Power transformer protection using chirplet
transform
ISSN 1751-8687 Received on 6th December 2015 Revised on 20th February 2016 Accepted on 4th March 2016 doi: 10.1049/iet-gtd.2015.1486 www.ietdl.orgSenthil Kumar Murugan
1✉, Sishaj Pulikottil Simon
1, Panugothu Srinivasa Rao Nayak
1,
Kinattingal Sundareswaran
1, Narayana Prasad Padhy
21Department of Electrical and Electronics Engineering, National Institute of Technology, Tiruchirappalli, India 2Department of Electrical and Electronics Engineering, Indian Institute of Technology, Roorkee, India
✉ E-mail: [email protected]
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
The power transformer plays a vital role in power system, since it handles large amounts of power between generation and distribution. Its outage rate has high impacts on power system reliability as well as power system economics. The outage rate of power transformer depends on several factors such as operating condition of power transformer, periodical maintenance, power transformer lifetime and maloperation of protection relay. However, the maloperation of the protection relay is the significant one. Therefore, it is necessary to use an appropriate protection relay to ensure the reliability. Current differential relaying method is the most commonly used approach for power transformer protection [1]. It measures the differential current in common base value and operates when differential current reaches the preset value. Whenever the internal fault occurs in the power transformer, differential current flows through the relay initiating the trip signal to the corresponding breakers. However in certain cases, the magnitude of the magnetising inrush current becomes ten times of the full load current which leads to maloperation of a differential relay [2, 3]. In addition, saturated current transformer (CT) during severe external fault (SEF) may have high-magnitude which will also cause a maloperation [4]. Therefore, discrimination between internal fault current and other disturbances during the operation of a power transformer has become a challenging task for the protection engineers.
Since the inrush current possesses a significant amount of the second-harmonic component, the conventional differential relay uses the second-harmonic restraint method to discriminate magnetising inrush current from internal fault current which is carried out through discrete Fourier transform [5]. It should be noted that CT saturation can be identified by the presence of the higher harmonic components. However, the core material of the modern power transformer produces less second-harmonic content during energisation. Therefore, accuracy of the conventional relay is not appreciable [5,6]. Also, since the internal and the inter-turn
fault currents may have harmonic content during fault inception and produce low-magnitude differential current, respectively, the sensitivity of the conventional relay is not enough to detect those faults at the earliest.
Though the newest techniques based on wavelet transform [7,8], neural network [9,10], fuzzy logic [11,12], adaptive relay [13,14] and combination of the above methods [15–17] are proposed, still the second-harmonic restraint method is widely used irrespective of its shortcomings [18]. Generally, the threshold setting for tripping condition is to be changed according to the power transformer rating (parameters). For instance, the percentage of second-harmonic content to prevent the relay operation is to be updated according to the transformer rating. Also, in case of neural network-based differential protection algorithm (DPA) [9, 10], the training data has to be created for each of the individual transformers separately. Therefore, in DPAs available in the literature, the protection system needs to be updated according to the power transformer parameters and is not system independent. Therefore, it is clear that there is a significant scope of research for developing new techniques in power transformer protection systems [19].
Recently, a new transform called chirplet transform (ChT) has found its application in fields such as instantaneous frequency estimation, classification of seismic waveforms [20, 21] etc. The ChT was introduced by Mann and Haykin in 1995 [22]. The ChT maps a mono-dimensional signal into a four-dimensional (4D) function: namely, time, scaling, chirping in frequency and chirping in time. The parameters are useful tools for properly shaping (rotating and shearing in frequency) each cell throughout the time–frequency (TF) plane. Since an additional parameter: namely, chirp rate is used along with time and frequency parameters, this paper attempts a new ChT-based method to discriminate the internal fault from the inrush currents and CT saturation cases irrespective of the current magnitude based on ChT energy distribution on the TF plane corresponding to time, frequency and chirp rate.
