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A virtual measurement instrument for electrical power quality analysis using wavelets
Measurement 42 (2009) 298–307
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A virtual measurement instrument for electrical power quality analysis using wavelets Julio Barros *, Matilde de Apraiz, Ramón I. Diego Department of Electronics and Computers, University of Cantabria, Escuela Técnica Superior de Náutica, Dique de Gamazo 1, Santander 39004, Spain
a r t i c l e
i n f o
Article history: Received 8 April 2008 Received in revised form 23 May 2008 Accepted 29 June 2008 Available online 11 July 2008
Keywords: Disturbances Harmonics Power quality Wavelet transforms
a b s t r a c t This paper presents a virtual measurement instrument for detection and analysis of power quality disturbances in voltage supply using wavelets. The instrument developed can operate in different working modes depending on the type of power quality disturbance to be detected and analyzed. In each mode different wavelet analysis (discrete or wavelet-packet transform), with different mother wavelet, decomposition tree and different sampling rate is performed on the input signal either in real-time or off-line. The instrument also permits the partial implementation of a wavelet decomposition tree when we are only interested in a specific frequency band in the input signal. The results obtained in simulation and using real signals demonstrate the good performance of the instrument developed for the detection and analysis of different power quality disturbances in voltage supply. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Electrical power quality is a general term used to designate a number of electromagnetic phenomena that cause voltage supply to deviate from its constant magnitude and frequency ideal sinusoidal waveshape. Two main groups of power quality disturbances can be defined: stationary (or quasi-stationary) and transient disturbances. Harmonic and interharmonic distortion, voltage fluctuation, voltage flicker and voltage unbalance make up the first group, whereas voltage transients, voltage dips, voltage swells, short interruptions in voltage supply and other high-frequency disturbances constitute the latter group. The root mean square magnitude (rms) is the most common signal processing tool used for estimation of voltage and current magnitude in power systems. Although the rms magnitude is defined for sinusoidal and periodic signals, it is also used in international power quality standards for estimation of non-periodic and time-varying signals such as voltage dips and swells or short interruptions in voltage supply [1]. * Corresponding author. E-mail address: [email protected] (J. Barros). 0263-2241/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2008.06.013
The discrete Fourier transform (DFT) should be used when we want to know the magnitude and phase-angle of the different frequency components of a periodic and stationary voltage or current waveform. IEC 61000-4-7 [2] proposes the use of rectangular sampling windows of 10-cycles’ width in 50-Hz power systems (12 cycles in 60-Hz systems) and the grouping of the output bins of DFT analysis to compute the harmonic distortion in voltage and current waveforms. DFT analysis only provides information in the frequency domain with a resolution that depends on the time window width used in the analysis (5 Hz resolution using the standard method for measurement of harmonics). No time information about the signal is provided. Wavelets are short-duration oscillating waveforms with zero mean and fast decay to zero amplitude, especially suited to analysis of non-stationary signals. Contrary to the use of DFT analysis, the use of wavelets allows the simultaneous evaluation of a signal in the time and frequency domains with different resolutions, making it very attractive for the analysis of electrical power quality disturbances. Wavelets are used in power quality when it is not important to know the exact frequency of a disturbance in voltage or current waveforms, but the time information is
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HP
2
LP
2
a2 (n)
d 2 (n) (fs /8)
0
d 1 (n) (fs /4)
(fs /2)
Frequency (Hz) Fig. 2. Output frequency bands of the wavelet decomposition tree in Fig. 1 for fs sampling rate.
HP
2
d 4 (n)
LP
2
d 3 (n)
HP
2
d 2 (n)
LP
2
d 1 (n)
2
HP x [n]
Input signal LP
2
Fig. 3. Two-level wavelet decomposition tree for WPT analysis.
Amplitude
important. An interesting review on the use of wavelets in power quality can be seen in [3–5]. The discrete wavelet transform (DWT) is the digital representation of the continuous wavelet transform (CWT). DWT can be implemented using a multi-stage filter bank with the wavelet function as the low-pass filter (LP) and it’s dual as the high-pass filter (HP), as is shown in Fig. 1 for a two-level decomposition tree. Downsampling by two at the output of the low-pass and high-pass filters scales the wavelet by two for the next stage. The output coefficients of the low-pass filter (the approximation coefficients) are again decomposed to produce a new representation of the signal and so on, producing a logarithmic decomposition of the frequency spectra of the input signal as is shown in Fig. 2 for the wavelet decomposition tree in Fig. 1 (fs/2 is the Nyquist frequency for fs sampling rate). High time resolution is obtained in higher frequency bands whereas low time resolution is provided in the lower frequency bands of the signal. The wavelet-packet transform (WPT) can be used to overcome the limitations of the DWT and to obtain a uniform frequency decomposition of the input signal. In the WPT, the output of both, the low-pass and the high-pass filters (the detail and the approximation coefficients) are decomposed to produce new coefficients, as is shown in Fig. 3 for a two-level wavelet decomposition tree, in this way enabling a uniform frequency decomposition of the input signal (Fig. 4). Using the wavelet-packet transform instead of DWT and adequately selecting the sampling frequency and the wavelet decomposition tree, the uniform output frequency bands can be selected to correspond with the frequency bands of the different harmonic groups in the input signal, as defined in the IEC standard 61000-4-7 [6]. Two main factors affect the successful application of wavelets in power quality applications: first, the extraction of specific features for detection and identification of the different power quality disturbances and second, the selection of the most adequate wavelet mother function and the selection of the decomposition tree and sampling frequency to obtain the time–frequency resolution required. In general, WPT provides more information for signal discrimination than DWT. This paper presents a virtual measurement instrument for detection and analysis of power quality disturbances in voltage supply in a low-voltage distribution system using wavelets. Three main characteristics presents the instrument developed: (1) different wavelet analysis can be applied on the input signal depending on the type of power quality disturbance under study, (2) real-time or
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d1 (n) 0
fs / 8
d 4(n)
d 3(n)
d2(n) fs /4
3f s /8
f s /2
Frequency (Hz) Fig. 4. Output frequency bands of the wavelet decomposition tree in Fig. 3 for fs sampling rate.
off-line application of wavelet transforms can be applied and (3) a partial implementation of wavelet transforms can be used to study only the time–frequency characteristics of the specific frequency band in the input signal selected by the user. The organization of this paper is as follows. Section 2 describes the hardware structure of the instrument and its different working modes depending on the power quality disturbance to be detected and analyzed. Section 3 presents the performance of the instrument under different measurement conditions using a programmable AC voltage supply and real voltage waveforms obtained from a lowvoltage distribution system. Finally, Section 4 presents the conclusions of the paper. 2. Virtual measurement instrument The single-phase version of the instrument developed is made up of a LEM LV 25-P Hall-effect voltage transducer, a NI USB-6009 and a laptop computer (Fig. 5). The voltage
d1 (n)
x [n]
Input signal
HP
LP
2 2
d 2 (n) a2 (n)
Fig. 1. Two-level wavelet decomposition tree for DWT analysis.
