DETECTION AND QUANTIFICATION OF HARMONIC EMISSIONS IN DOUBLY FED INDUCTION GENERATOR

International Journal of Electrical Engineering & Technology (IJEET) Volume 8, Issue 5, Sep-Oct 2017, pp. 20–31, Article ID: IJEET_08_05_003 Available online at http://www.iaeme.com/IJEET/issues.asp?JType=IJEET&VType=8&IType=5 ISSN Print: 0976-6545 and ISSN Online: 0976-6553 Journal Impact Factor (2016): 8.1891 (Calculated by GISI) www.jifactor.com © 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, http://www.iaeme.com/IJEET/index.asp 20 editor@iaeme.com Chandram Karri, Soujanya Kuchana 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. http://www.iaeme.com/IJEET/index.asp 21 editor@iaeme.com 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 nonlinear 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. http://www.iaeme.com/IJEET/index.asp 22 editor@iaeme.com Chandram Karri, Soujanya Kuchana 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.  Reconstruct coefficients.  Apply the corresponding wavelet transform to the distorted waveform input. Calculate RMS values of the coefficients thus obtained. http://www.iaeme.com/IJEET/index.asp 23 editor@iaeme.com Detection and Quantification of Harmonic Emissions in Doubly Fed Induction Generator  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-1D 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 denoised 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: √ ∑ [ ] http://www.iaeme.com/IJEET/index.asp (3) 24 editor@iaeme.com Chandram Karri, Soujanya Kuchana 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. 1 0.8 0.6 0.4 Input x 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.01 0.02 0.03 Time 0.04 0.05 0.06 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. Abs.Magnitude 150 100 50 0 0 100 200 300 400 500 Frequency(Hz) 600 700 800 900 Figure 4 FFT spectrum of standard signal. Magnitudes of each component from the FFT are shown in TABLE I http://www.iaeme.com/IJEET/index.asp 25 editor@iaeme.com Detection and Quantification of Harmonic Emissions in Doubly Fed Induction Generator Table 1 Imagnitudes Of Each Component By FFT Component Fundamental Third harmonic Fifth harmonic Seventh harmonic Magnitude 192 67 28 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 Frequency decomposition range a7 d7 d6 d5 0-1f 1f-2f 2f-4f 4f-8f d4 d3 d2 d1 8f-16f 16f-32f 32f-64f 64f-128f Presence of harmonics Third harmonic Fifth and seventh harmonic The total harmonic distortion is 0.3580.The comparison of THD for all three cases are summarized in TABLE III. http://www.iaeme.com/IJEET/index.asp 26 editor@iaeme.com Chandram Karri, Soujanya Kuchana Table 3 The Comparison Of Thd For All Three Cases Method Theoretical FFT Wavelet (dB 25)Level 7 THD 0.393 0.3909 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. http://www.iaeme.com/IJEET/index.asp 27 editor@iaeme.com Detection and Quantification of Harmonic Emissions in Doubly Fed Induction Generator 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 http://www.iaeme.com/IJEET/index.asp 28 editor@iaeme.com Chandram Karri, Soujanya Kuchana Figure 11 Energy levels of individual co-efficient of the imported signal Table 4 Frequency Range Of Each Coefficient Coefficient number CD1 CD2 CD3 CD4 CD5 CA5 Range of frequencies represented 16f-32f 8f-16f 4f-8f 2f-4f 1f-2f 0f-1f Energy relative to total signal ~0% 0.01% 0.02% 0.06% 0.61% 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 THD A 9.08% B 8.09% C 8.67% Table 6 THD of Current Waveform Phase THD A 1.74% http://www.iaeme.com/IJEET/index.asp B 1.49% 29 C 1.79% editor@iaeme.com Detection and Quantification of Harmonic Emissions in Doubly Fed Induction Generator 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. REFERENCES [1] Albegmprli, H.M., Çevik, A., Gülsan, M.E. and Kurtoglu,A.E. 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