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Transcript of Advanced Differential Protection
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VIII Seminrio Tcnico de Proteo e Controle28 de Junho a 1ode Julho de 2005
Rio de Janeiro RJ
Artigo: ST-3
ADVANCED POWER TRANSFORMER DIFFERENTIAL
PROTECTION
Zoran Gaji, Ivo Brni, Birger [email protected],[email protected],[email protected]
ABB Power Technologies AB, Vsters, Sweden
1. ABSTRACT
Three most typical weaknesses of the analogue
differential protection relays for power transformersand autotransformers have been:
1) Long operating time in case of heavy internalfaults followed by main CT saturation. Longdelays for heavy internal faultsthey can be of the
order of several tens of milliseconds are aconsequence of the harmonic distortion of the faultcurrents as they are seen by the differential relay.
The harmonic distortion is due to initial heavysaturation of the current transformers under faultconditions. Harmonic restrain criterion preventsimmediate operation of the differential protection.
2) Unwanted operations for external faults andtransformer inrush. Analogue differentialprotection relays for power transformers show atendency to unwanted operations for faults external
to the protected zone with the power transformerparticularly for external earth faults.
3) Bad sensitivity for low-level internal faults,
such as winding turn-to-turn faults. The low-level turn-to-turn faults typically cannot be detectedwith differential relay due to limited sensitivity ofthe relay operaterestraint characteristic. Even therelatively high sensitivity in the first section of the
differential relay characteristic of typically 30%may not be enough to detect a minor turn-to-turnfault, which initially only causes a differential
current of 10%, until it evolves into a more severefault with higher differential currents.
All these weaknesses can be successfully avoided if
the position of the fault (i.e. internal or external to
the differential protection zone) is quickly andcorrectly determined for all cases. The newprotection principle is based on the theory of
symmetrical components [1] and [2], or more exact,on the negative-sequence current theory.
Key Words: Protection, Transformer Protection,Differential Algorithm.
2. INTRODUCTION
The above-described problems can be effectivelysolved by the application of directional comparisonprinciple between the negative sequence currents
from all power transformer sides. Existence ofrelatively high negative-sequence currents is initself a proof of a disturbance on the power system,possibly a fault in the power transformer. Thenegative-sequence currents are measurableindications of abnormal conditions, similar to the
zero-sequence currents. One of the severaladvantages of the negative-sequence currentscompared to the zero-sequence currents is however
that they provide coverage for phase-to-phase andpower transformer turn-to-turn faults [4] as well,not only for earth-faults. Theoretically the negative
sequence currents do not exist during symmetrical
three-phase faults, however they do appear duringinitial stage of such faults [3] for long enough timefor the differential relay to make the properdecision. Further, the negative sequence currentsare not stopped at a power transformer of the Yd, or
Dy connection. The negative sequence currents arealways properly transformed to the other side ofany power transformer for any external disturbance.
Finally, the negative sequence currents are typicallynot affected by through-load currents.
The new algorithm for the internal/external fault
discriminator is based on the theory of symmetrical
components, or more exact, on the negative-sequence currents. Already in 1933, Wagner andEvans [1] stated that:
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected] -
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1) Source of the negative-sequence currents is atthe point of fault, (ENS= -INS* ZNS)
2)
Negative-sequence currents distribute throughthe negative-sequence network
3)
Negative-sequence currents obey the first
Kirchhoff's law
Similar statements are as well re-confirmed inreference [2].
The internal/external fault discriminator simplydetermines the position of the source of the
negative sequence currents with respect to theprotected zone. If the source of the negativesequence currents is found to be outside the zone,then the fault is external. If the source is found to be
inside the zone, the fault is internal.
The internal/external fault discriminator only worksif the protected power transformer is connected tosome load, so that currents can flow through the
protected power transformer, or at least through twowindings in case of a three-winding powertransformer. Thus, at an initial current inrush, theinternal/external fault discriminator algorithm
declares neither internal, nor external fault.
3. PRINCIPLES OF OPERATION
In order to avoid misunderstandings about what ismeant by the same direction and opposite
direction, an explanation of relay internally usedCT reference directions is shown in Figure 1.
Relay
E1S1
Z1S1
E1S2
Z1S2
IW1
IW2
IW1
IW2
Figure 1: Used reference connections of CTs, anddefinition of positive direction of currents
As shown in Figure 1 relay will always measure theprimary currents on all sides of the powertransformer with the same reference direction
towards the power transformer windings.