IET Generation, Transmission & Distribution Research Article
2
Chirplet transforms
The short-time Fourier transform (STFT) consists of a correlation of the signal with constant-size portions of a wave, whereas the wavelet transform consists of correlations with a constant-Q family of functions. The two transforms attempt to localise the signal in the TF plane. Both the modulated window of the STFT and the wavelet of the wavelet transform may be considered as ‘portions 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 family of Gaussian chirplet is given by the harmonic oscillation (wave) with a linear frequency modulation chirp
gt, f c, s, c(t) = 1 s√2p e−(1/2)(t−t/s)2ej2p[c(t−t) 2 +fc(t−t)] (1)
where t, fc, σ and c are the time-shift, centre-frequency, window
spread and chirp rate, respectively. The continuous ChT may be formulated as an inner product of the signal with the Gaussian chirplet functions as follows
Ct, f c, c= 1 −1 x(t)g∗t, f c, s, c(t) dt (2)
From (2), it can be understood that ChT is an extension of the Gabor transform, STFT and continuous wavelet transform. The time-shifting parameter ‘t’ is responsible for shifting the window along with a time axis. Here, ‘fc’ is the centre-frequency operator
to shift frequency. Here, ‘σ’ determines the window width corresponding to the frequency band. The chirp rate parameter ‘c’ causes a rotation of each cell on the TF plane as well as their shear along the frequency axis (Fig.1) [23].
The discrete version of the ChT (2) is given by [24]
C[n, k, l]= M −1 m=0 x[n − m] ∗ 1 2s p √ e −(1/2) ((M/2)−m)/s( )2 × ej2p (l/L)dmax((M /2)−m2)+ k((M/2)−m)(( )/K) (3) where n, k and l are the time, frequency and chirp rate indices, respectively. K is the number of frequencies and ‘k’ is the frequency bin index. The chirp rate index ‘l’ is ranging from 0 to L. The discrete smoothing window has M points.
3
Proposed methodology
The proposed DPA is implemented in two stages as shown in Fig.2a. In the first stage, the traditional dual slope biased restraint characteristic (BRC) is implemented with the division of zones.
The resultant of the first stage of the algorithm can make accurate decisions in three zones: namely, no-trip, trip and vulnerable zone. Since no tripping decision is possible in the vulnerable zone, further examination is needed. That is, in order to discriminate the operating conditions of the power transformer in the vulnerable zone, time domain to TF-domain transformation technique (ChT) is applied to extract some useful information in the second stage of the proposed DPA.
3.1 Division of zones on BRC plane
The first stage of the proposed DPA works based on the BRC with dual slopes whose operation is based on two quantities, i.e. IDand
IB. The IDis the difference between CT secondary current of high
voltage (HV) and low voltage (LV) sides of the power transformer in common base value. The IB is the average current flowing
through the power transformer [25,26].
The BRC plane is divided as three zones: namely, no-trip zone, HS zone and vulnerable zone as shown in Fig. 2b. The no-trip zone extends its periphery underneath the slope-1 and slope-2. Most of 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 vulnerable zone. The vulnerable zone covers a major part of the tripping region of the BRC which includes the cases of the inrush, major CT saturation and minor and moderate internal faults. Therefore, it requires an accurate discriminating algorithm to avoid maloperation. Hence, the ChT technique is applied to ID signal for
accurate discrimination in the second stage of the proposed DPA. In fact, the HS zone occupies the sliced area of the upper part of tripping region on the BRC plane which covers the area of severe faults. The required current for HS operation (IHO) is having a
constant HS threshold (IHS) till IR2 and follows the 100% slope
(HS-slope) with respect to IB. Here, the HS-slope ensures that no
CT saturation current enters into the HS zone.
3.2 Chirplet-based differential protection algorithm
The second stage of the proposed DPA uses the chirplet-based differential protection algorithm (CDPA). Applying ChT involves two steps: (i) selection of the ChT parameters such as time-shift, centre-frequency and chirp rate and (ii) decomposition of a signal into a sum of weighted chirps.
All the chirplet parameters are not fully independent to each other. Therefore, the selection process is carried out in a sequential manner 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 resolution. When the frequency domain of interest is wide, it can be explored in a logarithmic (log 10) or dyadic (log 2) basis in order to reduce computational effort. Here, the signal is sampled at the rate of 1600 Hz and thereby the maximum frequency of the sampled signal will be 800 Hz according to the Nyquist sampling
Fig. 1 Chirp wave a Mother chirplet b Its TF plane
criteria. Moreover, the frequency spectrum of power transformer transient signals will have the useful information up to fifth harmonic. Therefore, ChT centre-frequency is chosen in a dyadic base for four levels as 400, 200, 100 and 50 Hz.
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 has an equal volume on TF plane.
