Power Quality Analysis Using DSP Techniques

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ISSN (PRINT) : 2320 – 8945, Volume -1, Issue -3, 2013

80

Srividya T & A. Muni Sankar

Dept. of EEE, Sree Vidyanikethan Engineering College, Tirupati.

E-mail : [email protected], [email protected]

Abstract - Power Quality has become an important issue for electric utilities and the customers. Electronic devices are sensitive and can be easily disturbed by distortion like voltage sag, voltage swell, Interruptions etc.

in the electrical power supply. Power quality analysis has been of utmost importance to experts which helps in determining any disturbances in the network and proposes if any fault is present in the system. Through effective power monitoring, system errors can be classified at an earlier stage and thus the safety and reliability can be improved. This paper presents advanced DSP Techniques (Wavelet transform and S-transform) to identify and classify the power quality disturbances using MATLAB. The most widely used Techniques are FFT, STFT. Due to some of disadvantages and for the sake of quick power quality monitoring advanced DSP techniques are used and the analysis with advanced DSP Techniques (Wavelet transform and S-transform) provide accurate and fast detection of power quality disturbances.

Keywords: Power Quality, disturbance detection, Wavelet transform, S-transform

I. INTRODUCTION

An electrical power system is expected to deliver undistorted sinusoidal rated voltage and current continuously at rated frequency to the end users. . However, large penetration of power electronics based controllers and devices along with restructuring of the electric power industry and small-scale distributed generation have put more stringent demand on the quality of electric power supplied to the customers. To define power quality (PQ), the views of utilities, equipment manufacturers, and customers are completely different. Utilities treat PQ from the system reliability point of view. Equipment manufacturers, on the other hand, consider PQ as being that level of power supply allowing for proper operation of their equipment, whereas customers consider good PQ that ensures the

continuous running of processes, operations, and business.

Today Power Quality has captured increasing concern in recent years and has led to the development of various types of Digital Signal Processing Techniques to perform fast and accurate detection of power quality disturbances. Power Quality is defined as per IEEE,

“Power quality is the concept of powering and grounding sensitive equipment in a matter that is suitable to the operation of that equipment”[11].

Reliable and real-time monitoring of quality of electric power has become an important task in recent years and a major concern for consumers, manufacturers and distributors of the electric power. Several methods for detection and classification of power quality (PQ) disturbances that occur in a power system. As far as the detection of transients and similar disturbances is concerned these methods usually rely on some time- frequency representation of the power system’s voltage signal such as the Fast Fourier Transform or the short time Fourier transform. The Wavelet transform, S- transform which is more flexible and has gained the reputation of being very effective and efficient signal analysis techniques.

II. POWER QUALITY DISTURBANCES

The most common types of power quality disturbances are

Voltage sag is a reduction of AC voltage at a given frequency for the duration of 0.5 cycles to 1 minute of time. Sag are usually caused by system faults, and result of switching on loads with heavy start-up currents.

Voltage swell is the reverse form of a sag, having an increase in AC voltage for a duration of 0.5 cycles to 1 minute of time. Swell are usually caused by high impedance neutral, sudden load.

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ISSN (PRINT) :2320 – 8945, Volume -1, Issue -3, 2013

81 Interruption is defined as the complete loss of supply voltage or load current. Depending on its duration, an interruption is categorized as instantaneous, momentary, temporary or sustained.

Harmonics is defined as a sinusoidal component of a periodic wave having a frequency that is an integral multiple of the fundamental frequency usually 50Hz.

DC offset is the change in input voltage required to produce a zero output voltage when no signal is applied to an amplifier

2.1Drawbacks of Signal Processing (Transform) techniques used in PQ disturbances:

Various signal processing techniques used in power quality disturbances field are briefly discussed in following subsections.

1. There are number of transformations, among which the Fourier transforms are probably by far the most popular. If the FT of a signal in time domain is taken, the frequency-amplitude representation of that signal is obtained [1],[5]. This plot tells how much of each frequency exists in the signal. FT is a reversible transform. No frequency information is available in time-domain signal and no time information is available in Fourier transformed signal.

X (f) = dt ---- (1)

(t) = df ---- (2)

FT gives the spectral content of the signal, but it gives no information regarding where in time those spectral components appear. Fourier transform is not suitable if the signal has time varying frequency (Non-Stationary signals) because it just tells whether a certain frequency component exists or not.

2. A primary tool for the estimation of fundamental amplitude of a signal is the DFT (Discrete Fourier Transform) or its computationally efficient implementation called FFT (Fast Fourier Transform).

