IET Generation, Transmission & Distribution

Research Article

ISSN 1751-8687
Power transformer protection using chirplet Received on 6th December 2015
Revised on 20th February 2016
transform Accepted on 4th March 2016
doi: 10.1049/iet-gtd.2015.1486
www.ietdl.org

Senthil Kumar Murugan 1 ✉, Sishaj Pulikottil Simon 1, Panugothu Srinivasa Rao Nayak 1,
Kinattingal Sundareswaran 1, Narayana Prasad Padhy 2
1
Department of Electrical and Electronics Engineering, National Institute of Technology, Tiruchirappalli, India
2
Department of Electrical and Electronics Engineering, Indian Institute of Technology, Roorkee, India
✉ E-mail: senthil.pse@gmail.com

Abstract: This study presents a novel differential protection algorithm (DPA) for power transformer using chirplet
transform (ChT). The proposed method combines the features of biased restraint characteristic (BRC) of the
conventional differential relay and out-turn of ChT in a two-stage algorithm. In the first stage, the BRC plane is divided
into three zones: namely, high-set (HS), non-trip and vulnerable zones. The tripping decisions are carried out in the first
two zones based on differential and biased current. However, if the operating condition of the power transformer falls
in the vulnerable zone, then there is an ambiguity in discriminating internal fault, inrush current and current
transformer saturation cases. Therefore, in the second stage, ChT is applied to differential current signal to obtain an
energy distribution on the time-frequency plane with respect to time, frequency and chirp rate. Then, using the mean
and standard deviation of the normalised energy, power transformer operating conditions are classified. Also, most of
the DPAs available in the literature are system dependent. However, the proposed novel DPA can be effectively used
for any system. The proposed scheme is validated for two power transformer systems using PSCAD to simulate
various operating conditions and MATLAB to implement the algorithm.

1 Introduction fault currents may have harmonic content during fault inception
and produce low-magnitude differential current, respectively, the
The power transformer plays a vital role in power system, since it sensitivity of the conventional relay is not enough to detect those
handles large amounts of power between generation and faults at the earliest.
distribution. Its outage rate has high impacts on power system Though the newest techniques based on wavelet transform [7, 8],
reliability as well as power system economics. The outage rate of neural network [9, 10], fuzzy logic [11, 12], adaptive relay [13, 14]
power transformer depends on several factors such as operating and combination of the above methods [15–17] are proposed, still
condition of power transformer, periodical maintenance, power the second-harmonic restraint method is widely used irrespective
transformer lifetime and maloperation of protection relay. of its shortcomings [18]. Generally, the threshold setting for
However, the maloperation of the protection relay is the significant tripping condition is to be changed according to the power
one. Therefore, it is necessary to use an appropriate protection transformer rating (parameters). For instance, the percentage of
relay to ensure the reliability. Current differential relaying method second-harmonic content to prevent the relay operation is to be
is the most commonly used approach for power transformer updated according to the transformer rating. Also, in case of neural
protection [1]. It measures the differential current in common base network-based differential protection algorithm (DPA) [9, 10], the
value and operates when differential current reaches the preset training data has to be created for each of the individual
value. Whenever the internal fault occurs in the power transformers separately. Therefore, in DPAs available in the
transformer, differential current flows through the relay initiating literature, the protection system needs to be updated according to
the trip signal to the corresponding breakers. However in certain the power transformer parameters and is not system independent.
cases, the magnitude of the magnetising inrush current becomes Therefore, it is clear that there is a significant scope of research for
ten times of the full load current which leads to maloperation of a developing new techniques in power transformer protection
differential relay [2, 3]. In addition, saturated current transformer systems [19].
(CT) during severe external fault (SEF) may have high-magnitude Recently, a new transform called chirplet transform (ChT) has
which will also cause a maloperation [4]. Therefore, discrimination found its application in fields such as instantaneous frequency
between internal fault current and other disturbances during the estimation, classification of seismic waveforms [20, 21] etc. The
operation of a power transformer has become a challenging task ChT was introduced by Mann and Haykin in 1995 [22]. The ChT
for the protection engineers. maps a mono-dimensional signal into a four-dimensional (4D)
Since the inrush current possesses a significant amount of the function: namely, time, scaling, chirping in frequency and
second-harmonic component, the conventional differential relay chirping in time. The parameters are useful tools for properly
uses the second-harmonic restraint method to discriminate shaping (rotating and shearing in frequency) each cell throughout
magnetising inrush current from internal fault current which is the time–frequency (TF) plane. Since an additional parameter:
carried out through discrete Fourier transform [5]. It should be namely, chirp rate is used along with time and frequency
noted that CT saturation can be identified by the presence of the parameters, this paper attempts a new ChT-based method to
higher harmonic components. However, the core material of the discriminate the internal fault from the inrush currents and CT
modern power transformer produces less second-harmonic content saturation cases irrespective of the current magnitude based on
during energisation. Therefore, accuracy of the conventional relay ChT energy distribution on the TF plane corresponding to time,
is not appreciable [5, 6]. Also, since the internal and the inter-turn frequency and chirp rate.

