Simulated Events.
1. Introduction
Power transformers (PT) play an extremely important role on the reliability and energy supply continuity of Electric Power Systems (EPS). The inherent characteristic of power transformers introduce a number of unique problems that are not present in the protection of transmission lines, generators, motors or other power system apparatus (Horowitz & Phadke, 2008). When PT internal faults occur, immediate disconnection of the faulted transformer is necessary to avoid extensive damage and/or preserve power system stability and power quality (Harlow, 1999). Currently, percentage differential protection is a common practice for power transformer protection. However, nonlinearities in the transformer core, the current transformer (CT) core or in both, cause a substantial differential current to flow when there is no fault. Thus, these false differentials currents can cause a percentage differential relay miss trip. To mitigate some of these problems the differential relays are equipped with harmonic restraint, where the magnitudes of the second and fifth harmonic component are compared with the fundamental frequency component to discriminate internal faults from magnetizing inrush currents and transformer over-excitation, respectively (Anderson, 1999). However, performance limitations are still reported even for such phenomena. In order to overcome such limitation, a significant number of relaying formulations have been proposed (Abed & Mohammed, 2007; Eissa, 2005; Faiz & Lotfi-Fard, 2006; Mao & Aggarwal, 2000; Megahed et al., 2008; Morate & Nicoletti, 1999; Ngaopitakkul & Kunakorn, 2006; Saleh & Rahman, 2005. Thomas & Ozgönenel, 2007; Wang & Butler, 2001; Wiszniewski & Kasztenny, 1995; Zaman et al., 1996). These formulations are based on finite elements, artificial neural networks, fuzzy systems, dynamical principal components analysis, wavelet transforms (WTs) and hybrid systems. However, all mentioned relaying formulations have hard to design parameters, which make real life construction difficult.
In detecting faults in EPS and, specifically PT, frequency analysis is required so that the transient signal components can be isolated. This process helps to identify particular phenomena that generated the transient signals. It should be noted that the waveforms associated with electromagnetic transients are typically non-periodic in nature, containing both high-frequency oscillations as short duration pulses superimposed on low frequency signals. Still, need to know the fault occurrence instant encourages the application of techniques with precise time and frequency resolution.
In this chapter, a novel percentage differential relaying algorithm for three-phase power transformers protection based on Discrete Wavelet Transforms (DWT) is presented. The proposed algorithm’s formulation uses logical decision criteria based on wavelets coefficient spectral energy variation to identify and discriminate correctly external faults, inrush currents and incipient internal transformer faults. In order to analyze the proposed algorithms efficiency, it was built in MATLAB® platform (Matlab, 2010) and tested with simulated fault cases under BPA’s ATP/EMTP software (ATP/EMTP, 2002).
2. Wavelet Transform (WT)
The Wavelet Transform (WT) theory is based on signal analysis using varying scales in the time and frequency domain. Formalization was carried out in the 80s, based on the generalization of familiar concepts. The wavelet term was introduced by French geophysicist Jean Morlet. The seismic data analyzed by Morlet exhibit frequency component that changed rapidly over time, for which the Fourier Transform was not appropriate as an analysis tool. Thus, with the help of theoretical physicist Croatian Alex Grossmann, Morlet introduced a new transform which allows the high-frequency events identification with a better temporal resolution (Polikar, 1999).
Faulted EPS signals are associated with fast electromagnetic transients, are typically non-periodic and with high-frequency oscillations. This characteristic present a problem for traditional Fourier analysis because its assumes a periodic signal and a wide-band signal requires more dense sampling and longer time periods to maintain good resolution in the low frequencies (Robertson et al., 1996). Thus WT is a powerful tool in the power system transient phenomena analysis. It has the ability to extract information from the transient signals simultaneously in both time and frequency domains and has replaced the Fourier analysis in many applications (Phadke & Thorp, 2009).