Voltage supply
Voltage transducer LEM LV 25-P
NI USB-6009 Data Acquisition Board
Laptop computer
Fig. 5. Hardware structure of the virtual instrument developed.
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transducer used has an overall accuracy of ±0.6% and is useful for measuring nominal voltages from 10 to 500 V. The NI 6009 is a USB low cost data acquisition board with eight single-end/four differential analog input channels, 14-bit resolution, 48-kHz maximum sampling rate and ±10 V maximum input range. The software has been implemented using the LabVIEW 8.5 graphic programming environment. The instrument can operate in different working modes depending on the power quality disturbance to be detected and analyzed. In each case, different wavelet analysis, using different mother wavelet and different sampling rates are applied to the input signal. Two main basic working modes have been implemented at present: first, detection and analysis of transient power quality disturbances and second, analysis of stationary or quasi-stationary disturbances. 2.1. Transient power quality disturbances In this working mode the discrete wavelet transform or the wavelet-packet transform is performed using the wavelet decomposition tree, the mother wavelet and the sampling frequency selected by the user. In the current version of the instrument, voltage dips, voltage swells and short interruptions in voltage supply are studied using the two-level wavelet decomposition tree in Fig. 1, with Daubechies with four coefficients as the mother wavelet and 12.8 kHz sampling rate. According to [7] this selection shows the best performance in the detection of voltage events, but different selections could be made by the user in the front panel of the instrument. Fig. 6 shows the output frequency bands obtained using the DWT and the sampling rate selected. The coefficients of the highest frequency band of the decomposition tree d1(n), frequency band from 6.4 to 3.2 kHz, are insensitive to a steady-state signal but show a high variation in magnitude associated with the high-frequency transients present at the beginning and the end of a voltage event in voltage supply [7,8]. If these coefficients have sharp and short peaks in magnitude, then the disturbance is a short-duration voltage event, such as a voltage dip, swell or short interruption. Otherwise, if they present a long series of peaks then it corresponds to a repetitive high-frequency transient. In both cases the occurrence of
the disturbances is determined with high time resolution. The same can be applied to the 3.2–1.6 kHz frequency band for low-frequency transients. 2.1.1. Real time implementation of wavelet transforms In this working mode the wavelet transform is implemented in real-time using the method proposed in [9,10] to enable the use of the instrument as a protection scheme in power systems. In this method the input voltage samples are fragmented in sections of 2J samples, J being the maximum number of levels in the wavelet decomposition tree, it being necessary to maintain M 2 overlaps in memory (M being the size of the wavelet filter used) in the input vector and in each decomposition level in order to avoid the border effect of the data segment. Fig. 7 shows a graph with the implementation of the algorithm for one-level and two-level discrete decomposition trees, respectively. In our case, J = 2 is the maximum number of decomposition levels, so the data should be represented in sections of four samples (22). xn in Fig. 7 represents the input vector, c0 to c3 represent the coefficients of the wavelet function of size M = 4 used (c0, c1, c2, c3, are the coefficients of the low-pass filter and c3, c2, c1, c0 are the coefficients of the high-pass filter) and d(n) and a(n) represent the detail and approximation coefficients in each decomposition level. The input data are processed in pairs, as is shown in Fig. 7. (M 2) values (2 values in this case) of the input vector and of each of the approximation vectors are kept in memory to avoid the border effect. In each decomposition level the detail coefficients are provided as the outputs of the algorithm, as well as the approximation vector of the last level of the decomposition tree. The sequence of outputs
a
c 0 -c1 c 2 -c 3 c3 c2 c 1 c0 c 0 -c1 c 2 -c3 c 3 c 2 c 1 c0
previous section
(M-2) overlap
6.4 kHz
Level 1 detail coefficients d1 (n)
Nyquist frequency for 12.8 kHz sampling rate High- frequency transients
b
Low - frequency transients
d1 (0) a1 (0)
d1 (1) a1 (1)
(M-2) overlap
(M-2) overlaps
previous section
x -2 x -1 x0 x 1 x2 x 3
(M-2) overlaps
3.2 kHz Level 2 detail coefficients d 2(n)
next section
x -2 x -1 x 0 x1 x 2 x 3
d 1 (0)
d 1 (1)
a 1 (0)
a 1 (1)
next section
1.6 kHz Level 2 aprox. coefficients a2 (n) 0 Hz
Fundamental frequency and characteristic harmonics to order 30th
Fig. 6. Output frequency bands of the wavelet decomposition tree in Fig. 1 for 12.8 kHz sampling rate.
(M-2) overlaps d2 (0) a2 (0) Fig. 7. (a) One-level decomposition tree using the real-time method proposed, (b) two-level decomposition tree.
J. Barros et al. / Measurement 42 (2009) 298–307 1 1
HP
HP
2
LP
2
HP
2
LP
2
2
d4(n) 2
x [n]
d3(n) 3
Input signal 2
LP
2
d2(n) 4
Fig. 8. Partial implementation of a two-level WPT.
d1(n)
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produced by the algorithm in the two-level decomposition tree is as follows (Fig. 7b):
d1 ð0Þ; d1 ð1Þ; d2 ð0Þ; a2 ð0Þ; . . . Using this method a new magnitude of the detail and approximation coefficients in level 1 of the decomposition tree are obtained after two samples of the input signal and after four samples of the input signal in the second level. On the other hand, to perform the real-time implementation of the wavelet-packet transform (‘‘Running WPT”),
Fig. 9. Block diagram of the virtual instrument.
Fig. 10. ‘‘Running WT” VI.
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HP HP LP HP HP LP LP HP
d 32 (n) d 31 (n) d 30 (n) d 29 (n)
d´15 (n) 725 - 775 Hz
d´14 (n) 675 - 725 Hz
HP
LP
both, the detail and the approximation coefficients in each decomposition level should be decomposed, and M 2 overlaps of each array of coefficients should be stored in memory for processing the next section of data. Obviously, the computational load of this algorithm increases considerably in comparison with the ‘‘Running DWT” algorithm. The sequence of outputs produced in the case of a two-level wavelet packet decomposition tree is in this case as follows:
d1 ð0Þ; a1 ð0Þ; d1 ð1Þ; a1 ð1Þ; d2 ð0Þ; a2 ð0Þ; . . .
LP Input signal
HP
HP
HP LP HP
LP
HP LP LP LP HP HP LP LP HP LP LP
d´4 (n) d 8 (n) d 7 (n) d 6 (n) d 5 (n) d 4 (n) d 3 (n) d 2 (n)
175 - 225 Hz
d´3 (n) 125 - 175 Hz
d´2 (n) 75 - 125 Hz
d´1 (n) 25 - 75 Hz
d 1 (n)
Fig. 11. Five-level wavelet decomposition tree for time–frequency analysis of harmonic distortion.
2.1.2. Partial implementation of wavelet transforms An additional option provided by the program is the partial implementation of the wavelet decomposition tree when we are only interested in a specific frequency band in the input signal. To this end the user first selects the number of levels of the wavelet decomposition tree (J) and second, the required output frequency band in this level (numbered from 1 to 2J in ascending order with the lowest number corresponding to the high-frequency band, as is shown in Fig. 8). The program then generates an array with the correct sequence of HP or LP filters necessary to compute the coefficients of the output band selected. The array is generated starting from the output band x selected at level J and computing the function ceil(x/2) to obtain the output band at level J 1 and so on until the first level of the decomposition tree.