FFT transforms the signal from time domain to the frequency domain. Its fast computation is considered as an advantage. With this tool, it is possible to have an estimation of the fundamental amplitude and its harmonics with a reasonable approximation.

However, window dependency resolution is a disadvantage e.g. longer the sampling window better the frequency resolution. FFT performs well for estimation of periodic signals in stationary state; however it doesn’t perform well for detection of suddenly or fast changes in waveform e.g. transients, voltages dips or inter-

harmonics [4]. In some cases, results of the estimation can be improved with windowing or filtering, e.g.

hanning window, hamming window, low pass filter or high pass filter.

3. Finally, the STFT (Short Time Fourier Transform) is commonly known as a sliding window version of the FFT, which has shown better results in terms of resolution and frequency selectivity. In STFT the signal is divided into enough small segments, these segmented signals assumed stationary. A window function “ω” is chosen.

The width of this window must be equal to the segment of the signal where its stationary is valid. The disadvantage with STFT is width of window function is of finite length it covers only a few portion of the signal and it has no longer perfect frequency resolution(it has fixed resolution at all the time). Wavelet Transform overcome disadvantage of STFT to a certain extent.

III. WAVELET TRANSFORM

Wavelet Transform is developed as an alternative of STFT. It is capable of providing both frequency and time simultaneously (other transforms which gives this are STFT, Wigner distribution etc.,), hence giving a time-frequency representation of the signal. Wavelet Transform constitutes only a small portion of a huge list of transforms [1]. A wavelet is a wave-like oscillation with amplitude that starts out at zero, increases, and then decreases back to zero.

A wavelet transform is the representation of a function by wavelets [3]. The wavelets are scaled and translated copies of a finite-length or fast-decaying oscillating waveform (known as the "mother wavelet").

Wavelet transforms are classified into discrete wavelet transforms (DWTs) and continuous wavelet transforms (CWTs). CWTs operate over every possible scale and translation whereas DWTs use a specific subset of scale and translation values or representation grid.

3.1 CONTINUOUS WAVELET TRANSFORM

The CWT provides an approach that can be more flexible than the STFT. The CWT uses a time window function that changes with frequency, as opposed to the STFT for which the window function is fixed[9]. This adaptive time window function is derived from a prototype function called a mother wavelet. The mother wavelet is scaled and translated to provide information in the frequency and time domains.The continuous wavelet transform is defined as follows:

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82 ,s (τ) dτ --(4)

Where x(t) is a signal and Ψt,s (τ) is the wavelet basis function set which can be defined as follows

Ψt,s (τ) = 1/ Ψ((τ-t)/s) --- (5)

The factor 1/ 𝑠 is a scale-dependent normalization factor, employed so that all wavelets have the same enegy.where s is the scaling variable (s>0) and defined by s = fo/f.

(τ,s) = (τ,s) = 1/ ((τ-t)/s) --(6)

As seen in the above equation, the transformed signal is a function of two variables, tau and s , the translation and scale parameters, respectively. psi(t) is the transforming function, and it is called the mother wavelet. The term mother wavelet gets its name due to two important properties of the wavelet analysis as explained below: The term wavelet means a small wave. The term translation is used in the same sense as it was used in the STFT; it is related to the location of the window, as the window is shifted through the signal.

This term, obviously, corresponds to time information in the transform domain. However, we do not have a frequency parameter, as we had before for the STFT.

Instead, we have scale parameter which is defined as

$1/frequency$.

The parameter scale in wavelet analysis is similar to scale in maps. In practical applications, low scales(high frequencies) do not last for entire duration of the signal, they usually appear from time to time as short spikes and high scales(low frequencies) usually last for entire duration of the signal.Scaling either dilates or compresses a signal.In the definition of continuous wavelet transform , the scaling term is in the denominator and therefore,

for s > 1 , dilates the signals for s < 1 , compresses the signals

The multiresolution time-frequency plane of continuous wavelet transform The time and frequency plane chosen here contains boxes of different widths and heights, the area is constant. At low frequencies, the height of the boxes are shorter (which corresponds to better frequency resolutions, since there is less ambiguity regarding the value of the exact frequency), but their widths are longer (which correspond to poor time resolution, since there is more ambiguity regarding the value of the exact time). At higher frequencies the width of the boxes decreases, i.e., the time resolution gets better, and the heights of the boxes increase, i.e.,

the frequency resolution gets poorer. The Continuous Wavelet Transform (CWT) where one obtains the surface of the wavelet coefficients, for different values of scaling and translation factors.

3.2 DISCRETE WAVELET TRANSFORM 3.2.1 Why Discrete Wavelet Transform?

The continuous wavelet transform was developed as an alternative approach to the short time Fourier transforms to overcome the resolution problem. These days, computers are used to do almost all computations.

