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


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


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

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.

DIGITAL DIFFERENTIAL RELAYS FOR TRANSFORMER PROTECTION USING WALSH SERIES AND LEAST SQUARES...

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