Electrical Power and Energy Systems 32 (2010) 133–140

Contents lists available at ScienceDirect

Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

A new approach to voltage sag detection based on wavelet transform

Özgür Gencer, Semra Öztürk, Tarık Erfidan *

Kocaeli University, Faculty of Engineering, Department of Electrical Engineering, Veziroglu Kampüsü, Eski Gölcük Yolu, Kocaeli, Turkey

a r t i c l e i n f o

Article history:Received 9 September 2007Received in revised form 30 March 2008Accepted 8 June 2009

Keywords:Power systemsPower qualityWavelet transformVoltage sag detection

0142-0615/$ - see front matter � 2009 Published bydoi:10.1016/j.ijepes.2009.06.025

* Corresponding author. Tel.: +90 262 335 11 48.E-mail addresses: ogencer@kou.edu.tr (Ö. Gencer), s

tarik@kou.edu.tr (T. Erfidan).

a b s t r a c t

In this work, a new voltage sag detection method based on wavelet transform is developed. Voltage sagdetection algorithms, so far have proved their efficiency and computational ability. Using several win-dowing techniques take long computational times for disturbance detection. Also researchers have beenworking on separating voltage sags from other voltage disturbances for the last decade. Due to increasingpower quality standards new high performance disturbance detection algorithms are necessary to obtainhigh power quality standards. For this purpose, the wavelet technique is used for detecting voltage sagduration and magnitude. The developed voltage sag detection algorithm is implemented with high speedmicrocontroller. Test results show that, the new approach provides very accurate and satisfactory voltagesag detection.

� 2009 Published by Elsevier Ltd.

1. Introduction

The importance of power quality is increasing due to the factthat the equipments in power systems are much more sensitiveto power quality problems. Processes are interrupted; productivityis halted as a result of these disturbances. To avoid this, the powerquality problems, such as voltage sag, need to be identified first.Recent advances in signal analysis have led to the developmentof new methods for characterizing and identifying various powerquality problems. Today one of the most common power qualityproblems is voltage sag [1]. Voltage sags are the main cause ofmore than 80% of the problems experienced in power systems.Voltage sag is a short time (10 ms to 1 min) event during whicha reduction in RMS voltage magnitude occurs [2]. Despite of a shortduration, a small deviation from the rated voltage can result in lotsof cost effect disturbances. Because of the effect of voltage sag inmany cases, the production process comes to a halt. The distur-bance may be over within one second, but the restoration processmay take several hours. For many power system equipments, theeffect of voltage sag is the same as the effect of an interruption.The number of voltage sag is about 80–90 per year, where thenumber of interruptions is on average around one per year. So,the consequences due to voltage sags are more significant thandue to interruptions [2].

Voltage sag often sets only by two parameters, magnitude andduration [3]. Wavelet decomposition techniques provide a power-ful tool, which can be used to detect and localize voltage sags [4].

Elsevier Ltd.

emra@kou.edu.tr (S. Öztürk),

Wavelet analysis is becoming a common tool for analyzinglocalized variations of power within a time series. By decomposinga time series into time-frequency space, one is able to determineboth the dominant modes of variability and how those modes varyin time [5]. In power system analysis, wavelet transform have re-ceived attention because its efficiency for the analysis of transientscompared to other types transforms. The wavelet transform hasbeen used for numerous studies in power system protection,power quality, power system transients, load forecast and powersystem measurement [6].

Several studies have been done to show the identification andclassification of power quality problems using wavelet transform.Most of them use sampled voltage and current waveforms,based-on the Parseval’s theorem [7–10].

Ref. [10] is an excellent introduction to voltage sag detectiontechniques for dynamic voltage restorers, which are used to pro-tect sensitive loads from the effects of voltage sags. But this paperdid not provide all of the necessary essential details for waveletanalysis and avoided the issue of practical use with amicroprocessor.

Unfortunately, many studies using wavelet analysis have suf-fered from an apparent lack of quantitative results. The analysesare done via simulation and the theoretical results of the detectionmethods with wavelet analysis are not compared with practicalresults.

This paper presents a new algorithm to detect the starting andending points and the magnitude of the voltage sag. The discretewavelet transform (DWT) is used to detect fast changes in the volt-age signals, which allows time localization of differences frequencycomponents of a signal with different frequency wavelets. A digitalsignal microprocessor-based hardware system is used to test

134 Ö. Gencer et al. / Electrical Power and Energy Systems 32 (2010) 133–140

proposed algorithm in real-time with dsPIC. The algorithm is dem-onstrated via case studies.

