Stationary wavelet transform and single differentiator based decaying DC-offset filtering in post fault measurements

Measurement 47 (2014) 919–928

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Stationary wavelet transform and single differentiator based decaying DC-offset filtering in post fault measurements A.A. Yusuff, A.A. Jimoh ⇑, J.L. Munda Department of Electrical Engineering, Faculty of Engineering and the Built Environment, Tshwane University of Technology, Private Bag X680, Staatsartillerie Road, Pretoria West, Pretoria 0001, South Africa

a r t i c l e

i n f o

Article history: Received 10 January 2013 Received in revised form 24 June 2013 Accepted 10 October 2013 Available online 23 October 2013 Keywords: Decaying DC offset Stationary wavelet transform Wavelets packet decomposition Phasor estimation

a b s t r a c t This paper presents a novel scheme for removing a decaying DC-offset from both current and voltage measurements irrespective of the time constant.The technique is based on stationary wavelet transform (SWT) cascaded with a differentiator. The performance of the scheme on two study cases is investigated; the statistical performance in relation to noise on a hypothetical signal, and a modeled segment of a utility network in South Africa. The proposed scheme is practically applied by testing it on a real life data obtained from Eskom’s network. The result shows that the scheme is robust, and that it can remove any DC-offset. The output of the scheme can be used for fault detection, classification and location. Crown Copyright Ó 2013 Published by Elsevier Ltd. All rights reserved.

1. Introduction In power system transmission line protection, most relays use the system frequency component in voltage and current to estimate appropriate phasors for impedance calculation, every other frequencies or harmonics are treated as noise. Although it is possible to remove all harmonics higher than the system frequency, by using various kind of low pass filters, however during faults, except in few cases the fault current will always have a decaying DC offset, which could be up to 20% of the steady state current value. Various digital filtering techniques are used in extracting the fundamental frequency component. Various approaches have been put forward to minimize the influence of the decaying DC component on phasor. In [1], a cosine filter was used in estimating both direct and quadrature components of a phasor. Digital mimic filtering schemes [2] has also been used extensively for the removal of a decaying DC offset. In this scheme, a preset value is chosen between 30 ms and 50 ms which is the range of EHV ⇑ Corresponding author. Tel.: +27 827870251; fax: +27 123824964. E-mail addresses: [email protected] (A.A. Yusuff), [email protected] (A.A. Jimoh), [email protected] (J.L. Munda).

transmission line time constant, and the amplitude of the decaying DC offset is estimated. As long as there is no mismatch between the preset time constant and the actual time constant of the network, the scheme can totally remove the decaying DC offset. But in reality, since the time constant is dependent on the fault location and the network operating condition which are random variables, when the preset time constant is appreciably different from the network time constant, the error in the phasor estimate is appreciable. In [3], an adaptive mimic scheme was used to circumvent the deficiencies in using a pre-set time constant and the scheme produces a very accurate result irrespective of the time constant and the amplitude of the decaying DC offset. A few other techniques that have been used are Least Error Squares (LES) schemes [4,5], Kalman filtering techniques [6], as well as implementations in [7–13]. In recent times, time-scale and time–frequency signal decomposition techniques are used in the analysis and structural description of signals. The advances in computer hardware, software and mixed-domain signal transforms over the last decade has necessitated the need to rework the conventional approach to signals filtering and decomposition. These techniques expose Fourier transform

0263-2241/$ - see front matter Crown Copyright Ó 2013 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2013.10.022