Fig. 12. (a) Voltage notches in voltage supply due to a six-pulse converter, (b) frequency components in voltage supply.
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As an example, Fig. 8 shows the partial implementation of a two-level wavelet decomposition tree using the WPT to compute coefficients d3(n) (output frequency band number 2 at level 2). As can be seen in Fig. 8 in this case the filter sequence applied to the input signal is [HP in level 1 and LP in level 2]. 2.1.3. Implementation in LabVIEW Fig. 9 shows the block diagram of the virtual instrument developed using LabVIEW 8.5 graphic programming environment. Five main VIs make up this block diagram: ‘‘Input control parameters”, ‘‘Initialization”, ‘‘Running WT”, ‘‘Partial Running WT” and ‘‘Output Graphs”. ‘‘Input control parameters” is a VI that collects all the input data selected by the user using the controls on the front panel of the instrument. Wavelet function, maximum number of the wavelet decomposition tree, sampling frequency, discrete or packet wavelet transform, real-time or off-line implementation and partial or complete wavelet decomposition can be selected by the user. As a result the VI computes, among others, the output frequency bands and the number of coefficients in each level of the wavelet decomposition tree. ‘‘Initialization” selects from memory the appropriate wavelet filter coefficients (LP and HP, respectively) to per-
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form the wavelet transform and performs the initialization of all the data structures of the program. The VIs ‘‘Running WT” and ‘‘Partial Running WT” can be used in real-time or off-line depending on the selection made by the user on the front panel of the instrument. In the first case the input data are taken from the VI ‘‘DAQ”, otherwise the input data are taken from a data file (Input File) previously selected by the user, as is shown in Fig. 10. These VIs perform the convolutions, downsampling and the temporal storing in memory required for the implementation of the algorithm (described in Section 2.1.1), using the selection made by the user. In the case of the selection of ‘‘Partial Running WT”, the VI selects the correct sequence of high-pass and low-pass filters necessary for the computation of the coefficients of the required frequency band of the input signal, selected by the user on the front panel of the instrument as was described in Section 2.1.2. The VI ‘‘DAQ” controls the data acquisition of the input signal. This VI is programmed for continuous sampling of analog input channel 1 of the NI USB-6009 data acquisition board using the sampling frequency previously selected by the user. The voltage samples in pairs are sent to the data processing VI ‘‘WT”. Finally, ‘‘Output Graphs” is a VI that shows the waveform of the power quality disturbance and the coefficients
Fig. 13. (a) Waveform of voltage supply with a voltage dip, (b) magnitude of coefficients d1(n) obtained applying DWT.
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of the output frequency bands obtained applying the wavelet transform selected by the user. 2.2. Stationary or quasi-stationary power quality disturbances Two different power quality disturbances are considered in this working mode: harmonic distortion and voltage notching in voltage supply. 2.2.1. Harmonic distortion In the case of the estimation of harmonic distortion in voltage supply the WPT is applied to the voltage samples. The five-level wavelet decomposition tree in Fig. 11, with Vaidyanathan with 24 coefficients as the mother wavelet is used. This mother wavelet function has been proved in [11,12] as the most appropriate wavelet function for harmonic analysis (it has the best frequency characteristics, it is smoother in the passband and it shows less spectral leakage). Selecting 1.6 kHz sampling rate and using sampling window widths of 10 cycles of the fundamental frequency (200 ms in a 50-Hz power system), the output of the wavelet decomposition tree is formed by 32 bands of 25 Hz width, from 0 to 800 Hz (the Nyquist frequency for the sampling rate used), d1(n) to d32(n) in Fig. 11, which are grouped in 15 output bands of 50-Hz width centred on 0 0 each harmonic component, d1 ðnÞ to d15 ðnÞ in Fig. 11, mak-
ing the algorithm compatible with the harmonic groups defined in IEC 61000-4-7. As is reported in [6] this method presents an error in the acceptable range for a measurement instrument for the case of stationary harmonic distortion and better results than the standard method in the case of non-stationary harmonic distortion and in the case of the presence of non-synchronized interharmonic components. Furthermore, as is shown in [13], the method proposed enables the tracking of the time evolution of the odd harmonic frequency bands in the input signal using the outputs of the third level of the same wavelet decomposition tree. In this third level there are eight outputs bands with uniform 100-Hz width covering the frequency spectra from 0 to 800 Hz, with the odd harmonic frequencies from 1st to 15th order in the centre of each band. 2.2.2. Voltage notching Voltage notching is a type of periodic waveform distortion produced by the normal operation of power electronic devices when current commutates from one phase to another. During this period, there is a momentary short circuit between two phases being determined the severity of the notch by the source inductance between the converter and the point being monitored. Voltage notching represents a special case that falls between transient and harmonic distortion. Since notching
Fig. 14. (a) Waveform of voltage supply with a voltage swell, (b) magnitude of coefficients d1(n) obtained applying DWT.
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occurs continuously, it can be characterized through the harmonic spectrum. However, the frequency components associated with notching can be quite high and may not be readily characterized with measurement equipment normally used for harmonic analysis. Fig. 12a shows the waveform of a 460 V, 60 Hz, voltage supply with voltage notches due to a six-pulse converter [14] and Fig. 12b shows a zoom area of the frequency spectrum of the signal obtained applying DFT analysis. The sampling frequency used is 10.2 kHz (0.098 ms sampling period). As can be seen the spectrum of the signal is spread over the whole frequency range up to the harmonic of order 85, corresponding to 5.1 kHz in a 60 Hz system (the Nyquist frequency for the sampling rate used). The magnitude of the fundamental component using DFT was 462.4 V and the total harmonic distortion (THD) computed up to the harmonic of order 40 (maximum harmonic order for computation of THD in voltage supply in low-voltage and medium-voltage supply systems according to European Standard EN 50160 [15]) was 7.58%, whereas the high-frequency THD, computed from harmonic order 41 to order 85 was 4.57%. Two main features of this type of power quality disturbance can be highlighted: the transients associated with the beginning and the end of the commutation notches and the stationary high-frequency components in the spectrum of the signal.
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This time–frequency characteristic of the signal can be used as detection criteria. To this purpose the detail coefficients of the first level of the wavelet decomposition tree in Fig. 1, d1(n), using Daubechies with four coefficients as the mother wavelet, are computed for detection and assessment of voltage notches in voltage supply. The number of peaks in coefficients d1(n) over a specific threshold magnitude, computed in the case of no disturbance in the input signal, and the total energy of these coefficients have been used as detection criteria. In this working mode one-cycle window width and 40 kHz sampling frequency, as proposed in IEEE Std. 1159-1995 for assessment of voltage notching [16], are used. 3. Experimental results The instrument developed has been tested in simulation, using a single-phase/three-phase programmable power source [17] and using real voltage signals taken from the low-voltage distribution system of a building located in our campus. Three different groups of examples are considered in this section to show the performance of the instrument developed in the detection and analysis of transient and stationary power quality disturbances in voltage supply. The first group studies the detection and analysis of voltage events: a voltage dip, a voltage swell and of a short interruption in voltage supply are considered. The second
Fig. 15. (a) Waveform of voltage supply with a short interruption, (b) magnitude of coefficients d1(n) obtained applying DWT.
