABADI*, Mansooreh ZANGIABADI*,
Majid SANAYE-PASAND*, Majid SANAYE-PASAND*,
Gholam POURNAGHI**Gholam POURNAGHI**
* : ECE Dep., Faculty of Engg., University of * : ECE Dep., Faculty of Engg., University of Tehran,TehranTehran,Tehran, , IRAN IRAN
*:* Kerman Regional Electric Company (KREC), *:* Kerman Regional Electric Company (KREC), KermanKerman, , IRANIRAN
Differential ProtectionDifferential Protection
The fundamental principle of The fundamental principle of differential protection: sum of the differential protection: sum of the currents entering a device through currents entering a device through normal paths should be zero: normal paths should be zero: Kirchhoff's Current Law (KCL). Kirchhoff's Current Law (KCL).
If the currents enter (or leave) through If the currents enter (or leave) through abnormal paths, namely fault paths, abnormal paths, namely fault paths, then the sum of the currents through then the sum of the currents through normal paths will not be zero. normal paths will not be zero.
Differential Protection IllustrationDifferential Protection Illustration
6
1jj ?!0i
Problems in transformer Problems in transformer differential protection:differential protection:
inrush current, inrush current, CT inaccuracy, CT inaccuracy, CT saturation, CT saturation, over-excitation. over-excitation.
These problems produce fault trips (fault alarm These problems produce fault trips (fault alarm when there isn’t any trip) or no alarm when when there isn’t any trip) or no alarm when
there is a trip in transformer protection there is a trip in transformer protection functionfunction
DIFFERENTIAL RELAY DIFFERENTIAL RELAY IMPLEMENTATION:IMPLEMENTATION:
Current Sensor (CT)Current Sensor (CT): converts large : converts large amounts of current to small amountsamounts of current to small amounts
Data Acquisition SystemData Acquisition System: gathering data: gathering data FilterFilter: anti aliasing: anti aliasing Pre-processorPre-processor: scaling and so on : scaling and so on EstimatorEstimator: estimating peak & phase: estimating peak & phase Decision Maker (Classifier)Decision Maker (Classifier): fault/no fault: fault/no fault
Effect of CT Saturation on a Effect of CT Saturation on a Sinusoidal CurrentSinusoidal Current: :
-3 -2 -1 0 1 2 3-5
0
5Fl
ux [
V.S
]
Magnetizing Curve
0 1 2 3 4 5 6 7-1
0
1
Prim
ary
0 1 2 3 4 5 6 7-2
0
2
Time
Seco
ndar
y
Current [A]
WE HAVE USED TWO METHODS:WE HAVE USED TWO METHODS:
FOR ESTIMATING PEAK AND FOR ESTIMATING PEAK AND PHASE OF INPUT WAVE.PHASE OF INPUT WAVE.
Walsh coefficientsWalsh coefficients ::
Tt
tk
1
1
dt)T
t,K(Wal*)t(f
T
1W
)TK(Wal)TK(f2
1W
n2
1knn
Walsh Series (Ctd): Walsh Series (Ctd):
W=A * FW=A * F F=A-1*W F=A-1*W
where where F=[ F0 F1 F2 F3 F4 F5 F6 F7 F8]F=[ F0 F1 F2 F3 F4 F5 F6 F7 F8] A-1=ATA-1=AT
2
2
2
1peak1 FFI
2
4
2
3peak2 FFI
Least SquaresLeast Squares ::
A*X = BA*X = B E = A*X – B E = A*X – B
= LPI(A) * B= LPI(A) * B
LPI(A) = LPI(A) =
0X/E 2
estX
T1T A*)A*A(
Sampling:Sampling:
12 point window (for half cycle estimation) 12 point window (for half cycle estimation) or or
24 points (for full cycle estimation) 24 points (for full cycle estimation)
with with 24 sample/cycle sampling system 24 sample/cycle sampling system
Least square frequncy response for Least square frequncy response for fundamental frequencyfundamental frequency
0 500 1000 15000
0.5
1
1.5co
sine
fil
ter
0 500 1000 15000
0.5
1
1.5
frequency [HZ]
sine
fil
ter
Essential Harmonic Frequency response
The Decision SpaceThe Decision Space
0 50 100 1500
5
10
15
20
25
30
35
40
45
|Ires|
|Idif
|
Differential Relay Characteristics Curve
Fault Zone
Non-Fault Zone
Inrush Pattern RecognitionInrush Pattern Recognition
A significant second harmonic: A significant second harmonic:
Inrush Current Pattern RecognitionInrush Current Pattern Recognition
A CASE STUDYA CASE STUDY
Real recorded data:Real recorded data:
Transformer internal fault, Transformer internal fault, Transformer external fault, Transformer external fault, Transformer inrush currentTransformer inrush current
High and Low Voltage Side High and Low Voltage Side Currents for External FaultCurrents for External Fault
0 50 100 150-200
-100
0
100
200External Fault Currents, High and Low voltage Sides
Iha,
Ihb
, Ihc
Iha
Ihb
Ihc
0 50 100 150-200
-100
0
100
200
Ila,
Ilb
, Ilc
Sample (Time)
Ila
Ilb
Ilc
High and Low Voltage Side High and Low Voltage Side Currents for Internal FaultCurrents for Internal Fault
0 50 100 150-200
-100
0
100
200Internal Fault Currents, High and Low voltage Sides
Iha,
Ihb
, Ihc
Iha
Ihb
Ihc
0 50 100 150-50
0
50
Ila,
Ilb
, Ilc
Sample (Time)
Ila
Ilb
Ilc
High and Low Voltage Side High and Low Voltage Side Currents for Inrush CurrentCurrents for Inrush Current
0 50 100 150 200 250-100
-50
0
50
100Inrush Currents, High and Low voltage Sides
Iha,
Ihb
, Ihc
Iha
IhbIhc
0 50 100 150 200 250-0.04
-0.02
0
0.02
