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An improved fault-location method for distribution system using wavelets and support vector regression
Electrical Power and Energy Systems 55 (2014) 467–472
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
An improved fault-location method for distribution system using wavelets and support vector regression Lei Ye ⇑, Dahai You, Xianggen Yin, Ke Wang, Junchun Wu State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e
i n f o
Article history: Received 17 December 2012 Received in revised form 5 September 2013 Accepted 25 September 2013
Keywords: Fault location Distribution system Wavelet transform Support vector regression
a b s t r a c t This paper presents a wavelets and support vector regression (SVR) based method for locating grounded faults in radial distribution systems. The method utilizes traveling wave data recorded at the substation only. After modal transformation on three-phase traveling waves, the arrival time and amplitude information of modal components are extracted using discrete wavelet transform (DWT). In particular, time delay and ratio between the first Wavelet Transform Modulus Maxima (WTMM) of modal components in each scale are the candidate features for training a SVR which will be used for fault distance prediction. The simulation and SVR process are performed respectively using PSCAD/EMTDC and MATLAB. The result shows the method has high accuracy and good stability. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Localization of faults on power transmission lines is one of the main concerns for all electric utilities, as accurate fault location can lead to reduction of outage time and costs. So far, various fault location methods have been proposed and can be classified as fundamental components based methods [1–8] and traveling wave based methods [9–16]. All the above methods use the measured data either from single end of the transmission line or from multi-ends. The multi-end method requires synchronized measurement with time stamping and online communication to locate the fault. On the other hand, the single-end method just requires measurement at one end and is suitable for fault location in distribution networks which always only have measurement at substation end. In recent years, more efforts are devoted to the research on fault location techniques for distribution systems. Many distribution networks are non-effectively earthed systems, which make fundamental components based methods impractical to locate singleline to ground (SLG) fault. Although traveling wave based method is applicable in distribution network, two or multi-end method is expensive to implement because of the inadequate measurements in distribution network. Thus, single-end traveling wave based method is very practical to locate fault in distribution network. Wavelet transform (WT) is most common tool for analysis on traveling waves in power system. The time, frequency and amplitude (represented by wavelet transform modulus) information of ⇑ Corresponding author. Tel.: +86 13476074611. E-mail address: [email protected] (L. Ye). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.09.027
transient traveling waves can be extracted by wavelets analysis. Time-domain reflectometry (TDR) is one of the most common traveling-wave based fault location methods on transmission lines [9–11]. But in distribution network, TDR are not easy to interpret due to reflections in discontinuity points. Regardless of the reflection of traveling waves, grounded fault can be located utilizing time delay of modal components, assuming that the velocities of modal components are constant [12]. But velocity of zero mode component is not stable actually. Recently, by mapping TDR in frequency domain using continuous wavelet transform (CWT), a new approach discussed a correlation between characteristic frequencies and fault location, and showed reduction in the complexity of TDR-based fault location methods in distribution systems [13–16]. But due to the attenuation of traveling waves in propagation and insufficient frequency resolution of wavelets analysis in high frequency spectrum, accurate characteristic frequencies are difficult to obtain and the error is still significant. Moreover, the energy of SLG fault-originated traveling wave in neutral non-effectively earthed system is not large enough to be used to undertake the detection of characteristic frequency in any fault location because of serious refractions and reflections in distribution system with laterals. To fix the complexity of traveling wave reflection in distribution network, various Artificial Intelligence approaches which employ high-frequency component of fault-originated waveforms have been published [17–20]. In [19], ANN training is performed using the modal frequency and amplitude of the transient current waveform. In [20], the energy information in each scale (frequency band) provided by wavelet multi-resolution analysis (MRA) of the recorded transient voltage is used as training input of ANN.
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L. Ye et al. / Electrical Power and Energy Systems 55 (2014) 467–472
The method in [19,20] just utilize the information of frequency and amplitude extracted by DWT analysis. Since the scale in DWT analysis represents a frequency band in frequency domain, the frequency information extracted by DWT analysis is not in high frequency resolution, and the relation between the inputs and outputs of ANN in [19,20] are not clear, as a result, a large amount of samples must be obtained for seeking this relation in training process of ANN. This paper is aimed to locate grounded faults in distribution systems of all grounding types. The proposed method is a single-end method using wavelets and SVR, which makes full use of the time, frequency and amplitude information of traveling waves. It is found the time delay and ratio between the first WTMM of modal components in each scale are related with fault distance. Moreover, these relations with fault distance are very clear and these features are very suitable as training input of SVR for fault location. In comparison with former methods, the SVR which integrate these strong relations achieves very good performance with few training samples. At the meantime, the method is accurate and irrespective to the effects of fault inception angle, fault distance and fault impedance.
DDWT is adopted, and wavelet function is quadratic B-spline wavelet. 2.2. Support vector regression
2. Wavelet transform and SVR
Support vector machines (SVMs) were first developed as a support vector classification (SVC) to solve classification problems, within the area of statistical learning theory and structural risk minimization [22–24] . Although SVMs have been used for fault classification, and transmission lines parameter estimation for fault locations, it can also be applied to regression problems by an alternative loss function. These SVMs are called support vector regression. SVR uses structural minimization principles to choose discriminative functions that have minimal risk bound, and the necessary training sample size is smaller. Therefore SVRs are less likely to over-fitting data than other classification algorithms such as multilayer perceptron (MLP) neural network classifiers. SVR results in a global solution because they are trained as a convex optimization problem. They have been shown to be an attractive and more systematic approach to learn linear or nonlinear decision boundaries [25]. SVR includes linear SVR and nonlinear SVR. In this paper, nonlinear SVR is used for estimating fault locations.