It is evident that neither the FT, nor STFT, nor the CWT can be practically computed by using analytical equations, integrals, etc. It is therefore necessary to discretize the transforms. As the discretize CWT enables the computation of the continuous wavelet transform by computers, it is not a true discrete transform. As a matter of fact, the wavelet series is simply a sampled version of the CWT, and the information it provides is highly redundant as for as the reconstruction of the signal is concerned. This redundancy, on the other hand, requires a significant amount of computation time and resources. The discrete wavelet transform DWT provides sufficient information both for analysis and the synthesis of the original signal, with a significant reduction in the computation time. The DWT is considerably easier to implement when compared to the CWT.

Discrete wavelet is written as

--- (7)

j and k are integers and s0 > 1 is a fixed dilation step.

The translation factor t₀ depends on the dilation step. A time-scale representation of a digital signal is obtained using digital filtering techniques.

3.2.2 Discrete Wavelet Transform Algorithm

The discrete wavelet transform (DWT) uses filter banks for the construction of the multi-resolution time- frequency plane.In the discrete case, filters of different cut-off frequencies are used to analyze the signal at different scales. The signal is passed through a series of high pass filters to analyze the high frequencies, and it is passed through a series of low pass filters to analyze the low frequencies. A low pass filter removes the high frequency components, while the high pass filter picks out the high-frequency contents in the signal being analyzed. Filter bank consists of filters which separate a signal into frequency bands. The resolution of the signal, which is a measure of the amount of detail information in the signal, is changed by the filtering operations. The split of signal into two different versions of same signal, thus obtained is decomposed signal. The

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 

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   _j ^j

k j

j s

s k t s t

0 0 0 0

,

) 1

(  

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83 process may continue until the decomposed signal match the pre-determined value.

To apply wavelet to identify time intervals of disturbances following steps are taken:

(i) Generate a signal with actual data or developed in any software with known initial and final times.

(ii) Apply different wavelet transform with suitable mother wavelet.

(iii) Identify the disturbances intervals with the help of wavelet coefficients.

3.2.2 Choice of Analyzing Mother Wavelet

Choice of analyzing mother wavelets plays a significant role in detecting various types of power quality disturbances. Especially when considering small scale signal decompositions. There are many different mother wavelets like Haar, Morlet, and Daubechies. In this paper Daubechies1 is used. As the wavelet goes to higher scales, the analyzing wavelets become less localized in time and oscillate less due to the dilation nature of the wavelet transform analysis.. As a result of higher scale signal decomposition, fast and short transient disturbances will be detected at lower scales, whereas slow and long transient disturbances will be detected at higher scales.

IV. S-TRANSFORMS

The extension of wavelet transform and Fourier transform is the S-transform (ST) introduced by Stockwell and other scholars. A Key feature of the S- transform is that it uniquely combines a frequency dependent resolution of the time-frequency space and absolutely referenced local phase information [7]. This allows one to define the meaning of phase in a local spectrum setting, and results in many desirable characteristics.

ST has been applied in classification of power quality disturbances and the results of ST of signals are analyzed by different time frequency analysis method to realize the classification and recognition of power quality disturbances.

Why S-transform?

S-transform uniquely combines progressive resolution with absolutely referenced phase information, which means that the phase information given by the S- transform is always referenced to time t=0, which is also true for the phase given by the Fourier transform. This is true for each S-transform sample of the time-frequency space. This is in contrast to a wavelet approach, where the phase of the wavelet transform is relative to the

centre of analyzing wavelet. The unique feature of S- transform is it uniquely combines frequency resolution with absolutely reference phase, and therefore the time average the S-transform equals the Fourier spectrum [2].

The S-transform expression becomes

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where f is the frequency, t and τ, are both time. The normalizing factor of f / 2π in (1) ensures that, when integrated over all τ , S(τ, f ) converges to X(f ) , the Fourier transform of x(t ).

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Therefore, S-transform is invertible. In this improved ST scheme the window function has been considered as the same Gaussian window but, an additional parameter δ is introduced into the Gaussian window where its width varies with frequency as follows

(10) The generalized ST becomes

(11) The adjustable parameter δ represents the number of periods of Fourier sinusoid that are contained within one standard deviation of the Gaussian window. If δ is too small the Gaussian window retains very few cycles of the sinusoid. Hence the frequency resolution degrades at higher frequencies. If δ is too high the window retains more sinusoids within it. As a result the time resolution degrades at lower frequencies. It indicates that the δ value should be varied judiciously so that it would give better energy distribution in the time-frequency plane.