2.1. Continuous Wavelet Transform (CWT)
The Short-Time Fourier Transform (STFT) of the continuous signal
In the FT case the base function are complex sinusoid
The main characteristic of the WT is that it uses a variable window to scan the frequency spectrum, increasing the temporal resolution of the analysis. The wavelets are represented by:
In the equation (1), the constant
where
Thus, it is evident that WT has a zero rating, property that increases the degrees of freedom, allowing the introduction of the dilation parameter of the window (Sarkar & Su, 1998).
The Continuous Wavelet Transform (CWT) of the continuous signal
where the scale factor
The WT coefficient is an expansion and a particular shift represents how well the original signal
2.2. Discrete Wavelet Transform (DWT)
2.2.1. Why is DWT needed?
Although the discretized continuous wavelet transform enables the computation of the continuous wavelet transform by computers, it is not a true discrete transform. As a matter of fact, the wavelet series is simply a sampled version of the CWT, and the information it provides is highly redundant as far as the reconstruction of the signal is concerned. This redundancy, on the other hand, requires a significant amount of computation time and resources. The Discrete Wavelet Transform (DWT), on the other hand, provides sufficient information both for analysis and synthesis of the original signal, with a significant reduction in the computation time. The DWT is considerably easier to implement when compared to the CWT. The basic concepts of the DWT will be introduced in this section along with its properties and the algorithms used to compute it (Polikar, 1999).
2.2.2. DWT definition
The redundancy of information and the enormous computational effort to calculate all possible translations and scales of CWT restricts its use. An alternative to this analysis is the discretization of the scale and translation factors, which leads to the DWT. There are several ways to introduce the concept of DWT, the main are the decomposition bands and the decomposition pyramid (or Multi-Resolution Analysis -MRA), developed in the late 70's (Rioul & Vetterli, 1991). The DWT of the continuous signal
where
Thus,
The DWT of a discrete signal
where
The mother wavelet may be dilated and translated discretely by selecting the scaling and translation parameters
2.3. Multi-Resolution Analysis (MRA)
The problems of temporal and frequency resolution found in the analysis of signals with the STFT (best resolution in time at the expense of a lower resolution in frequency and vice-versa) can be reduced through a Multi-Resolution Analysis (MRA) provided by WT. The temporal resolutions,
where
The main difference between DWT and STFT is the time-scaling parameter. The result is geometric scaling, i.e. 1, 1/
The CWT follows exactly these concepts and adds the simplification of the scale, where all the impulse responses of the filter bank are defined as dilated versions of a mother wavelet
(Rioul & Vetterli, 1991). The CWT is a correlation between a wavelet at different scales and the signal with the scale (or the frequency) being used as a measure of similarity. The CWT is computed by changing the scale of the analysis window, shifting the window in time, multiplying by the signal, and integrating over all times. In the discrete case, filters of different cut-off frequencies are used to analyze the signal at different scales. The signal is passed through a series of high pass filters to analyze the high frequencies, and it is passed through a series of low pass filters to analyze the low frequencies. Thus, the DWT can be implemented by multistage filter bank named MRA (Mallat, 1999), as illustrated on Fig. 2. The Mallat algorithm consists of series of high-pass and the low-pass filters that decompose the original signal
The resolution of the signal, which is a measure of the amount of detail information in the signal, is changed by the filtering operations, and the scale is changed by up-sampling and down-sampling (sub-sampling) operations. Sub-sampling a signal corresponds to reducing the sampling rate, or removing some of the samples of the signal. On the other hand, up-sampling a signal corresponds to increasing the sampling rate of a signal by adding new samples to the signal.
The procedure starts with passing this signal
A half band low-pass filter removes all frequencies that are above half of the highest frequency in the signal. For example, if a signal has a maximum of 1000 Hz component, then half band low-pass filtering removes all the frequencies above 500 Hz. However, it should always be remembered that the frequency unit for discrete time signals is radians.