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
2520 & The Institution of Engineering and Technology 2016
2 Chirplet transforms The resultant of the first stage of the algorithm can make accurate
decisions in three zones: namely, no-trip, trip and vulnerable zone.
The short-time Fourier transform (STFT) consists of a correlation of Since no tripping decision is possible in the vulnerable zone,
the signal with constant-size portions of a wave, whereas the wavelet further examination is needed. That is, in order to discriminate the
transform consists of correlations with a constant-Q family of operating conditions of the power transformer in the vulnerable
functions. The two transforms attempt to localise the signal in the zone, time domain to TF-domain transformation technique (ChT)
TF plane. Both the modulated window of the STFT and the is applied to extract some useful information in the second stage
wavelet of the wavelet transform may be considered as ‘portions of the proposed DPA.
of waves’. Similarly, chirplet may be considered as ‘portions of
chirps’. The mother chirplets are generated by different windowing
function, much like the mother wavelet of wavelet theory. The 3.1 Division of zones on BRC plane
family of Gaussian chirplet is given by the harmonic oscillation
The first stage of the proposed DPA works based on the BRC with
(wave) with a linear frequency modulation chirp
dual slopes whose operation is based on two quantities, i.e. ID and
IB. The ID is the difference between CT secondary current of high
1 2 j2p[c(t−t)2 +fc (t−t)]
gt, fc , s, c (t) = √



e−(1/2)(t−t/s) e (1) voltage (HV) and low voltage (LV) sides of the power transformer
s 2p in common base value. The IB is the average current flowing
through the power transformer [25, 26].
where t, fc, σ and c are the time-shift, centre-frequency, window The BRC plane is divided as three zones: namely, no-trip zone, HS
spread and chirp rate, respectively. The continuous ChT may be zone and vulnerable zone as shown in Fig. 2b. The no-trip zone
formulated as an inner product of the signal with the Gaussian extends its periphery underneath the slope-1 and slope-2. Most of
chirplet functions as follows the CT saturated cases will be plunged into this zone. The worst
case of CT saturation due to high remanent flux may enter into the
1 vulnerable zone. The vulnerable zone covers a major part of the
Ct, fc , c = x(t)gt∗, fc , s, c (t) dt (2) tripping region of the BRC which includes the cases of the inrush,
−1
major CT saturation and minor and moderate internal faults.
Therefore, it requires an accurate discriminating algorithm to avoid
From (2), it can be understood that ChT is an extension of the Gabor maloperation. Hence, the ChT technique is applied to ID signal for
transform, STFT and continuous wavelet transform. The accurate discrimination in the second stage of the proposed DPA.
time-shifting parameter ‘t’ is responsible for shifting the window In fact, the HS zone occupies the sliced area of the upper part of
along with a time axis. Here, ‘fc’ is the centre-frequency operator tripping region on the BRC plane which covers the area of severe
to shift frequency. Here, ‘σ’ determines the window width faults. The required current for HS operation (IHO) is having a
corresponding to the frequency band. The chirp rate parameter ‘c’ constant HS threshold (IHS) till IR2 and follows the 100% slope
causes a rotation of each cell on the TF plane as well as their (HS-slope) with respect to IB. Here, the HS-slope ensures that no
shear along the frequency axis (Fig. 1) [23]. CT saturation current enters into the HS zone.
The discrete version of the ChT (2) is given by [24]


M −1
1 −(1/2)(((M /2)−m)/s)
2 3.2 Chirplet-based differential protection algorithm
C[n, k, l] = x[n − m] ∗ 






√

e
m=0 2s p The second stage of the proposed DPA uses the chirplet-based
 
differential protection algorithm (CDPA). Applying ChT involves
× ej2p (l/L)dmax ((M /2)−m )+((k((M /2)−m))/K )
2
(3) two steps: (i) selection of the ChT parameters such as time-shift,
centre-frequency and chirp rate and (ii) decomposition of a signal
where n, k and l are the time, frequency and chirp rate indices, into a sum of weighted chirps.
respectively. K is the number of frequencies and ‘k’ is the All the chirplet parameters are not fully independent to each other.
frequency bin index. The chirp rate index ‘l’ is ranging from 0 to Therefore, the selection process is carried out in a sequential manner
L. The discrete smoothing window has M points. with respect to other parameters. The centre-frequency translation
parameter for the kth level ‘fck ’ is chosen so that it is possible to
cover the Fourier domain of interest with an appropriate
3 Proposed methodology resolution. When the frequency domain of interest is wide, it can
be explored in a logarithmic (log 10) or dyadic (log 2) basis in
The proposed DPA is implemented in two stages as shown in order to reduce computational effort. Here, the signal is sampled at
Fig. 2a. In the first stage, the traditional dual slope biased restraint the rate of 1600 Hz and thereby the maximum frequency of the
characteristic (BRC) is implemented with the division of zones. sampled signal will be 800 Hz according to the Nyquist sampling