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group considers the case of the time–frequency analysis of a fluctuating harmonic component and finally, the third example describes the detection and analysis of the voltage notching produced by a six-pulse converter. 3.1. Voltage events Fig. 13 shows the waveform of voltage supply with a 132 V magnitude and 100 ms voltage dip and the magnitude of the detail coefficients of the first level of the wave-
let decomposition tree in Fig. 1, d1(n), obtained applying DWT with Daubechies with four coefficients to voltage samples and 12.8 kHz sampling frequency. Fig. 14 presents the case of a 270 V magnitude, 72 ms duration voltage swell and the magnitude of coefficients d1(n). Both voltage events have been generated using the AC programmable voltage source using 230 V, 50-Hz fundamental component and a harmonic distortion of 1% of 3rd order harmonic, 3% of 5th order harmonic and 1.5%, 1% and 0.9% of 7th, 9th and 11th order harmonic components, respectively (this har-
Fig. 16. Voltage waveform with a 5th order harmonic fluctuation and time evolution of the corresponding output coefficients in level 3 of the wavelet decomposition tree in Fig. 11.
Fig. 17. Magnitude of coefficients d1(n) for the voltage waveform in Fig. 12a.
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monic distortion is the typical harmonic distortion measured in our low-voltage distribution system during the afternoon on a week day). Finally, Fig. 15 shows the waveform of voltage supply with a 106.09 ms short interruption and the magnitude of the detail coefficients d1(n). This short interruption has been recorded in the low-voltage distribution network of our building. As can be seen in all the examples considered, coefficients d1(n) are insensitive to the steady-state magnitude of voltage supply but show sharp variation in magnitude corresponding to the beginning and end of the voltage event. Therefore, using these coefficients the beginning, the end and the duration of the voltage event can be accurately detected. 3.2. Non-stationary harmonic distortion As an example of the time–frequency characteristics of the method proposed in the analysis of stationary or quasistationary power quality disturbances, this example studies the case of a fluctuating harmonic component. Fig. 16a shows 10 cycles of voltage supply measured in a low-voltage distribution system, with a predominant fifth-order harmonic of 3.15% magnitude. A change in magnitude of this harmonic component from 3.15% magnitude to 6% magnitude (compatibility level for low-voltage supply distribution systems according to European standard EN50160) is produced at instant 75 ms of the record. Fig. 16b shows the magnitude of the output coefficients of level 3 of the wavelet decomposition tree in Fig. 11 corresponding to the output band from 200 to 300 Hz, where the fifth harmonic component is predominant. As can be seen the change in magnitude of the fifthorder harmonic can be accurately detected using these coefficients. 3.3. Voltage notching Finally, the performance of the instrument developed is shown in the detection and analysis of voltage notching. Fig. 17 shows the magnitude of the detail coefficients of the first level of the wavelet decomposition tree in Fig. 1 obtained applying DWT with Daubechies with four coefficients to voltage waveform in Fig. 12a. As can be seen the magnitude of coefficients d1(n) shows a long series of peaks (six peaks/cycle) exactly corresponding to the notches in voltage supply. The beginning, the end and the duration of voltage notches can be determined with a time resolution double of the sampling period of the signal due to the downsampling by two associated with the computation of the coefficients of the first level of the wavelet decomposition tree (0.196 ms in this case). 4. Conclusion The paper presents the structure and the performance of a virtual measurement instrument for detection and analysis of power quality disturbances in power systems
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using wavelets. Depending on the working mode selected as a function of the type of power quality disturbance to be detected and analyzed, the instrument implements in real time or off-line, different wavelet analysis on the input signal. An additional feature of the instrument is the partial implementation of wavelet analysis to study only a specific frequency band in the input signal. The results obtained demonstrate the good performance of the instrument in the detection and analysis of power quality disturbances as well as showing its possible use in relaying applications. Acknowledgements The authors thank the Spanish Ministry of Science and Technology, National Plan R+D+I (2004–2007), for its support of this research project under Grant DPI2006-15083C02, of which the present paper is a part. References [1] International Electrotechnical Commission, IEC 61000-4-30. Electromagnetic compatibility (EMC). Part 4-30: Testing and measurement techniques. Power quality measurement methods, Switzerland, 2003. [2] International Electrotechnical Commission, IEC 61000-4-7. Electromagnetic compatibility (EMC). Part 4-7: Testing and measurement techniques. General guide on harmonics and interharmonics measurement and instrumentation, for power supply systems and equipment connected thereto, Switzerland, 2002. [3] S. Chen, H.Y. Zhu, Wavelet transform for processing power quality disturbances, EURASIP Journal on Advances in Signal Processing (2007) 1–20, doi:10.1155/2007/47695. [4] N.C.F. Tse, L.L. Lai, Wavelet-based algorithm for signal analysis, EURASIP Journal on Advances in Signal Processing (2007) 1–20, doi: 10.1155/2007/38916. [5] C.H. Lee, Y.J. Wang, W.L. Huang, A literature survey of wavelets in power engineering applications, Proceedings of the National Science Council, Republic of China Part B 24 (4) (2000) 249–258. [6] J. Barros, R.I. Diego, A new method for measurement of harmonic groups in power systems using wavelet analysis in the IEC standard waveform, Electric Power Systems Research 74 (4) (2006) 200–208. [7] J. Barros, E. Pérez, A combined wavelet – Kalman filtering scheme for automatic detection and analysis of voltage dips in power systems, in: IEEE PowerTech2005, St. Petersburg, Russia, 2005. [8] A.C. Parsons, W.M. Grady, E.J. Powers, A wavelet-based procedure for automatically determining the beginning and end of transmission system voltage sags, in: Proceedings of IEEE Power Engineering Society Winter Meeting, New York, USA, 1999, vol. 2, pp. 1310–1315. [9] H. Mota, F.H. Vasconcelos, R.M. da Silva, Real-time wavelet transform algorithms for the processing of continuous streams of data, in: IEEE International Workshop on Intelligent Signal Processing, Faro, Portugal, 2005, pp. 346–351. [10] J. Barros, M. de Apraiz, R.I. Diego, Real-time implementation of wavelet transforms for electrical power quality applications, in: 14th IEEE Mediterranean Electrotechnical Conference, Ajaccio, France, 2008, pp. 635–639. [11] E.Y. Hamid, Z. Kawasaki, Wavelet packet transform for rms values and power measurements, IEEE Power Engineering Review 21 (9) (2001) 49–51. [12] J. Barros, R.I. Diego, Analysis of harmonics in power systems using the wavelet-packet transform, IEEE Transactions on Instrumentation and Measurement 57 (1) (2008) 63–69. [13] J. Barros, R.I. Diego, Time–frequency analysis of harmonics in power systems using wavelets, WSEAS Transactions on Power Systems 1 (11) (2006) 1924–1929. [14] http://grouper.ieee.org/groups/harmonic/iharm/docs/data/. [15] European Standard EN 50160, Voltage characteristics of electricity supplied by public distribution systems, CENELEC, 1999. [16] IEEE Std. 1159-1995, IEEE Recommended practice for monitoring electric power quality, IEEE, New York, USA, 1995. [17] HP 6800 Series AC power source/analyzer. User’s guide, Hewlett– Packard Company, 1995.
