Detection of Dynamic Power Quality Disturbance based on Lifting Wavelet

Jian-ping ZHOU School of Power and Automation Engineering,

Shanghai University of Electric Power Shanghai,China

zhoujianping@shiep.edu.cn

Zhi-ping WANG School of Power and Automation Engineering,

Shanghai University of Electric Power Shanghai,China

wangzhiping@shiep.edu.cn

Abstract— Lifting wavelet is a useful method to analyze the abrupt signal because lifting wavelet can simultaneously show the local characteristic of time domain signal and frequency domain signal. The dynamic power quality disturbance in modern power supply can usually engender the fault signal such as voltage sag, voltage swell and voltage interruption. Lifting wavelet and Fourier transform are used respectively to detect these three fault signals of dynamic power quality disturbance. The simulation results show that lifting wavelet can accurately and effectively detect the singularity of fault signals, but Fourier transform fails to detect these fault signals. Lifting wavelet is a very good tool to detect the singularity of dynamic power quality disturbance.

Keywords-lifting wavelet; dynamic power quality disturbance; voltage; detect

I. INTRODUCTION Science and technology development requires better

power quality and more reliability than before. Therefore, modern power supply must be stable, flexible and reliable. Traditional power only focuses on stable voltage quality, harmonic analysis and power reliability, while modern power supply includes dynamic power quality besides these. In recent years, much attention is paid to dynamic power quality disturbance such as voltage sag, voltage swell and voltage interruption [1]. At present, there are no unified detection standard and method because disturbance is short and random. Wavelet transform shows the local characteristic of signal both in time and frequency domain and is suitable to deal with the abrupt signal. Therefore, it is widely used to detect and recognize dynamic power quality disturbance [2]-[5].

The wavelet transform based on lifting scheme is presented by Sweldens, namely lifting wavelet [6]. The lifting scheme is a simple construction of the second generation wavelets. These wavelets are not necessarily translation and dilation of one fixed function. The lifting scheme allows one to design the filters needed in the transform algorithms. The lifting scheme also leads to a fast in-place calculation of the wavelet transform, i.e., an implementation that does not require additional memory, since fast calculation is important in power system, especially when a real-time operation is needed. In the present paper, simulation is made according to the actual dynamic power quality disturbance. Lifting wavelet and

Fourier transform are adopted respectively to detect the singularity when voltage sag, voltage swell and voltage interruption occur in the power grid.

II. FIRST GENERATION WAVELET Although the original idea can be traced back to the

Haar transform first introduced at the beginning of the last century, wavelets were not popular until at the early eighties when researchers from geophysics, theoretical physics, and mathematics developed a mathematical foundation. Since then, this topic has been treated in considerable detail by numerous researchers in both the mathematics and engineering literature. In particular, Mallat and Meyer discovered a close relationship between wavelets and the structure of multi-resolution analysis. Their work, multi-resolution analysis, not only led to a simple way of calculating the mother wavelet, but also established a connection between continuous-time wavelets and digital filter banks. Following Mallat and Meyer’s work, Daubechies further developed a systematic technique for generating finite-duration orthonormal wavelets with FIR

finite impulse response filter banks. Wavelets are well-known for their capability to deal

with transient signals. For the continuous wavelet transform takes the form [7].

,a b R,

1( , ) ( ) ( ) , 0t bCWT a b x t dt a

aa (1)

Because all marks are simply dilated and translated versions of a single prototype function ( )t , traditionally

( )t in equation is called the mother wavelet. The parameter represents the scale index, determining the

center frequency of the function

a1( ( )a t b ) . The

parameter b indicates the time shifting (or translation). The wavelet transform (1) takes x(t), a member of the set of square integrable functions of one real variable t in ,

and transforms it to , a member of the set of functions of two real variables (a, b). A critical feature of the wavelet transform is that the width of the time or space window narrows when the wavelet is assessing the high

2 ( )L R( , )CWT a b

2010 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-4225-6/10 $26.00 © 2010 IEEE

DOI 10.1109/AICI.2010.142

93

2010 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-4225-6/10 $26.00 © 2010 IEEE

DOI 10.1109/AICI.2010.142

93

frequency, and it expands when assessing the lower frequencies.

III. WAVELET TRANSFORM BASED ON LIFTING WAVELET

Sweldens [6] presented the lifting scheme, a simple construction of the second generation wavelet. The lifting scheme is a spatial or time-domain construction of biorthogonal wavelets. The basic idea behind lifting is that it provides a simple relationship between all multi-resolution analysis that shares the same low-pass filter or high-pass filter. The low-pass filter gives the coefficients of the refinement relation, which entirely determines the scaling functions where the coefficients are given by the high-pass filter. The lifting scheme consists of iterations of the following three basic operations, as shown in Fig. 1. Firstly, the original data is divided into two subsets. The original signal is often split to the even indexed points and the odd indexed points, that is, [ ] [2 ]ex n x n and

. Secondly, this generates the wavelet coefficients d[n] as the error by the predicting operator P:

[ ] [2 1]ox n x n

[ ] [ ] ( [ ])o ed n x n P x n (2) The prediction and recording process is called a lifting

step. The original signal is transformed from ( , )o ex x to

( , )ox d . There is aliasing in the even samples due to the subsample. The lifting step is introduced to solve the problem. Finally, the update combines xe[n] and d[n] to obtain the scaling coefficients c[n] that represents the coarse approximation in the original signal. The updated operator U is used with the wavelet coefficients for xe[n].