Fig. 1 Chirp wave

a Mother chirplet
b Its TF plane

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
& The Institution of Engineering and Technology 2016 2521
 consecutive centre-frequencies. Therefore, each centre-frequency
will have its own distinct chirp rate. That is, the first sample
instant will have fck as the instantaneous frequency and the Mth
sample will have fck+1 as the instantaneous frequency. For
example, the chirp rate of the fourth level will have values
between 0 and 3.125 in order to vary the instantaneous frequency
from 50 to 100 Hz with respect to the sampling instant. The
choice of the chirp rate vector size depends on the trade-off
between accuracy and computation burden. Here, the size of the
chirp rate vector (vk) is chosen as five. Therefore, the chirp rate
vectors for the four levels are given as follows

v1 = [0, 12.5, 25.0, 37.5, 50]

v2 = [0, 6.25, 12.5, 18.75, 25.0]
v3 = [0, 3.125, 6.25, 9.375, 12.5]
v4 = [0, 1.5625, 3.125, 4.6875, 6.25]

The result of the ChT is represented as the energy distribution on the

TF plane corresponding to three parameters: namely, time, frequency
and chirp rate. To extract the useful information from the three
dimensional energy matrix, it undergoes a statistical evaluation
process in determining the mean and standard deviation after
normalisation of energy. Here, the mean of normalised energy
(NE) for each level mC[n,

k] is calculated using (4)

L

 C [n, k, l]
mC[n,

k] = (4)
l=1
L

where C
[n, k, l] is the NE. Then, the mean of overall NE mC[n]

and the
standard deviation of overall NE sC[n]
are calculated using (6) and
(7), respectively


K
mC[n,

k]
mC[n]

= (5)
k=1
K




































K  2

1 
sC[n]

=  m
− mC[n]

(6)
K − 1 k=1 C[n, k]

Furthermore, the z-score of mC[n,

k] is calculated with respect to mC[n]


and sC[n]

using (7)


mC[n.k]

− mC[n]


ZSC[n.k]

= (7)
sC[n]

It should be noted that the value of z-score of the second, third and
fourth (fundamental) level NEs are used as a key factor to
Fig. 2 Proposed DPA implementation discriminate the internal faults from other disturbances. It is
a Flowchart obvious that the domains of internal fault, inrush current and CT
b Division of zones on BRC plane saturation will have its own distinct characteristics with respect to
c Gaussian energy distribution curve the chirp rate. These characteristics can be deciphered from the
distribution of z-scores of each level on the Gaussian curve as in
Fig. 2c.
criteria. Moreover, the frequency spectrum of power transformer The Gaussian curve is divided into two regions with one region
transient signals will have the useful information up to fifth enveloping half energy bandwidth (HEBW), i.e. (0 dB ≥ mC[n,
k] ≥
harmonic. Therefore, ChT centre-frequency is chosen in a dyadic −3 dB) and other lies outside of HEBW, i.e. (mC[n,
k] < −3 dB).
base for four levels as 400, 200, 100 and 50 Hz.
The HEBW is calculated by the following equation given in (8)
The time-shift ‘t’ describes the position of the chirplet. It is
mainly controlled by the time interval of interest and the sampling √







rate of the signal. Time-shift has been chosen in such a way that it HEBW = sC[n]

· 2 2 ln 2 (8)
has an equal volume on TF plane.
The dimensionless parameter, chirp rate ‘c’ allows linear The pseudo-code for the proposed DPA is given below (see Fig. 3).
frequency modulation and shaping of each cell on the TF plane. The NE during internal fault highly concentrates on the
Its value permits to calculate the frequency range of the chirp fourth-level centre-frequency ‘fc4 ’, particularly on the zero chirp
around its centre-frequency ‘fck ’ within the time boundaries rate. The energy level decreases along the chirp rate from the zero
imposed by σ. Since the centre-frequency is chosen as a dyadic chirp rate. Since the energy distribution during the internal fault
base, the frequency translation has distinct translation between highly concentrates on fc4 , the mC[n]

will be far away from mC[n,

4] .

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
2522 & The Institution of Engineering and Technology 2016
 Fig. 4 Single line schematic diagram of PTM-1

4.1 System schematic

The system model consists of a single source at HV bus; two parallel

connected power transformers T1 and T2 between HV and LV buses;
a single transmission line and a load at LV bus. Current transformers
CT1 and CT2 are connected to T1 through HV and LV terminals,
respectively. It is considered that the transformer T2 also has the
similar CT connections. Since the power transformer has +30°
phase shift from HV to LV terminals, the phase correction should
be included in the LV-CT secondary terminals. Therefore, LV-CT
secondary terminals are delta connected not only to incorporate the
phase correction, but also to eliminate the zero sequence current.
As per IEEE recommendation [25], the CT ratio of HV and LV
terminals are chosen as 200/1 and 3500/1, respectively. Also, the
ratio correction for both HV-CT and LV-CT is adopted as 1.143
and 1.006, respectively. Once the phase shift and CT ratio
correction is carried out, both HV and LV sides of CT secondary
currents will be sampled at 1600 Hz. Furthermore, the sampled
signals ID and IB are exported to the MATLAB platform for
Fig. 3 Pseudo-code for the proposed DPA implementing the proposed DPA.