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Measurement journal homepage: www.elsevier.com/locate/measurement
A virtual measurement instrument for electrical power quality analysis using wavelets Julio Barros *, Matilde de Apraiz, Ramón I. Diego Department of Electronics and Computers, University of Cantabria, Escuela Técnica Superior de Náutica, Dique de Gamazo 1, Santander 39004, Spain
a r t i c l e
i n f o
Article history: Received 8 April 2008 Received in revised form 23 May 2008 Accepted 29 June 2008 Available online 11 July 2008
Keywords: Disturbances Harmonics Power quality Wavelet transforms
a b s t r a c t This paper presents a virtual measurement instrument for detection and analysis of power quality disturbances in voltage supply using wavelets. The instrument developed can operate in different working modes depending on the type of power quality disturbance to be detected and analyzed. In each mode different wavelet analysis (discrete or wavelet-packet transform), with different mother wavelet, decomposition tree and different sampling rate is performed on the input signal either in real-time or off-line. The instrument also permits the partial implementation of a wavelet decomposition tree when we are only interested in a specific frequency band in the input signal. The results obtained in simulation and using real signals demonstrate the good performance of the instrument developed for the detection and analysis of different power quality disturbances in voltage supply. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Electrical power quality is a general term used to designate a number of electromagnetic phenomena that cause voltage supply to deviate from its constant magnitude and frequency ideal sinusoidal waveshape. Two main groups of power quality disturbances can be defined: stationary (or quasi-stationary) and transient disturbances. Harmonic and interharmonic distortion, voltage fluctuation, voltage flicker and voltage unbalance make up the first group, whereas voltage transients, voltage dips, voltage swells, short interruptions in voltage supply and other high-frequency disturbances constitute the latter group. The root mean square magnitude (rms) is the most common signal processing tool used for estimation of voltage and current magnitude in power systems. Although the rms magnitude is defined for sinusoidal and periodic signals, it is also used in international power quality standards for estimation of non-periodic and time-varying signals such as voltage dips and swells or short interruptions in voltage supply [1]. * Corresponding author. E-mail address: [email protected] (J. Barros). 0263-2241/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2008.06.013
The discrete Fourier transform (DFT) should be used when we want to know the magnitude and phase-angle of the different frequency components of a periodic and stationary voltage or current waveform. IEC 61000-4-7 [2] proposes the use of rectangular sampling windows of 10-cycles’ width in 50-Hz power systems (12 cycles in 60-Hz systems) and the grouping of the output bins of DFT analysis to compute the harmonic distortion in voltage and current waveforms. DFT analysis only provides information in the frequency domain with a resolution that depends on the time window width used in the analysis (5 Hz resolution using the standard method for measurement of harmonics). No time information about the signal is provided. Wavelets are short-duration oscillating waveforms with zero mean and fast decay to zero amplitude, especially suited to analysis of non-stationary signals. Contrary to the use of DFT analysis, the use of wavelets allows the simultaneous evaluation of a signal in the time and frequency domains with different resolutions, making it very attractive for the analysis of electrical power quality disturbances. Wavelets are used in power quality when it is not important to know the exact frequency of a disturbance in voltage or current waveforms, but the time information is
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HP
2
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2
a2 (n)
d 2 (n) (fs /8)
0
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Frequency (Hz) Fig. 2. Output frequency bands of the wavelet decomposition tree in Fig. 1 for fs sampling rate.
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2
d 4 (n)
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2
d 3 (n)
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d 2 (n)
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Fig. 3. Two-level wavelet decomposition tree for WPT analysis.
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important. An interesting review on the use of wavelets in power quality can be seen in [3–5]. The discrete wavelet transform (DWT) is the digital representation of the continuous wavelet transform (CWT). DWT can be implemented using a multi-stage filter bank with the wavelet function as the low-pass filter (LP) and it’s dual as the high-pass filter (HP), as is shown in Fig. 1 for a two-level decomposition tree. Downsampling by two at the output of the low-pass and high-pass filters scales the wavelet by two for the next stage. The output coefficients of the low-pass filter (the approximation coefficients) are again decomposed to produce a new representation of the signal and so on, producing a logarithmic decomposition of the frequency spectra of the input signal as is shown in Fig. 2 for the wavelet decomposition tree in Fig. 1 (fs/2 is the Nyquist frequency for fs sampling rate). High time resolution is obtained in higher frequency bands whereas low time resolution is provided in the lower frequency bands of the signal. The wavelet-packet transform (WPT) can be used to overcome the limitations of the DWT and to obtain a uniform frequency decomposition of the input signal. In the WPT, the output of both, the low-pass and the high-pass filters (the detail and the approximation coefficients) are decomposed to produce new coefficients, as is shown in Fig. 3 for a two-level wavelet decomposition tree, in this way enabling a uniform frequency decomposition of the input signal (Fig. 4). Using the wavelet-packet transform instead of DWT and adequately selecting the sampling frequency and the wavelet decomposition tree, the uniform output frequency bands can be selected to correspond with the frequency bands of the different harmonic groups in the input signal, as defined in the IEC standard 61000-4-7 [6]. Two main factors affect the successful application of wavelets in power quality applications: first, the extraction of specific features for detection and identification of the different power quality disturbances and second, the selection of the most adequate wavelet mother function and the selection of the decomposition tree and sampling frequency to obtain the time–frequency resolution required. In general, WPT provides more information for signal discrimination than DWT. This paper presents a virtual measurement instrument for detection and analysis of power quality disturbances in voltage supply in a low-voltage distribution system using wavelets. Three main characteristics presents the instrument developed: (1) different wavelet analysis can be applied on the input signal depending on the type of power quality disturbance under study, (2) real-time or
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d1 (n) 0
fs / 8
d 4(n)
d 3(n)
d2(n) fs /4
3f s /8
f s /2
Frequency (Hz) Fig. 4. Output frequency bands of the wavelet decomposition tree in Fig. 3 for fs sampling rate.
off-line application of wavelet transforms can be applied and (3) a partial implementation of wavelet transforms can be used to study only the time–frequency characteristics of the specific frequency band in the input signal selected by the user. The organization of this paper is as follows. Section 2 describes the hardware structure of the instrument and its different working modes depending on the power quality disturbance to be detected and analyzed. Section 3 presents the performance of the instrument under different measurement conditions using a programmable AC voltage supply and real voltage waveforms obtained from a lowvoltage distribution system. Finally, Section 4 presents the conclusions of the paper. 2. Virtual measurement instrument The single-phase version of the instrument developed is made up of a LEM LV 25-P Hall-effect voltage transducer, a NI USB-6009 and a laptop computer (Fig. 5). The voltage
d1 (n)
x [n]
Input signal
HP
LP
2 2
d 2 (n) a2 (n)
Fig. 1. Two-level wavelet decomposition tree for DWT analysis.