[ ] [ ] ( [ ])ec n x n U d n (3) These three steps form the lifting stage. The iterations

of the lifting stage on the output samples create the complete set of discrete wavelet transform scaling and wavelet coefficients cj[n]and dj[n] at each scale j.

The lifting steps can be easily inverted. The following equations for invertible lifting are derived:

[ ] [ ] ( [ ]), [ ] [ ] ( [ ])e o ex n c n U d n x n d n P x n (4) The lifting scheme proposed by Sweldens [6] is an

efficient tool to construct the second generation wavelets, with advantages such as faster implementation, full in-place calculation, reversible integer-to-integer transforms, and so on [8].

IV. SINGULARITY DETECTION OF VOLTAGE SAG In recent years, voltage sag mainly causes the

dysfunction of voltage-sensitive equipments. It’s generally considered that voltage sag lead to 70% ~90% power quality problem [1][9]. Therefore, it is necessary to detect the singularity of the voltage sag. The power voltage wave is sine when the power grid is stable. The voltage sag is emulated when the sine wave drops from 180 to 200ms. The original signal is detected with Fourier transform, as demonstrated in Fig.2. Fig.2 shows that Fourier transform fails to detect the singularity. Fig. 3 shows the detail signal of 4 layers with lifting wavelet. The original signal detection with lifting wavelet includes the following three steps. Firstly, the lifting scheme is made of Haar wavelet. Secondly, the original signal is decomposed into 4 layers

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Figure 3. Detection of voltage sag using lifting wavelet

Figure 2. Detection of voltage sag using Fourier transform

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and the coefficient is distracted using the lifting wavelet function. Finally, the detail signal of 4 layers can be obtained. Fig. 3 shows that the abrupt change is located accurately in the first layer of detail signal cd1=180, 200ms . The simulation result suggests that the point of the voltage fall can be quickly located by lifting wavelet.

V. SINGULARITY DETECTION OF VOLTAGE SWELL AND VOLTAGE INTERRUPTION

Analogously, we also simulated the fault signals of voltage swell and voltage interruption with Fourier transform and lifting wavelet. The voltage wave is set up to rise from 370 to 400ms and break off from 480 to 500ms, respectively. The simulation results show that Fourier transform still can not detect the singularity of voltage swell and voltage interruption (not shown). However, the voltage swell and voltage interruption can successfully be detected with lifting wavelet, as demonstrated in Fig.4 and Fig.5. The singularity of voltage swell and voltage interruption are accurately located in the first layer of Fig.4 (cd1=370,400ms) and in the first layer of Fig.5 (cd1=480,500ms), respectively. The detected fault points coincide with the predetermined parameters.

VI. CONCLUSION According to the above theory analysis and simulation

result, the conclusion can be drawn as follows: 1) Lifting wavelet can accurately and quickly detect the singularity of voltage sag, voltage swell and voltage interruption. 2) Compared with Fourier transform, lifting wavelet is more suitable to detect the dynamic power quality disturbance in modern power supply.

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Figure 5.Detection of voltage interruption using lifting wavelet

ACKNOWLEDGMENT This paper is supported by Leading Academic Discipline

Project of Shanghai Municipal Education Commission (J51303) and the Natural Science Foundation of China (60771030).

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[3] Chen Xiang-xun, “Wavelet-based measuring and classification of short duration power quality disturbances,” Proceedings of the CSEE, 2002, vol.22, No.10, pp.l–6.

[4] Zhang Yu-hui, Chen Xiao-dong, Wang Hong-yi, “Continuous wavelet-based measuring and classification of short duration power quality disturbances,” Electric Power Automation Equipment, 2004, vol.24, No.3, pp.17–21

[5] Wang Cheng-shan, Wang Ji-dong, “Classification on the method of power quality disturbance based on wavelet packet decomposition ,” Power System Technology, 2004, vol.28, No.15, pp.78–82

[6] Sweldens W, “The lifting scheme: A construction of second generation wavelet,” SIAM J.Math.Anal.,1998, vol.29, No.2, pp.511–546.

[8] H.X. Chen, Patrick S.K. Chua, G.H. Lim., “Vibration analysis with lifting scheme and generalized cross validation in fault diagnosis of water hydraulic system,” Journal of Sound and Vibration ,Vol.301, pp. 458–480, 2007.

[9] Gomez J C, Morcos M M., “Voltage Sag and Recovery Time in Repetitive Events.,” IEEE Transactions on Power Delivery, 2002, vol.17, No.4, pp.1037–1043.

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Figure 4.Detection of voltage swell using lifting wavelet

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