Digital Differential protection of power transformer using Matlab
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ABSTRACT: A comparative study of algorithms for digital differential protection of power transformers is reported. The mathematical basis for each algorithm is described. The algorithms are compared as to their speed of response, computational burden and capability to distinguish between an inrush and transformer internal faultIEEE Transactions on Power Delivery 05/1988; · 1.52 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: First Page of the ArticleTransactions of the American Institute of Electrical Engineers 07/1941;  SourceAvailable from: ieeexplore.ieee.org[Show abstract] [Hide abstract]
ABSTRACT: Electric power utilities use differential relays for detecting faults in power transformers. Conventional designs of these relays use second harmonic, third harmonic or total harmonic current as a restraining quantity. This inhibits the relay operation during magnetizing inrush conditions. Initial designs of digital differential relays also used similar approaches. Most designs used the second harmonic component of the current to block trippings during the magnetizing inrush conditions. As the operating voltages and lengths of transmission lines have increased substantially, currents during internal transformer faults can contain large harmonic components. Therefore, the security of differential relays using harmonic restraint is a matter of concern. However, some recently reported algorithms do not use second harmonic restraint to block trippings during magnetizing inrush conditions. They use winding currents. In most situations, the currents in a delta winding are not readily available. The algorithms based on transformer models need equivalent circuit parameters of the transformer. The relay engineer must determine the equivalent parameters of the transformer before using these algorithms. This paper presents a new digital algorithm for detecting winding faults in singlephase and threephase transformers. The proposed algorithm does not use harmonic component of current to block trippings during magnetizing inrush conditions. It is applicable to situations where it is and it is not possible to measure winding currents. The algorithm does not require the BH curve data and takes hysteresis losses of the transformer into account. The algorithm was tested using a variety of operating conditions simulated on a digital computer.IEEE Power Engineering Review 08/1989; 9(7):4950.
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Chapter 10
© 2012 Aktaibi and Rahman, licensee InTech. This is an open access chapter distributed under the terms of
the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits
unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Digital Differential Protection of
Power Transformer Using Matlab
Adel Aktaibi and M. Azizur Rahman
Additional information is available at the end of the chapter
http://dx.doi.org/10.5772/48624
1. Introduction
Power system development is reflected in the development of all the power system devices
generators, transformers with different sizes, transmission lines and the protection
equipment. Modern power transformer is one of the most vital devices of the electric power
system and its protection is critical. For this reason, the protection of power transformers has
taken an important consideration by the researchers. One of the most effective transformer
protection methods is the differential protection algorithm. Typically, transformer
protection is focused on discriminating the internal faults from the magnetizing inrush
currents in the power transformers and overcoming the CTs related issues [1 5].
2. Conventional differential protection scheme
This scheme is based on the principle that the input power to the power transformer under
normal conditions is equal to the output power. Under normal conditions, no current will flow
into the differential relay current coil. Whenever a fault occurs, within the protected zone, the
current balance will no longer exist, and relay contacts will close and release a trip signal to
cause the certain circuit breakers (CBs) to operate in order to disconnect the faulty
equipment/part. The differential relay compares the primary and secondary side currents of
the power transformer. Current transformers (CTs) are used to reduce the amount of currents
in such a way their secondary side currents are equal. Fig. 1 shows the differential relay in its
simplest form. The polarity of CTs is such as to make the current circulate normally without
going through the relay, during normal load conditions and external faults.
Current transformers ratings are selected carefully to be matched with the power
transformer current ratings to which they are connected so as the CTs secondary side
currents are equal. However, the problem is that the CTs ratios available in the market have
standard ratings. They are not available exactly as the desired ratings. Therefore, the
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primary ratings of the CTs are usually limited to those of the available standard ratio CTs.