For an external fault the fictitious negativesequence source will be located outside thedifferential protection zone at the fault point. Thusthe negative sequence currents will enter the
healthy power transformer on the fault side, andleave it on the other side, properly transformed.According to the current direction definitions in
Figure 1, the negative sequence currents on therespective power transformer sides will have
opposite directions. In other words, the
internal/external fault discriminator sees thesecurrents as having a relative phase displacement ofexactly 180oas shown in Figure 2.
Relay
ENS
ZNSS1
ZNSS2
Yy0; 1:1INS
S1 INS
S1 INS
S2
INSS1
INSS1
Negative Sequence
Zero Potential
Figure 2:Flow of negative sequence currents forpower transformer external fault
For an internal fault (with the fictitious negativesequence source within protected power
transformer) the negative sequence currents willflow out of the faulty power transformer on both
sides. According to the definitions in Figure 1, thenegative sequence currents on the respective powertransformer sides will have the same direction. Inother words, the internal/external fault
discriminator sees these currents as having arelative phase displacement of zero electricaldegrees, as shown in Figure 3. In reality, for aninternal fault, there might be some small phase shiftbetween these two currents due to possible differentnegative sequence impedance angles of the source
equivalent circuits on the two power transformersides.
Relay
ENS
Yy0; 1:1
ZNSS1
ZNSS2
INSS2
INSS1
INSS2INSS1
Negative Sequence
Zero Potential
Figure 3: Flow of negative sequence currents for
power transformer internal fault
3.1 Negative sequence differential current
Modern numerical transformer differential relaysuse matrix equations to automatically compensatefor any power transformer vector group and turnsratio [6]. This compensation is done automaticallyin the on-line process of calculating the traditional
differential currents. It can be shown, that thenegative-sequence differential currents can be
calculated by using exactly the same matrixequations, which are used to calculate thetraditional differential currents. However, the sameequation shall be fed by the negative-sequence
currents from the two power transformer sidesinstead of individual phase currents, as shown in
the following matrix equation for a case of two-winding, Yd5 power transformer.
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2 2
_ 1 _ 2 1 1 _ 1 0 1 _
1 _ 1_ 2 _ 1 2 1 _ 1 1 0 _
3 _ 3_ 3 _ 1 1 2 _ 0 1 1 _
Id L N S IH V N S IL V N S
U r L V
Id L N S a IH V N S a IL V N S
U r H V
Id L N S a IH V N S a IL V N S
(0.1)
where:
Id_L1_NS is the negative sequence differentialcurrent in phase L1 (in HV side primary amperes).IHV_NS is HV side negative sequence current in
HV side primary amperes (phase L1 reference).ILV_NS is LV side negative sequence current inLV side primary amperes (phase L1 reference).
Ur_HV is transformer rated phase-to-phase voltageon HV side (setting parameter).Ur_LV is transformer rated phase-to-phase voltageon LV side (setting parameter).
a is the well-known complex operator for sequence
quantities; a=0,5+j*0,866.
In reality only the first negative sequence
differential current, e.g. Id_L1_NS, needs to becalculated, because the negative sequence currentsalways form the symmetrical three phase current
system on each transformer side. Consequentlythree negative sequence differential currents willalways have the same magnitude and be phase
displaced for 120 electrical degrees from eachother.
As marked in matrix equation, the first term on theright hand side of the equation, represents the totalcontribution of the negative sequence current from
HV side compensated for eventual powertransformer phase shift. The second term on theright hand side of the equation, represents the totalcontribution of the negative sequence current from
LV side compensated for eventual powertransformer phase shift and transferred to the powertransformer HV side.
When above compensation is made, then the 0-180
degree rule is again valid between negativesequence current contributions from the two sides.For example, for any unsymmetrical external fault,the respective negative sequence current
contributions from the HV and LV powertransformer sides will be exactly 180 degrees apart
and equal in magnitude, regardless the powertransformer turns ratio and phase displacement, asin example shown in Figure 4.
0.1 kA
30
210
60
240
90
270
150
330
180 0
Contribution to neg. seq. differential current from HV side
Contribution to neg. seq. differential current from LV side
0.2 kA0.3 kA
0.4 kA
"steady state"
for HV side
neg. seq. phasor
"steady state"
for LV side
neg. seq. phasor
10ms
10ms
Figure 4: Trajectories of Negative SequenceCurrent Contributions from HV and LV sides of
Yd5 power transformer during external fault
Figure 4 shows trajectories of the two separate
phasors representing the negative-sequence currentcontributions from HV and LV sides of an Yd5power transformer (e.g. after the compensation of
the transformer turns ratio and phase displacementby using previous matrix equation) for anunsymmetrical external fault. Observe that the
relative phase angle between these two phasors is180 electrical degrees at any point in time. There isnot any current transformer saturation for this case.