After passing the signal through a half band low-pass filter, half of the samples can be eliminated according to the Nyquist’s rule. Simply discarding every other sample will subsample the signal by two, and the signal will then have half the number of points. The scale of the signal is now doubled. Note that the low-pass filtering removes the high frequency information, but leaves the scale unchanged. Only the sub-sampling process changes the scale. Resolution, on the other hand, is related to the amount of information in the signal, and therefore, it is affected by the filtering operations. Half band low-pass filtering removes half of the frequencies, which can be interpreted as losing half of the information. Therefore, the resolution is halved after the filtering operation. Note, however, the sub-sampling operation after filtering does not affect the resolution, since removing half of the spectral components from the signal makes half the number of samples redundant anyway. Half the samples can be discarded without any loss of information.
This procedure can mathematically be expressed as (Polikar, 1999):
The decomposition of the signal into different frequency bands is simply obtained by successive highpass and lowpass filtering of the time domain signal. The original signal
where
2.4. Energy and power of discrete signal
The total energy of a discrete signal
and the average power is defined as:
For a periodic signal of fundamental period
3. Differential protection of power transformers using DWT
3.1. Percentage differential protection
Differential protection schemes are widely used by electric companies to protect EPS equipments. This relaying technique is applied on power transformers protection, buses protection, and large motors and generators protection among others (Anderson, 1999). Considering power transformers rated above 10 MVA, the percentage differential relay with harmonic restraint is the most used protection scheme (Horowitz & Phadke, 2008). The percentage differential relay can be implemented with an over-current relay (R) and operation (o) and restriction coils (r), as illustrated on Fig. 3, connected between Current Transformer (CTs).
Under normal operating conditions or external faults, the CTs secondary currents,
The relay identifies an internal fault when the differential current exceeds the percentage value
3.2. Proposed protection algorithm using DWT
A change in the spectral energy of the wavelets components of the current differential is noted when different electrical events (external faults, internal faults and/or inrush current) occur on the power transformers (Megahed et al., 2008). In this sense, the discrimination criterion of the proposed protection algorithm in this work is based in the spectral energy level generated by the electrical event type. The flow chart of the proposed algorithm is presented on Fig. 4.
In the disturbance detection (BLOCK 1) the activation current is calculated. The activation current is calculated for each phase through the percentage characteristic
where
In the disturbance identification (BLOCK 2) the three-phase differential currents are initially processed through a DWT implemented as filter bank. After, a restraint index
where
The proposed algorithm was implemented in MATLAB® platform (Matlab, 2010). Fig. 5 presents the graphical interface developed with three input block: 1) selecting the disturbance type; 2) selecting of the wavelet analysis characteristics; 3) analyzed results outputs.
4. Case study
Fig. 6. illustrates the studied electrical power system. The studied system consists of:
Generator: 13.8 kV, 30 MVA, 50 Hz;
Power Transformer (PT): 35 MVA, 13.8/138 kV, Yg–∆;
Current Transformers (CT) with 1200/5 and 200/5 turns ratio;
Transmission line: with a length of 100 km;
Variable Load of 3, 10 or 25 MVA all with a 0.92 power factor.
The switches shown in Fig. 6, S1 and S4, are used to simulate the energization operation of the PT. In this phenomenon the transformer is connected without load. The switch S3 simulates external faults through a fault resistor Rf. The closing of the switch S2 simulates an internal faults to the PT in both the primary and secondary windings.
4.1. Types of analyzed events
The proposed algorithm operates through three-phase differential currents. The simulations performed are presented on Table 1:
Nº |
|
|
Different energization cases, comprising different switching inception angles (0°, 30°, 60° and 90°) by closing the switch S1 in the Low Voltage (LV) side. |
|
Internal faults in both primary and secondary sides of the transformer. These faults were simulated with a fault resistance Rf values of 0 Ω, 0.01 Ω, 10 Ω, and 100 Ω. |
|
Several cases of external faults with fault resistances Rf values: 0 Ω, 0.01 Ω, 10 Ω, and 100 Ω. |
|
Faults applied between the PT and the CTs. |
|
Energizing the PT with the presence of internal faults |
|
Energizing the PT with the presence of external faults. |
5. Simulation and analysis result
In order to evaluate the proposed protection algorithm efficiency, internal faults and transient inrush currents have been simulated. For each simulation, the proposed algorithm used different mother wavelets to evaluate accuracy and speed. The mother wavelets tested in this study were: Daubechies (Db), Symlet (Sy), Haar (Hr), Coiflet (Coif) and Morlet (Mo).