Ila,
Ilb
, Ilc
Sample (Time)
Ila
Ilb
Ilc
Three Phases Differential Currents Three Phases Differential Currents in External Faultin External Fault
0 50 100 1500
10
20
30
40
50
60
70
80Differential Currents Vs. Sample (time)
Sample (Time)
IdiffaIdiffb
Idiffc
. Three Phases Differential . Three Phases Differential Currents in Internal FaultCurrents in Internal Fault
0 50 100 1500
20
40
60
80
100
120
140
160Differential Currents Vs. Sample (time)
Sample (Time)
Idiffa
IdiffbIdiffc
Three Phases Differential Currents Three Phases Differential Currents in Inrush Currentin Inrush Current
0 50 100 150 200 2500
10
20
30
40
50
60
70
80
90Differential Currents Vs. Sample (time)
Sample (Time)
Idiffa
Idiffb
Idiffc
Decision Space in External Fault Decision Space in External Fault for three Phasesfor three Phases
0 100 200 300 400 500 600 700 8000
100
200
300Fault Zone Bound:Solid line ,Idiff Locus:Dotted line
|Idif
fa|
0 100 200 300 400 500 600 700 8000
100
200
300
|Idif
fb|
0 100 200 300 400 500 600 700 8000
100
200
300
|Idif
fc|
Irest1
Decision Space in Internal Fault for Decision Space in Internal Fault for Three PhasesThree Phases
0 50 100 150 200 250 300 3500
100
200Fault Zone Bound:Solid line ,Idiff Locus:Dotted line
|Idif
fa|
0 50 100 150 200 250 300 3500
50
100
150
|Idif
fb|
0 50 100 150 200 250 300 3500
50
100
150
|Idif
fc|
Irest1
Decision Space in Inrush Current Decision Space in Inrush Current for Three Phasesfor Three Phases
0 50 100 150 2000
50
100Fault Zone Bound:Solid line ,Idiff Locus:Dotted line
|Idif
fa|
0 50 100 150 2000
20
40
60
|Idif
fb|
0 50 100 150 2000
20
40
60
|Idif
fc|
Irest1
Second/Fundamental Harmonic Second/Fundamental Harmonic Ratio for External FaultRatio for External Fault
0 50 100 150 200 2500
0.5
1
1.5
Samples (Time)
Ires
t2/I
rest
1
Ratio of Second Harmonic to Fundamental (External Fault)
Second/Fundamental Harmonic Second/Fundamental Harmonic Ratio for Internal FaultRatio for Internal Fault
0 50 100 150 200 2500
0.5
1
1.5
Samples (Time)
Ires
t2/I
rest
1
Ratio of Second Harmonic to Fundamental (Internal Fault)
Second/Fundamental Harmonic Second/Fundamental Harmonic Ratio for Inrush CurrentRatio for Inrush Current
0 50 100 150 200 2500
0.5
1
1.5
Samples (Time)
Ires
t2/I
rest
1
Ratio of Second Harmonic to Fundamental (Inrush)
General Trip Alarm for External General Trip Alarm for External FaultFault
0 50 100 150-1
-0.5
0
0.5
1
1.5
2Tripping Command of Phases(External Fault)
Samples
Tri
p Si
gnal
No Trip Command
General Trip Alarm for Internal General Trip Alarm for Internal FaultFault
0 50 100 150-1
-0.5
0
0.5
1
1.5
2Tripping Command of Phases(Internal Fault)
Samples
Tri
p Si
gnal
Trip command begins at sample 95
General Trip Alarm for Inrush General Trip Alarm for Inrush CurrentCurrent
0 50 100 150 200 250-1
-0.5
0
0.5
1
1.5
2Tripping Command of phases (Inrush)
Samples
Tri
p Si
gnal
No Trip Command
SummarySummary
A digital differential relay for transformer A digital differential relay for transformer protection was presented. protection was presented.
Two estimator systems: Walsh series and least Two estimator systems: Walsh series and least squares algorithms were formulated and squares algorithms were formulated and designed. designed.
The differential protection decision maker The differential protection decision maker subsystem was introduced. subsystem was introduced.
Current signals harmonic components and Current signals harmonic components and second harmonic restraint concept were utilized second harmonic restraint concept were utilized in decision maker subsystem. in decision maker subsystem.
Conclusion Conclusion
In a practical case study, the designed In a practical case study, the designed relay performance was tested under three relay performance was tested under three real circumstances: external fault, internal real circumstances: external fault, internal fault and inrush current. fault and inrush current.
It was shown -using graphs and It was shown -using graphs and illustrations- that the presented relay illustrations- that the presented relay issues trip alarm for transformer internal issues trip alarm for transformer internal fault, and does not issue trip alarm for fault, and does not issue trip alarm for external fault and inrush current situations.external fault and inrush current situations.
Conclusion (Ctd)Conclusion (Ctd)
It were seen that both estimation It were seen that both estimation algorithms perform their job correctly. algorithms perform their job correctly.
Walsh series acts better than least Walsh series acts better than least squares algorithm, especially on second squares algorithm, especially on second harmonic estimation. harmonic estimation.
An anti alias filter (for example a An anti alias filter (for example a Butterworth one) will improve response of Butterworth one) will improve response of the estimator. the estimator.