assesment of power quality through wavelet entropy

8/14/2019 ASSESMENT OF POWER QUALITY THROUGH WAVELET ENTROPY

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ASSESSMENT OF POWER QUALITY THROUGH

WAVELET ENTROPY

By Under Esteemed Guidance of

D Siva Krishna Reddy L09EE133 G. Subba ReddyM tech

DVV Satyanarayana Y08EE027

A Manoj Kumar Y08EE001

K Aswani Kumar Y08EE058


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INTRODUCTION

As it is well known, an ideal three-phase AC supply consists of three phase voltages that are 120

degrees out of phase and have identical magnitudes. Above all, these voltages should be

sinusoidal and should be available continuously. Any diversion from these requirements is

considered as poor quality of power. One of the major causes of disturbances in AC power

system is the electronic switching circuits, which are widely used both in industry and in

household systems. Most of the power electronic equipments are manufactured based on the

available standards, but due to increase in the numbers of such equipments there are also an

increase in disturbances in the power system. While the sources of disturbances in AC power

systems increase continuously, the electric utilities and end users of electrical power have

become more concerned about the quality issues of the AC power.

The term entropy is a measure of energy required to do useful work in thermodynamic process.

In any power system network, the energy is consumed by loads and some energy is wasted in

elements during the process of power flow. This concept of energy deviation in system may be

used to extract significant information with respect to power quality at the load end.

Wavelet entropy is one such important tool for obtaining useful energy of given system. The test

system includes a distribution system with different loads. Power quality issues and indices are

obtained by wavelet entropy. The results will be presented to validate the proposed concept.


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OBJECTIVE


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LITERATURE SURVEY:

1. Power quality event classification: an overview and key issuesD. Saxena, K.S. Verma and S.N. Singh

Department of Electrical and Electronics Engineering, Invertis Inst. of Engg. Bareilly (UP)INDIA.

Department of Electrical Engineering, CET, Denmark Technical University,Lyngby,DENMARK.

Department of Electrical Engineering, K.N.I.T Sultanpur (UP), INDIA.

A PQ problem can be defined as any power problem manifested in voltage, current and/or

frequency deviations that result in failure or mal-operation of customers equipment. In early

days, power quality issues were concerned with the power system transient arising due to

switching and lightning surges, induction furnace and other cyclic loads. Increasedinterconnection, widespread use of power electronics devices with sensitive and fast control

schemes in electrical power networks have brought many technical and economic advantages,along with a need for maintenance of good power quality.


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2. Signal Processing Techniques used in Power Quality Monitoring

Umar Naseem KhanWroclaw University of Technology, Poland, in 2007

The majority of power quality problems can be characterized through measurements of voltageand current. To distinguish the type of disturbances, monitoring systems require the processing

of signals, which concern the extraction of features and information from measured digital

signals. In fact, the use of signal processing techniques can influence the way that voltage and

current signals are measured and analyzed in power system field.

DETECTION METHODS OF POWER QUALITY DISTURBANCES:

1. Rms value Voltage magnitude variation

Voltage frequency variation

3-phase unbalance

2. Fourier analysis3. Short time Fourier transform analysis4. Wavelet transform

The wavelet transform is based on the decomposition of a signal in terms of small waves

(daughter wavelets) derived from translation (shifting in time) and dilation (sealing) of a

fixed wavelet function called the "mother wavelet". The main advantage of the wavelettransform is its varying-length window. The general formula of the continuous wavelet

transform (VWT) of a signal v (k) is given by

VWT (a, b) =

Wavelets havebeen very useful in electrical transients analysis. According to the type of

disturbance, a different type of wavelet is used.5. S- transform

6. Parks vector approach

7. Kalman filters


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3. POWER QUALITY ASSESSMENT VIA WAVELET TRANSFORM ANALYSIS

Surya Santoso (Student Member), Edward J. Powers(Fellow) and W. Mack Grady Senior Member)

The University of Texas at AustinAustin, Texas 78712-1084Department of Electrical and computer Engineering

Peter Hofmann (Member)Consolidated Edison Company

New York, NY 10017

The approach is based on wavelet transform analysis, particularly the dyadic-ortho normalwavelet transform. The key idea underlying the approach is to decompose a given disturbance

signal into other signals which represent a smoothed version and a detailed version of the

original signal. The decomposition is performed using multi resolution signal decompositiontechniques

The above technique is used to detect and localize disturbances with actual power line

disturbances. In order to enhance the detection outcomes, the squared wavelet transform

coefficients of the analyzed power line signal are utilized. Based on the results of the detectionand localization, an initial investigation of the ability to uniquely characterize various types of

power quality disturbances is carried out. This investigation is based on characterizing the

uniqueness of the squared wavelet transform coefficients for each power quality disturbance.