Fig. 1. Basic level of wavelet transform filtering process.

2. Wavelet transform

In this section we review the necessary information on wavelettransforms (WT) for the decomposition and the detection of tem-poral structures such as the voltage Sag data that we analyze.

Power quality problems are characterized by their maximumamplitudes, crest voltages, RMS, frequency, statistics of wavelettransform coefficients, instantaneous voltage drops, number ofnotches, duration of transients, etc. [11]. These characteristics areunique to identify features for different power quality problems,and introduced signal processing tools in power quality analysis.

The WT has been applied to signal processing in various fieldssince 1980s. Time series with time-varying frequencies can befound in many power quality problems, i.e. voltage flicker, loadand capacitor switching, inrush current, fault signals, etc. Thistechnique is particularly suitable for non-stationary process andcan yield localized time-frequency information that is not availablefrom the traditional Fourier transform. The windowed Fouriertransform achieves location in time by windowing the data at var-ious times and then taking the Fourier transform. In this procedurehowever, precision in time and frequency are fixed in the chosenwindow function and therefore arrival time detection of transientcomponents with different scales is not possible. On the otherhand, WT are essentially applied to extract information and as abasis for signal representation to achieve both good time and fre-quency position. The choice of the basis function determines theinformation to be extracted from the process and allows the studyof different signal structures, such as non-stationary short-timetransient components, features at different scales. The process rep-resentation using wavelets is provided by a series expansion of di-lated and translated versions of the basis function, also called themother wavelet, multiplied by appropriate coefficients. So, the firststep of the wavelet transform is to determine the mother wavelet.For a wavelet of order N, the basis function can be represented as

wðnÞ ¼XN�1

j¼0

ð�1Þjcjð2nþ j� N þ 1Þ ð1Þ

where cj is coefficient. The basis function should satisfy some con-ditions [12,13]: The basic function integrates to zero, i.e.Z 1

�1wðtÞdt ¼ 0 ð2Þ

The basis function must be oscillators or have a wave shape. Forprocesses with finite energy the wavelet series expansion gives anoptimal approximation to the original series [14].

Many different wavelet bases can be used for the transforma-tion attaining the properties above. The selection of a basic func-tion is motivated by the data features to be extracted. Alternativefunctions move different characteristics of the raw data set be-tween scales. In this paper, we adopt Daub4 mother wavelet,which is the most compact wavelet and it has a much simpleimplementation [14].

The multiresolution decomposition separates the signal into‘‘details” at different scales, the remaining part, being a coarserrepresentation of the signal, is called ‘‘approximation”. Each detail(Dj) and approximation signal (Aj) can be obtained from the previ-ous approximation Aj-1 via a convolution with high-pass and low-pass filters, respectively (Fig 1).

The wavelet transform can be done in three different ways,which are, discrete wavelet transform, continuous wavelet trans-form and wavelet series. Discrete wavelet transform (DWT) is suf-ficient to decompose and reconstruct most power quality

problems. It provides enough information, and offers high reduc-tion in the computational time [14].

Discrete wavelet transforms are suitable for processing realdata in which the signal f(t) is known only at sampling points withspacing dependent on the sampling rate. The WT in this case hasdiscretized scale k and location u parameters. Using a logarithmicuniform spacing in the discretization of the scale and location do-mains provides an orthonormal wavelet basis which characterisescompletely N signal observations with N wavelet coefficients [15].

For any signal, f(t) 2 L2(R), the DWT analysis equations are givenby:

aj;k ¼Z

f ðtÞ2j=2/ð2j t�kÞdt

bj;k ¼Z

xðtÞ2j=2wð2j t�kÞdtð3Þ

f ðtÞ ¼ 2N=2X

k

aN;k/ð2Nt � kÞ þXM�1

j¼N

2j=2X

k

bN;kwð2Nt � kÞ ð4Þ

/(t) and w(t) are scalling and wavelet functions. ai, k and bi, k arethe corresponding scalling and wavelet coefficients.

The WT assumes that the full period of the signal is being ana-lyzed. Discontinuity of high frequency components are occurringwhen the analyzed section is different value at the beginning andat the end of two consecutive windows, so the high frequency ef-fects can be recognized [16].

There are some works on how to determine and appropriate itfrom other disturbances. Most of them use the multiresolution-analysis technique of DWT and the Parseval’s theorem. These the-orems are employed at different resolution levels to extract the en-ergy distribution features of the sag signal. Then, some methods,such as the Artificial Neural Networks classify these extracted fea-tures to identify the disturbance type according to the transientduration and the energy features [17,18].