4.2 Transformer modelling

Therefore, the z-score of mC[n,

4] , and both mC[n,

3] and mC[n,

2] will lie
The transformer model is carried out using RL matrix representation
outside HEBW and on the negative side of HEBW, respectively. In
with saturated core on the HV side. The BCTRAN routine in
the case of inrush current, the presence of the harmonic component is
PSCAD enables to calculate the 6 × 6 RL matrix of three-phase
higher than the internal fault, whereas the fundamental component is
two-winding transformer by taking the open- and short-circuit test
merely equal to the internal fault current. Hence, the NE during
data of the power transformer [27]. The 6 × 6 RL matrix is
inrush case concentrates together on fc4 and fc3 with the occurrence
modified as 7 × 7 and 8 × 8 RL matrices to simulate the
of peak energy on zero chirp rate. Therefore, the z-score of mC[n,

4] ,
turn-to-Earth fault and turn-to-turn fault, respectively [28]. The
mC[n,

3] and mC[n,
2] will lie close to the positive side of HEBW
following three cases of the internal faults are simulated. (a) Faults
boundary, on the positive and negative sides of HEBW, at LV terminals with different fault resistances and fault inception
respectively. In case of inrush current with the presence of less angles, (b) turn-to-turn faults and (c) turn-to-Earth faults at
amount of second-harmonic components, the conventional DPA different locations of winding and fault inception angles. For cases
fails to restrict the trip. However, the NE concentration remains (b) and (c), simulations are performed at both HV and LV
same even though the presence of the energy peaks (fc4 and fc3 ) do windings at 20–80% in steps of 20% winding location along with
not occur at the zero chirp rate. In the case of CT saturation, the changes in fault inception angle of 0°–330° in steps of 30°.
presence of high-frequency components is found to be significant. Generally, the inrush current occurs during re-energising the
Its NE will be spread over fc4 and fc3 . Owing to the presence of already de-energised power transformer. The inrush current is
high-frequency components, mC[n,
2] , mC[n,

3] and mC[n,

4] lie within greatly influenced by the switching angle and residual flux of the
HEBW and mC[n]
is found closer to mC[n,

2] than mC[n,

3] . Therefore, power transformer [29]. The simulation of inrush currents is
the z-score of mC[n,
2] , mC[n,

3] and mC[n,

4] will lie closer to the performed, for various cases of switching angles and remanence,
positive side of HEBW, around mC[n]
and negative side of HEBW, from 0° to 330° in steps of 30° and from ±10 to ±80% in steps of
respectively. Thus, the chirplet parameters help to discriminate the 10%, respectively. Also, the power transformer energisation with
internal fault from other disturbances. various cases of internal faults are simulated.
Furthermore, on observing CTs in the system, CT saturation
occurs due to the presence of DC component in fault current and
remanent flux in the CT core. This condition will generate
significant distortion in the secondary current, thereby leading to
4 System simulation an increase in the ID. In the system simulation, Lucas CT model
[30] is used to simulate the CT saturation which is available in the
The proposed DPA is tested for two systems: namely, power PSCAD master library. Various cases of CT saturations are
transformer model-1 (PTM-1), PTM-2 and power auto simulated by changing the remanent flux in CT core and the
transformer model (PATM). The single line schematic diagram of burden on the CT secondary. In addition, the CT saturations
PTM-1 consists of two similar rating transformers T1 and T2 as during inrush with various cases of internal faults and during
shown in Fig. 4. The power transformer parameters are given in the inrush currents are simulated.
Appendix of Section 8. The system modelling is carried out using Besides the above simulation studies, a typical fault phenomenon
PSCAD. called cross-country fault is also simulated to validate the proposed

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
& The Institution of Engineering and Technology 2016 2523
Fig. 5 Internal fault case
a ID waveform
b ID trajectories
c NE distribution on Gaussian curve during MIF

algorithm. A cross-country fault is one where there are two faults PTM-1 and PTM-2 is shown in Fig. 5a. The three-phase SIF on
affecting the same circuit, but in different locations and possibly the LV terminal of the power transformer with a fault resistance
involving different phases [31]. The simulation is carried out by Rf = 0.5 Ω has ID ≥ IHS (6.0 pu) and IB < 3.0 pu. Since ID falls on
creating an external fault which causes an internal fault such that the HS zone, the trip command is enabled in the first stage of the
both external and internal exist. algorithm.
Also, the single-phase MIF (at 80% winding from phase end) has
ID < IHO and ID ≥ IDO. Since ID falls on the vulnerable zone, the
5 Results and discussion second stage of the DPA is enabled. The trajectories (starting with a
diamond head and ending with a round head) of ID for both PTM-1
The validation of the proposed DPA is carried out for individual events and PTM-2 are plotted in the BRC plane and are shown in Fig. 5b.
of internal faults, inrush currents, CT saturations and occurrence of The resultant of the CDPA gives the mean of NE for three levels:
the above multiple events on PTM-1, PTM-2 and PATM. mC[n,

2] , mC[n,

3] and mC[n,

4] which are shown in Fig. 5c. Here, the
z-score of mC[n,

4] always falls outside HEBW and z-scores of
5.1 Internal fault mC[n,

3] and mC[n,

2] lie on the negative side of HEBW. Even though
the current trajectories of PTM-1 and PTM-2 follow different
Depending on the magnitude of the internal fault currents, ID may paths, the energy distributions on the Gaussian curve remains in
fall either on vulnerable or HS zone of the BRC plane. Therefore, the same region. Therefore, it is obvious that the change in the
two typical cases of internal faults: namely, severe internal fault z-score is independent of the fault current magnitude and
(SIF) and minor internal fault (MIF) are illustrated to validate represents explicitly the waveform characteristics. Similarly, the
tripping decision for HS zone and vulnerable zone, respectively. proposed DPA is able to successfully discriminate various cases of
The ID obtained during the simulation of the SIF and MIF for internal faults as discussed in Section 4.2.