2.1. Wavelet transforms
3. Fault distance estimation
Wavelet transform (WT) is a power tool in signal processing and can realize both the time and frequency localization. Wavelet transform of sampled waveforms can be obtained by implementing the discrete wavelet transform (DWT). Given a digital signal function f(k), its DWT will be calculated as follows [9]:
3.1. Basic ideas
m 1 X n ka0 DWTðf ; m; nÞ ¼ pffiffiffiffiffiffi f ðkÞw am am 0 0 k
ð1Þ
m
where the am 0 and ka0 corresponds to the scale factor and shifting factor. If a0 = 2, it is called discrete dyadic wavelet transform (DDWT) which is fast and popular in singular detection [21]. Implementation of the discrete wavelet transform, involves successive pairs of high-pass and low-pass filters at each scaling stage of the wavelet transform. This can be thought of as successive approximations of the same function, each approximation providing the incremental information related to a particular scale. The first scale will cover a broad frequency range at the high frequency end of the spectrum, and the higher scales will cover the lower end of the frequency spectrum with progressively shorter bandwidths. Conversely, the first scale will have the highest time resolution and lowest frequency resolution and higher scales will cover longer time intervals and shorter frequency ranges [9]. DDWT is utilized for the singular detection of signals in this paper. As illustrated in [21], the WTMM which is a strict local maximum of the wavelet transform modulus is used to detect singular point. Assuming Wf(m, n) represents wave transform coefficient, the definition of WTMM is: (1) WTMM is a local extremum at any point (m0, n0) such that (oWf(m0, n))/(on) has a zero-crossing at n = n0, when n varies. (2) WTMM is modulus maximum at any point (m0, n0) such that |Wf(m0, n)| < |Wf(m0, n0)| when n belongs to either a right or the left neighborhood of n0, and |Wf(m0, n)| 6 |Wf(m0, n0)| when n belongs to the other side of the neighborhood of n0. The time and value of WTMM represent arrival time and amplitude of traveling waves. In addition, the choice of different wavelet functions has a great impact on singularity detection. In this paper,
The proposed method utilizes the sampled signals at substation end only. After modal transformation, the three-phase voltage waves recorded at substation are transformed to aerial mode component which is present for any kind of fault and zero mode component whose magnitude is significant only during faults having a path to ground. The main idea of this paper is to use the inherent difference between modal components to locate SLG fault. Single-end methods [11,12] based on time delay between modal components was presented before, and its fault location formula is given as follows:
s ¼ v 1 v 0 ðt 0 t 1 Þ=ðv 1 v 0 Þ
ð2Þ
where v1 and v0 is the velocity of the aerial mode component and zero mode component of traveling waves separately, accordingly t1 and t0 are the arrival times of the two mode components, s is the estimated fault distance. It is necessary to obtain the arrival times and velocities of aerial mode component and zero mode component accurately in (2). The time delay between modal components can be obtained by wavelet analysis, but the velocity of zero mode component is difficult to be estimated accurately as it varies with fault distance and frequency. In [9], the velocity of zero mode component is considered as a constant, which may result in significant error. To avoid the complex estimation of the velocity of zero mode component, a SVR based fault location method is presented in this paper. Besides time information, SVR integrates the information of amplitude and frequency, which improve its accuracy and stability. The training samples of SVR are constructed with the features extracted from recorded traveling waves by wavelet analysis and SVR outputs the fault distance at last. 3.2. Features extraction It is important for SVR to choose the proper and typical training feature which is closely related with fault distance. For each mode component, its propagating constant c and velocity v is expressed as follows:
L. Ye et al. / Electrical Power and Energy Systems 55 (2014) 467–472
pffiffiffiffiffiffi c ¼ a þ jb ¼ ZY
ð3Þ
v ¼ x=b
ð4Þ
where a is the attenuation coefficient, b is the phase coefficient, Z, Y is impedance and admittance of each mode after modal transformation, x is angular frequency, and v is the velocity of traveling wave. Thus, eax represents the attenuation of amplitude, which varies with frequency and propagating distance. The time delay between modal components exists because of the different velocities. It is also known that, with the increasing of propagating distance, both of two mode components will attenuate, but zero mode will attenuate more rapidly, as a result that the amplitude (which can be represented by WTMM) of each components will vary with fault distance, and amplitude ratio between modal components will change regularly. On the other hand, the attenuation coefficient and phase coefficient are related to the frequency of traveling waves, as a result that the time delay and amplitude ratio between modal components will vary with scales. To prove the validity of the analysis above, a typical distribution system as shown in Fig. 1 is simulated by PSCAD/EMTDC in the paper. Considering that the velocity of zero mode component is very unstable at low frequency, the analysis scales are chosen from scale 1 to scale 6 in the total 8 scales. As shown in Figs. 2 and 3, the results support that the first WTMM ratio and time delay between modal components are related with scale and fault distance. The first WTMM ratio between modal components decreases monotonously when the fault distance increases, and increases when scale increases (frequency decreases). Time delay between modal components increases monotonously when the fault distance increases, and increases when the analyzed scale increases. It can be inferred that the fault distance can be estimated based on features of the first WTMM ratio and time delay between modal components in different scales.
469
Fig. 2. The first WTMM ratio between modal components within 1–6 scales in different fault distances.