3.2 Internal / external fault discriminator
The internal/external fault discriminator is based onthe above-explained facts. Its operation is based onthe relative position of the two phasors representing
HV and LV negative-sequence currentcontributions, defined by matrix expression. Itpractically performs directional comparisonbetween these two phasors. First, the LV sidephasors is positioned along the zero degree line.After that the relevant position of the HV side
phasor in the complex plain is determined. Theoverall directional characteristic of theinternal/external fault discriminator is shown in
Figure 5.
Figure 5: Operating characteristic of theinternal/external fault discriminator
Neg. Seq. currentcontribution from
HV side
Neg. Seq. currentcontribution from
LV side
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In order to perform directional comparison of the
two phasors their magnitudes must be high enoughso that one can be sure that they are due to a fault.On the other hand, in order to guarantee a goodsensitivity of the internal/external fault
discriminator, the value of this minimum limit must
not be too high. Therefore this limit value, calledIminNegSeq, is settable in the range from 1% to
20% of the differential protections base current,which is in our case the power transformer HV side
rated current. The default value is 4%. Only ifmagnitudes of both negative sequence currentcontributions are above the set limit, the relative
position between these two phasors is checked. Ifeither of the negative sequence currentcontributions, which should be compared, is toosmall (less than the set value for IminNegSeq), no
directional comparison is made in order to avoid thepossibility to produce a wrong decision. This
magnitude check, as well guarantee stability of thealgorithm, when power transformer is energized.
The setting NegSeqROA represents the so-calledRelay Operate Angle, which determines theboundary between the internal and external faultregions. It can be selected in the range from 30
degrees to 90 degrees, with a step of 1 degree. Thedefault value is 60 degrees. The default settingsomewhat favours security in comparison to
dependability.
If the above condition concerning magnitudes is
fulfilled, the internal/external fault discriminatorcompares the relative phase angle between thenegative sequence current contributions from the
HV side and LV side of the power transformerusing the following two rules:
If the negative sequence currents contributionsfrom HV and LV sides are in phase, the fault isinternal (i.e. both phasors are within internal fault
region)
If the negative sequence currents contributionsfrom HV and LV sides are 180 degrees out of
phase, the fault is external (i.e. HV phasors isoutside internal fault region)
Therefore, under all external fault condition, therelative angle is theoretically equal to 180 degrees.
During internal fault, the angle shall ideally be 0degrees, but due to possible different negativesequence source impedance angles on HV and LV
side of power transformer, it may differ somewhatfrom the ideal zero value. However, during heavyfaults, CT saturation might cause the measured
phase angle to differ from 180 degrees for external,and from about 0 degrees for internal fault. See
Figure 6 for an example of a heavy internal faultwith transient CT saturation.
0.5 kA
30
210
60
240
90
270
120
300
150
330
180 0
HV side contribution t o the t otal negative sequence differential current in kA
Directional limit (within the region delimited by 60 degrees is internal fault)
1 .0 kA
1 .5 kA
definitely
an internal
fault
Internal
fault
declared
7 ms after
internal
fault
occurred
trip command
in 12 ms
excursion
from 0 degrees
due to
CT saturation
external
fault
region
35 ms
Directional Comparison Criterion: Internal fault as seen from the HV s ide
Figure 6:Operation of the internal/external faultdiscriminator for internal fault with CT saturation
4. IMPROVEMENT OF THE PROTECTION
The internal/external fault discriminator is a verypowerful and reliable supplementary criterion to thetraditional power transformer differential
protection. It detects even minor faults, with a highsensitivity and a high speed, and at the same timediscriminates with a high degree of dependability
between internal and external faults. When goodproperties of traditional power transformerdifferential protection are combined together with
advanced features of internal/external faultdiscriminator a high performance differential
protection for power transformers andautotransformers is achieved.
4.1 No extra delays at heavy internal faults
As the newly introduced internal/external faultdiscriminator has proved to be very reliable, it has
been given a great power. If, for example, a faulthas been detected, i.e. start signals set by ordinarydifferential protection, and at the same time the
internal/external fault discriminator characterisedthis fault as internal, then any eventual blocksignals produced by either the harmonic or the
waveform restraints, are ignored. This assures theresponse times of the new and advanced differentialprotection below one power system cycle (i.e.below 20ms for 50Hz system) for all internal faults.Even for heavy internal faults with severelysaturated current transformers new differential
protection operates well below one cycle becausethe harmonic distortions in the differential currentsdo not slow down the differential protection
operation. Practically, an unrestrained operation isachieved for all internal faults.