Commonly the primary side of the current transformer has only one turn (1) and the
secondary side has many turns depending on the transformation ratio (N) of the CT, which
is selected to match the ratings of the power transformer. Since the transformation ratio of
transformers is the ratio between the number of turns in the primary side to the number of
the turns in the secondary side. Therefore, the turn ratio of the primary current transformer
is
?
?? and the turn ratio of the secondary side current transformer is??
current of the CT located in the primary side of the power transformer is [2], [67];
???. The secondary
??=?
??
??? (1)
Where:
?? : the primary side current of the power transformer,
?? : the secondary side current of????.
?? : the number of turns in the secondary side of????
In the same manner for the CT located at the secondary side of the power transformer, the
CT secondary current is:
??=?
??
??? (2)
Where:
?? : secondary side current of the power transformer,
?? : secondary side current of????.
?? : number of turns in the secondary side of????
Figure 1. Differential protection for single phase two winding transformer
?2
??
??
?1
CT1
CT2
SinglePhase Power
Transformer
Np :Ns
??= ?1− ?2
Differential Relay
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Since the differential current is: ??= ??− ??, then, from equation (1) and equation (2) the
differential current flowing in the relay operating coil current ?? can be calculated as;
??=
??
??−???
??? (3)
If there is no internal fault occurring within the power transformer protected zone, the
currents ????????? are assumed equal in magnitude and opposite in direction. That means the
differential current???= 0 as shown in figure 2. The primary and secondary side current of
the power transformer are related to each other by equation (4);
??
??=???
??? (4)
Where:
???and???: primary and secondary side turns of the power transformer, respectively
??
?? : power transformer transformation ratio.
Figure 2. Output currents of the CTs are equal in magnitude and opposite in direction
If there is any fault in the power transformer protected zone, the currents ????????? are no
longer equal in magnitude and opposite in direction. That means the differential
current???= ??∠? has a significant value as shown in figure 3.
Figure 3. Output currents of the CTs are not equal in magnitude and not opposite in direction
The amount of current ???= ??∠? induces the relay operating coil to operate in order to send
a trip signal to the circuit breakers to isolate the transformer.
From equation (4) the secondary current with respect to the primary current of the power
transformer is [2], [67];
??=?
??×??
??
? (5)
Therefore, by manipulating equations (3) and (5),
?2 180o ?1
??
??
?2
?1
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??=
??
??−?
??×?????
??
⁄
?
?.
??=
??
???1 −?
????
⁄
????
⁄
?? (6)
? = ?1 −?
????
⁄
????
⁄
?.
From equation (6) it is obvious that the term ? must be equal to zero in order to make
??= 0
( 1 −?
????
⁄
????
⁄
) = 0
??
??=
??
?? (7)
Equation (7) gives the condition for the security of the differential relay, which means the
reciprocal of the ratio of the secondary side turns of the CTs must equal to the turns ratio of
the power transformer.
In power transformers, the input power is equal to the output power. However, the voltage
and the current in both the primary and secondary sides are different depending on
whether the transformer is step up or step down. For instance, if the transformer is step up
that means; the input voltage of the power transformer is low and the current is high,
meantime the voltage in the secondary side is high and the current is low. This action makes
both the input and output power equal. Due to this nature the CTs in the primary and the
secondary sides of the power transformer do not have same turn ratio. However, they are
carefully selected, in terms of turn ratio and magnetizing characteristics, so that they have
the same output current at normal conditions of operations. If identical CTs are not
available, the closer ones are chosen and then the mismatch between them is compensated
by using the interposing CTs. The interposing CTs can fix the mismatch in the CTs; however
they add their own burden to the output of the main CTs.
The same argument is applied for three phase (3?) transformers, except some extra issues
may appear in polyphase transformers. Figure 4 shows the schematic diagram of the 3?
differential protection.
In some cases, of 3? power transformer connections as shown in figure 5, a 30? phase shift
between primary and secondary currents is taking place. This phase shift occurs in the Y
or Y connected transformers due to the transformation of the current from Y or Y as
illustrated in the figure 4. This phase shift can be corrected easily by connecting the CTs
secondary circuits in opposite way to the way that the power transformer phases are
connected. I.e. if the transformer windings are connected in Y the CTs secondary windings
should be connected in Y and vice versa [20]. As shown in figure 4 the relation between
the linetoline voltage (???) to the phase voltage (???) can explain the phase shift between
the Y transformer connection. The following equation gives the relationship between the