3.3. Procedure of fault location Based on the above analysis, the first WTMM ratio and time delay between modal components in different scales are chosen as the input features, and the actual fault distance is chosen as the output. Thus, training samples of SVR can be constructed with this inputs and output at different fault points. In the last, a SVR for fault location will be trained by these training samples which make full use of the time, frequency and amplitude information extracted from traveling waves recorded at substation end. When a fault occurs on the distribution line, an input sample can be obtained at substation end by wavelet analysis. Then, the fault distance as an output can be predicted by SVR which has been trained in advance.
F
110kv/10kv 4km
3km
5km
A
B E
2km
6km fault
C
D
Fig. 3. The time delay between modal components within 1–6 scales in different fault distances.
The procedure of fault location is as follows: (1) Establish simulation model of distribution network by PSCAD/EMTDC, based on the detail parameters of line and ground. (2) Through simulation results at different fault point, obtain enough training samples by wavelet analysis. It is better to take 0.5 km or smaller as the interval of fault points for high accuracy. (3) Training a SVR for fault location. (4) To a SLG fault, the input vector is formed with the first WTMM ratio and time delay between modal components in 1–6 scales using wavelet analysis. Through trained SVR, the fault distance as an output is predicted. The method also can realize to locate faults which have significant zero mode component like line to line to ground (LLG) fault and unbalanced three-phase fault. Therefore, the method can locate most faults in distribution networks which are generally vulnerable to grounded fault.
4. Simulation result and discussion
Fig. 1. Single-supply distribution network with 2 branches.
A typical radial distribution system as shown in Fig. 1 is modeled in PSCAD/EMPDC. There are two laterals on the main feeder.
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The conductor geometric mean radius is 7.95 mm. The conductor DC resistance is 0.394 ohm/km. The ground resistivity is 100 ohm m. The tower parameters are shown in Fig. 4. SLG faults earthed directly are simulated at the interval of 0.5 km. Three-phase voltage traveling waves are sampled at bus A with the sampling frequency of 10 MHz and then transformed into mode components with Karenbauer modal transformation. Choosing the quadratic B-spline wavelet as the mother wavelet, the WTMMs and arrival time of zero mode component and aerial mode component can be extracted by DDWT. The total length of lines is 20 km and the number of training samples for SVR is 40. At the meantime, the SVR process is established by MATLAB. To evaluate the proposed method, the error is defined as follows:
error ¼ jdestimated dactual j
ð5Þ Fig. 5. Training set regression predict by SVR.
where destimated is estimated fault distance, dactual is actual fault distance. Mean square error (MSE) and mean error (ME) also are criteria generally used in assessing the quality of the fault location results. They are calculated as follows:
ME ¼
n 1X errori n i¼1
MSE ¼
ð6Þ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn ðerrori MEÞ2 i¼1 n1
ð7Þ
In general, ME represents the prediction accuracy of SVR, and the MSE represents the prediction stability of SVR. Smaller value of them represents better performance.
4.1. Effect of fault distance The prediction results of training samples are shown in Fig. 5. ME and MSE of training samples set are 0.0321 and 0.0920 with the distance unit of km. It can be proved from the results that the performance of SVM in training samples is very good. To verify unknown samples prediction accuracy of SVR, the test samples set is established by 19 samples which are formed by SLG faults at 19 random different points of the distribution lines (main feeder ABCD, lateral BE and CF). The prediction results of test set by SVR are shown as Fig. 6 and Table 1. The maximum error of test samples is only 214 m, and ME and MSE of test set are 0.0943 and 0.0664 with the distance unit of km. It is verified that the fault distance can be estimated accurately by SVR.
0.7m
Fig. 6. Test set regression predict by SVR.
4.2. Effect of fault impedance and fault inception angle Because proposed method utilizes the amplitude information of traveling wave, it is necessary to evaluate the effect of fault impedance and fault inception angle. The faults with different fault impedance and fault inception angle at the same fault point are simulated and analyzed. As shown in Table 2, the error is small and stable, which verify that the method is also irrespective to fault impedance and fault inception. 4.3. The stability of proposed method
0.76m
7.5m
Fig. 4. Parameters of distribution line tower.
Because the training samples are mostly obtained by software simulation, the input information obtained from actual measurement device may have a certain deviation with the input of training samples, especially for the amplitude information. In this paper, the additive errors of information of amplitude and time delay are evaluated as in Table 3. The result indicates that errors of amplitude information have insignificant effect on the accuracy of proposed method, but errors of time information contribute significant effect on the accuracy of proposed method. When the error of time delay is up to 50%, ME of the method is 2.01 with the distance unit of km and MSE is 1.039.
L. Ye et al. / Electrical Power and Energy Systems 55 (2014) 467–472
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Table 1 The performance of proposed method in different fault distances. Fault section
Fault distance (km)
Estimated fault distance (km)
Error (m)
Feeder ABCD
0.7 1.3 2.4 3.6 4.7 5.8 6.1 7.9 8.2 9.3 10.4 11.3 12.3 13.2
0.697 1.315 2.614 3.509 4.553 5.687 6.133 7.773 8.121 9.374 10.472 11.477 12.179 13.206
2.9 15.4 214.0 91.4 147.5 112.6 33.1 127.4 79.1 74.2 72.0 177.4 120.9 6.2
Branch BE
4.7 5.3
4.553 5.480
146.8 180.3
Branch CF
9.7 10.3 11.4
9.692 10.274 11.244
7.7 26.4 155.6
Table 2 Estimated results with samples in different fault resistance and reception in 4 km. Fault resistance (X)
Fault inception angle (°)
Estimated fault distance (km)
Error (m)
0 0 0 10 20 50 100
30 60 90 30 30 30 30
3.9902 3.9904 3.9905 3.9902 3.9902 3.9901 3.99
9.8 9.6 9.5 9.8 9.8 9.9 10
Table 3 Estimated results with samples in different additive error in 4 km. Additive error of time delay
Additive error of first WTMM ratio
ME
MSE
0 0 0 0 0 +10% +20% +30% +40% +50%
+10% +20% +30% +40% +50% 0 0 0 0 0
0.0959 0.0969 0.0962 0.0977 0.1037 0.04841 0.9308 1.2393 1.6274 2.010
0.0639 0.0630 0.0644 0.0635 0.0596 0.2599 0.4656 0.6066 0.7675 1.039
Fig. 7. Comparison with other methods.