The dimensionless parameter, chirp rate ‘c’ allows linear frequency modulation and shaping of each cell on the TF plane. Its value permits to calculate the frequency range of the chirp around its centre-frequency ‘fck’ within the time boundaries
imposed by σ. Since the centre-frequency is chosen as a dyadic base, the frequency translation has distinct translation between
consecutive centre-frequencies. Therefore, each centre-frequency will have its own distinct chirp rate. That is, the first sample instant will have fc
k as the instantaneous frequency and the Mth
sample will have fc
k+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 v 1= 0, 12.5, 25.0, 37.5, 50[ ] v 2= 0, 6.25, 12.5, 18.75, 25.0[ ] v 3= 0, 3.125, 6.25, 9.375, 12.5[ ] v 4= 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)
mC[n, k] = L l=1 C[n, k, l] L (4)
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 mC[n] = K k=1 mC[n, k] K (5) sC[n] = 1 K − 1 K k=1 mC[n, k] − mC[n] 2 (6)
Furthermore, the z-score of mC[n, k]is calculated with respect to mC[n]
and sC[n] using (7) ZSC[n.k] = mC[n.k] − mC[n] sC[n] (7)
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 discriminate the internal faults from other disturbances. It is obvious that the domains of internal fault, inrush current and CT saturation will have its own distinct characteristics with respect to 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.
The Gaussian curve is divided into two regions with one region enveloping half energy bandwidth (HEBW), i.e. (0 dB ≥ mC[n, k] ≥
−3 dB) and other lies outside of HEBW, i.e. (mC[n, k] < −3 dB).
The HEBW is calculated by the following equation given in (8) HEBW = sC[n] · 2
2 ln 2 √
(8) The pseudo-code for the proposed DPA is given below (see Fig.3). The NE during internal fault highly concentrates on the fourth-level centre-frequency ‘fc4’, particularly on the zero chirp
rate. The energy level decreases along the chirp rate from the zero chirp rate. Since the energy distribution during the internal fault highly concentrates on fc
4, the mC[n] will be far away from mC[n, 4] .
Fig. 2 Proposed DPA implementation a Flowchart
b Division of zones on BRC plane c Gaussian energy distribution curve
Therefore, the z-score of mC[n, 4] , and both mC[n, 3] and mC[n, 2] will lie
outside HEBW and on the negative side of HEBW, respectively. In the case of inrush current, the presence of the harmonic component is higher than the internal fault, whereas the fundamental component is merely equal to the internal fault current. Hence, the NE during inrush case concentrates together on fc
4 and fc3 with the occurrence
of peak energy on zero chirp rate. Therefore, the z-score of mC[n, 4] ,
mC[n, 3] and mC[n, 2] will lie close to the positive side of HEBW
boundary, on the positive and negative sides of HEBW, respectively. In case of inrush current with the presence of less amount of second-harmonic components, the conventional DPA fails to restrict the trip. However, the NE concentration remains same even though the presence of the energy peaks (fc
4 and fc3) do
not occur at the zero chirp rate. In the case of CT saturation, the presence of high-frequency components is found to be significant. Its NE will be spread over fc
4 and fc3. Owing to the presence of
high-frequency components, mC[n, 2] , mC[n, 3] and mC[n, 4] lie within
HEBW and mC[n] is found closer to mC[n, 2] than mC[n, 3] . Therefore,
the z-score of mC[n, 2] , mC[n, 3] and mC[n, 4] will lie closer to the
positive side of HEBW, around mC[n] and negative side of HEBW,
respectively. Thus, the chirplet parameters help to discriminate the internal fault from other disturbances.
4
System simulation
The proposed DPA is tested for two systems: namely, power transformer model-1 (PTM-1), PTM-2 and power auto transformer model (PATM). The single line schematic diagram of PTM-1 consists of two similar rating transformers T1 and T2 as
shown in Fig.4. The power transformer parameters are given in the Appendix of Section 8. The system modelling is carried out using PSCAD.
4.1 System schematic
The system model consists of a single source at HV bus; two parallel connected power transformers T1and T2between HV and LV buses;
a single transmission line and a load at LV bus. Current transformers CT1and CT2are 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
implementing the proposed DPA.