linetoline voltage (???) to the phase voltage (???) [2], [3], [6], [7]:
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Digital Differential Protection of Power Transformer Using Matlab 223
???
??=????????.?
???
??=?????√?
? (8)?
????= √3?????
Y
Figure 4. Connection of differential protection of 3phase Y transformer
Figure 5. The relationship between line to line voltage and the phase to neutral voltage and the phase
shift between them which reflects the phase shift in Y or Y connected transformers
1
???
???
???
???
???
???
??
′
??
′
??
′
??
′
??
′
??′
??1
??2?
??3
30o
a
b
c
n
???
???
???
???
???
???
½???
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3. Differential protection difficulties
Generally, three main difficulties handicap the conventional differential protection. They
induce the differential relay to release a false trip signal without the existing of any fault.
These complications must be overcome in order to make the differential relay working
properly [2], [3]:
Magnetizing inrush current during initial energization,
CTs Mismatch and saturation,
Transformation ratio changes due to Tap changer.
3.1. Magnetizing inrush current
This phenomenon, the transient magnetizing inrush or the exciting current, occurs in the
primary side of the transformer whenever the transformer is switched on (energized) and
the instantaneous value of the voltage is not at?90?. At this time, the first peak of the flux
wave is higher than the peak of the flux at the steady state condition. This current appears as
an internal fault, and it is sensed as a differential current by the differential relay. The value
of the first peak of the magnetizing current may be as high as several times the peak of the
full load current. The magnitude and duration of the magnetizing inrush current is
influenced by many factors, some of these factors are [2], [6], [7];
The instantaneous value of the voltage waveform at the moment of closing CB,
The value of the residual (remnant) magnetizing flux,
The sign of the residual magnetizing flux,
The type of the iron laminations used in the transformer core,
The saturation flux density of the transformer core,
The total impedance of the supply circuit,
The physical size of the transformer,
The maximum fluxcarrying capability of the iron core laminations,
The input supply voltage level,
The effect of the inrush current on the differential relay is false tripping the transformer
without of any existing type of faults. From the principle of operation of the differential
relay, the relay compares the currents coming from both sides of the power transformer as
explained above. However, the inrush current is flowing only in the primary side of the
power transformer. So that, the differential current will have a significant value due to the
existence of current in only one side. Therefore, the relay has to be designed to recognize
that this current is a normal phenomenon and to not trip due to this current.
3.2. False trip due to C.T characteristics
The performance of the differential relays depends on the accuracy of the CTs in
reproducing their primary currents in their secondary side. In many cases, the primary
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Digital Differential Protection of Power Transformer Using Matlab 225
ratings of the CTs, located in the high voltage and low voltage sides of the power
transformer, does not exactly match the power transformer rated currents. Due to
this discrepancy, a CTs mismatch takes place, which in turn creates a small false
differential current, depending on the amount of this mismatch. Sometimes, this amount
of the differential current is enough to operate the differential relay. Therefore, CTs ratio
correction has to be done to overcome this CTs mismatch by using interposing CTs of
multi taps [8].
Another problem that may face the perfect operation of the CTs is the saturation problem.
When saturation happens to one or all CTs at different levels, false differential current
appears in the differential relay. This differential current could cause maloperation of the
differential relay. The dc component of the primary side current could produce the worst
case of CT saturation. In which, the secondary current contains dc offset and extra
harmonics [9], [10].
3.3. False trip due to tap changer
OnLoad TapChanger (OLTC) is installed on the power transformer to control
automatically the transformer output voltage. This device is required wherever there are
heavy fluctuations in the power system voltage. The transformation ratio of the CTs can be
matched with only one point of the tapchanging range. Therefore, if the OLTC is changed,
unbalance current flows in the differential relay operating coil. This action causes CTs
mismatches. This current will be considered as a fault current which makes the relay to
release a trip signal [11], [12].
4. Digital differential protection
Many digital algorithms have been used so far after the invention of the computer. These
algorithms do the same job with different accuracy and speed. The acceptable speed
according to IEEE standard for transformer protection is 100 msec. All modern algorithms