Voltage supply
Voltage transducer LEM LV 25-P
NI USB-6009 Data Acquisition Board
Laptop computer
Fig. 5. Hardware structure of the virtual instrument developed.
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transducer used has an overall accuracy of ±0.6% and is useful for measuring nominal voltages from 10 to 500 V. The NI 6009 is a USB low cost data acquisition board with eight single-end/four differential analog input channels, 14-bit resolution, 48-kHz maximum sampling rate and ±10 V maximum input range. The software has been implemented using the LabVIEW 8.5 graphic programming environment. The instrument can operate in different working modes depending on the power quality disturbance to be detected and analyzed. In each case, different wavelet analysis, using different mother wavelet and different sampling rates are applied to the input signal. Two main basic working modes have been implemented at present: first, detection and analysis of transient power quality disturbances and second, analysis of stationary or quasi-stationary disturbances. 2.1. Transient power quality disturbances In this working mode the discrete wavelet transform or the wavelet-packet transform is performed using the wavelet decomposition tree, the mother wavelet and the sampling frequency selected by the user. In the current version of the instrument, voltage dips, voltage swells and short interruptions in voltage supply are studied using the two-level wavelet decomposition tree in Fig. 1, with Daubechies with four coefficients as the mother wavelet and 12.8 kHz sampling rate. According to [7] this selection shows the best performance in the detection of voltage events, but different selections could be made by the user in the front panel of the instrument. Fig. 6 shows the output frequency bands obtained using the DWT and the sampling rate selected. The coefficients of the highest frequency band of the decomposition tree d1(n), frequency band from 6.4 to 3.2 kHz, are insensitive to a steady-state signal but show a high variation in magnitude associated with the high-frequency transients present at the beginning and the end of a voltage event in voltage supply [7,8]. If these coefficients have sharp and short peaks in magnitude, then the disturbance is a short-duration voltage event, such as a voltage dip, swell or short interruption. Otherwise, if they present a long series of peaks then it corresponds to a repetitive high-frequency transient. In both cases the occurrence of
the disturbances is determined with high time resolution. The same can be applied to the 3.2–1.6 kHz frequency band for low-frequency transients. 2.1.1. Real time implementation of wavelet transforms In this working mode the wavelet transform is implemented in real-time using the method proposed in [9,10] to enable the use of the instrument as a protection scheme in power systems. In this method the input voltage samples are fragmented in sections of 2J samples, J being the maximum number of levels in the wavelet decomposition tree, it being necessary to maintain M 2 overlaps in memory (M being the size of the wavelet filter used) in the input vector and in each decomposition level in order to avoid the border effect of the data segment. Fig. 7 shows a graph with the implementation of the algorithm for one-level and two-level discrete decomposition trees, respectively. In our case, J = 2 is the maximum number of decomposition levels, so the data should be represented in sections of four samples (22). xn in Fig. 7 represents the input vector, c0 to c3 represent the coefficients of the wavelet function of size M = 4 used (c0, c1, c2, c3, are the coefficients of the low-pass filter and c3, c2, c1, c0 are the coefficients of the high-pass filter) and d(n) and a(n) represent the detail and approximation coefficients in each decomposition level. The input data are processed in pairs, as is shown in Fig. 7. (M 2) values (2 values in this case) of the input vector and of each of the approximation vectors are kept in memory to avoid the border effect. In each decomposition level the detail coefficients are provided as the outputs of the algorithm, as well as the approximation vector of the last level of the decomposition tree. The sequence of outputs
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d 1 (1)
a 1 (0)
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1.6 kHz Level 2 aprox. coefficients a2 (n) 0 Hz
Fundamental frequency and characteristic harmonics to order 30th
Fig. 6. Output frequency bands of the wavelet decomposition tree in Fig. 1 for 12.8 kHz sampling rate.
(M-2) overlaps d2 (0) a2 (0) Fig. 7. (a) One-level decomposition tree using the real-time method proposed, (b) two-level decomposition tree.
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d4(n) 2
x [n]
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LP
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Fig. 8. Partial implementation of a two-level WPT.
d1(n)
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produced by the algorithm in the two-level decomposition tree is as follows (Fig. 7b):
d1 ð0Þ; d1 ð1Þ; d2 ð0Þ; a2 ð0Þ; . . . Using this method a new magnitude of the detail and approximation coefficients in level 1 of the decomposition tree are obtained after two samples of the input signal and after four samples of the input signal in the second level. On the other hand, to perform the real-time implementation of the wavelet-packet transform (‘‘Running WPT”),
Fig. 9. Block diagram of the virtual instrument.
Fig. 10. ‘‘Running WT” VI.
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HP HP LP HP HP LP LP HP
d 32 (n) d 31 (n) d 30 (n) d 29 (n)
d´15 (n) 725 - 775 Hz
d´14 (n) 675 - 725 Hz
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both, the detail and the approximation coefficients in each decomposition level should be decomposed, and M 2 overlaps of each array of coefficients should be stored in memory for processing the next section of data. Obviously, the computational load of this algorithm increases considerably in comparison with the ‘‘Running DWT” algorithm. The sequence of outputs produced in the case of a two-level wavelet packet decomposition tree is in this case as follows:
d1 ð0Þ; a1 ð0Þ; d1 ð1Þ; a1 ð1Þ; d2 ð0Þ; a2 ð0Þ; . . .
LP Input signal
HP
HP
HP LP HP
LP
HP LP LP LP HP HP LP LP HP LP LP
d´4 (n) d 8 (n) d 7 (n) d 6 (n) d 5 (n) d 4 (n) d 3 (n) d 2 (n)
175 - 225 Hz
d´3 (n) 125 - 175 Hz
d´2 (n) 75 - 125 Hz
d´1 (n) 25 - 75 Hz
d 1 (n)
Fig. 11. Five-level wavelet decomposition tree for time–frequency analysis of harmonic distortion.
2.1.2. Partial implementation of wavelet transforms An additional option provided by the program is the partial implementation of the wavelet decomposition tree when we are only interested in a specific frequency band in the input signal. To this end the user first selects the number of levels of the wavelet decomposition tree (J) and second, the required output frequency band in this level (numbered from 1 to 2J in ascending order with the lowest number corresponding to the high-frequency band, as is shown in Fig. 8). The program then generates an array with the correct sequence of HP or LP filters necessary to compute the coefficients of the output band selected. The array is generated starting from the output band x selected at level J and computing the function ceil(x/2) to obtain the output band at level J 1 and so on until the first level of the decomposition tree.
Fig. 12. (a) Voltage notches in voltage supply due to a six-pulse converter, (b) frequency components in voltage supply.