4.2 Transformer modelling
The transformer model is carried out using RL matrix representation with saturated core on the HV side. The BCTRAN routine in PSCAD enables to calculate the 6 × 6 RL matrix of three-phase two-winding transformer by taking the open- and short-circuit test data of the power transformer [27]. The 6 × 6 RL matrix is modified as 7 × 7 and 8 × 8 RL matrices to simulate the turn-to-Earth fault and turn-to-turn fault, respectively [28]. The following three cases of the internal faults are simulated. (a) Faults at LV terminals with different fault resistances and fault inception angles, (b) turn-to-turn faults and (c) turn-to-Earth faults at different locations of winding and fault inception angles. For cases (b) and (c), simulations are performed at both HV and LV windings at 20–80% in steps of 20% winding location along with changes in fault inception angle of 0°–330° in steps of 30°.
Generally, the inrush current occurs during re-energising the already de-energised power transformer. The inrush current is greatly influenced by the switching angle and residual flux of the power transformer [29]. The simulation of inrush currents is performed, for various cases of switching angles and remanence, from 0° to 330° in steps of 30° and from ±10 to ±80% in steps of 10%, respectively. Also, the power transformer energisation with 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 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 PSCAD master library. Various cases of CT saturations are simulated by changing the remanent flux in CT core and the burden on the CT secondary. In addition, the CT saturations during inrush with various cases of internal faults and during inrush currents are simulated.
Besides the above simulation studies, a typical fault phenomenon called cross-country fault is also simulated to validate the proposed
Fig. 3 Pseudo-code for the proposed DPA
algorithm. A cross-country fault is one where there are two faults affecting the same circuit, but in different locations and possibly involving different phases [31]. The simulation is carried out by creating an external fault which causes an internal fault such that both external and internal exist.
5
Results and discussion
The validation of the proposed DPA is carried out for individual events of internal faults, inrush currents, CT saturations and occurrence of the above multiple events on PTM-1, PTM-2 and PATM.
5.1 Internal fault
Depending on the magnitude of the internal fault currents, ID may
fall either on vulnerable or HS zone of the BRC plane. Therefore, two typical cases of internal faults: namely, severe internal fault (SIF) and minor internal fault (MIF) are illustrated to validate tripping decision for HS zone and vulnerable zone, respectively. The ID obtained during the simulation of the SIF and MIF for
PTM-1 and PTM-2 is shown in Fig. 5a. The three-phase SIF on the LV terminal of the power transformer with a fault resistance Rf= 0.5 Ω has ID≥IHS (6.0 pu) and IB< 3.0 pu. Since IDfalls on
the HS zone, the trip command is enabled in the first stage of the 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
second stage of the DPA is enabled. The trajectories (starting with a diamond head and ending with a round head) of IDfor both PTM-1
and PTM-2 are plotted in the BRC plane and are shown in Fig.5b. The resultant of the CDPA gives the mean of NE for three levels: 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
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 paths, the energy distributions on the Gaussian curve remains in the same region. Therefore, it is obvious that the change in the z-score is independent of the fault current magnitude and represents explicitly the waveform characteristics. Similarly, the proposed DPA is able to successfully discriminate various cases of internal faults as discussed in Section 4.2.
Fig. 5 Internal fault case a IDwaveform
b IDtrajectories
5.2 Inrush
The switching on the power transformer from the HV side (primary of power transformer) before closing the LV breaker is an usual practice in a real-time power system operation. While energising the power transformer, the inrush current will always fall on the vulnerable zone of the BRC plane. Here, a typical case of the inrush current is illustrated with a remanent flux of ±80% and a 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 operating zones on the BRC plane remain same (see Fig.6b) and the current trajectories lie on the single end feed line of the vulnerable zone. Since ID lies on the vulnerable zone, the CDPA
is enabled.
The resultant of the CDPA gives the mean of NE for three levels, mC[n, 2] , mC[n, 3] and mC[n, 4] which are shown in Fig.6c. Here, the
z-score of mC[n, 4] always falls within the positive side and near to
HEBW boundary. In the worst of inrush current cases, the mC[n, 4]
may fall outside the HEBW in between the consecutive time-shift ‘t’. However, it will not fall continuously outside HEBW for all time-shifts. Also, the three tripping conditions: (a) ZSC[n, 4] ≥ sC[n] ·
2 ln 2 √
, (b) ZSC[n, 3] , 0 and (c) ZSC[n, 2] , 0
will not satisfy simultaneously which prevents the maloperation. Also, it should be noted that the z-scores of mC[n, 3] and mC[n, 2] lie
on the positive side and negative side of HEBW, respectively.