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limitations, and point to techniques that are impossible using the Fourier tools. However, the computational burden of mixed domain signal filtering and decomposition is larger compared to its frequency domain counterparts. Unlike 4 decades ago, when computational power was a major problem in implementing algorithms, in the recent time computational power is now cheap, hence there might be a need to venture into untrodden path in filtering, provided we will get a better result in terms of time response albeit with more computational power. Hilbert–Huang Transform (HHT) based on Empirical Mode Decomposition (EMD) has been used to decompose non-stationary signals into a number of Intrinsic Mode Functions (IMFs), and subsequently Hilbert transform is used to calculate the instantaneous frequency and instantaneous amplitude of the IMFs [14–16]. However the major challenge of EMD is the inability to separate modes whose instantaneous frequencies simultaneously lie with an octave. In order to circumvent this deficiency, the use of masking was proposed in [17], while Olhede and Walden proposed a method based on wavelet packet decomposition to get the Hilbert spectrum on the narrow-band decomposition of the signal, with an appreciable performance compared to EMD based techniques [18,19].

Wavelets transform is a time scale technique that has been used extensively in multi resolution analysis of non-stationary signals. A typical example of its use in phasor amplitude estimation is given in [20–22]. However, this claims were debunked by Brahma and Kavasseri in [23]. They observed that the signal used in [20] is not realistic in power system, and that the assumptions of complete removal of decaying dc offset by a band pass anti aliasing filter in [22] or High pass 4th order Butterworth filter in [21] introduced unnecessary delays, without any appreciable performance justification. Stationary wavelet transform (SWT) was used in [24] for filtering and feature extraction of post fault measurements on power transmission lines. We propose the use of stationary wavelet transform (SWT) in cascade with a differentiator in removing decaying dc offset as well as other harmonics in both current and voltage measurements at the terminals of a transmission line. In this work we present a scheme for removing a decaying DC offset and estimation of the amplitude of the system fundamental frequency component that is applicable to both voltage and current. This could consequently be used in fault classification and estimating fault location. In Section 2, the theoretical background of the scheme was laid down. We look at the performance of our scheme for an hypothetical waveform with a decaying

Fig. 1. Stationary wavelet transform decomposition.

Fig. 2. The proposed scheme.

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dc offset as well as noise level varying from 20 dB to 80 dB, in Section 3. In Section 4, we show the application of our scheme, to a segment of a power utility network in South Africa (Eskom) by simulating a phase to ground fault. In addition, the performance of the scheme is checked on a real life data from a digital fault recorder (DFR). And conclusions are made in Section 5.

2. Stationary wavelet transform Stationary wavelet transform, unlike discrete wavelet transform (DWT) is time invariant caused by decimation [25]. It has been used in denoising, singularity detection [26], sharp transient detection [27] as well as HVDC line protection [28].

signal

det level 2

200

40

150

20 0 Amplitude

Amplitude

100 50 0

−40 −60

−50 −100 0

−20

−80 0.05

0.1

0.15 0.2 time

0.25

−100 0

0.3

0.05

0.1

300

100

200

50

100

0

−100

−100

−200

0.05

0.1

0.15 0.2 time

0.3

0.25

0.3

0.25

0.3

0

−50

−150 0

0.25

det level 4

150

Amplitude

Amplitude

det level 3

0.15 0.2 time

0.25

−300 0

0.3

0.05

0.1

app level 5

0.15 0.2 time

det level 5

600

400 300

500 200 100 Amplitude

Amplitude

400 300 200

0 −100 −200 −300

100 −400 0 0

0.05

0.1

0.15 0.2 time

0.25

0.3

−500 0

0.05

0.1

Fig. 3. Stationary wavelet transform decomposition.

0.15 0.2 time

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Table 1 Normalization constants Kc:fs is sampling frequency and di are detail coefficients at various levels. fs (kHz)

d1

d2

d3

d4

d5

d6

0.8 1.6 3.2 6.4 12.8 20.6

36.9411 73.5265 146.8759 293.6629 587.2815 945.1426

13.0922 26.0583 52.0538 104.0760 208.1364 334.9647

4.6737 9.3024 18.5823 37.1534 74.3012 119.5767

1.7178 3.4190 6.8298 13.6554 27.3088 43.9495

0.7115 1.4162 2.8290 5.6563 11.3117 18.2045

0.5031 1.0014 2.0004 3.9996 7.9986 12.8725

DC offset filtering using SWT based scheme for 20dB awgn

DC offset filtering using SWT based scheme for 40dB awgn

Amplitude estimate Orignal signal the proposed scheme output

5

Amplitude estimate Orignal signal the proposed scheme output

2

4 Amplitude (p.u)

Amplitude (p.u)