A fast algorithm is actually available to compute the wavelettransform of a signal. Even though the discretized wavelet trans-form can be computed on a computer or a microprocessor, thiscomputation depends on the signal size and the resolution that isneeded. The DWT provides sufficient information both for analysisand synthesis of the original signal, with a significant reduction inthe computation time.

3. Wavelet based detection of voltage sags

As mentioned in [19], high frequency resolution of transformedsignal can detect transient disturbances better than low resolu-tions. The scaling (A5) and wavelet signals (D1-D5) of a voltage sig-nal (S), when it is subjected to sag for 4 cycles are shown in Fig. 2.Daub4 wavelet is used in computation here. It can be seen that the

Fig. 2. Multiresolution voltage signal decomposition.

Ö. Gencer et al. / Electrical Power and Energy Systems 32 (2010) 133–140 135

first level of the transformed signal clearly shows a peak at thebeginning and end of the voltage sag. The other wavelet levels havealso experienced variations at this same instant. Therefore, it canbe said that the disturbance can be detected with high frequencywavelet levels better.

Because the microcontroller A/D channel is used bidirectional, itcan read only the positive values of AC voltage signal. The negativealternances of the signal is converted to positive with a full bridgeconverter. So, the frequency of monitored signal becomes 100 Hz.

Fig. 3a shows the pure sine wave and (c) its D1 wavelet. Thehorizontal axis presents sampling point and the vertical axis pre-sents the magnitude of wavelet coefficient. The first 4 points andlast 2 sample magnitudes are different from zero and the othersare very close to zero. The pure sine wave will be used as a refer-ence in comparison with sag cases. Fig. 3b shows a voltage signaldistorted with sag and (d) shows its first decomposition level. Itis clear from the figure that if there is a decrease in voltage signal,the wavelet coefficients around sag starting point differs from zero.A spike is seen at the initial point in wavelet.

The sag can occur at any point of voltage signal. To determinethe effects of voltage sag starting point on the magnitude of thespike in the wavelet, the same magnitude of sags were applied atdifferent points on voltage wave.

The magnitudes of the spikes are different and not symmetricalaccording to 900 as shown in Fig. 4. So only the occurrence of sagcan be determined but it cannot give direct information aboutthe magnitude of sag.

Fig. 4 also shows that the first 4 points of the wavelets are thesame. So an approximation can be defined to find how it changes

according to sag magnitude. Fig. 5 shows the magnitude of spikesas a function of voltage sag magnitude.

A function for sag magnitude according to D11 coefficients canbe determined by regression analysis. In this work power regres-sion model is used (solid line in Fig. 5). So, the magnitude of volt-age sag can be calculated by determining only the D11 coefficientof decomposed voltage signal. The point of sag starting point isthe location of peak occurrence. The peak will also occur at theend of the voltage sag. Hence, voltage sag classification parameters,magnitude and duration are identified and the voltage disturbanceis classified with this method.

The disadvantage of this method is discretization of the signal.The calculation of the voltage sag parameters can be done at theend of the cycle. It would be faster to determine and turn on therestorer system, if the calculations of the parameters are done atthe half period of one cycle, For this purpose, the voltage signalis divided into two regions, called here as A and B shown in Fig. 6.

Fig. 6 depicts the decomposition of voltage signal. A critical va-lue of D11 must be calculated for each region first. For example ifabove 20% magnitude of voltage sag is critical and the voltage re-storer must compensate above this level, the critical value is deter-mined for 20% of voltage for each region. In Fig. 6 after samplingthe voltage signal for Region A, the wavelet transform is doneand the peak at D1 is observed. Then the magnitude of the voltagesag is calculated according to D11 coefficient. The sampling iscontinuing for Region B, and the same calculations are repeated.A peak at D1 coefficient is not observed, but D11 coefficient is be-low critical value of this region, so the restorer continue to workuntil next calculation.

Fig. 3. (a) Pure sine voltage signal, (b) voltage signal distorted with sag, (c) decomposition of pure sine voltage signal, (d) decomposition of distorted voltage signal.

Fig. 4. The magnitude of spikes according to sag starting point.