are faster than this IEEE standard. Nowadays, there are some algorithms performs their
function in less than 10 msec. In this chapter, a fast algorithm is introduced. Its speed is in
the range of 1 to 15 msec. This algorithm is based on the Fast Fourier algorithm (FFT). This
algorithm is not new, however, significant changes has been introduced to make it much
faster.
The proposed digital differential relay is designed using a simulation technique in Matlab
Simulink environment. The design is implemented to protect the power transformer against
internal faults and prevent interruption due to inrush currents.
This algorithm is built on the principle of harmoniccurrent restraint, where
the magnetizinginrush current is characterized by large harmonic components
content that are not noticeably present in fault currents. Due to the saturated condition of
the transformer iron, the waveform of the inrush current is highly distorted. The
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amplitude of the harmonics, compared with the fundamental is somewhere between 30%
to 60% and the third harmonic 10% to 30%. The other harmonics are progressively less [3]
[6], [13]. Fast Fourier Transform (???) is used to implement this approach.
In general, any periodic signal ?(?) can be decomposed to its sine and cosine components
as follows:
f(t) =a?
2+ ?C?cos(kwt)
???
?
+ S?sin(kwt)
Where: ?? is the DC component of the f (t), and???, ?? are the cosine and sine coefficients of
the frequencies present in ?(?), respectively. The discrete forms of the coefficients???, ???are
expressed in the following equations:
C?=2
N? x(n)cos?2kwt
???
N
?
???
S?=2
N? x(n)sin?2kwt
???
N
?
???
The Fourier harmonic coefficients can be expressed as [13]:
F?=??S?
?+ C?
?
Where: ??is the ??? harmonic coefficient for k = 1, 2,...,N and ?(?) is the signal ?(?) in its
discrete form. The ??? produces exactly the same results as the ???; however, the ???
is much faster than DFT, where the speed of calculation is the main factor in this process
[1316].
Fig 6 illustrates the flow chart of the designed digital Fourier Transform based logic
technique algorithm. In this algorithm the output currents of the ??? undergo over two
analysis processes, amplitude comparison process and harmonic content calculation
process. The amplitude comparison between the ??? values of the ??? output currents (
????–???? ) is in the left hand side of the flowchart, and the harmonic calculation is in the
right hand side of the flowchart.
The software is implemented according to the following steps [1517]:
Step 1. Reading data from the????.
Step 2. Data calculation, which is given as follows;
For the amplitude calculation, if the absolute difference (????–???? ) between the ??? output
currents is greater than zero the logic (1) takes place, which indicates the case of an inrush
current or an internal fault. Otherwise, the logic (0) takes place, which indicates a detection
of an external fault.
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Digital Differential Protection of Power Transformer Using Matlab 227
Figure 6. Flow chart of the proposed Digital Differential Relay Scheme
Data entry coming from C.Ts
Calculation of 1st
& 2nd Harmonics
Detection of Internal,
external fault
or increase of load
(1)
0.3F1<F2<0.7F1
Detection of inrush
(0)
Yes
No
Detection of inrush
or internal fault
(1)
Detection of
external fault or
increase of load
(0)
=
>
Detection of
Internal fault
Detection of inrush
or external fault
Yes
No
Trip signal released
No Trip
Stop simulation
START
Return to Process
The next sample
Id1 – Id2 : 0
Both logics are (1)
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In the meantime, the harmonic calculation is performed. If the percentage value of the
second harmonic amplitude is in the range of (0.3 to 0.6) of the fundamental component
amplitude, then the logic (0) occurs, that means recognition of inrush current. Otherwise, the
logic (1) takes place, which indicates a detection of an internal or external fault.
Step 3. Taking the final decision:
If the logic cases received from both cases (a & b) in step two are both (1), that indicates a
detection of an internal fault. Then a trip signal is released to stop the simulation.
For the other logic options of (0,1) means an external fault, (1,0) means an inrush current, or
(0,0) indicate an occurrence of an inrush current or an external fault, and the simulation goes
back to step two to start the calculation again for the next sample.
5. Implementation of the digital differential protection using matlab
This implementation is done using Matlab/Simulink environment. Figure 7 shows the
simulated power system built in Matlab/Simulink environment. In which a three phase,
250MVA, 60Hz, (735/315) kV, Y/ power transformer is used in this system. The contents of
each designed block are illustrated in separate figs. 8 to 12.
There are some coefficients are kept hidden for the reader to find them. These coefficients
can change the behavior of the design.
Figure 7. Matlab/Simulink Model of the proposed system
Power Transformer
CTs
CTs
Diff. Relay
fault
scope 1
scope 2
scope 3
scope 4
scope 5
Discrete,
Ts = 5e005 s.
A
B
C
a
b
c
Trip
I1I2I3I4I5I6
i
+

