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International Journal of Electrical Engineering & Technology (IJEET)

Volume 8, Issue 5, Sep-Oct 2017, pp. 20–31, Article ID: IJEET_08_05_003

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© IAEME Publication

DETECTION AND QUANTIFICATION OF

HARMONIC EMISSIONS IN DOUBLY FED

INDUCTION GENERATOR

Chandram Karri, Soujanya Kuchana

S R Engineering College, Warangal, India

ABSTRACT

In this paper, Discrete wavelet transform available in Wavelet toolbox,

MATLAB/SIMULNIK has been used to analyze harmonics presented in DFIG. The

wavelet toolbox is successfully used to calculate the energy levels presented in the

harmonics of the voltage and current waveforms generated in the DFIG. A technique

to find out the THD independent of FFT is implemented in MATLAB and the THD for

all the phases in both the current and voltage waveforms are computed and tabulated

in the simulation results. It is observed from the case study that the discrete wavelet

transform is an effective tool to detect and quantify the harmonics present in the

DFIG. The simulation results in each phase are presented in the simulation results.

The results of the proposed approach has been compared with theoretical result and

FFT and it is found from the results that the proposed approach provides better

results.

Key words: Discrete Wavelet Transform, Doubly fed Induction generator.

Cite this Article: Chandram Karri, Soujanya Kuchana, Detection and Quantification

of Harmonic Emissions in Doubly Fed Induction Generator. International Journal of

Electrical Engineering & Technology, 8(5), 2017, pp. 20–31.

http://www.iaeme.com/IJEET/issues.asp?JType=IJEET&VType=8&IType=5

1. INTRODUCTION

The main objective of electric utilities is to supply reliable power to the consumers by

maintaining voltage and frequency magnitudes specified by standards [1]. However, this has

become a difficult task because the ratings of non-linear loads have been increased rapidly[2].

Power quality has been adversely affected due to the power disturbances such as harmonics,

notches, outages of various power system components, flicker, swells, sags transients

frequency, voltage disturbances etc. Effects of these problems are overloading of neutral

conductors, heating of induction motors, transformers, capacitors, voltage dips, shutdowns,

fluctuations, protection tripping, variable speed drives failure and tripping etc[3]. Wind power

is actively growing to be a significant contributor to the field of renewable, clean energy[4].

One of the major reasons for the significant growth in wind power contribution is

development of new technologies such as doubly fed induction machines and permanent

magnet synchronous machines and power electronic converters. Due to these developments,



the harmonics present in the system is much more, as the harmonic effect is more in the

power electronic converters [5]. Hence, it is necessary to identify the harmonics [6,7] present

in the system. In the literature survey, Fourier transform, Short Term Fourier transform and

Fast Fourier transform were applied for detection of harmonics [8,9,10]. The most preferred

tool is the Fourier analysis, which gives quantitative information about all the frequencies

present in the system. However, the Fourier analysis has one serious deficiency that all time

information is lost when the transform is applied. The next logical step would be to then pick

a certain window or time frame from the time signal and then apply Fourier transform; this is

the Short Time Fourier Transform (STFT), a sort of a compromise between the frequency and

time domains as the output would be plotted between these two. Thus, the signal would

provide information about when a particular frequency appeared in the signal as well.

However, it is obvious that the accuracy of the information would depend largely on the size

of the window that was used. Also, when the size of the window is fixed, it is the same for all

frequencies, it is not possible to vary the window length and obtain more accuracy for

particular frequencies. Of course, the obvious modification to the above would be to make the

lengths of those windows time varying in nature. The windows are kept longer for obtaining

low frequency information and are kept shorter for determining high frequency information.

The Wavelet technique[11, 12,13] is a fast becoming tool of choice for most power systems

analysts for harmonic analysis due its inherent flexibility and the wonderful insight it offers

into the behavior of multi-frequency systems. The objective this paper is to detect and

quantify the harmonics present in the DFIG using Wavelet. Rest of the paper is organized as

follows. Harmonics distortion in a doubly fed induction generator is given in section II.

Description on wavelet is provided in section III. Harmonic analysis on DFIG using wavelet

in MATLAB is provided in section IV. Simulation results are given in Section V. Conclusion

of the paper is given in section VI.

2. HARMONICS DISTORTIONS IN A DOUBLY-FED INDUCTION

GENERATOR

Doubly-Fed Induction Generator (DFIG)[14] is an entire system consisting of a wound rotor

induction machine and a variable frequency (AC-DC-AC) IGBT convertor. The stator is

always connected to the grid, while the rotor is fed with variable frequency currents through

the power convertor network connected to the grid.