samples is just 40. The error is evaluated by kilometer as (5), not by percentage of whole line length, because whatever the length of line is, the estimated fault distance must be accuracy and can instruct workers to the fault point in a small region. The test samples in different fault distances are simulated in neutral non-effectively earthed distribution system as Fig. 1. The result of the comparison is shown in Fig. 7. It shows that the proposed method has best performance than other methods in accuracy. In addition, to method [14], the characteristic frequency in two points (9.3 km and 13.2 km) are failed to be detected. The characteristic frequency–distance curve in [16] is also failed to obtain because of the missing of characteristic frequencies in some fault distances. So methods just using sole frequency information like [13–16] are not suitable for fault location for SLG fault in neutral non-effectively earthed distribution system. And method [20] has bad performance in insufficient training samples (just 40 samples) due to the lack of strong relation between energy and distance.
5. Conclusion
The operating experiences of traveling wave based fault location devices in transmission system shows that the time information is credible [9,10]. So the method have very high stability for the additive errors from measurement devices. 4.4. Comparison with recent presented methods In order to demonstrate the superiority of the proposed method, some former methods in this topic are examined. The main differences of these methods are: method [12] just utilizes the time delay between modal components in time domain to locating fault with assuming constant velocities of modal components, method [14] and method [16] take characteristic frequency in sole frequency domain for fault location, and method [20] integrates amplitude and frequency information by ANN with a large amount of training samples. In this comparison, the number of training
In this paper, a method using wavelets and SVR is proposed for locating grounded faults in radial distribution systems of all grounding types, which only utilizes traveling wave recorded at the substation. It is found that with the increase of fault distance, the first WTMM ratio between modal components decreases monotonously, and time delay between modal components increases monotonously. In this paper, it is original that time delay and ratio between the first WTMM of modal components in each scale are chosen as the candidate feature for training a SVR for fault location. This SVR integrates the characteristic information of amplitude, time and frequency extracted by wavelets analysis. Simulation studies demonstrate that SVR can predict the fault distance accurately and is irrespective to fault inception angle, fault distance and fault impedance. Moreover, the SVR shows good stability with the additive error from measurement devices. Reference [1] Takagi T, Yamakoshi Y, Yamaura M, Kondow R, Matsushima T. Development of a new fault locator using the one-terminal voltage and current data. IEEE Trans Power Appl Syst PAS 1982;101(8). [2] Zhu J, Lubkeman DL, Girgis AA. Automated fault location and diagnosis on electric power distribution feeders. IEEE Trans Power Del 1997;12(2):801–9. [3] Choi Myeon-Song, Lee Seung-Jae, Lee Duck-Su, Jin Bo-Gun. A new fault location algorithm using direct circuit analysis for distribution systems. IEEE Trans Power Del 2004;19(1):35–41.
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[4] Salim RH, Resener M, Filomena AD, Oliveira KRC, Bretas AS. Extended faultlocation formulation for power distribution systems. IEEE Trans Power Del 2009;24(2):508–16. [5] Nouri H, Alamuti MM. Comprehensive distribution network fault location using the distributed parameter model. IEEE Trans Power Del 2011;26(4):2154–62. [6] Ngu EE, Ramar K. A combined impedance and traveling wave based fault location method for multi-terminal transmission lines. Int J Power Energy Syst 2011;33(10):1767–75. [7] Ngu EE, Ramar K, Eisa A. One-end fault location method for untransposed fourcircuit transmission lines. Int J Power Energy Syst 2012;43(1):660–9. [8] Jiang Z, Miao SH, Xu H, et al. An effective fault location technique for transmission grids using phasor measurement units. Int J Power Energy Syst 2012;42(1):653–60. [9] Eee F, Magnago H, Abur A. Fault location using wavelets. IEEE Trans Power Del 1998;13(4):1475–80. [10] Navaneethan S, Soraghan JJ, Siew WH, et al. Automatic fault location for underground low voltage distribution networks. IEEE Trans Power Del 2001;16(2):346–51. [11] Abur A, Magnago FH. Use of time delays between modal components in wavelet based fault location. Int J Power Energy Syst 2000;22(6):397–403. [12] Mardiana R, Al Motairy H, Su CQ. Ground fault location on a transmission line using high-frequency transient voltages. IEEE Trans Power Del 2011;26(2):1298–9. [13] Borghetti A, Corsi S, Nucci CA, et al. On the use of continuous-wavelet transform for fault location in distribution power networks. Int J Power Energy Syst 2006;28(9):608–17. [14] Borghetti A, Bosetti M, Di Silvestro M, et al. Continuous-wavelet transform for fault location in distribution power networks: definition of mother wavelets inferred from fault originated transients. IEEE Trans Power Syst 2008;23(2):380–8.