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
2524 & The Institution of Engineering and Technology 2016
Fig. 6 Inrush current case
a ID waveform
b ID trajectories
c NE distribution on Gaussian curve

5.2 Inrush Though, the maximum inrush current of PTM-2 is less than the
PTM-1, the NE distribution on the Gaussian curve remains same.
The switching on the power transformer from the HV side (primary This characteristic of the proposed DPA makes the relay stable
of power transformer) before closing the LV breaker is an usual during inrush. In addition, the proposed DPA is validated with the
practice in a real-time power system operation. While energising various cases of the inrush currents as discussed in Section 4.2.
the power transformer, the inrush current will always fall on the However, the conventional method issue the tripping command
vulnerable zone of the BRC plane. Here, a typical case of the when the SHR fall below the second-harmonic setting at 0.13 and
inrush current is illustrated with a remanent flux of ±80% and a 0.14 s in PTM-1 and PTM-2, respectively.
switching angle of 30°. The ID during inrush currents for PTM-1
and PTM-2 are shown in Fig. 6a.
The inrush current magnitude in the case of low remanent flux will
be always less than the case of high remanent flux. However, the 5.3 Internal fault with inrush
operating zones on the BRC plane remain same (see Fig. 6b) and
the current trajectories lie on the single end feed line of the When the power transformer is energised with an SIF, the ID is
vulnerable zone. Since ID lies on the vulnerable zone, the CDPA highly dominated by the internal fault current than the inrush
is enabled. current. Fig. 7a shows that the ID during inrush with internal fault
The resultant of the CDPA gives the mean of NE for three levels, for PTM-1 and PTM-2. The current trajectory of ID lies on the
mC[n,

2] , mC[n,

3] and mC[n,

4] which are shown in Fig. 6c. Here, the vulnerable zone and enables the CDPA. The resultant of the
z-score of mC[n,

4] always falls within the positive side and near to
CDPA gives the mean of NE for three levels: mC[n,
2] , mC[n,

3] and

HEBW boundary. In the worst of inrush current cases, the mC[n,
4]

mC[n,

4] which are shown in Fig. 7b. It is found that the z-score of
mC[n,

4] always falls outside HEBW and z-scores of mC[n,
3] and
may fall outside the HEBW in between the consecutive time-shift
‘t’. However, it will not fall continuously outside HEBW for all mC[n,

2] lie on the negative side of HEBW. The z-scores of mC[n,
4] ,

time-shifts. Also, the three tripping conditions: (a) mC[n,

3] and mC[n,

2] satisfy the trip condition and enables the trip
√






command. However, when the power transformer is energised

4] ≥ sC[n]
ZSC[n,
· 2 ln 2, (b) ZSC[n,

3] , 0 and (c) ZSC[n,

2] , 0
with an MIF, the magnitude of ID is dominated by the inrush
will not satisfy simultaneously which prevents the maloperation. current replicating the inrush waveform characteristics. Therefore,
Also, it should be noted that the z-scores of mC[n,

3] and mC[n,

2] lie
the CDPA can detect the internal fault, only after the inrush
on the positive side and negative side of HEBW, respectively. current decay, introducing a time delay.

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
& The Institution of Engineering and Technology 2016 2525
Fig. 7 Internal fault with inrush case
a ID waveform
b NE distribution on Gaussian curve

5.4 CT saturation 5.6 Inrush with internal fault and CT saturation

CT saturation (minor and major levels) may occur due to SIF and When the power transformer is energised with an SIF, CT saturation
external fault on the power transformer, which produces the may occur. As a result of CT saturation, the ID waveform is distorted
transient ID in the protection relay. The distorted CT secondary as shown in Fig. 10. The root mean square value of the ID forces the
current (I1) during CT saturation is shown in Fig. 8a. In case of current trajectory to fall on the HS zone. Therefore, the trip
CT saturation due to SIF, IB will be low, and therefore ID enters command is enabled at 0.105 ms in the first stage of the algorithm.
into the HS zone enabling the tripping condition. However, CT
saturation during SEF may lead ID to fall on either vulnerable or
non-trip zone. During SEF, the minor level of CT saturation will 5.7 Cross-country fault
fall on the non-trip zone. However, the major CT saturation will
not fall on the HS zone, since HS zone adopts HS-slope in the When a cross-country fault occurs in a power transformer, CT
area of CT saturation, i.e. IB ≥ IR2.To illustrate, a typical CT saturation leads to spurious and distorted ID waveform during
saturation case due to SEF with 80% remanent flux and 5 Ω external and internal faults, respectively. Fig. 11a shows the ID
burden is considered. The trajectories of ID for PTM-1 and during the cross-country fault with CT saturation. The external and
PTM-2 during major CT saturation pass through the vulnerable internal faults occur at 0.1 and 0.2 s, respectively.
zone, but do not enter into the HS zone (see Fig. 8b) and The resultant of the CDPA gives the mean of NE for three levels:
enabling the CDPA. mC[n,