1.5 3 2 1 0

1 0.5 0 −0.5

−1

−1

−2

−1.5

−3 0

0.02

0.04

0.06

0.08

0.1 time (s)

0.12

0.14

0.16

0.18

0.2

0

DC offset filtering using SWT based scheme for 20dB awgn

0.5 0

−1

0.06

0.08

0.1 time (s)

0.12

0.14

0.16

0.18

0

−1 0.06

0.08

0.1 time (s)

0.12

0.14

0.16

0.18

0.08

0.1 0.12 time (s)

0.14

0.16

0.18

0.2

Amplitude estimate Orignal signal the proposed scheme output

0

−1 0.04

0.06

0.5

−0.5

0.02

0.2

1

−0.5

0

0.04

1.5 Amplitude (p.u)

Amplitude (p.u)

0.5

0.18

DC offset filtering using SWT based scheme for 40dB awgn

Amplitude estimate Orignal signal the proposed scheme output

1

0.16

Amplitude estimate Orignal signal the proposed scheme output

0.02

DC offset filtering using SWT based scheme for 20dB awgn 1.5

0.14

0

−1 0.04

0.1 0.12 time (s)

0.5

−0.5

0.02

0.08

1

−0.5

0

0.06

1.5

Amplitude (p.u)

Amplitude (p.u)

1

0.04

DC offset filtering using SWT based scheme for 40dB awgn

Amplitude estimate Orignal signal the proposed scheme output

1.5

0.02

0.02

0.04

0.06

0.08

Fig. 4. Levels 3–5 performance with respect to 20 dB and 40 dB SNR.

0.1 0.12 time (s)

0.14

0.16

0.18

0.2

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A.A. Yusuff et al. / Measurement 47 (2014) 919–928 80

150

140

70

120

60

100

100

50

80

40 60

30

50

40

20

20

10 0

0

0.5

1

1.5

2

0 0.8

2.5

0.9

1

1.1

0

1.2

120

140

140

100

120

120

100

100

80

80

60

60

40

40

20

20

20

0

0

80

0.99

0.995

1

60 40

0.5

1

1.5

0 0.95

100

1

1.05

1.1

70

0.99

0.995

1

150

60

80

50 60

40

40

30

100

50

20 20

10

0 0.8

0.9

1

1.1

0 0.98 0.985 0.99 0.995 1

1.2

0

1.005 1.01

0.99

0.995

1

1.005

Fig. 5. Histogram of the amplitude estimates of the scheme.

Kendal

For any continuous time signal x(t), the discrete stationary wavelet coefficient at level i and sub-band k is [29]

Duvha L1

G1

G2 L2 Minerva

L3 Vulcan

wi;k ðtÞ ¼

Q i 1 X

fi;k ðqÞx½ðt  qÞmod N

ð1Þ

q¼0

where {fi,k(q)} is the stationary wavelet packet filter at level i and sub-band k. Thus the component at level i and subband k, with the number of 2i  1 + k, is

di;k ðtÞ ¼

Q i 1 X

fi;k ðqÞwi;k ½ðt  qÞmod N

ð2Þ

q¼0

Load1

Load2

Fig. 6. The simulated power system (Eskom subnetwork).

Stationary wavelet transform can decompose a signal into narrow-band components, which will meet singlecomponent signal analysis requirements like in phasor

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estimation. Fig. 1 shows the SWT decomposition tree and the up sampling of the filters.

4. Simulation and results In order to check the performance of the proposed scheme, we used two study cases as given below:

3. The proposed scheme

i Statistical performance analysis with dc offset and various noise levels. ii Simulation of a phase to ground fault in power system.