5.1. Transient signal and fault current simulation
The transient signal (inrush current) and fault current simulated are concentrated in the following situations:
Fig. 7 presents an energization case. Part (a) illustrates the voltages in the secondary side of the PT. Part (b) the differential current are presented.
Fig. 8 illustrates a case of energization with internal fault (concurrent event). The internal fault was simulated in the A phase with fault resistance Rf = 10 Ω.
Fig. 9 illustrates a case of external fault removal. The faults occurring at 3 km to the PT on the transmission line.
5.2. Algorithm proposed analysis
Depending on the voltage angle in which the transformer is connected to the EPS, its residual flux can cause transient inrush currents which are correctly discriminated by the proposed protection algorithm.
Fig. 10 shows the algorithm response to a transient inrush current. Fig. 10(a) presents the inrush current in differential circuit of the power transformer. Fig. 10(b) shows the first detail of the DWT decomposition where a maximum number of three windows analyses are implemented on detail coefficient of the WT. Three windows analyses (Nw) are necessary to guarantee a correct decision by the methodology. The window analysis is moving 1/4 cycle for each restraint index (
5.3. Obtained results
The magnitude and shape of inrush current changes depending on several factors such as energization instant, core remnant flux, saturation of CTs and non-linearities of transformer core. However, in this work only the switching instant was evaluated. 12 energization cases were simulated for each switching angle and evaluated with the following mother wavelet: Daubechies (Db), Harr (Hr), Symlet (Sy), Coiflet (Coif) and Morlet (Mo).
Table 2 shows the proposed algorithm performance in correct operation number (OC[%]) for transformer energization. In test development, the Daubechies mother wavelets presented the best performance for all switching angles with 97.11% correct diagnosis. The Harr mother wavelet type appeared as the least efficient with 18.75% of correct diagnosis. Furthermore, at 90° switching angle presented the worse energization condition because it was the least correctly identified (56.66%). However, others switches angles tested did presented a significant effect on the inrush current identification.
Switch Angle |
|
OC [%] | ||||
|
|
|
|
|
||
|
12 | 7 | 12 | 12 | 12 | 91.66 |
|
12 | 2 | 12 | 12 | 12 | 83.33 |
|
12 | 0 | 10 | 12 | 10 | 73.33 |
|
11 | 0 | 9 | 8 | 6 | 56.66 |
OC [%] | 97.11 | 18.75 | 89.58 | 91.66 | 85.41 |
Table 3 summarizes the methodology efficiency in percentage of correct operation of the proposed algorithm for different internal faults types and different fault resistances (RF). The performance was evaluated considering a constant load of 10 MVA on the end of the transmission line. There was an important drop in accuracy of the protection algorithm to internal fault cases in faults type A-B and A-B-C. However, the discrimination of faults type A-G (phase-ground) and A-B-G showed little sensitivity to Rf variation.
It was noted that the mother wavelet Daubechies showed an excellent performance and high efficiency in discrimination of simulated disturbances. This is because the decomposition solutions using Daubechies wavelet function are orthogonal and no marginal overlaps will happen during the signal reconstruction. The mother wavelet Symlet and Coiflet presented a satisfactory performance with a greater efficiency than the Morlet type. On the other hand, the wavelet Haar type did not achieved a good performance, presenting many inaccuracies in the discrimination of all simulated disturbances.
To verify the wavelet function type effect on the proposed formulation, 3 wavelets function were compared with conventional protection methodology based in Fourier Analysis (FTT). The wavelet type used in the comparison study were: Daubechies, Haar and Symlet. The Fig. 11 shows the test results and the comparison between the proposed algorithm, a conventional percentage differential protection relay. It can be observed that the conventional technique based on FTT obtained a lower efficiency than the proposed algorithm.