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As an example, Fig. 8 shows the partial implementation of a two-level wavelet decomposition tree using the WPT to compute coefficients d3(n) (output frequency band number 2 at level 2). As can be seen in Fig. 8 in this case the filter sequence applied to the input signal is [HP in level 1 and LP in level 2]. 2.1.3. Implementation in LabVIEW Fig. 9 shows the block diagram of the virtual instrument developed using LabVIEW 8.5 graphic programming environment. Five main VIs make up this block diagram: ‘‘Input control parameters”, ‘‘Initialization”, ‘‘Running WT”, ‘‘Partial Running WT” and ‘‘Output Graphs”. ‘‘Input control parameters” is a VI that collects all the input data selected by the user using the controls on the front panel of the instrument. Wavelet function, maximum number of the wavelet decomposition tree, sampling frequency, discrete or packet wavelet transform, real-time or off-line implementation and partial or complete wavelet decomposition can be selected by the user. As a result the VI computes, among others, the output frequency bands and the number of coefficients in each level of the wavelet decomposition tree. ‘‘Initialization” selects from memory the appropriate wavelet filter coefficients (LP and HP, respectively) to per-
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form the wavelet transform and performs the initialization of all the data structures of the program. The VIs ‘‘Running WT” and ‘‘Partial Running WT” can be used in real-time or off-line depending on the selection made by the user on the front panel of the instrument. In the first case the input data are taken from the VI ‘‘DAQ”, otherwise the input data are taken from a data file (Input File) previously selected by the user, as is shown in Fig. 10. These VIs perform the convolutions, downsampling and the temporal storing in memory required for the implementation of the algorithm (described in Section 2.1.1), using the selection made by the user. In the case of the selection of ‘‘Partial Running WT”, the VI selects the correct sequence of high-pass and low-pass filters necessary for the computation of the coefficients of the required frequency band of the input signal, selected by the user on the front panel of the instrument as was described in Section 2.1.2. The VI ‘‘DAQ” controls the data acquisition of the input signal. This VI is programmed for continuous sampling of analog input channel 1 of the NI USB-6009 data acquisition board using the sampling frequency previously selected by the user. The voltage samples in pairs are sent to the data processing VI ‘‘WT”. Finally, ‘‘Output Graphs” is a VI that shows the waveform of the power quality disturbance and the coefficients
Fig. 13. (a) Waveform of voltage supply with a voltage dip, (b) magnitude of coefficients d1(n) obtained applying DWT.
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of the output frequency bands obtained applying the wavelet transform selected by the user. 2.2. Stationary or quasi-stationary power quality disturbances Two different power quality disturbances are considered in this working mode: harmonic distortion and voltage notching in voltage supply. 2.2.1. Harmonic distortion In the case of the estimation of harmonic distortion in voltage supply the WPT is applied to the voltage samples. The five-level wavelet decomposition tree in Fig. 11, with Vaidyanathan with 24 coefficients as the mother wavelet is used. This mother wavelet function has been proved in [11,12] as the most appropriate wavelet function for harmonic analysis (it has the best frequency characteristics, it is smoother in the passband and it shows less spectral leakage). Selecting 1.6 kHz sampling rate and using sampling window widths of 10 cycles of the fundamental frequency (200 ms in a 50-Hz power system), the output of the wavelet decomposition tree is formed by 32 bands of 25 Hz width, from 0 to 800 Hz (the Nyquist frequency for the sampling rate used), d1(n) to d32(n) in Fig. 11, which are grouped in 15 output bands of 50-Hz width centred on 0 0 each harmonic component, d1 ðnÞ to d15 ðnÞ in Fig. 11, mak-
ing the algorithm compatible with the harmonic groups defined in IEC 61000-4-7. As is reported in [6] this method presents an error in the acceptable range for a measurement instrument for the case of stationary harmonic distortion and better results than the standard method in the case of non-stationary harmonic distortion and in the case of the presence of non-synchronized interharmonic components. Furthermore, as is shown in [13], the method proposed enables the tracking of the time evolution of the odd harmonic frequency bands in the input signal using the outputs of the third level of the same wavelet decomposition tree. In this third level there are eight outputs bands with uniform 100-Hz width covering the frequency spectra from 0 to 800 Hz, with the odd harmonic frequencies from 1st to 15th order in the centre of each band. 2.2.2. Voltage notching Voltage notching is a type of periodic waveform distortion produced by the normal operation of power electronic devices when current commutates from one phase to another. During this period, there is a momentary short circuit between two phases being determined the severity of the notch by the source inductance between the converter and the point being monitored. Voltage notching represents a special case that falls between transient and harmonic distortion. Since notching
Fig. 14. (a) Waveform of voltage supply with a voltage swell, (b) magnitude of coefficients d1(n) obtained applying DWT.
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occurs continuously, it can be characterized through the harmonic spectrum. However, the frequency components associated with notching can be quite high and may not be readily characterized with measurement equipment normally used for harmonic analysis. Fig. 12a shows the waveform of a 460 V, 60 Hz, voltage supply with voltage notches due to a six-pulse converter [14] and Fig. 12b shows a zoom area of the frequency spectrum of the signal obtained applying DFT analysis. The sampling frequency used is 10.2 kHz (0.098 ms sampling period). As can be seen the spectrum of the signal is spread over the whole frequency range up to the harmonic of order 85, corresponding to 5.1 kHz in a 60 Hz system (the Nyquist frequency for the sampling rate used). The magnitude of the fundamental component using DFT was 462.4 V and the total harmonic distortion (THD) computed up to the harmonic of order 40 (maximum harmonic order for computation of THD in voltage supply in low-voltage and medium-voltage supply systems according to European Standard EN 50160 [15]) was 7.58%, whereas the high-frequency THD, computed from harmonic order 41 to order 85 was 4.57%. Two main features of this type of power quality disturbance can be highlighted: the transients associated with the beginning and the end of the commutation notches and the stationary high-frequency components in the spectrum of the signal.
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This time–frequency characteristic of the signal can be used as detection criteria. To this purpose the detail coefficients of the first level of the wavelet decomposition tree in Fig. 1, d1(n), using Daubechies with four coefficients as the mother wavelet, are computed for detection and assessment of voltage notches in voltage supply. The number of peaks in coefficients d1(n) over a specific threshold magnitude, computed in the case of no disturbance in the input signal, and the total energy of these coefficients have been used as detection criteria. In this working mode one-cycle window width and 40 kHz sampling frequency, as proposed in IEEE Std. 1159-1995 for assessment of voltage notching [16], are used. 3. Experimental results The instrument developed has been tested in simulation, using a single-phase/three-phase programmable power source [17] and using real voltage signals taken from the low-voltage distribution system of a building located in our campus. Three different groups of examples are considered in this section to show the performance of the instrument developed in the detection and analysis of transient and stationary power quality disturbances in voltage supply. The first group studies the detection and analysis of voltage events: a voltage dip, a voltage swell and of a short interruption in voltage supply are considered. The second
Fig. 15. (a) Waveform of voltage supply with a short interruption, (b) magnitude of coefficients d1(n) obtained applying DWT.