4.2 Stability against external faults
External faults happen ten to hundred times moreoften than internal ones. Many power transformer
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differential protection relays have a rather poor
stability against external faults. If a disturbance hasbeen detected and the internal/external faultdiscriminator characterised this fault as externalfault, the additional criteria are posed on the
differential relay before its trip is allowed. This
assures high stability against external faults.However, in the same time the differential relay is
still capable to trip for evolving faults. Example ofsuch evolving fault is shown in Figure 7.
0.2
0.4 kA
30
210
60
240
90
270
120
300
150
330
180 0
Magnitude of contribution from the HV (Y) side (in kA)
Directional limit (within 60 degrees is internal fault)
only
ext.
fault
ext.
and
int.
faults
int.
only
internal -
external
fault
boundary
A
B
C
internal
faults
external
faults
Figure 7:Operation for evolving fault
Point A in Figure 7 corresponds to the external faultonly. Point B corresponds to simultaneous external
and internal faults. The internal fault occurred 20msafter the external one. Point C corresponds to thesituation after the external fault has been cleared by
some other protection in 128 ms, while the internalfault persists. The advanced differential protectionwould actually operates already at point B and
disconnects the power transformer, in spite of thefact that the point B is deep in the external faultarea because of the more dominant (heavier)external fault.
4.3 Detection of minor internal faults
The internal/external fault discriminator has shownextreme capability to detect low-level faults such as
winding turn-to-turn faults. For more information
on this subject please refer to reference [4].
5. OPERATING PRINCIPLES FOR THREE-
WINDING TRANSFORMERS
The principle of the internal/external faultdiscriminator can be extended to powertransformers and autotransformers with three
windings. If all three windings are connected totheir respective networks, then three directionalcomparisons can be done, but only twocomparisons are necessary in order to positively
determine the position of the fault with respect to
the protected zone. The directional comparisons,which are possible, are: primary - secondary,
primary - tertiary, and secondary - tertiary. The rule
applied by the internal / external fault discriminator
in case of three-winding power transformers is:
If all comparisons indicate an internal fault,then it is an internal fault.
If any comparison indicates an external fault,
then it is an external fault
If one of the windings is not connected, thealgorithm automatically reduces to the two-windingversion. Nevertheless, the whole power transformer
is protected, inclusive the non-connected winding.
5.1 Example of unsymmetrical internal fault for
three-winding transformer
An internal fault L2-L3-Ground on the secondary
winding (d1) of a three-winding power transformer,connection group Yd1d5, has been simulated by
ATP [7].
0 10 20 30 40 50 60 70 80-4
-2
0
2
4
PrimarycurrentsinkA
iA
iB
iC
iN
0 10 20 30 40 50 60 70 80-50
0
50
100
SecondarycurrentsinkA
ia
ib
ic
0 10 20 30 40 50 60 70 80-5
0
5
10
Time in ms, internal fault at t = 13 ms
Inst.diff.curr.in
kA
inst diff L1inst diff L2
inst diff L3
int. fault
int. faultint. fault
int. fault
iB = primary (Y) line current L2
ib = secondary (d1) line current L2
instaneous diff. curr. L2
Figure 8:Currents for an L2-L3-E internal fault onthe secondary winding (d1) of an Yd1d5 power
transformer. Differential currents are in primary kA
The currents on the primary- and secondary sides,
and the instantaneous differential currents, areshown in Figure 8. The two directional
comparisons, made by the internal/external faultdiscriminator on the contributions to the totalnegative sequence differential current from theprimary, secondary and tertiary are shown in Figure9 and Figure 10.
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Figure 9:Internal/external fault discriminator
operation between primary and secondary windings
Figure 10:Internal/external fault discriminatoroperation between primary and tertiary windings
Obviously both of them steadily indicate that the
fault is internal. Deviations of the relative phaseangle from zero degrees in Figure 9 and Figure 10were mainly due to current transformer saturation.Severe current transformer saturation is actually the
most dangerous enemy of the internal/external faultdiscriminator. However very effective means tocounteract the negative effects of main CTsaturation have been integrated in advanceddifferential protection algorithm.