Consider a faulted phase current ip(t) that has a decaying DC offset component ie(t) and the sinusoidal components is(t) as given by (3)–(5)

ie ðtÞ ¼ Aet=s is ðtÞ ¼

ð3Þ

4.1. Statistical performance analysis

M X In cosðnxt þ /n Þ

ð4Þ Consider a hypothetical signal y(t) given by

n¼1

ip ðtÞ ¼ Aet=s þ

M X

In cosðnxt þ /n Þ

ð5Þ

yðtÞ ¼ Ie et=s þ IA cosðxt þ /n Þ þ

n¼2

n¼1

A is the magnitude of exponential decaying DC offset, s is the time constant of the decaying DC offset, In is the amplitude of the nth harmonics, /n is the phase angle of the nth harmonics, x is the electrical angular frequency. If we pre-process ip(t) in (5) with an anti-aliasing filter to band limit the signal, such that we have

if ðtÞ ¼ Ie et=s þ IA cosðxt þ /n Þ þ

Q X In cosðnxt þ /n Þ

ð6Þ

n¼2

The scheme shown in Fig. 2 can be used in totally removing a decaying dc offset and most of the high order harmonics. Consider t

if ðtÞ ¼ IA ½sinðxt þ h  /Þ þ sinðh  /Þes 

ð7Þ

where h, / and s are phase angle, fault incidence angle and the decaying dc offset time constant respectively. Fig. 3 shows a 5 level stationary wavelet decomposition of a sinusoidal signal (7) with an amplitude IA = 100, s = 0.127 s, h = 12°, and / = 88.57°. Haar wavelet is used in the decomposition. It is easily observed from Fig. 3 that, the amplitude of detail coefficients at various levels greatly differ from the amplitude of the input signal which is 100, except for level 3 detail coefficients which gives a very close approximation. In addition the SWT decomposition has introduced a constant dc in the detail coefficients of levels 2, 4 and 5 as could be seen in Fig. 3b, d and f respectively. There is also a slight constant dc offset at level 3. It is apparent that the amplification factors for levels 2–5 are 0.4, 1, 2.5 and 3.5 respectively. Although, the detail coefficients at level 3 of SWT using Haar wavelet can completely filter a decaying dc offset and give a good representation of the original signal, however we will show later that level 3 does not have a good noise immunity when the signal to noise ratio (SNR) is 20 dB. In order to ensure that all amplitudes of the detail coefficients at various levels have a correlation with the amplitude of the input signal, a normalization constant Kc is introduced. Kc for various sampling rate and Haar wavelet based SWT levels is given in Table 1. This will ensure that the amplification factor is 1 irrespective of the level of the detail coefficients used.

Q X In cosðnxt þ /n Þ þ ðtÞ

ð8Þ y(t) can represent the current or voltage measurements from instrumentation devices in substations, in general they are not clean. The signals are perturbed by various noises in such an hostile environment. In order to check the effect of noise perturbations on the proposed scheme, an additive white Gaussian noise (t) of signal to noise ratio (SNR) between 20 dB and 80 dB is added to y(t) using the awgn function in MATLAB. The following signal parameters are used in the simulation: Ie = 1 p.u., IA = 1 p.u., the sampling frequency fs = 3.2 kHz. Fig. 4 illustrate the removal of decaying dc offset and various distortions in the amplitude estimates with a SNR of 20 dB and 40 dB. Although, the detail coefficients at level 3 is able to remove the decaying dc offset, however the sensitivity of the coefficient to noise is higher compared to the detail coefficients at level 5. Fig. 5 shows the histograms of amplitude estimates obtained from various SWT detail levels. Level 3 gives the worst estimate of the signal amplitude at 20 dB SNR. For

Table 2 Transmission lines parameter.