2] , mC[n,

3] and mC[n,

4] which are shown in Fig. 11b during

The resultant of the CDPA gives the mean of NE for three internal fault consequence event of external fault. Here, the
levels: mC[n,

2] , mC[n,

3] and mC[n,

4] which are shown in Fig. 8c. z-score of mC[n,

4] always falls outside HEBW and the z-scores of
Here, the z-scores of mC[n,
2] and mC[n,

4] always fall on the
mC[n,

3] and mC[n,

2] lie on the negative side of HEBW during the

positive side and negative side of HEBW, respectively. internal fault condition. Since the trip conditions are satisfied, a
Similarly, the z-score of mC[n,

3] lie on both sides of HEBW, i.e. trip command is enabled during the internal fault. However,
around mC[n]

. Therefore, the trip conditions are not satisfied and during the external fault, the z-scores of mC[n,
2] , mC[n,

3] and
maloperation is prevented. mC[n,

4] do not satisfy the trip conditions. Therefore, the trip
command is prevented during the external fault. It should be
noted that the conventional method initiates false tripping for
PTM-2 at 0.12 ms.
5.5 Inrush with CT saturation
5.8 Performance comparison
During energisation of the power transformer, the low-rated
high-burden CT may get saturated due to inrush current. It causes The proposed DPA is compared with the conventional
the distortion in CT response, thereby increasing the magnitude of second-harmonic method in terms of trip time and accuracy. The
ID in irregular form as shown in Fig. 9a. The waveform resembles trip time results in various cases of internal faults as given in
the characteristic of both inrush and CT saturation currents. This Table 1. The conventional method generally introduces a time
phenomenon leads the current trajectory to fall on the vulnerable delay greater than one cycle period due to the presence of the
zone enabling the CDPA. second-harmonic component during the fault inception [6].
The resultant of the CDPA gives the mean of NE for three levels: In the proposed DPA, the trip time for the HS and vulnerable
mC[n,

2] , mC[n,

3] and mC[n,

4] which are shown in Fig. 9b. Here, the zones varies between 5 to 10 and 10 to 15 ms, respectively. It
z-scores of mC[n,

3] and mC[n,

4] always fall on the positive side and should be noted that the overall trip time of the proposed method
negative side of HEBW, respectively. Similarly, the z-score of will not be delayed >15 ms even in the worst case of an MIF and
mC[n,

2] lies on both sides of HEBW. Therefore, the trip conditions internal fault with inrush current (Fig. 7). It is evident that the
are not satisfied preventing maloperation. It should be noted that proposed DPA has a faster response time than the conventional
the conventional method initiates false tripping for PTM-1 and method. The computational burden of the algorithms is also
PTM-2 at 0.12 and 0.11 ms, respectively. evaluated in terms of time taken to estimate their respective output

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
2526 & The Institution of Engineering and Technology 2016
Fig. 8 CT saturation due to external fault case
a I1 waveform
b ID trajectories
c NE distribution on Gaussian curve

coefficients. The time taken to process a one window sample for the than the conventional method, the trip time and accuracy of the
proposed and conventional methods is 2 and 0.1 ms, respectively. proposed method is found to be advantageous. The evaluation of
Though the computation time of the proposed method is greater the computation time is carried out with Intel core i7260 central

Fig. 9 Inrush with CT saturation case

a ID waveform
b NE distribution on Gaussian curve

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
& The Institution of Engineering and Technology 2016 2527
Fig. 10 ID waveform during inrush with internal fault and CT saturation

Table 1 Comparison of trip time

Fault type (A, B, C – HV side, a, b, c – LV side and G, g – Operating zone H –HS V – Trip time, ms
ground) vulnerable
Proposed method Conventional method

PTM-1 PTM-2 PATM PTM-1 PTM-2 PATM

ABCG with 0.1 Ω H 5 5 5 14 13 12

ABCG with 20 Ω V 10 10 10 21 23 19
AB with 0.1 Ω H 5 5 5 15 16 14
AB with 20 Ω V 15 15 15 23 26 20
AG at 10% winding V 15 15 15 17 18 16
AG at 50% winding V 15 15 15 21 21 19
abcg with 0.1 Ω H 5 5 5 16 15 13
Abcg with 20 Ω V 10 10 10 23 24 20
ab with 0.1 Ω H 5 5 5 18 16 13
ab with 20 Ω V 10 10 10 25 23 21
ag at10% winding V 15 15 15 21 22 19
ag at 50% winding V 15 15 15 22 24 21
ABCG with 1 Ω during inrush V 10 10 10 23 21 20
AG with 1 Ω during inrush V 15 15 15 37 38 29
abcg with 1 Ω during inrush V 10 10 10 24 25 21
ag with 1 Ω during inrush V 15 15 15 43 39 35

Fig. 11 Cross-country fault case

a ID waveform
b NE distribution on Gaussian curve

processing unit at 3.40 GHz, 3.23 GB of random access memory and (TP), true negative, false positive and false negative is carried out.
MATLAB 2011b. The accuracy (% μ) is defined as the ratio of TP to the total
The accuracy of the proposed DPA and the conventional method number of cases. It is observed from Table 2 that the proposed
is presented in Table 2. The accuracy of the algorithm is evaluated DPA for all the cases of PTM-1, PTM-2 and PATM gives a better
through confusion matrix analysis [32]. Here, more detailed performance when compared with the conventional method.
analysis of the accuracy of an algorithm based on the true positive Moreover, the inrush current and CT saturation cases are very