Fig. 5. Values of first coefficients of D1 wav

136 Ö. Gencer et al. / Electrical Power and Energy Systems 32 (2010) 133–140

4. Implementation of sag detector

The implemented system to detect voltage sag and compensateit is shown in Fig. 7. The voltage restorer components (shown inFig. 7) are the VSC, the injection transformer, the energy storageand the bypass switch. The measured voltages and currents arethe inputs to the wavelet based detector, which gives signals tothe voltage restorer to function when the measured quantities dif-fer from the settings. The wavelet based detector module triggersthe start of the compensation when the supply voltage comes out-side of a pre-defined range. The energy storage provides the re-quired active power to compensate the identified voltage sag.The voltage is injected into the distribution system by the series-injecting transformer. The bypass switch is normally closed toshort-circuit the voltage restorer. When the sag detector unit de-tects voltage sag, the bypass switch is opened and the voltage re-storer starts the compensation process.

elet according to different voltage sags.

Ö. Gencer et al. / Electrical Power and Energy Systems 32 (2010) 133–140 137

Developed sag detector using DWT consists of two parts. One ofthem is zero-crossing detection and the other is dsPIC microcon-troller unit. Transformer and full bridge converter is used for sam-pling AC line voltage and feeding zero-crossing circuit. A zero-

Fig. 6. Analyzing voltage signal into 2 region a

Fig. 7. Single line diagram of wa

crossing circuit generates pulse whenever AC line voltage reducesto zero. Then sampling starts. Flow chart of proposed Waveletbased sag detector is shown in Fig. 8. The number of samplingfor a cycle is chosen as 64, which is enough to calculate the

nd the wavelet transform of these regions.

velet based voltage restorer.

138 Ö. Gencer et al. / Electrical Power and Energy Systems 32 (2010) 133–140

DWT, so that the sampling time is set to 156 ls in dsPIC timer 0module. At the beginning of each sampling interval, then timer sets

Fig. 8. Flow chart of proposed wavelet based voltage sag detector.

Fig. 9. Behaviour of microcontroller at different voltage s

an interrupt flag then A/D channel begins to acquire new analogvalue.

After taking 64 samples, dsPIC calculates critical value usingDWT. This calculating process is about 32 ls and it is less thansampling time. The less sampling time gives a more accurate solu-tion. But it needs more calculation time. If critical value is less thanthe desired value, it can be observed that voltage sag occurred andall process restarts for a new period. So, developed detector systemcan identify and characterize voltage sags.

5. Test results

To recognize the distorted signal and test the proposed algo-rithm a voltage sag identifier system is developed. In order to allowthe voltage beginning and recovery at different points during volt-age sags, tests were performed with rectangular voltage sags by afully programmable power source with an integrated arbitrarywaveform generator. The programmable ac power source enablesa flexible, variable amplitude and frequency voltage output. Theoutput voltage can be transiently changed. This is useful for spec-ifying exact sag magnitude and for transient state conditions [20].A 200 MHz scopmeter is configured to measure the outputs ofpower source and dsPIC.

dsPIC 30F4011 16-bit microcontroller, manufactured by Micro-chip was chosen to implement DWT. It has also three channels of10 bit analog to digital (A/D) converter, five 16 bit timers, six motorcontrol PWM channels with DSP engine. This device can be run atspeeds of up to 120 MHz.

ag points for Region A (a) 15� (b) 30� (c) 45� (d) 60�.

Fig. 10. Behaviour of microcontroller at different voltage sag points for Region B (a) 105� (b) 120� (c) 135� (d) 150�.

Ö. Gencer et al. / Electrical Power and Energy Systems 32 (2010) 133–140 139

The interruption pin of the microcontroller detects the funda-mental zero-crossing let A/D port to sample the voltage inputwaveform. For each sag duration that is tested, voltage data havebeen acquired with a sampling frequency of 6.4 kS/s. The micro-controller gets 32 samples per a region and 64 samples per a per-iod. Then the wavelet transform is acquired if related region andif it is lower than threshold value, dsPIC turn on the voltagerestorer.

The computation time of the algorithm is approximately 50 ls.It is minimum 2 cycles for conventional methods. Wavelet baseddetection system can be faster with using higher clock signals.Higher computational times according to conventional methodsresults uninterrupted energy for critical loads which is the mainpurpose of these voltage restorer systems.

The proposed sag detection algorithm is tested for differentpoints of voltage signal for each region. Fig. 9 shows the resultsfor region A. The sag starting points are (a) 15� (b) 30� (c) 45� (d)60� of the voltage signal. The sag magnitude is 50% but the definedcritical value for the sag is 20%. The microprocessor calculates theD11 value and compares it with critical value. If it is below the de-sired value, microprocessor trigs the voltage restorer until at theend of the sag.

The tests are repeated for the Region B. The sag starting pointsare (a) 105� (b) 120� (c) 135� (d) 150� of voltage signal for Region Ba shown in Fig. 10. If the critical value of this region is belowthreshold value the microprocessor trigs the voltage restorer afterthe sampling is finished.