4. Power Quality Problems and New Solutions

A. de Almeida, L. Moreira. J. Delgado

ISRDepartment of Electrical and Computer EngineeringUniversity of Coimbra, Plo II

3030-290 Coimbra (Portugal)

In this paper, the main Power Quality (PQ) problems are presented with their associated causes

and consequences. Some solutions to mitigate the PQ problems are presented.


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The mitigation of PQ problems may take place at different levels: transmission, distribution

andthe end- use equipment several measures can be taken at these levels.

PROPOSED WORK

1. THE WAVELET TRANSFORMThe Wavelet transform is a transform of this type. It provides the time-frequency representation.(There are other transforms which give this information too, such as short time Fourier

transforms, Wigner distributions, etc.)

Often times a particular spectral component occurring at any instant can be of particular interest.In these cases it may be very beneficial to know the time intervals these particular spectral

components occur. For example, in EEGs, the latency of an event-related potential is ofparticular interest (Event-related potential is the response of the brain to a specific stimulus like

flash-light, the latency of this response is the amount of time elapsed between the onset of the

stimulus and the response).

Wavelet transform is capable of providing the time and frequency information simultaneously,

hence giving a time-frequency representation of the signal.

How wavelet transform works is completely a different fun story, and should be explained after

short time Fourier Transform (STFT). The WT was developed as an alternative to the STFT.The STFT will be explained in great detail in the second part of this tutorial. It suffices at thistime to say that the WT was developed to overcome some resolution related problems of the

STFT, as explained in Part II.

To make a real long story short, we pass the time-domain signal from various high pass and low

pass filters, which filter out either high frequency or low frequency portions of the signal. This


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procedure is repeated, every time some portion of the signal corresponding to some frequencies

being removed from the signal.

Here is how this works: Suppose we have a signal which has frequencies up to 1000 Hz. In the

first stage we split up the signal in to two parts by passing the signal from a high pass and a low

pass filter (filters should satisfy some certain conditions, so-called admissibility condition)which results in two different versions of the same signal: portion of the signal corresponding to

0-500 Hz (low pass portion), and 500-1000 Hz (high pass portion).

Then, we take either portion (usually low pass portion) or both, and do the same thing again.

This operation is called decomposition.

Assuming that we have taken the low pass portion, we now have 3 sets of data, each

corresponding to the same signal at frequencies 0-250 Hz, 250-500 Hz, 500-1000 Hz.

Then we take the low pass portion again and pass it through low and high pass filters; we now

have 4 sets of signals corresponding to 0-125 Hz, 125-250 Hz, 250-500 Hz, and 500-1000 Hz.We continue like this until we have decomposed the signal to a pre-defined certain level. Thenwe have a bunch of signals, which actually represent the same signal, but all corresponding to

different frequency bands. We know which signal corresponds to which frequency band, and if

we put all of them together and plot them on a 3-D graph, we will have time in one axis,frequency in the second and amplitude in the third axis. This will show us which frequenciesexist at which time ( there is an issue, called "uncertainty principle", which states that, we cannot

exactly know what frequency exists at what time instance , but we can only know what

frequency bands exist at what time intervals , more about this in the subsequent parts of thistutorial).

However, I still would like to explain it briefly:

The uncertainty principle, originally found and formulated by Heisenberg, states that, themomentum and the position of a moving particle cannot be known simultaneously. This applies

to our subject as follows:

The frequency and time information of a signal at some certain point in the time-frequency plane

cannot be known. In other words: We cannot know what spectral component exists at any

given time instant. The best we can do is to investigate what spectral components exist at any

given intervalof time. This is a problem of resolution, and it is the main reason why researchershave switched to WT from STFT. STFT gives a fixed resolution at all times, whereas WT gives

a variable resolution as follows:

Higher frequencies are better resolved in time, and lower frequencies are better resolved in

frequency. This means that, a certain high frequency component can be located better in time

(with less relative error) than a low frequency component. On the contrary, a low frequencycomponent can be located better in frequency compared to high frequency component.