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group considers the case of the time–frequency analysis of a fluctuating harmonic component and finally, the third example describes the detection and analysis of the voltage notching produced by a six-pulse converter. 3.1. Voltage events Fig. 13 shows the waveform of voltage supply with a 132 V magnitude and 100 ms voltage dip and the magnitude of the detail coefficients of the first level of the wave-
let decomposition tree in Fig. 1, d1(n), obtained applying DWT with Daubechies with four coefficients to voltage samples and 12.8 kHz sampling frequency. Fig. 14 presents the case of a 270 V magnitude, 72 ms duration voltage swell and the magnitude of coefficients d1(n). Both voltage events have been generated using the AC programmable voltage source using 230 V, 50-Hz fundamental component and a harmonic distortion of 1% of 3rd order harmonic, 3% of 5th order harmonic and 1.5%, 1% and 0.9% of 7th, 9th and 11th order harmonic components, respectively (this har-
Fig. 16. Voltage waveform with a 5th order harmonic fluctuation and time evolution of the corresponding output coefficients in level 3 of the wavelet decomposition tree in Fig. 11.
Fig. 17. Magnitude of coefficients d1(n) for the voltage waveform in Fig. 12a.
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monic distortion is the typical harmonic distortion measured in our low-voltage distribution system during the afternoon on a week day). Finally, Fig. 15 shows the waveform of voltage supply with a 106.09 ms short interruption and the magnitude of the detail coefficients d1(n). This short interruption has been recorded in the low-voltage distribution network of our building. As can be seen in all the examples considered, coefficients d1(n) are insensitive to the steady-state magnitude of voltage supply but show sharp variation in magnitude corresponding to the beginning and end of the voltage event. Therefore, using these coefficients the beginning, the end and the duration of the voltage event can be accurately detected. 3.2. Non-stationary harmonic distortion As an example of the time–frequency characteristics of the method proposed in the analysis of stationary or quasistationary power quality disturbances, this example studies the case of a fluctuating harmonic component. Fig. 16a shows 10 cycles of voltage supply measured in a low-voltage distribution system, with a predominant fifth-order harmonic of 3.15% magnitude. A change in magnitude of this harmonic component from 3.15% magnitude to 6% magnitude (compatibility level for low-voltage supply distribution systems according to European standard EN50160) is produced at instant 75 ms of the record. Fig. 16b shows the magnitude of the output coefficients of level 3 of the wavelet decomposition tree in Fig. 11 corresponding to the output band from 200 to 300 Hz, where the fifth harmonic component is predominant. As can be seen the change in magnitude of the fifthorder harmonic can be accurately detected using these coefficients. 3.3. Voltage notching Finally, the performance of the instrument developed is shown in the detection and analysis of voltage notching. Fig. 17 shows the magnitude of the detail coefficients of the first level of the wavelet decomposition tree in Fig. 1 obtained applying DWT with Daubechies with four coefficients to voltage waveform in Fig. 12a. As can be seen the magnitude of coefficients d1(n) shows a long series of peaks (six peaks/cycle) exactly corresponding to the notches in voltage supply. The beginning, the end and the duration of voltage notches can be determined with a time resolution double of the sampling period of the signal due to the downsampling by two associated with the computation of the coefficients of the first level of the wavelet decomposition tree (0.196 ms in this case). 4. Conclusion The paper presents the structure and the performance of a virtual measurement instrument for detection and analysis of power quality disturbances in power systems
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using wavelets. Depending on the working mode selected as a function of the type of power quality disturbance to be detected and analyzed, the instrument implements in real time or off-line, different wavelet analysis on the input signal. An additional feature of the instrument is the partial implementation of wavelet analysis to study only a specific frequency band in the input signal. The results obtained demonstrate the good performance of the instrument in the detection and analysis of power quality disturbances as well as showing its possible use in relaying applications. Acknowledgements The authors thank the Spanish Ministry of Science and Technology, National Plan R+D+I (2004–2007), for its support of this research project under Grant DPI2006-15083C02, of which the present paper is a part. References [1] International Electrotechnical Commission, IEC 61000-4-30. Electromagnetic compatibility (EMC). Part 4-30: Testing and measurement techniques. Power quality measurement methods, Switzerland, 2003. [2] International Electrotechnical Commission, IEC 61000-4-7. Electromagnetic compatibility (EMC). Part 4-7: Testing and measurement techniques. General guide on harmonics and interharmonics measurement and instrumentation, for power supply systems and equipment connected thereto, Switzerland, 2002. [3] S. Chen, H.Y. Zhu, Wavelet transform for processing power quality disturbances, EURASIP Journal on Advances in Signal Processing (2007) 1–20, doi:10.1155/2007/47695. [4] N.C.F. Tse, L.L. Lai, Wavelet-based algorithm for signal analysis, EURASIP Journal on Advances in Signal Processing (2007) 1–20, doi: 10.1155/2007/38916. [5] C.H. Lee, Y.J. Wang, W.L. Huang, A literature survey of wavelets in power engineering applications, Proceedings of the National Science Council, Republic of China Part B 24 (4) (2000) 249–258. [6] J. Barros, R.I. Diego, A new method for measurement of harmonic groups in power systems using wavelet analysis in the IEC standard waveform, Electric Power Systems Research 74 (4) (2006) 200–208. [7] J. Barros, E. Pérez, A combined wavelet – Kalman filtering scheme for automatic detection and analysis of voltage dips in power systems, in: IEEE PowerTech2005, St. Petersburg, Russia, 2005. [8] A.C. Parsons, W.M. Grady, E.J. Powers, A wavelet-based procedure for automatically determining the beginning and end of transmission system voltage sags, in: Proceedings of IEEE Power Engineering Society Winter Meeting, New York, USA, 1999, vol. 2, pp. 1310–1315. [9] H. Mota, F.H. Vasconcelos, R.M. da Silva, Real-time wavelet transform algorithms for the processing of continuous streams of data, in: IEEE International Workshop on Intelligent Signal Processing, Faro, Portugal, 2005, pp. 346–351. [10] J. Barros, M. de Apraiz, R.I. Diego, Real-time implementation of wavelet transforms for electrical power quality applications, in: 14th IEEE Mediterranean Electrotechnical Conference, Ajaccio, France, 2008, pp. 635–639. [11] E.Y. Hamid, Z. Kawasaki, Wavelet packet transform for rms values and power measurements, IEEE Power Engineering Review 21 (9) (2001) 49–51. [12] J. Barros, R.I. Diego, Analysis of harmonics in power systems using the wavelet-packet transform, IEEE Transactions on Instrumentation and Measurement 57 (1) (2008) 63–69. [13] J. Barros, R.I. Diego, Time–frequency analysis of harmonics in power systems using wavelets, WSEAS Transactions on Power Systems 1 (11) (2006) 1924–1929. [14] http://grouper.ieee.org/groups/harmonic/iharm/docs/data/. [15] European Standard EN 50160, Voltage characteristics of electricity supplied by public distribution systems, CENELEC, 1999. [16] IEEE Std. 1159-1995, IEEE Recommended practice for monitoring electric power quality, IEEE, New York, USA, 1995. [17] HP 6800 Series AC power source/analyzer. User’s guide, Hewlett– Packard Company, 1995.