0 10 20 30 40 50 60 70 80
0
2
4
6
8
10
12
14
16
18
Time in ms, internal fault at t = 13 ms
Binary signals of the power transformer differential protection
fault
start-L1
start-L2
start-L3
trip
tripRestrained
tripUnrestrained
tripNegSeqUnrestrained
tripNegSeqSensitive
blockDueToCurr2ndHarm-L1
blockDueToCurr2ndHarm-L2
blockDueToCurr2ndHarm-L3blockDueToCurr5thHarm-L1
blockDueToCurr5thHarm-L2
blockDueToCurr5thHarm-L3
blockDueToWaveAnalysis-L1
blockDueToWaveAnalysis-L2
blockDueToWaveAnalysis-L3
InternalFault
ExternalFaultint. fault declared
trip in 15 ms
Figure 11: Binary output signals of the advanceddifferential protection during internal fault in 3-
winding power transformer.
It shall be noticed that in Figure 11 the usual
restrained differential protection (signal namedtripRestrained) was delayed due to harmonic andwaveform block criteria. Besides, this signal wasunstable (onoffon, etc). The usual unrestraineddifferential protection limit, which had been set to10 times transformer rated current, was not
exceeded due to heavy ct saturation, and thus nohelp from the unrestrained differential protectionwas obtained either. Only the new advanced
differential protection was capable to quickly detectand trip the faulty power transformer in 15 ms afterthe fault inception.
5.3 Example of two simultaneous external faults
A case with two simultaneous external faults, the
first one L1Ground fault on the secondary side andthe second fault L1Ground on the tertiary side of
an Yd1d5 power transformer, is presented here.
0.2 kA0.4 kA
30
210
60
240
90
270
120
300
150
330
180 0
Contribution to t otal neg. seq. diff. current from tertiary
Contribution to total neg. seq. diff. current from primary
Contribution to t otal neg. seq. diff. current from secondary
0 .6 kA
fromsecondary
side
from tertiary
side
Figure 12. Trajectories of the contributions to thetotal negative sequence differential current for thefirst 25 ms during two simultaneous external faults
From Figure 12 it is obvious that the new
internal/external fault discriminator will securely
0.2
0.4
0.6 kA
30
210
60
240
90
270
120
300
150
180 0
Comparison Between Contributions: Primary - Secondary
Negative sequence differential current phasor (in kA)
Directional limit (within 60 degrees is internal fault)
57 ms
after
fault
internal
fault
declared
here
external
fault
zone
external
fault
zone
0.2
0.4
0.6 kA
30
210
60
240
90
270
120
300
150
330
180 0
Negative sequence differential current phasor (in kA)
Directional limit (within 60 degrees is internal fault)
Comparison Between Contributions: Primary - Tertiary
57 ms
after
fault
trip
external
fault
zone
external
fault
zone
internal
fault
zone
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declare this fault as external for this complicated
test case.
5.4 Example of three-phase internal fault
The negative-sequence-current-based directional
principle yields a fast and reliable discriminationbetween external and internal faults. This is easy to
understand in case of unsymmetrical faults, wherethe negative sequence system is expected to exist.
But the principle is just as efficient in case ofwholly symmetrical three-phase faults as well. Thereason is that when a (symmetrical) three-phase
fault occurs, the negative sequence current sourceappears at the fault for a while, more exactly, untilthe dc components in the fault currents die out [3].As far as advanced power transformers differential
algorithm is concerned, this interval of time is longenough for the directional criterion to declare either
an internal or an external fault.
Figure 13 shows magnitudes of the negative
sequence differential current, and its components,for an absolutely symmetrical internal three-phasefault on the Y side of an Yd1d5 power transformeras they were calculated by the differential relay. It
took in this example about 20 ms for currenttransformers to reach heavy saturation. Theexistence of the false negative sequence currents
after CT saturation was not a surprise. However,much more interesting was that the negativesequence system appeared immediately following
the inception of the internal symmetrical fault.
Figure 14 shows that during 22 ms after the fault
inception, both directional tests correctly indicatedan internal fault, which was long enough time todisconnect the faulty power transformer in 14 ms
(output relay make time not included) as shown inFigure 15.
0 10 20 30 40 50 60 70 800
0.2
0.4
0.6
0.8
1
1.2
1.4The total negative sequence differential current and its three components
CurrentsinkA
(transformerratedcurrentI1=0.5
23kA)
Time in ms, internal symmetrical fault at t = 13 ms
IdifNegSeqTotal
IdifNegSeqContrPri
IdifNegSeqContrSec
IdifNegSeqContrTer
total negative
sequencedifferential
current
current transformer
saturation sets in
heavy ct saturation
3-phase
internal
fault
rated current
Figure 13:Magnitudes of the negative sequencedifferential current, and its components, for an
internal three-phase fault on an Yd1d5 transformer.