[15] Borghetti A, Bosetti M, Nucci CA, et al. Integrated use of time-frequency wavelet decompositions for fault location in distribution networks: theory and experimental validation. IEEE Trans Power Del 2010;25(4):3139–46. [16] Sadeh J, Bakhshizadeh E, Kazemzadeh R. A new fault location algorithm for radial distribution systems using modal analysis. Int J Power Energy Syst 2013;45(1):271–8. [17] Moshtagh J, Aggarwal RK. A new approach to ungrounded fault location in a three-phase underground distribution system using combined neural networks & wavelet analysis. In: IEEE Can conf electrical and computer engineering (CCECE); 2006. p. 376–81. [18] Ngaopitakkul A, Pothisarn C. Discrete wavelet transform and back-propagation neural networks algorithm for fault location on single-circuit transmission line. In: Proc IEEE int conf robotics and biomimetics (ROBIO); 2008. p. 1613– 18. [19] Tawfik MM, Morcos MM. On the use of Prony method to locate faults in loop systems by utilizing modal parameters of fault current. IEEE Trans Power Del 2005;20(1):532–4. [20] Pourahmadi-Nakhli M, Safavi AA. Path characteristic frequency-based fault locating in radial distribution systems using wavelets and neural networks. IEEE Trans Power Del 2011;26(2):772–81. [21] Mallat S, Hwang WL. Singularity detection and processing with wavelets. IEEE Trans Inform Theor 1992;38(2):617–43. [22] Hearst MA, Dumais ST, Osman E, Platt J, Scholkopf B. Support vector machines. IEEE Intell Syst Appl 1998;13(4):18–28. [23] Vapnik V. The nature of statistical learning theory. Springer; 1995. [24] Gunn SR. In: Support vector machines for classification and regression technical report. University of Southampton; 1998. [25] Yusuff AA, Fei C, Jimoh AA, et al. Fault location in a series compensated transmission line based on wavelet packet decomposition and support vector regression. Electr Power Syst Res 2011;81(7):1258–65.
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
An improved fault-location method for distribution system using wavelets and support vector regression Lei Ye ⇑, Dahai You, Xianggen Yin, Ke Wang, Junchun Wu State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e
i n f o
Article history: Received 17 December 2012 Received in revised form 5 September 2013 Accepted 25 September 2013
Keywords: Fault location Distribution system Wavelet transform Support vector regression
a b s t r a c t This paper presents a wavelets and support vector regression (SVR) based method for locating grounded faults in radial distribution systems. The method utilizes traveling wave data recorded at the substation only. After modal transformation on three-phase traveling waves, the arrival time and amplitude information of modal components are extracted using discrete wavelet transform (DWT). In particular, time delay and ratio between the first Wavelet Transform Modulus Maxima (WTMM) of modal components in each scale are the candidate features for training a SVR which will be used for fault distance prediction. The simulation and SVR process are performed respectively using PSCAD/EMTDC and MATLAB. The result shows the method has high accuracy and good stability. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Localization of faults on power transmission lines is one of the main concerns for all electric utilities, as accurate fault location can lead to reduction of outage time and costs. So far, various fault location methods have been proposed and can be classified as fundamental components based methods [1–8] and traveling wave based methods [9–16]. All the above methods use the measured data either from single end of the transmission line or from multi-ends. The multi-end method requires synchronized measurement with time stamping and online communication to locate the fault. On the other hand, the single-end method just requires measurement at one end and is suitable for fault location in distribution networks which always only have measurement at substation end. In recent years, more efforts are devoted to the research on fault location techniques for distribution systems. Many distribution networks are non-effectively earthed systems, which make fundamental components based methods impractical to locate singleline to ground (SLG) fault. Although traveling wave based method is applicable in distribution network, two or multi-end method is expensive to implement because of the inadequate measurements in distribution network. Thus, single-end traveling wave based method is very practical to locate fault in distribution network. Wavelet transform (WT) is most common tool for analysis on traveling waves in power system. The time, frequency and amplitude (represented by wavelet transform modulus) information of ⇑ Corresponding author. Tel.: +86 13476074611. E-mail address: [email protected] (L. Ye). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.09.027
transient traveling waves can be extracted by wavelets analysis. Time-domain reflectometry (TDR) is one of the most common traveling-wave based fault location methods on transmission lines [9–11]. But in distribution network, TDR are not easy to interpret due to reflections in discontinuity points. Regardless of the reflection of traveling waves, grounded fault can be located utilizing time delay of modal components, assuming that the velocities of modal components are constant [12]. But velocity of zero mode component is not stable actually. Recently, by mapping TDR in frequency domain using continuous wavelet transform (CWT), a new approach discussed a correlation between characteristic frequencies and fault location, and showed reduction in the complexity of TDR-based fault location methods in distribution systems [13–16]. But due to the attenuation of traveling waves in propagation and insufficient frequency resolution of wavelets analysis in high frequency spectrum, accurate characteristic frequencies are difficult to obtain and the error is still significant. Moreover, the energy of SLG fault-originated traveling wave in neutral non-effectively earthed system is not large enough to be used to undertake the detection of characteristic frequency in any fault location because of serious refractions and reflections in distribution system with laterals. To fix the complexity of traveling wave reflection in distribution network, various Artificial Intelligence approaches which employ high-frequency component of fault-originated waveforms have been published [17–20]. In [19], ANN training is performed using the modal frequency and amplitude of the transient current waveform. In [20], the energy information in each scale (frequency band) provided by wavelet multi-resolution analysis (MRA) of the recorded transient voltage is used as training input of ANN.