This proposed sag detection algorithm is working perfectly forany instant of the voltage sag.

Computation and detection of voltage sag magnitudes anddurations with using proposed method provides a great advantageto DVR systems on other conventional sag restorers. It can be

implemented to such a system easily and decreases costs mostly.Existing detection methods cannot gives a satisfaction results likethis for this purpose.

6. Conclusions

Utilities record power quality data, especially voltage, to iden-tify the origins of power quality problems in order to improvethe reliability of electrical systems. This paper presents a practi-cally efficient method for the voltage sag detection. The methoduses discrete wavelet transforms to determine beginning and end-ing of the voltage sag with sag magnitude. A dsPIC-based hardwareidentification system for voltage sag is implemented. The proposedmethod is successfully tested for different voltage sag instantsof voltage. It has the advantage of finding voltage sag magni-tude and duration with real time operation and low costimplementation.

References

[1] Khan AK. Monitoring power for the future. Power Eng J 2001;15(2):81–5.[2] Bollen MHJ. Understanding power quality problems: voltage sags and

interruptions. New York: IEEE Press; 1999.[3] Yalçınkaya G, Bollen MHJ, Crossley PA. Characterization of voltage sags in

industrial distribution systems. IEEE Trans Ind Appl 1998;34(4):682–8.[4] Parsons AC, Grady WM, Powers EJ. A wavelet-based procedure for

automatically determining the beginning and end of transmission systemvoltage sags. In: Proc. IEEE-PES Winter Meeting, vol. 2; 1999. p. 1310–5.

[5] Gu IYH, Bollen MHJ. Time-frequency and time-scale domain analysis of voltagedisturbances. IEEE Trans Power Delivery 2000;15(4):1279–84.

[6] Fernandez RM, Rojas HND. An overview of wavelet transforms applications inpower systems. 14th PSCC, Sevilla, 24–28 June 2002.

[7] Gaouda M, Salama MA, Sultan MR, Chikhani AY. Power quality detection andclassification using wavelet-multiresolution signal decomposition. IEEE TransPower Delivery 1999;14(4):1469–76.

140 Ö. Gencer et al. / Electrical Power and Energy Systems 32 (2010) 133–140

[8] Gaouda AM, Salama MMA, Sultan MR, Chikhani AY. Application of multi-resolution signal decomposition for monitoring short duration variations indistribution systems. IEEE Trans Power Delivery 2000;15(2):478–85.

[9] Resende JW, Chaves MLR, Penna C. Identification of power qualitydisturbances using the MATLAB wavelet transform toolbox. In: IPSTConference, 2001.

[10] Gaouda AM, Salama MMA, Sultan MR, Chikhani AY. Application ofmultiresolution signal decomposition for monitoring short-durationvariations in distribution systems. IEEE Trans Power Delivery 2000;15(2).

[11] Parsons AC, Grady WM, Powers EJ. A wavelet-based procedure forautomatically determining the beginning and end of transmission systemvoltage sags. Power Engineering Society 1999 winter meeting, IEEE, vol. 2, 31January–4 February 1999; p. 1310–5. vol. 2.

[12] Arrillaga J, Watson NR, Chen S. Power system quality assessment. Chichester:Wiley; 2000.

[13] Daubechies I. Ten lectures on wavelets. Philadelphia, PA: SIAM; 1992.

[14] Chui CK. Wavelets. A mathematical tool for signal processing. Philadelphia,PA: SIAM; 1997.

[15] Burrus CS, Gopinath RH, Guo H. Introduction to wavelets and wavelettransforms, a primer. Englewood Clis, NJ: Prentice-Hall Press; 1998.

[16] A Wavelet-based Differential Transformer Protection. IEEE Trans PowerDelivery 14(4) (1999).

[17] Zhu TX, Tso SK, Lo KL. Wavelet-based fuzzy reasoning approach to power-quality disturbance recognition. IEEE Trans Power Delivery 2004;19(4):1928–35.

[18] Huang S, Yang T, Huang J. FPGA realization of power quality disturbancedetection: an approach with wavelet, ANN and fuzzy logic Neural Networks”,2005. In: Proceedings 2005 IEEE international joint conference on vol. 4, 31July–4 August 2005; p. 2613–8 vol. 4.

[19] Parameswariah C, Cox M. Frequency characteristics of wavelets. IEEE TransPower Delivery 2002;17(3).

[20] California Instruments, Operating Manual: LX Series AC Power Source, 2003.