A spectrogram, or sonogram, is a visual representation of the spectrum of frequencies.

Spectrograms are usually created in one of two ways:

approximated as a filter bank that results from a series of band pass filters (this was the only way before the advent of modern digital signal processing), or calculated from the time signal using the short-time Fourier transform (STFT). These two methods actually form two different Time-Frequency Distributions, but are equivalent under some conditions. S-transform using spectrogram analysis provides better visual analyzation of the siganal.

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84 V. SIMULATION RESULTS

The power quality disturbances like Voltage sag, voltage swell, Momentary interruption, harmonics, and DC offset has been analyzed using two techniques i.e., Wavelet transform and S-transform. The Comparison simulation results of power quality disturbances like Voltage sag, voltage swell, Momentary interruption, harmonics, and DC offset using continuous wavelet transform and discrete wavelet transform technique are as shown in below Fig:1, 2, 3,4,5.

Fig:1 Signal with sag disturbance detection using CWT and DWT

Fig:2 Signal with swell disturbance detection using CWT and DWT

Fig:3 Signal with momentary interruption disturbance detection using CWT and DWT

Fig:4 Signal with harmonic disturbance detection using CWT and DWT

Fig:5 Signal with DC offset disturbance detection using CWT and DWT

The simulation results of power quality disturbances like Voltage sag, voltage swell, Momentary interruption, harmonics, and DC offset using S- Transform is as shown in below Fig:6,7,8,9,10.

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85 Fig:6 Signal with sag disturbance detection using S-

transform

Fig:7 Signal with swell disturbance detection using S- transform

Fig:8 Signal with momentary interruption disturbance detection using S-transform

Fig:9 Signal with harmonic disturbance detection using S-transform

Fig:10 Signal with DC offset disturbance detection using S-transform

VI. CONCLUSION

In this paper the Wavelet transform and S-transform provides fast and accurate power quality disturbances detection. The power quality disturbances like voltage sag, voltage swell, momentary interruption, harmonics and Dc offset are identified and classified. Wavelet transform is better for analyzing power quality signals which uses variable window lengths. S-transform uniquely provides frequency resolution while maintaining a direct relationship with the Fourier spectrum. It can be extended to classify the disturbances Using Adaptive neuro fuzzy inference system (ANFIS), provides faster results than with DSP techniques.

VII. REFERENCES

1. Robi Polikar, “Fundamental Concepts and an Overview of Wavelet Theory”.

2. R.G. Stockwell, “A basis for efficient representation of the S-transform”.

3. T. Lachman, A.P.Memon, T.R. Mohamad, Z.A.

Memon, “Detection of Power Quality Disturbances Using Wavelet Transform Technique” Vol. 1, No. 1, 2010.

4. P. Kailasapathi and D. Sivakumar, “Methods to Analyze Power Quality Disturbances” European Journal of Scientific Research, Vol.47 No.1 (2010), pp.06-016.

5. Emanuel Fuchs, Beti Trajanoska, Sarah Orhouzee, and Herwig Renner, “Comparison of Wavelet and Fourier Analysis in Power Quality”, IEEE certified Journal, 2012.

6. Fanibhushan Sharma, A. K. Sharma, Ajay Sharma, Nirmala Sharma, “Recent Power Quality Techniques A Comparative Study”, Vol. 1, No. 6, October 2010

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86 7. Yu-Hsiang Wang, “The Tutorial S-transform”.

8. D. Saxena, K.S. Verma and S.N. Singh, “Power quality event classification: an overview and key issues” International Journal of Engineering, Science and Technology, Vol. 2, No. 3, 2010, pp.

186-199.

9. Mohammed E Salem, Azab Mohamed and salina Abdul Samad, “Power Quality Disturbance Detection using DSP Based Continuous Wavelet Transform”, Vol.7, No.6, 2007.

10. Zahra Moravej, Mohammad Pazoki and Ali Akba Abdoos, “Application of Signal Processing in Power Quality Monitoring”.

11. Math H.J. Bollen, “Understanding Power Quality Problems”, IEEE Power Engineering society.

12. Gabriel Gaşparesc “Methods of power quality analysis” University of Timişoara, Romania.

13. P.K. Dash, B.K. Panigrahi, and G. Panda, “Power Quality Analysis using S-transform”, to appear in IEEE Trans. on Power Delivery,vol.8, no.2, April 2003, pp.406-412.

14. Flores, R.A, “State of the Art in the Classification of Power Quality Events, An Overview”.

Harmonics and Quality of Power, 2002, 10th International Conference on Volume 1, issue, 6-9, pp. 17-20, Oct. 2002.

https://www.ufjf.br/pscope_eng/

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