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The method in [19,20] just utilize the information of frequency and amplitude extracted by DWT analysis. Since the scale in DWT analysis represents a frequency band in frequency domain, the frequency information extracted by DWT analysis is not in high frequency resolution, and the relation between the inputs and outputs of ANN in [19,20] are not clear, as a result, a large amount of samples must be obtained for seeking this relation in training process of ANN. This paper is aimed to locate grounded faults in distribution systems of all grounding types. The proposed method is a single-end method using wavelets and SVR, which makes full use of the time, frequency and amplitude information of traveling waves. It is found the time delay and ratio between the first WTMM of modal components in each scale are related with fault distance. Moreover, these relations with fault distance are very clear and these features are very suitable as training input of SVR for fault location. In comparison with former methods, the SVR which integrate these strong relations achieves very good performance with few training samples. At the meantime, the method is accurate and irrespective to the effects of fault inception angle, fault distance and fault impedance.
DDWT is adopted, and wavelet function is quadratic B-spline wavelet. 2.2. Support vector regression
2. Wavelet transform and SVR
Support vector machines (SVMs) were first developed as a support vector classification (SVC) to solve classification problems, within the area of statistical learning theory and structural risk minimization [22–24] . Although SVMs have been used for fault classification, and transmission lines parameter estimation for fault locations, it can also be applied to regression problems by an alternative loss function. These SVMs are called support vector regression. SVR uses structural minimization principles to choose discriminative functions that have minimal risk bound, and the necessary training sample size is smaller. Therefore SVRs are less likely to over-fitting data than other classification algorithms such as multilayer perceptron (MLP) neural network classifiers. SVR results in a global solution because they are trained as a convex optimization problem. They have been shown to be an attractive and more systematic approach to learn linear or nonlinear decision boundaries [25]. SVR includes linear SVR and nonlinear SVR. In this paper, nonlinear SVR is used for estimating fault locations.
2.1. Wavelet transforms
3. Fault distance estimation
Wavelet transform (WT) is a power tool in signal processing and can realize both the time and frequency localization. Wavelet transform of sampled waveforms can be obtained by implementing the discrete wavelet transform (DWT). Given a digital signal function f(k), its DWT will be calculated as follows [9]:
3.1. Basic ideas
m 1 X n ka0 DWTðf ; m; nÞ ¼ pffiffiffiffiffiffi f ðkÞw am am 0 0 k
ð1Þ
m
where the am 0 and ka0 corresponds to the scale factor and shifting factor. If a0 = 2, it is called discrete dyadic wavelet transform (DDWT) which is fast and popular in singular detection [21]. Implementation of the discrete wavelet transform, involves successive pairs of high-pass and low-pass filters at each scaling stage of the wavelet transform. This can be thought of as successive approximations of the same function, each approximation providing the incremental information related to a particular scale. The first scale will cover a broad frequency range at the high frequency end of the spectrum, and the higher scales will cover the lower end of the frequency spectrum with progressively shorter bandwidths. Conversely, the first scale will have the highest time resolution and lowest frequency resolution and higher scales will cover longer time intervals and shorter frequency ranges [9]. DDWT is utilized for the singular detection of signals in this paper. As illustrated in [21], the WTMM which is a strict local maximum of the wavelet transform modulus is used to detect singular point. Assuming Wf(m, n) represents wave transform coefficient, the definition of WTMM is: (1) WTMM is a local extremum at any point (m0, n0) such that (oWf(m0, n))/(on) has a zero-crossing at n = n0, when n varies. (2) WTMM is modulus maximum at any point (m0, n0) such that |Wf(m0, n)| < |Wf(m0, n0)| when n belongs to either a right or the left neighborhood of n0, and |Wf(m0, n)| 6 |Wf(m0, n0)| when n belongs to the other side of the neighborhood of n0. The time and value of WTMM represent arrival time and amplitude of traveling waves. In addition, the choice of different wavelet functions has a great impact on singularity detection. In this paper,
The proposed method utilizes the sampled signals at substation end only. After modal transformation, the three-phase voltage waves recorded at substation are transformed to aerial mode component which is present for any kind of fault and zero mode component whose magnitude is significant only during faults having a path to ground. The main idea of this paper is to use the inherent difference between modal components to locate SLG fault. Single-end methods [11,12] based on time delay between modal components was presented before, and its fault location formula is given as follows:
s ¼ v 1 v 0 ðt 0 t 1 Þ=ðv 1 v 0 Þ
ð2Þ
where v1 and v0 is the velocity of the aerial mode component and zero mode component of traveling waves separately, accordingly t1 and t0 are the arrival times of the two mode components, s is the estimated fault distance. It is necessary to obtain the arrival times and velocities of aerial mode component and zero mode component accurately in (2). The time delay between modal components can be obtained by wavelet analysis, but the velocity of zero mode component is difficult to be estimated accurately as it varies with fault distance and frequency. In [9], the velocity of zero mode component is considered as a constant, which may result in significant error. To avoid the complex estimation of the velocity of zero mode component, a SVR based fault location method is presented in this paper. Besides time information, SVR integrates the information of amplitude and frequency, which improve its accuracy and stability. The training samples of SVR are constructed with the features extracted from recorded traveling waves by wavelet analysis and SVR outputs the fault distance at last. 3.2. Features extraction It is important for SVR to choose the proper and typical training feature which is closely related with fault distance. For each mode component, its propagating constant c and velocity v is expressed as follows:
L. Ye et al. / Electrical Power and Energy Systems 55 (2014) 467–472
pffiffiffiffiffiffi c ¼ a þ jb ¼ ZY
ð3Þ
v ¼ x=b
ð4Þ
where a is the attenuation coefficient, b is the phase coefficient, Z, Y is impedance and admittance of each mode after modal transformation, x is angular frequency, and v is the velocity of traveling wave. Thus, eax represents the attenuation of amplitude, which varies with frequency and propagating distance. The time delay between modal components exists because of the different velocities. It is also known that, with the increasing of propagating distance, both of two mode components will attenuate, but zero mode will attenuate more rapidly, as a result that the amplitude (which can be represented by WTMM) of each components will vary with fault distance, and amplitude ratio between modal components will change regularly. On the other hand, the attenuation coefficient and phase coefficient are related to the frequency of traveling waves, as a result that the time delay and amplitude ratio between modal components will vary with scales. To prove the validity of the analysis above, a typical distribution system as shown in Fig. 1 is simulated by PSCAD/EMTDC in the paper. Considering that the velocity of zero mode component is very unstable at low frequency, the analysis scales are chosen from scale 1 to scale 6 in the total 8 scales. As shown in Figs. 2 and 3, the results support that the first WTMM ratio and time delay between modal components are related with scale and fault distance. The first WTMM ratio between modal components decreases monotonously when the fault distance increases, and increases when scale increases (frequency decreases). Time delay between modal components increases monotonously when the fault distance increases, and increases when the analyzed scale increases. It can be inferred that the fault distance can be estimated based on features of the first WTMM ratio and time delay between modal components in different scales.