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
2528 & The Institution of Engineering and Technology 2016
Table 2 Confusion matrix analysis
Cases Total cases Proposed DPA Conventional method

TP %μ TP %μ

PTM-1 PTM-2 PATM PTM-1 PTM-2 PATM PTM-1 PTM-2 PATM

internal fault 288 288 288 288 288 288 100 265 261 263 91.32
inrush current 96 96 96 96 96 96 100 76 75 77 79.17
internal fault with inrush 48 48 48 48 48 48 100 41 40 42 85.41
CT saturation 40 40 40 38 39 39 96.67 31 30 30 77.5
inrush and CT saturation 48 48 48 47 46 47 97.22 39 40 38 81.25
internal fault with inrush and CT saturation 48 48 48 48 48 48 100 41 41 40 84.72
cross-country fault 32 32 32 32 32 32 100 27 28 26 84.37
total cases 600 600 600 587 587 588 99.55 520 515 516 86

prone for maloperation in the conventional method. However, the 8 Ghunem, R.A., El-Shatshat, R., Ozgonenel, O.: ‘A novel selection algorithm of a
proposed DPA offers a promising accuracy of 99.55%. wavelet-based transformer differential current features’, IEEE Trans. Power Deliv.,
2014, 29, (3), pp. 1120–1126
Generally, the conventional relays maloperate when ID has a low 9 Perez, L.G., Flechsig, A.J., Meador, J.L., et al.: ‘Training an artificial neural
magnitude of the second-harmonic component in modern power network to discriminate between magnetizing inrush and internal faults’, IEEE
transformers during energisation [6]. However, the proposed DPA Trans. Power Deliv., 1994, 9, (1), pp. 434–441
discriminates the operating conditions based on the time-varying 10 Tripathy, M., Maheshwari, R.P., Verma, H.K.: ‘Probabilistic neural-network-based
frequency characteristics irrespective of magnitude of the protection of power transformer’, IET Electr. Power Appl., 2007, 1, (5),
pp. 793–798
second-harmonic component. Also, the CDPA discriminates the 11 Shin, M.C., Park, C.W., Kim, J.H.: ‘Fuzzy logic-based for large power transformer
disturbances with respect to energy distribution on the Gaussian protection’, IEEE Trans. Power Deliv., 2003, 18, (3), pp. 718–724
curve, which is not influenced by the magnitude of ID. Moreover, 12 Barbosa, D., Netto, U.C., Coury, D.V., et al.: ‘Power transformer differential
the proposed DPA does not require any threshold settings for its protection based on Clarke’s transform and fuzzy systems’, IEEE Trans. Power
discrimination process. Therefore, the proposed DPA exhibits the Deliv., 2011, 26, (2), pp. 1212–1220
13 Zhang, W., Tan, Q., Miao, S., et al.: ‘Self-adaptive transformer differential
system independent feature. protection’, IET Gener. Transm. Distrib., 2013, 7, (1), pp. 61–68
14 Dashti, H., Sanaye-Pasand, M.: ‘Power transformer protection using a multiregion
adaptive differential relay’, IEEE Trans. Power Deliv., 2014, 29, (2), pp. 777–785
15 Pan, C., Chen, W., Yun, Y.: ‘Fault diagnostic method of power transformers based
6 Conclusion on hybrid genetic algorithm evolving wavelet neural network’, IET Electr. Power
Appl., 2008, 2, (1), pp. 71–76
16 Barbosa, D., Coury, D.V., Oleskovicz, M.: ‘New approach for power transformer
This paper concludes that the proposed DPA is a system independent protection based on intelligent hybrid systems’, IET Gener. Transm. Distrib.,
approach for detecting the power transformer internal faults without 2012, 6, (10), pp. 1009–1018
any maloperation. This algorithm possesses the advantages of both 17 Shah, A.M., Bhalja, B.R.: ‘Discrimination between internal faults and other
BRCs in the first stage and ChT technique in the second stage. disturbances in transformer using the support vector machine-based protection
scheme’, IEEE Trans. Power Deliv., 2013, 28, (3), pp. 1508–1515
The BRC improves the speed of operation in the HS zone and 18 Baoming, G., Almeida, A.T., Qionglin, Z., et al.: ‘An equivalent instantaneous
non-trip zone, whereas the second stage of the proposed DPA inductance-based technique for discrimination between inrush current and
ensures the discrimination accuracy based on time-varying internal faults in power transformers’, IEEE Trans. Power Deliv., 2005, 20, (4),
frequency characteristics. Since the operating conditions of power pp. 2473–2482
transformers have its own distinct characteristics, with respect to 19 Tripathy, M., Maheshwari, R.P., Verma, H.K.: ‘Advances in transformer
protection: a review’, Electr. Power Compon. Syst., 2005, 33, (11), pp. 1203–1209