i
+

i
+

i

+
i

+
i

+
Iabc_B2
Iabc_B3
A
B
C
a
b
c
CB2
A
B
C
a
b
c
CB1
A
a
A1
a1
A
a
A1
a1
A
a
A1
a1
A
A1
aa1
A
A1
aa1
A
A1
aa1
A
B
C
a
b
c
A
B
C
a
b
c
N
A
B
C
A
B
C
45 kW
A
B
C
C
A
B
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Digital Differential Protection of Power Transformer Using Matlab 229
Figure 8. The differential relay block contents
Figure 9. The comparator block contents
comparatorcomparator comparator
1
Trip
6
I6
5
I5
4
I4
3
I3
2
I2
1
I1
In2
In1
Out1
In2
In1
Out1
In2
In1
Out1
i
+

i
+

i
+

i

+
i
+

i
+

i
+

i
+

i
+

1
Out1
AND
IA
Ia
y
amplitude
comparator
Id1
Id2
y2
Harmonic
Calculation
2
In1
1
In2
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Figure 10. The amplitude comparator block contents
Figure 11. The harmonic comparator block contents
Figure 12. The ratio block contents
1
y
signal
magnitude
angle
h2
signal
magnitude
angle
h1
z1
z2
y
ratio
C
1
Id1
2
ratio
1
y
<
<
<
C
C
C
2
z2
1
z1
1
y
signal rms
signal rms
<=
In1
Out2
Out1
Filter
u
2
Ia
1
IA
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Digital Differential Protection of Power Transformer Using Matlab 231
6. The results and discussions
The results will be given for different cases:
Case 1: magnetizing inrush current,
Case 2: magnetizing inrush with adding load,
Case 3: Three phase to ground fault at loaded transformer,
Case 4: Phase A to ground external fault at loaded transformer,
Other cases of different types of faults and inrush currents such as single line to ground
fault, linetoline fault, line to line to ground fault and three phase fault in both cases loaded
and unloaded transformer are illustrated.
Case 1: Magnetizing inrush current:
In this section of simulation, when the primary side CB1 is closed at 0.1 sec, only the inrush
current flows in the primary circuit of the power transformer and no current passes through
the power transformer to the secondary side as shown in Fig. 13. The harmonic comparator
shows in Fig. 14 that the value of the 2nd harmonic is higher than 0.3 of the fundamental
component.
Figure 13. Inrush currents waveforms of the three phases at the primary side of the power transformer.
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Figure 14. Harmonic comparator result: the 2nd harmonic and the fundamental component for the 1st
case.
Figure 15. Amplitude comparator results for the 1st case.
In this case the harmonic calculation part released logic (0) but the amplitude comparator
showed in Fig. 15 that the differential current is equal to the inrush current, where both
curves are drown over each other, then the amplitude comparator release logic (1). For this
logic coordination (0,1) no trip signal is released.
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Digital Differential Protection of Power Transformer Using Matlab 233
Case 2: Magnetizing inrush with adding load:
This test is carried out after the energization of the power transformer by switching ON the
CB1 at 0.1sec and CB2 at 0.3 sec from the beginning of the simulation to see the effect of load
excursion on the accuracy of the designed approach. Therefore, a 500W resistive load is
added to the system at 0.3 sec. Consequently, the inrush current disappeared and load
current started to flow in the primary and secondary circuits of the transformer according to
the transformation ratio of the power transformer as shown in Fig. 16. However, the
amplitude of the output currents of the primary and secondary CTs are equal due to the
proper selection of the transformation ratio of the primary and secondary CTs, which can
obviously noticed in Fig. 18. Where, before the time 0.3 sec the differential current was equal
to the inrush current, but after the swathing ON of the load the differential current went to
zero and the primary and secondary currants became equal.
Figure 16. Normal load current starts flowing at 0.3sec.
As shown in Fig. 17, after the switching of CB2, the value of the 2nd harmonic become lower
than 0.3 of the fundamental component. Accordingly, the harmonic calculation part released
logic (1) but the amplitude comparator released logic (0). Consequently, for this logic
coordination (1,0) no trip signal is released. Figure 18 shows the amplitude comparator
results.