469
Fig. 2. The first WTMM ratio between modal components within 1–6 scales in different fault distances.
3.3. Procedure of fault location Based on the above analysis, the first WTMM ratio and time delay between modal components in different scales are chosen as the input features, and the actual fault distance is chosen as the output. Thus, training samples of SVR can be constructed with this inputs and output at different fault points. In the last, a SVR for fault location will be trained by these training samples which make full use of the time, frequency and amplitude information extracted from traveling waves recorded at substation end. When a fault occurs on the distribution line, an input sample can be obtained at substation end by wavelet analysis. Then, the fault distance as an output can be predicted by SVR which has been trained in advance.
F
110kv/10kv 4km
3km
5km
A
B E
2km
6km fault
C
D
Fig. 3. The time delay between modal components within 1–6 scales in different fault distances.
The procedure of fault location is as follows: (1) Establish simulation model of distribution network by PSCAD/EMTDC, based on the detail parameters of line and ground. (2) Through simulation results at different fault point, obtain enough training samples by wavelet analysis. It is better to take 0.5 km or smaller as the interval of fault points for high accuracy. (3) Training a SVR for fault location. (4) To a SLG fault, the input vector is formed with the first WTMM ratio and time delay between modal components in 1–6 scales using wavelet analysis. Through trained SVR, the fault distance as an output is predicted. The method also can realize to locate faults which have significant zero mode component like line to line to ground (LLG) fault and unbalanced three-phase fault. Therefore, the method can locate most faults in distribution networks which are generally vulnerable to grounded fault.
4. Simulation result and discussion
Fig. 1. Single-supply distribution network with 2 branches.
A typical radial distribution system as shown in Fig. 1 is modeled in PSCAD/EMPDC. There are two laterals on the main feeder.
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L. Ye et al. / Electrical Power and Energy Systems 55 (2014) 467–472
The conductor geometric mean radius is 7.95 mm. The conductor DC resistance is 0.394 ohm/km. The ground resistivity is 100 ohm m. The tower parameters are shown in Fig. 4. SLG faults earthed directly are simulated at the interval of 0.5 km. Three-phase voltage traveling waves are sampled at bus A with the sampling frequency of 10 MHz and then transformed into mode components with Karenbauer modal transformation. Choosing the quadratic B-spline wavelet as the mother wavelet, the WTMMs and arrival time of zero mode component and aerial mode component can be extracted by DDWT. The total length of lines is 20 km and the number of training samples for SVR is 40. At the meantime, the SVR process is established by MATLAB. To evaluate the proposed method, the error is defined as follows:
error ¼ jdestimated dactual j
ð5Þ Fig. 5. Training set regression predict by SVR.
where destimated is estimated fault distance, dactual is actual fault distance. Mean square error (MSE) and mean error (ME) also are criteria generally used in assessing the quality of the fault location results. They are calculated as follows:
ME ¼
n 1X errori n i¼1
MSE ¼
ð6Þ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn ðerrori MEÞ2 i¼1 n1
ð7Þ
In general, ME represents the prediction accuracy of SVR, and the MSE represents the prediction stability of SVR. Smaller value of them represents better performance.
4.1. Effect of fault distance The prediction results of training samples are shown in Fig. 5. ME and MSE of training samples set are 0.0321 and 0.0920 with the distance unit of km. It can be proved from the results that the performance of SVM in training samples is very good. To verify unknown samples prediction accuracy of SVR, the test samples set is established by 19 samples which are formed by SLG faults at 19 random different points of the distribution lines (main feeder ABCD, lateral BE and CF). The prediction results of test set by SVR are shown as Fig. 6 and Table 1. The maximum error of test samples is only 214 m, and ME and MSE of test set are 0.0943 and 0.0664 with the distance unit of km. It is verified that the fault distance can be estimated accurately by SVR.
0.7m
Fig. 6. Test set regression predict by SVR.