210
240
90
270
120
330
150
180
Primary - Secondary Primary - Tertiary
Magnitude of negative sequence differential current (in kA)
Directional limit (within 60 degrees is internal fault)
60
30
0
300
0
30
60
90
120
150
180
210
240270
300
330
Figure 14: Directional tests for an internal three-phase fault on an Yd1d5 transformer, first 25 ms.
0 10 20 30 40 50 60 70 80 90
0
2
4
6
8
10
12
14
16
18
Time in ms, internal fault occured at t = 13 ms
Binary output signals of the differential protection for 3-phase internal fault
fault
start-L1
start-L2
start-L3
trip
tripRestrained
tripUnrestrained
tripNegSeqUnrestrained
tripNegSeqSensitive
blockDueToCurr2ndHarm-L1blockDueToCurr2ndHarm-L2
blockDueToCurr2ndHarm-L3
blockDueToCurr5thHarm-L1
blockDueToCurr5thHarm-L2
blockDueToCurr5thHarm-L3
blockDueToWaveAnalysis-L1
blockDueToWaveAnalysis-L2
blockDueToWaveAnalysis-L3
InternalFault
ExternalFaultint. fault found, 9 ms
trip in 14 ms
12 ms
Figure 15: Output signals for an internal whollysymmetrical three-phase fault.
As shown in Figure 15 the internal fault was
declared in 9 ms, the negative sequence differentialprotection issued a trip request after 12 ms, and the
final trip command to the power transformer circuitbreakers was given in 14 ms after the faultinception by the advanced differential protection.
6. CONCLUSIONS
This paper shows, that by using advanced
numerical technology, it is now possible to protectpower transformers with advanced differentialprotection principle, which has much higheroperation speed, security and sensitivity thantraditional transformer differential protection.
Operation of new internal/external faultdiscriminator for power transformers has been
successfully tested, by using simulation filesproduced by ATP [7], disturbance recording filescaptured during independent transformerdifferential protection testing on the analogue
network simulator [5] and finally from thedisturbance recordings captured in the field. Allthese tests indicate excellent performance of the
internal/external fault discriminator for power
transformers and autotransformers. It detects evenminor faults, with a high sensitivity and a highspeed, and at the same time discriminates with a
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high degree of dependability between internal and
external faults. The only shortcomings of this newdirectional comparison algorithm are that it onlyoperates when power transformer is loaded and itdoes not provide indication of the faulty phase(s).
However, for internal faults power transformers are
always tripped three-phase, while from the captureddisturbance record at the moment of tripping the
faulty phase(s) can be identified.
7. REFERENCES
[1] C.F. Wagner, R.D. Evans, Book:Symmetrical Components", McGraw-Hill,New York & London, 1933
[2] J.L. Blackburn, Book: SymmetricalComponents for Power System Engineering,
Marcel Dekker, New York, Basel, HongKong, 1993; ISBN: 0-8247-8767-6
[3] Jonas Johansson, Master Thesis: FastEstimation of Symmetrical Components,Department of Industrial ElectricalEngineering and Automation, Lund
University, Sweden 2002.
[4] Z. Gaji, I. Brni, B. Hillstrm, I. Ivankovi"Sensitive Turn-to-Turn Fault protection forPower Transformers", CIGRE SC B5Colloquium, September 2005, Calgary-
Canada
[5] Z. Gaji, G.Z. Shen, J.M. Chen, Z.F. Xiang,"Verification of utility requirements onmodern numerical transformer protection bydynamic simulation" presented at the IEE
Conference on Developments in PowerSystem Protection, Amsterdam, Netherlands,2001
[6] F. Meki, Z. Gaji and S. Ganesan, "AdaptiveFeatures of Numerical Differential Relays,"presented at the 29th Annual Conference for
Protective Relay Engineers, Spokane,Washington, USA, October 2002
[7] ATP is the royalty-free version of theElectromagnetic Transients Program (EMTP).
For more info please visit the following websites: http://www.eeug.de/ orhttp://www.ee.mtu.edu/atp/
http://www.eeug.de/http://www.eeug.de/http://www.ee.mtu.edu/atp/http://www.ee.mtu.edu/atp/http://www.ee.mtu.edu/atp/http://www.eeug.de/