L1 L2 L3

Length (km)

R0 (X)

R1 (X)

X0 (X)

X1 (X)

84.74 96.23 39.18

32.50 35.98 15.27

1.91 1.44 0.88

92.82 104.11 43.01

27.32 26.76 12.48

Table 3 Generators parameter x00d ¼ x00q ¼ x0 ¼ x2 .

G1 G2

xd

xq

x0d

x0q

x0d

MVA

2.23 1.95

2.13 1.9

0.28 0.35

0.42 0.5

0.27 0.258

810 666

Table 4 Scheduled loads, at load buses.

Load1 Load2

Active (MW)

Reactive (MVar)

534.6 945.4

19.9 201.8

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a waveform having 1 as the amplitude, and a decaying dc offset, the amplitude estimate by using level 3 detail coefficients is between 0.4 and 2.5 for a noise level of 20 dB SNR, see Fig. 5a. However for the same noise level, the SWT detail level 5 gives amplitude estimate whose values lie between 0.9 and 1.1 as can be seen in Fig. 5g. If the noise level is around 40 dB SNR, we have amplitude estimates of 0.85–1.2, 0.95–1.05 and 0.985–1.01 for SWT detail levels 3–5 respectively. The practical implication of this is that the accuracy of the amplitude estimates

could be graded by using different detail levels. Using the level 3 detail coefficients gives the fastest result as could be seen in the phase difference between the original signal and the scheme output for various levels in Fig. 4b, d and f. 4.2. Simulated power system A segment of Eskom network simulated is shown in Fig. 6 to illustrate the performance of the scheme, the data used for simulation are given in Tables 2–4. The fault

Voltage amplitude estimation

Current dc−offset filtering

Amplitude estimate proposed scheme faulted voltage waveform

Amplitude estimate proposed scheme faulted current waveform

1

10

0.5

5

Amplitude (p.u)

Amplitude (p.u)

1.5

0

0

−0.5 −5

−1

1.9

1.92 1.94 time (s)

1.96

−10 1.88

1.98

1.9

Voltage amplitude estimation 2

1.92 1.94 time (s)

1.96

Current dc−offset filtering

Amplitude estimate proposed scheme faulted voltage waveform

Amplitude estimate proposed scheme faulted current waveform 10

1.5

1 Amplitude (p.u)

Amplitude (p.u)

5

0.5

0

−0.5

0

−5

−1 −10 1.88

1.9

1.92

1.94 time (s)

1.96

1.98

1.9

1.92

1.94 time (s)

Fig. 7. The proposed scheme with levels 2 and 3 on a LN fault at 53 km.

1.96

1.98

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Current dc−offset filtering

Amplitude estimate proposed scheme faulted voltage waveform

Amplitude estimate proposed scheme faulted current waveform

15

1 10

Amplitude (p.u)

Amplitude (p.u)

0.5

0

5

0

−5 −0.5 −10

−1 1.88

1.9

1.92

1.94 time (s)

1.96

1.98

−15 1.88

1.9

Voltage amplitude estimation 1.5

1.92

1.94 time (s)

1.96

1.98

Current dc−offset filtering 15

Amplitude estimate proposed scheme faulted voltage waveform

Amplitude estimate proposed scheme faulted current waveform

1 10

Amplitude (p.u)

Amplitude (p.u)

0.5

0

5

0

−0.5

−5 −1

1.9

1.92

1.94 time (s)

1.96

1.98

1.88

1.9

1.92 1.94 time (s)

1.96

1.98

Fig. 8. The proposed scheme with levels 4 and 5 on a LN fault at 53 km.