Though, the maximum inrush current of PTM-2 is less than the PTM-1, the NE distribution on the Gaussian curve remains same. This characteristic of the proposed DPA makes the relay stable during inrush. In addition, the proposed DPA is validated with the various cases of the inrush currents as discussed in Section 4.2. However, the conventional method issue the tripping command when the SHR fall below the second-harmonic setting at 0.13 and 0.14 s in PTM-1 and PTM-2, respectively.
5.3 Internal fault with inrush
When the power transformer is energised with an SIF, the ID is
highly dominated by the internal fault current than the inrush current. Fig.7a shows that the IDduring inrush with internal fault
for PTM-1 and PTM-2. The current trajectory of ID lies on the
vulnerable zone and enables the CDPA. The resultant of the CDPA gives the mean of NE for three levels: mC[n, 2] , mC[n, 3] and
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
mC[n, 2] lie on the negative side of HEBW. The z-scores of mC[n, 4] ,
mC[n, 3] and mC[n, 2] satisfy the trip condition and enables the trip
command. However, when the power transformer is energised with an MIF, the magnitude of ID is dominated by the inrush
current replicating the inrush waveform characteristics. Therefore, the CDPA can detect the internal fault, only after the inrush current decay, introducing a time delay.
Fig. 6 Inrush current case a IDwaveform
b IDtrajectories
5.4 CT saturation
CT saturation (minor and major levels) may occur due to SIF and external fault on the power transformer, which produces the transient ID in the protection relay. The distorted CT secondary
current (I1) during CT saturation is shown in Fig.8a. In case of
CT saturation due to SIF, IBwill be low, and therefore IDenters
into the HS zone enabling the tripping condition. However, CT saturation during SEF may lead IDto fall on either vulnerable or
non-trip zone. During SEF, the minor level of CT saturation will 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 area of CT saturation, i.e. IB≥IR2.To illustrate, a typical CT
saturation case due to SEF with 80% remanent flux and 5 Ω burden is considered. The trajectories of ID for PTM-1 and
PTM-2 during major CT saturation pass through the vulnerable zone, but do not enter into the HS zone (see Fig. 8b) and enabling the CDPA.
The resultant of the CDPA gives the mean of NE for three levels: mC[n, 2] , mC[n, 3] and mC[n, 4] which are shown in Fig. 8c.
Here, the z-scores of mC[n, 2] and mC[n, 4] always fall on the
positive side and negative side of HEBW, respectively. Similarly, the z-score of mC[n, 3] lie on both sides of HEBW, i.e.
around mC[n] . Therefore, the trip conditions are not satisfied and
maloperation is prevented.
5.5 Inrush with CT saturation
During energisation of the power transformer, the low-rated high-burden CT may get saturated due to inrush current. It causes the distortion in CT response, thereby increasing the magnitude of IDin irregular form as shown in Fig.9a. The waveform resembles
the characteristic of both inrush and CT saturation currents. This phenomenon leads the current trajectory to fall on the vulnerable zone enabling the CDPA.
The resultant of the CDPA gives the mean of NE for three levels: mC[n, 2] , mC[n, 3] and mC[n, 4] which are shown in Fig. 9b. Here, the
z-scores of mC[n, 3] and mC[n, 4] always fall on the positive side and
negative side of HEBW, respectively. Similarly, the z-score of mC[n, 2] lies on both sides of HEBW. Therefore, the trip conditions
are not satisfied preventing maloperation. It should be noted that the conventional method initiates false tripping for PTM-1 and PTM-2 at 0.12 and 0.11 ms, respectively.
5.6 Inrush with internal fault and CT saturation
When the power transformer is energised with an SIF, CT saturation may occur. As a result of CT saturation, the IDwaveform is distorted
as shown in Fig.10. The root mean square value of the IDforces the
current trajectory to fall on the HS zone. Therefore, the trip command is enabled at 0.105 ms in the first stage of the algorithm.
5.7 Cross-country fault
When a cross-country fault occurs in a power transformer, CT saturation leads to spurious and distorted ID waveform during
external and internal faults, respectively. Fig. 11a shows the ID
during the cross-country fault with CT saturation. The external and internal faults occur at 0.1 and 0.2 s, respectively.