The net rotor current frequency would be the sum of the frequencies fed in by the

convertor network and the frequency of the currents induced by rotation due to the wind speed

input. The model is represented as follows:

The rotation speed of the blades is given as an input to the convertor network show.

Whenever the wind speed is slow, the AC-DC-AC convertors automatically increase the

frequency of currents they feed into the rotor; making sure the frequency of stator current and

voltage is always kept constant at 50Hz. The convertors achieve this by first converting the

AC input from the grid into DC, changing the DC voltage levels by suitable switching

techniques based on the wind speed input, and reconverting it back to AC at the requisite

frequency.

Detection and Quantification of Harmonic Emissions in Doubly Fed Induction Generator


Figure 1 Configuration of a DFIG wind turbine

Since the operation of the DFIG is heavily dependent on the power convertors, the current

drawn and supplied would have some amount of harmonics[15,16] present in them, due to the

peaky currents drawn in. Thus, some harmonics can be expected in the system due to presence

of the power convertor circuit. Not just the power convertors, even the load connected to the

DFIG network would introduce significant amount of harmonics, especially due to their non-

linear nature. Even linear loads present some sort of distortion in the voltage and current

waveforms, as no load can be completely linear in nature.

3. DISCRETE WAVELET TRANSFORM

Wavelet transforms [17, 18] are functions defined over a finite interval and having an average

value of zero. The basic idea of the wavelet transform is representation of any arbitrary

function as a superposition of set of such wavelets or basis functions. These basis functions or

baby wavelets are obtained from a single proto-type wavelet called the mother

wavelet, by dilations (scaling) and translations (shifts). In Wavelet Transform, the width of

the wavelet function changes with each spectral component. At high frequencies, the wavelet

analysis gives good time resolution and poor frequency resolution, while at low frequencies,

good frequency resolution and poor time resolution are observed. Mathematically, the wavelet

transform is a convolution of the wavelet function with the given signal. The wavelets are

classified in to continuous and discrete wavelets. The brief description is given below.

3.1. Continuous Wavelet Transform

The Continuous Wavelet Transform (CWT) is provided by the equation,

( )

√ ∫ ( ) (

)

(1)

Where,

x(t) is the signal to be analysed

ψ(t) is the mother wavelet or the basis function

a is the dilation parameter

b is the location parameter

All the wavelet functions used in the transformation are derived from the mother wavelet

through translation (shifting) and scaling (dilation or compression). Computing the CWT

takes a lot of time, as the signal is continuously analysed, taking high computation times.



3.2. Discrete Wavelet Transform

The Discrete Wavelet Transform (DWT), which is based on sub-band coding, yields a fast

computation of the Wavelet Transform (Sub-band coding is any form of transform coding that

breaks a signal into a number of different frequency bands and encodes each one

independently). A time-scale representation of the digital signal is obtained using digital

filtering techniques.

3.3. Multi-Level Decomposition

Generally, for many signals, the most important part, which gives the signal its identity, is the

low-frequency content. The high-frequency content, on the other hand, imparts flavor or

nuance. In wavelet analysis, approximations and details are often spoken of. The

approximations are the high-scale, low-frequency components of the signal, whereas, the

details are the low-scale, high-frequency components. The original signal passes through two

complementary filters (one low pass and the other high pass) and emerges as two signals, A

and D, doubling the number of samples. So, the signals A and D are then down-sampled to

approximately half their size by keeping only one point of the two in all the samples, thereby

giving cA and cD. The decomposition process can be iterated, with successive

approximations being decomposed in turn, so that one signal is broken down into many lower

resolution components. This is called the wavelet decomposition tree. The high frequency

content (mostly noise) will be removed in the successive iterations. The decomposition of the

approximations can proceed until the individual details consist of a single sample or pixel.

This is the technique that has been adopted for in this work.MRA using Wavelet Transform is

shown in Fig. 2

Figure 2 MRA using Wavelet Transform

3.4. Wavelet Selection

There are many possible „mother‟ wavelets for wavelet analysis, and selecting one is entirely

dependent on the task at hand. Different wavelets [19] give different accuracies for various

tasks, and several papers have been published about the way to go about choosing the correct

one. The favorite way for comparing wavelets seem to be by checking the RMS error the

transform induces between the actual signal and the reconstructed signal using the

coefficients.

The algorithm used is as follows:

Choose any arbitrary mother wavelet.

Apply the corresponding wavelet transform to the distorted waveform input.

Reconstruct coefficients.

Calculate RMS values of the coefficients thus obtained.



Calculate the difference in the computed RMS values and the actual RMS values. Less the

error, the better approximation the wavelet provides to the actual wave.