Mother Wavelet |
|
|
|||
|
|
|
|
||
|
0.01 | 100.0 | 100.0 | 100.0 | 100.0 |
10 | 100.0 | 100.0 | 100.0 | 100.0 | |
50 | 99.22 | 98.28 | 100.0 | 100.0 | |
100 | 98.90 | 97.66 | 98.44 | 100.0 | |
|
0.01 | 82.36 | 81.65 | 83.15 | 84.15 |
10 | 76.32 | 76.54 | 75.18 | 75.36 | |
50 | 72.65 | 71.54 | 73.21 | 73.26 | |
100 | 70.18 | 69.32 | 70.15 | 70.15 | |
|
0.01 | 99.38 | 100.0 | 100.0 | 100.0 |
10 | 98.75 | 98.75 | 99.68 | 100.0 | |
50 | 97.81 | 97.65 | 98.75 | 98.75 | |
100 | 97.18 | 97.03 | 98.12 | 95.75 | |
|
0.01 | 100.0 | 100.0 | 100.0 | 100.0 |
10 | 99.38 | 98.75 | 100.0 | 97.34 | |
50 | 98.75 | 91.25 | 97.50 | 92.81 | |
100 | 97.65 | 87.66 | 96.87 | 88.28 | |
|
0.01 | 97.21 | 96.54 | 94.65 | 94.36 |
10 | 96.24 | 95.64 | 95.63 | 94.62 | |
50 | 95.12 | 96.35 | 94.32 | 93.12 | |
100 | 90.15 | 84.71 | 85.63 | 89.34 |
6. Conclusions
In this chapter a novel formulation for differential protection of three-phase transformers, based on the differential current transient analysis is proposed. The algorithms performance is evaluated using fault simulations in a typical electrical system under BPA’s ATP/EMTP software. The algorithm considers the different magnitudes assumed by the DWT coefficients, induced by internal faults and inrush currents. The wavelet decomposition allows good time and frequency precision to characterize the transient events.
The proposed algorithm is comprehensible and feasible for implementation showing a correct operation with the adaptive threshold value. The obtained results through various simulated fault cases and non-fault disturbances showed that the proposed algorithm is robust and accurate.
Based on these tests and after critical evaluation of the proposed protection algorithm important conclusions could be observed:
The use of Wavelet Transforms to analyze differential signals produced by transient phenomenon proved to be an effective and robust tool.
The variation of wavelets spectral energy coefficients proved to be an effective measure of discrimination.
The proposed algorithm presents a perspective of practical application given the simplicity under which the methodology is based.
The performance comparison made between the wavelet types: Daubechies (Db), Harr (Hr), Symlet (Sy), Coiflet (Coif) and Morlet (Mo), showed that the use of the Daubechies wavelet is the most appropriated.
The comparative study with the conventional differential protection algorithm showed that the proposed formulation presents greater performance.
References
- 1.
Abed N. Y. . Mohammed O. A. 2007 Modeling and Characterization of Transformer Internal Faults Using Finite Element and Discrete Wavelet Transforms. ,43 4 April 2007),1425 1428 0018-9464 - 2.
Aggarwal R. Kim C. H. 2000 Wavelet Transform in Power System : part 1-gene ral introduction to the wavelet transform. ,14 2 April 2007),81 87 - 3.
Anderson P. M. 1999 Power System Protection Wiley-Interscience: IEEE Press with McGraw-Hill.0-78033-427-2 Jersey, USA. - 4.
Bentley P. M. Mc Donnell J. T. E. 1994 Wavelets Transform: an introduction. ,6 4 August 1994),175 186 0954-0695 - 5.
Bonneville Power Administration. 2002 . Retrieved from: http://www.emtp.rog/. - 6.
Daubechies I. 1990 The Wavelet Transform, Time-Frequency Localization and Signal Analysis. ,36 5 September 1990),961 1005 0018-9448 - 7.
Eissa M. M. 2005 A Novel Digital Directional Transformer Protection Technique Based on Wavelet Packet 20 3 July 2005),1830 1836 0885-8977 - 8.