the chirplet parameters irrespective of the current magnitude, the 20 Peng, Z.K., Meng, G., Chu, F.L., et al.: ‘Polynomial chirplet transform with
proposed DPA is robust. The simulation studies show that the application to instantaneous frequency estimation’, IEEE Trans. Instrum. Meas.,
proposed algorithm has high sensitivity toward MIFs, faster 2011, 60, (9), pp. 3222–3229
response during SIFs and good stability during CT saturation and 21 Bardainne, T., Gaillot, P., Dubos-Sall, N., et al.: ‘Characterization of seismic
inrush currents. In view of the fact that ChT is capable of waveforms and classification of seismic events using chirplet atomic
decomposition. Example from the Lacq gas field (Western Pyrenees, France)’,
analysing the power transformer transient signals, the proposed Geophys. J. Int., 2006, 166, (2), pp. 699–718
algorithm can be effectively implemented for a wide range of 22 Mann, S., Haykin, S.: ‘The chirplet transform: physical considerations’, IEEE
power transformer ratings. Trans. Signal Process., 1995, 43, (11), pp. 2745–2761
23 Angrisani, L., D’Arco, M.: ‘A measurement method based on a modified version of
the chirplet transform for instantaneous frequency estimation’, IEEE Trans.
Instrum. Meas., 2002, 51, (4), pp. 704–711
24 Millioz, F., Davies, M.: ‘Sparse detection in the chirplet transform: application to
7 References FMCW radar signals’, IEEE Trans. Signal Process., 2012, 60, (6), pp. 2800–2813
25 IEEE Std. C37.91™-2008: ‘IEEE guide for protecting power transformers’, 2008
1 Guzman, A., Zocholl, S., Benmouyal, G., et al.: ‘A current based solution for 26 ‘Transformer Protection RET650, Application Manual, 1MRK 504 134-UEN,
transformer differential protection – part I: problem statement’, IEEE Trans. Product version 1.3’, (ABB Inc., 2012.)
Power Deliv., 2001, 16, (4), pp. 485–491 27 Brandwajn, V., Dommel, H.W., Dommel, I.I.: ‘Matrix representation of
2 Sonnemann, W.K., Wagner, C.L., Rockefeller, G.D.: ‘Magnetizing inrush three-phase N-winding transformers for steady-state and transient studies’, IEEE
phenomena in transformer banks’, AIEE Trans., 1958, 77, (III), pp. 884–892
Trans. Power Appl. Syst., 1982, 101, (6), pp. 1369–1378
3 Guzman, A., Zocholl, S., Benmouyal, G., et al.: ‘A current based solution for
28 Bastard, P., Bertrand, P., Meunier, M.: ‘A transformer model for winding fault
transformer differential protection – part II: relay description and evaluation’,
studies’, IEEE Trans. Power Deliv., 1994, 9, (2), pp. 690–699
IEEE Trans. Power Deliv., 2002, 17, (4), pp. 485–491
4 Gangadharan, P.K., Sidhu, T.S., Klimek, A.: ‘Influence of current transformer 29 Chiesa, N., Mork, B.A., Hoidalen, H.K.: ‘Transformer model for inrush current
saturation on line current differential protection algorithms’, IET Gener. Transm. calculations: simulations, measurements and sensitivity analysis’, IEEE Trans.
Distrib., 2007, 1, (2), pp. 270–277 Power Deliv., 2010, 25, (4), pp. 2599–2608
5 Sharp, R.L., Glassburn, W.E.: ‘A transformer differential relay with 30 Lucas, J.R., McLaren, P.G., Keerthipala, W.W.L., et al.: ‘Improved simulation
second-harmonic restraint’, AIEE Trans., 1958, 77, (III), pp. 913–918 models for current and voltage transformers in relay studies’, IEEE Trans. Power
6 Liu, P., Malik, O.P., Chen, D., et al.: ‘Improved operation of differential protection Deliv., 1992, 7, (1), pp. 152–159
of power transformers for internal faults’, IEEE Trans. Power Del., 1992, 17, (4), 31 Lin, X., Weng, H., Wang, B.: ‘Identification of cross-country fault of power
pp. 1912–1919 transformer for fast unblocking of differential protection’, IEEE Trans. Power
7 Gaouda, A.M., Salama, M.M.A.: ‘DSP wavelet-based tool for monitoring Deliv., 2009, 24, (3), pp. 1079–1086
transformer inrush currents and internal faults’, IEEE Trans. Power Deliv., 2010, 32 Ting, K.M.: ‘Confusion matrix’, in Sammut, C., Webb, G.I. (Eds.): ‘Encyclopedia
25, (3), pp. 1258–1268 of Machine Learning’ (Springer, New York, NY, USA, 2010), p. 209

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
& The Institution of Engineering and Technology 2016 2529
8 Appendix PTM-2: 50 MVA, 132/12 kV, 50 Hz, YNd1, %Z = 35.64%,
magnetising current = 0.14%.
PTM-1: 40 MVA, 132/11.5 kV, 50 Hz, Dyn11, %Z = 13.56%, PATM: 100 MVA, 230/110/11 kV, 50 Hz, YNynd1, %Z = 11.41%,
magnetising current = 0.10%. magnetising current = 0.1%.

IET Gener. Transm. Distrib., 2016, Vol. 10, Iss. 10, pp. 2520–2530
2530 & The Institution of Engineering and Technology 2016