The case studies were performed on harmonic and inter-harmonic distortion, and the

subsequent results plotted. Though it may appear that „dmey‟ wavelet would give the least

amount of error, and indeed it is an excellent approximation, other research has shown that on

an average, the db10 wavelet gives the least amount of RMS error for most applications. The

example shown here is only to illustrate the technique of finding out the best wavelet. These

calculations are to be carried out when the user is unsure of the amount of error the wavelet is

going to induce in the analysis. Hence, the analysis used in this report utilizes the db10

wavelet, which can be easily changed to any other wavelet.

4. HARMONIC ANALYSIS ON DFIG USING WAVELETS IN

MATLAB/SIMULINK

MATLAB wavelet toolbox offers a lot of options on wavelet analysis. All types of analysis on

one dimensional and multi dimensional signals are allowed, allowing one special multiple-1-

D signal analysis, which allows the user to load a signal matrix and analyze it row-by-row.

This is the technique used in the report, as each phase of voltage/current has been stored as a

separate element in a matrix which is loaded by the toolbox. Further, the signal can be de-

noised or compressed, and various estimation procedures can be carried out on them. The

wavelet to be used differs widely from application to application. A few techniques will be

described to choose the best kind of wavelet. And finally, the wavelet will be used to actually

perform the analysis on voltage and current waveforms, displaying the various energies

present in the various frequency bands. The THD is calculated extracting the wavelets into the

MATLAB workspace. Voltage and current waveforms are extracted from the DFIG model on

SIMULINK. The waveforms are stored as a matrix, and can be extracted one-by-one as

necessary. For harmonic analysis, we load these waveforms into the wavelet toolbox of

MATLAB by choosing the multi-signal 1D analysis option. Once there, we select the db10

wavelet as the mother wavelet of choice and go for a 5-level decomposition. Higher order

decomposition can be opted for, but that would lead to unnecessary increase in the

computation time without significant increase in accuracy. Hence, we stick to a 5-level

decomposition.

The wavelet toolbox allows the user to see all the 5 levels of decompositions and the final

reconstructed signal as well, along with a host of other results and statistics on the same. The

energy in the waveforms can be directly seen from the energy of the coefficients.

4.1. Extracting THD from Wavelets

Though the THD can be extracted from the powergui block of SIMULINK, which uses FFT

to compute the signal, we will be aiming to extract the THD from the wavelet decomposition

itself. First, about the basic definition of THD:

√

(2)

In the above formula, all the Hi are the RMS values of the „i‟th harmonic component.

Hence, we first need to compute the RMS values of the coefficients. That can be done by

using the following formulae:

√

∑ [ ( )]

(3)



Once this is done, we can calculate the THD as follows:

√

∑ [ ( )]

√

∑ [ ( )]

(4)

In the above formulae, „N‟ refers to the number of samples in that particular frequency.

5. SIMULATION RESULTS

The suggested approach has been implemented in MATLAB (Version 7) and applied on a

standard signal and doubly fed induction generator.

5.1. Case IA Simple case with First, third, fifth and seventh harmonics

In this case, the waveform contains the fundamental (50Hz) with 1 volt amplitude, third

harmonic component with 0.35 volts amplitude, fifth harmonic component with 0.15 volts

amplitude and seventh harmonic component with 0.1 volts amplitude. The waveform with all

harmonics is shown in Fig. 3. Sampling frequency is taken as 6400 Hz.

Figure 3 Sample waveform with different harmonics

Initially, FFT is applied on standard signal and the spectrum of FFT is shown in Fig. 4. It

is clear from Fig. 4 that the harmonics are presented at 150 Hz, 250 Hz and 350 Hz.

Figure 4 FFT spectrum of standard signal.

Magnitudes of each component from the FFT are shown in TABLE I

0 0.01 0.02 0.03 0.04 0.05 0.06-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Input x

Time

0 100 200 300 400 500 600 700 800 9000

50

100

150

Abs.Magnitude

Frequency(Hz)



Table 1 Imagnitudes Of Each Component By FFT

Component Magnitude

Fundamental 192

Third harmonic 67

Fifth harmonic 28

Seventh harmonic 19

Total harmonic distortion from FFT is 0.3909. Wavelet has been applied on the same

standard signal. In this study, db20 mother wavelet has been chosen.

The level of decomposition for this case is calculated as follows.

(

) (

)

Sampling frequency is 6400 Hz and fundamental frequency is 50 Hz and hence level is 7.

The above calculations are essentially required to select the level of decomposition in order to

localize the harmonic components with the distorter signal.

Wavelet decompositions of the signal are shown in Fig 5.