Faiz J. Lotfi-Fard S. 2006 A Novel Wavelet-Based Algorithm for Discrimination of Internal Faults From Magnetizing Inrush Currents in Power Transformer. ,21 4 October 2006),1989 1996 ISNN 0885-8977. - 9.
Harlow J. H. 2007 (2nd Edition), CRC Press Taylor & Francis Group.100849391865 Raton, USA. - 10.
Haykin S. Veen B. V. 2001 (2nd Edition), Jhon Wiley & Sons Inc.8-57307-741-7 Alegre, Brazil. - 11.
Horowitz S. H. Phadke A. G. 2008 (3nd Edition), Ed. Research Studies Press Ltd.978-0-47005-712-4 Baldock, England. - 12.
Mallat S. 1999 (2nd Edition), Academic Press.012466606 California, USA. - 13.
Mao P. L. . Aggarwal R. K. 2000 A Wavelets Transform Based Decision Making Logic Method for Discrimination Between Internal Faults and Inrush Currents in Power Transformer. ,22 6 August 2000),389 395 0142-0615 - 14.
Megahed A. I. Ramadan A. El Mahdy W. 2008 Power Transformer Differential Relay Using Wavelet Transform Energies, in the Power and Energy Society General Meeting IEEE,1 6 978-1-42441-905-0 Pittsburgh, USA, July 20-24, 2008. - 15.
Morate M. G. Nicoletti D. W. 1999 A Wavelet-Based Differential Transformer Protection. ,14 4 November 1999),1351 1358 0885-8977 - 16.
Ngaopitakkul A. Kunakorn A. 2006 Internal Faults Classification in Transformer Windings Using Combination of Discrete Wavelet Transform and Back-Propagation Neural Networks ,4 3 June 2006),365 371 1598-6446 - 17.
Phadke A. G. . Thorp J. S. 2009 (2nd Edition), Ed. Research Studies Press Ltd.978-0-47005-713-1 Baldock, England. - 18.
Polikar R. 1999 The Story of Wavelets, , World Scientific and Eng. Society Press,192 197 USA, Retrieved from: http://www.public.iastate.edu/~rpolikar. - 19.
Rioul O. Vetterli M. 1991 Wavelets and Signal Processing. ,8 4 October 1994),14 38 1053-5888 - 20.
Robertson D. C. . Camps O. I. . Mayer J. S. . Gish W. B. 1996 Wavelets and Electromagnetic Power System Transient. 11 2 April 1996),1050 1058 0885-8977 - 21.
Saleh S. A. Rahman M. A. 2005 Modeling and Protection of Three-Phase Power Transformer Using Wavelet Packet Transform. ,20 2 April 2005),1273 1282 0885-8977 - 22.
Sarkar T. K. Su C. 1998 A Tutorial on Wavelets from an Electrical Engineering Perspective, Part 2: The Continuous Case 40 6 December 1998),36 49 1045-9243 - 23.
Simpson D. M. 1993 An Introduction to the Discrete Orthogonal Wavelet Transform. ,9 1 July 1993),57 81 - 24.
The Mathworks Inc. 2010 Mathworks Matlab. Retrieved from: http://www.mathworks.com/ - 25.
Thomas W. Ozgönenel O. 2007 Diagnostic of transformer internal faults through ANN based on radial basis functions and dynamical principal component analysis. & Distribution,1 11 - 26.
Vetterli M. . Herley C. 1992 Wavelets and Filter Banks: Theory and Design ,40 9 September 1992),2207 1992 0105-3587 X. - 27.
Wang H. Butler K. L. 2001 Finite Element Analysis of Internal Winding Faults in Distribution Transformer.16 3 July 2001),422 428 0885-8977 - 28.
Wiszniewski A. Kasztenny B. 1995 A Multi-Criteria Differential Transformer Relay Based on Fuzzy Logic 10 4 October 1995),1786 1792 0885-8977 - 29.
Zaman M. A. Hoque M. A. Rahman M. A. 1996 On-line Implementation of the Artificial Neural Network Based Protection for Power Transformer, of NECEC,5 11 NL, Canada, May 17-22, 1996.