Take a look at the following grid:


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f ^|******************************************* continuous

|* * * * * * * * * * * * * * * wavelet transform

|* * * * * * *|* * * *|* *

--------------------------------------------> Time

Interpret the above grid as follows: The top row shows that at higher frequencies we have more

samples corresponding to smaller intervals of time. In other words, higher frequencies can beresolved better in time. The bottom row however, corresponds to low frequencies, and there are

less number of points to characterize the signal, therefore, low frequencies are not resolved well

in time.

^frequency|

|

|| *******************************************************

|

|

|| * * * * * * * * * * * * * * * * * * * discrete time

| wavelet transform

| * * * * * * * * * *|

| * * * * *

| * * *|----------------------------------------------------------> time

In discrete time case, the time resolution of the signal works the same as above, but now, the

frequency information has different resolutions at every stage too. Note that, lower frequencies

are better resolved in frequency, where as higher frequencies are not. Note how the spacingbetween subsequent frequency components increase as frequency increases.

Below, are some examples of continuous wavelet transform:

Let's take a sinusoidal signal, which has two different frequency components at two differenttimes:


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Note the low frequency portion first, and then the high frequency.

Figure 1.10

The continuous wavelet transform of the above signal:


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Figure 1.11

Note however, the frequency axes in these plots are labeled as scale. The concept of the scale

will be made clearer in the subsequent sections, but it should be noted at this time that the scale

is inverse of frequency. That is, high scales correspond to low frequencies, and low scalescorrespond to high frequencies. Consequently, the little peak in the plot corresponds to the high

frequency components in the signal, and the large peak corresponds to low frequency

components (which appear before the high frequency components in time) in the signal.

You might be puzzled from the frequency resolution shown in the plot, since it shows goodfrequency resolution at high frequencies. Note however that, it is the good scale resolution that

looks good at high frequencies (low scales), and good scale resolution means poor frequency

resolution and vice versa.


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2. THE WAVELET ENTROPY:The power quality signals have the imbalance, the non-stationary, the different frequencycomponent and the different energy distribution, Shannon entropy is used to extract the features

from different power quality disturbance signals as a measurement of these irregularities. Let the

disturbance signal be

U= { j=1, 2, .N}.The Shannon (non normalized) entropy of the j point is represented asN

S = log

k=1

Where is the wavelet energy spectrum at scale j and instant k and is defined as follows.

The wavelet energy spectrum for detail and approximation coefficients in each decompositionlevel is obtained from the wavelet multi-resolution analysis of different disturbances and can becalculated as follows:

E= | (k)|^2

E = | (k)|^2

Where j=1, 2J

EE

is the energy spectrum for detail and approximation coefficients respectively. (K) is

the detailed coefficients and (k) is the approximation coefficients Where J represents the totalnumber of resolution levels. The extracted features help to distinguish a disturbance signal from

another.

WORK TO BE DONE

1. VARIOUS WAVELET ENTROPY MEASURES AND THEIR CALCULATIONMETHODS

Wavelet energy entropy

Wavelet time entropy Wavelet singular entropy

Wavelet time frequency entropy

Wavelet average entropy

Wavelet distance entropy


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2. APPLICATION OF VARIOUS WAVELET ENTROPY METHODS ON ASIMPLE POWER SYSTEM NETWORK WITH DIFFERENT LOADS

REFERENCES

1. T.Y. Vega, V.F. Riog, H.B.S Segundo, Evolution of Signal Processing Techniques in

Power Quality 9th

International Conference Electrical Power, Barcelona 9-11 October

2007.

2. Rioul, O. and vetteril, M., Wavelets and Signal Processing, IEEE Tran. Signal

Processing, vol-8, pp.14-38, 1991.

3. S. Mallat, A theory for multi resolution signal decomposition: the wavelet representation,

IEEE Trans. On Pattern Anal and Mach. Intell., vol 11, pp. 674-693, July 1989.

4. MATLAB 7.0.1 help tools

5. Wavelet theory by robi polikar.

assesment of power quality through wavelet entropy

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