4.2. Effect of fault impedance and fault inception angle Because proposed method utilizes the amplitude information of traveling wave, it is necessary to evaluate the effect of fault impedance and fault inception angle. The faults with different fault impedance and fault inception angle at the same fault point are simulated and analyzed. As shown in Table 2, the error is small and stable, which verify that the method is also irrespective to fault impedance and fault inception. 4.3. The stability of proposed method
0.76m
7.5m
Fig. 4. Parameters of distribution line tower.
Because the training samples are mostly obtained by software simulation, the input information obtained from actual measurement device may have a certain deviation with the input of training samples, especially for the amplitude information. In this paper, the additive errors of information of amplitude and time delay are evaluated as in Table 3. The result indicates that errors of amplitude information have insignificant effect on the accuracy of proposed method, but errors of time information contribute significant effect on the accuracy of proposed method. When the error of time delay is up to 50%, ME of the method is 2.01 with the distance unit of km and MSE is 1.039.
L. Ye et al. / Electrical Power and Energy Systems 55 (2014) 467–472
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Table 1 The performance of proposed method in different fault distances. Fault section
Fault distance (km)
Estimated fault distance (km)
Error (m)
Feeder ABCD
0.7 1.3 2.4 3.6 4.7 5.8 6.1 7.9 8.2 9.3 10.4 11.3 12.3 13.2
0.697 1.315 2.614 3.509 4.553 5.687 6.133 7.773 8.121 9.374 10.472 11.477 12.179 13.206
2.9 15.4 214.0 91.4 147.5 112.6 33.1 127.4 79.1 74.2 72.0 177.4 120.9 6.2
Branch BE
4.7 5.3
4.553 5.480
146.8 180.3
Branch CF
9.7 10.3 11.4
9.692 10.274 11.244
7.7 26.4 155.6
Table 2 Estimated results with samples in different fault resistance and reception in 4 km. Fault resistance (X)
Fault inception angle (°)
Estimated fault distance (km)
Error (m)
0 0 0 10 20 50 100
30 60 90 30 30 30 30
3.9902 3.9904 3.9905 3.9902 3.9902 3.9901 3.99
9.8 9.6 9.5 9.8 9.8 9.9 10
Table 3 Estimated results with samples in different additive error in 4 km. Additive error of time delay
Additive error of first WTMM ratio
ME
MSE
0 0 0 0 0 +10% +20% +30% +40% +50%
+10% +20% +30% +40% +50% 0 0 0 0 0
0.0959 0.0969 0.0962 0.0977 0.1037 0.04841 0.9308 1.2393 1.6274 2.010
0.0639 0.0630 0.0644 0.0635 0.0596 0.2599 0.4656 0.6066 0.7675 1.039
Fig. 7. Comparison with other methods.
samples is just 40. The error is evaluated by kilometer as (5), not by percentage of whole line length, because whatever the length of line is, the estimated fault distance must be accuracy and can instruct workers to the fault point in a small region. The test samples in different fault distances are simulated in neutral non-effectively earthed distribution system as Fig. 1. The result of the comparison is shown in Fig. 7. It shows that the proposed method has best performance than other methods in accuracy. In addition, to method [14], the characteristic frequency in two points (9.3 km and 13.2 km) are failed to be detected. The characteristic frequency–distance curve in [16] is also failed to obtain because of the missing of characteristic frequencies in some fault distances. So methods just using sole frequency information like [13–16] are not suitable for fault location for SLG fault in neutral non-effectively earthed distribution system. And method [20] has bad performance in insufficient training samples (just 40 samples) due to the lack of strong relation between energy and distance.
5. Conclusion
The operating experiences of traveling wave based fault location devices in transmission system shows that the time information is credible [9,10]. So the method have very high stability for the additive errors from measurement devices. 4.4. Comparison with recent presented methods In order to demonstrate the superiority of the proposed method, some former methods in this topic are examined. The main differences of these methods are: method [12] just utilizes the time delay between modal components in time domain to locating fault with assuming constant velocities of modal components, method [14] and method [16] take characteristic frequency in sole frequency domain for fault location, and method [20] integrates amplitude and frequency information by ANN with a large amount of training samples. In this comparison, the number of training
In this paper, a method using wavelets and SVR is proposed for locating grounded faults in radial distribution systems of all grounding types, which only utilizes traveling wave recorded at the substation. It is found that with the increase of fault distance, the first WTMM ratio between modal components decreases monotonously, and time delay between modal components increases monotonously. In this paper, it is original that time delay and ratio between the first WTMM of modal components in each scale are chosen as the candidate feature for training a SVR for fault location. This SVR integrates the characteristic information of amplitude, time and frequency extracted by wavelets analysis. Simulation studies demonstrate that SVR can predict the fault distance accurately and is irrespective to fault inception angle, fault distance and fault impedance. Moreover, the SVR shows good stability with the additive error from measurement devices. Reference [1] Takagi T, Yamakoshi Y, Yamaura M, Kondow R, Matsushima T. Development of a new fault locator using the one-terminal voltage and current data. IEEE Trans Power Appl Syst PAS 1982;101(8). [2] Zhu J, Lubkeman DL, Girgis AA. Automated fault location and diagnosis on electric power distribution feeders. IEEE Trans Power Del 1997;12(2):801–9. [3] Choi Myeon-Song, Lee Seung-Jae, Lee Duck-Su, Jin Bo-Gun. A new fault location algorithm using direct circuit analysis for distribution systems. IEEE Trans Power Del 2004;19(1):35–41.
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