Figure 5 Wavelet decompositions of the signal

Here the decomposition level is 7. The range of frequencies is shown in TABLE II

Table 2 The Range Of Frequencies

Level of

decomposition

Frequency

range

Presence of

harmonics

a7 0-1f

d7 1f-2f

d6 2f-4f Third harmonic

d5 4f-8f Fifth and seventh

harmonic

d4 8f-16f

d3 16f-32f

d2 32f-64f

d1 64f-128f

The total harmonic distortion is 0.3580.The comparison of THD for all three cases are

summarized in TABLE III.



Table 3 The Comparison Of Thd For All Three Cases

Method THD

Theoretical 0.393

FFT 0.3909

Wavelet (dB 25)Level 7 0.3580

5.2. Case II DFIG Model in SIMULINK

A 9 MW wind farm [20] consisting of six 1.5 MW wind turbines connected to a 25 kV

distribution system exports power to a 120 kV grid through a 30 km, 25 kV feeder developed

in MATLAB is considered in this study.In this model the wind speed is maintained constant

at 15 m/s. The control system uses a torque controller in order to maintain the speed at 1.2 pu.

The reactive power produced by the wind turbine is regulated at 0 Mvar. For a wind speed of

15 m/s, the turbine output power is 1 pu of its rated power, the pitch angle is 8.7 deg and the

generator speed is 1.2 pu.The example here loads the signal „Volt‟ from the output of the

SIMULINK DFIG model. As can be clearly seen, the 4 vectors present in the signal (the time

axis and the 3 voltage phases) have been decomposed and the energies are on display. Various

statistics such as mean deviation, range etc. and a host of graphs can be viewed about the

signals. Imported voltage signal is shown in Fig. 6.

Figure 6 Imported voltage signal of DFIG

Energy levels of individual co-efficients of the imported signal of DFIG are shown in Fig

7.

Figure 7 Energy levels of individual co-efficients of the imported signal of DFIG

Decomposition level and Selection of individual phase of the three phase voltage supply

of imported signal are shown in Fig 8 and Fig 9.



Figure 8 Decomposition level of imported signal

Figure 9 Selection of individual phase of the three phase voltage supply of imported signal

Voltage and current waveforms are extracted from the DFIG model in SIMULINK. The

waveforms are stored as a matrix, and can be extracted one-by-one as necessary. The

simulation is run for 0.2 seconds, with the fundamental frequency of the system being 60Hz.

CD5 represents the energy present in the lowest frequency range, and CD1 that in the

highest frequency range. Thus the energy present in the various harmonics can be easily found

out. For a five level decomposition, the frequencies represented by the coefficients are given

in TABLE IV. Here, „f‟ is the fundamental frequency of the system=60Hz.The CD4

coefficient represents the range of frequencies consisting of the troublesome third harmonic.

Similarly, the energies of the requisite harmonics can be found out. Various other statistics

can be found out as well, such as the FFT graph, histograms, mean, range etc.

Figure 10 Decomposition of the imported signal



Figure 11 Energy levels of individual co-efficient of the imported signal

Table 4 Frequency Range Of Each Coefficient

Coefficient

number

Range of frequencies

represented

Energy relative to

total signal

CD1 16f-32f ~0%

CD2 8f-16f 0.01%

CD3 4f-8f 0.02%

CD4 2f-4f 0.06%

CD5 1f-2f 0.61%

CA5 0f-1f 99.3%

The signals are extracted row wise from the .mat file that was created in the SIMULINK

simulation. First, the variables are loaded into the workspace, and then extract the signal of

interest. The RMS value is calculated by summing up the squares of each element of the row

and then dividing it by the total number of elements in that row, finally taking the square root

of the entire thing. Summing up the RMS values of the harmonics and taking the square,

further dividing by the RMS value of the fundamental wave (CA5). The values thus found

are:

Table 5 THD of Voltage Waveform

Phase A B C

THD 9.08% 8.09% 8.67%

Table 6 THD of Current Waveform

Phase A B C

THD 1.74% 1.49% 1.79%



It can be seen from the TABLE V and TABLE VI that the THD values are slightly

different. It shows that the individual phases are unbalanced. Harmonic severity can be

measured by THD calculations.

6. SIMULATION RESULTS

In this paper, wavelet has been used to detect and quantify the harmonic distortion in doubly

fed induction generator in MATLAB/SIMULINK. The harmonic emission in DFIG is

analyzed. The Wavelet transform was used successfully to calculate the energies present in

the harmonics of the voltage and current waveforms. A technique to find out the THD

independent of FFT was implemented in MATLAB and the THD for all the phases in both the

current and voltage waveforms was computed and tabulated in the simulation results. This

paper is dealt with only the detection of harmonic issues in a DFIG. This concept can be

further extended to mitigate those issues, with the help of certain filter components or

something on similar lines. Also, this analysis has been performed only keeping in mind the

harmonic sources within the DFIG.

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