current at Kendal bus is first preprocessed through an antialiasing filter, a 2nd order Butterworth filter with cutoff frequency of 200 Hz was used for the anti-aliasing. The output of the anti-aliasing filter was then fed into the proposed scheme as shown in Fig. 2. The outputs of the scheme for a line to neutral fault on the simulated power system are shown in Figs. 7 and 8. Fig. 7a has the fastest response in terms of the time lag between the actual simulated measurements and the scheme output as could be seen in the current and the voltage plot. But this is at the expense of noise immunity and the over

shoot in the voltage amplitude estimates. The time lag is clearly evident SWT detail coefficients at level 5 in Fig. 8b, however there is no overshoot in the voltage amplitude estimate, and it seems to have a better noise immunity compared to the other levels. 4.3. A phase to ground fault current from digital fault recorder (DFR) in Eskom Eskom has DFRs installed on most of their transmission lines to record disturbances. These records are used for

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A.A. Yusuff et al. / Measurement 47 (2014) 919–928 Record from a DFR

Record from a DFR 300

8000

200 Amplitude (A)

Amplitude (A)

6000 4000 2000 0 −2000

100 0 −100 −200 −300 −400

−4000

−500

−6000

−600 −700 0.54

−8000 0.4

0.5

0.6

0.7

0.8 time (s)

0.9

1

1.1

0.6

0.62 time (s)

0.64

0.66

0.68

10000 ia ib ic

swt ia swt ib swt ic ia ib ic

8000

6000

6000 Amplitude (A)

Amplitude (A)

0.58

Plot of fault voltage with fault location 53.5 km

Plot of fault current with fault location 53.5 km 8000

0.56

4000 2000 0

4000 2000 0

−2000

−2000

−4000

−4000 −6000

−6000

−8000

−8000 0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

0.93

0.94

0.95

0.96

0.97

time (s)

0.98 time (s)

0.99

1

1.01

1.02

Fig. 9. The output of the proposed scheme in response to the DFR record.

post disturbance analysis of various relays operations. We tested the performance of the scheme on real life data recorded by one of the DFR for Duvha – Kendal 400 kV transmission line. The data is for a phase to ground fault on red phase at a fault location of 53.5 km from Duvha substation. The DFR record is first converted from a proprietary format to IEEE COMTRADE and ASCII format, which then are later imported into MATLAB workspace. as shown in Fig. 9a. The scanning frequency of the DFR is 2.5 kHz, which translate to a sampling frequency of 2.5 kHz for the measurement. The measurement is re sampled to give a sampling rate of 3.2 kHz using ‘‘resample’’ function in MATLAB. The reason for this is based on the fact that SWT needs a data length of 2Q, where Q is an integer. A sampling rate of 3.2 kHz give 64 samples per cycle. The expanded views of Fig. 9a before the fault and after the fault are given in Fig. 9b and c respectively. It is easily seen that the current measurement is corrupted by noise even before the fault and by a decaying DC offset after the fault. The output of the proposed scheme in response to the DFR record is shown in Fig. 9d. The proposed scheme is able to totally remove the decaying dc offset in addition to high frequency noise in the measurements. However, there is a phase shift between the original measurement and the output of the scheme.

5. Conclusion The paper presents a new scheme based on stationary wavelet transform for a complete removal of a decaying dc offset from fault current and voltage measurements irrespective of the time constant of the network. The scheme is able to achieve this at various accuracy depending on the level of SWT detail coefficients used. The delay is lowest when level 3 detail coefficients are used, however this comes at a cost of a poor noise immunity. Although, the delay in level 5 is appreciable compared to the others, level 5 offers a better noise immunity. Based on the three study cases investigated, the detail level used in filtering should be based on the SNR prevalent in the application context. The new scheme is robust and efficient even in the presence of noise level 20 dB. References [1] E.O. Schweitzer, D. Hou, Filtering for protective relays, in: Proceedings of the 19th Western Protective Relay Conference, Spokane, Washington, 1992. [2] Gabriel, Benmouyal, Removal of dc offset in current waveforms using digital mimic filtering, IEEE Transactions Power Delivery 10 (2) (1995) 621–630. [3] Chi, Shan, Yu, A discrete-fourier-transform based adaptive mimic phasor estimator for distance relaying applications, IEEE Transactions on Power Delivery 21 (4) (2006) 1836–1846.

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