The resultant of the CDPA gives the mean of NE for three levels: mC[n, 2] , mC[n, 3] and mC[n, 4] which are shown in Fig. 11b during
internal fault consequence event of external fault. Here, the z-score of mC[n, 4] always falls outside HEBW and the z-scores of
mC[n, 3] and mC[n, 2] lie on the negative side of HEBW during the
internal fault condition. Since the trip conditions are satisfied, a trip command is enabled during the internal fault. However, during the external fault, the z-scores of mC[n, 2] , mC[n, 3] and
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.
5.8 Performance comparison
The proposed DPA is compared with the conventional second-harmonic method in terms of trip time and accuracy. The trip time results in various cases of internal faults as given in Table 1. The conventional method generally introduces a time delay greater than one cycle period due to the presence of the second-harmonic component during the fault inception [6].
In the proposed DPA, the trip time for the HS and vulnerable zones varies between 5 to 10 and 10 to 15 ms, respectively. It should be noted that the overall trip time of the proposed method will not be delayed >15 ms even in the worst case of an MIF and internal fault with inrush current (Fig. 7). It is evident that the proposed DPA has a faster response time than the conventional method. The computational burden of the algorithms is also evaluated in terms of time taken to estimate their respective output
Fig. 7 Internal fault with inrush case a IDwaveform
coefficients. The time taken to process a one window sample for the proposed and conventional methods is 2 and 0.1 ms, respectively. Though the computation time of the proposed method is greater
than the conventional method, the trip time and accuracy of the proposed method is found to be advantageous. The evaluation of the computation time is carried out with Intel core i7260 central
Fig. 9 Inrush with CT saturation case a IDwaveform
b NE distribution on Gaussian curve
Fig. 8 CT saturation due to external fault case a I1waveform
b IDtrajectories
processing unit at 3.40 GHz, 3.23 GB of random access memory and MATLAB 2011b.
The accuracy of the proposed DPA and the conventional method is presented in Table2. The accuracy of the algorithm is evaluated through confusion matrix analysis [32]. Here, more detailed analysis of the accuracy of an algorithm based on the true positive
(TP), true negative, false positive and false negative is carried out. The accuracy (% μ) is defined as the ratio of TP to the total number of cases. It is observed from Table 2 that the proposed DPA for all the cases of PTM-1, PTM-2 and PATM gives a better performance when compared with the conventional method. Moreover, the inrush current and CT saturation cases are very
Table 1 Comparison of trip time
Fault type (A, B, C – HV side, a, b, c – LV side and G, g – ground)
Operating zone H –HS V – vulnerable
Trip time, ms
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. 10 IDwaveform during inrush with internal fault and CT saturation
Fig. 11 Cross-country fault case a IDwaveform
prone for maloperation in the conventional method. However, the proposed DPA offers a promising accuracy of 99.55%.
Generally, the conventional relays maloperate when IDhas a low
magnitude of the second-harmonic component in modern power transformers during energisation [6]. However, the proposed DPA discriminates the operating conditions based on the time-varying frequency characteristics irrespective of magnitude of the second-harmonic component. Also, the CDPA discriminates the disturbances with respect to energy distribution on the Gaussian curve, which is not influenced by the magnitude of ID. Moreover,
the proposed DPA does not require any threshold settings for its discrimination process. Therefore, the proposed DPA exhibits the system independent feature.
6
Conclusion
This paper concludes that the proposed DPA is a system independent approach for detecting the power transformer internal faults without any maloperation. This algorithm possesses the advantages of both BRCs in the first stage and ChT technique in the second stage. The BRC improves the speed of operation in the HS zone and non-trip zone, whereas the second stage of the proposed DPA ensures the discrimination accuracy based on time-varying frequency characteristics. Since the operating conditions of power transformers have its own distinct characteristics, with respect to the chirplet parameters irrespective of the current magnitude, the proposed DPA is robust. The simulation studies show that the proposed algorithm has high sensitivity toward MIFs, faster response during SIFs and good stability during CT saturation and inrush currents. In view of the fact that ChT is capable of analysing the power transformer transient signals, the proposed algorithm can be effectively implemented for a wide range of power transformer ratings.
7
References
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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
8
Appendix
PTM-1: 40 MVA, 132/11.5 kV, 50 Hz, Dyn11, %Z = 13.56%, magnetising current = 0.10%.
PTM-2: 50 MVA, 132/12 kV, 50 Hz, YNd1, %Z = 35.64%, magnetising current = 0.14%.
PATM: 100 MVA, 230/110/11 kV, 50 Hz, YNynd1, %Z = 11.41%, magnetising current = 0.1%.
