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Journal of Applied Sciences Research, 4(11): 1561-1568, 2008 © 2008, INSInet Publication A New Harmonic Detection Method for Shunt Active Filter Based on Wavelet Transform 1 K. G. Firouzjah, 1A. Sheikholeslami, 1M. R. Karami-Mollaei, 2M. Khaleghi 1 Nushirvani University of Technology, P. O. Box 47135-484, Babol, Iran 2 Islamic Azad University of Khamene, Iran Abstract: This paper deals with two popular and powerful methods in noise and harmonic detection field of digital signal processing. The first one is the W indowing technique and the other one is wavelet transform. The proposed method uses these methods in the traditional synchronous fundamental dqframe algorithm. In other words, a windowing-wavelet based method is formed as a low pass filter. The Hamming window is adopted as windowing aspect to reduce its effete in frequency domain. The used mother wavelet is selected in terms of their effectiveness on transient response, low overshot and oscillation at frequency domain. Due to these concepts, the db8 is selected as mother wavelet. This method is superior to traditional FFT based and wavelet based filters because of fast transient response and small negligible sidelobes. The presented method has been verified with MATLABSIMULINK model and wavelet toolbox. Simulation results confirm the ability of this technique in power system harmonic detection. Key words: Shunt Active Filter, W avelet Transform, Harmonic Detection, W indowing, Hamming, DQ method INTRODUCTION An unavoidable proliferation of nonlinear loads in industrial, commercial, and residential applications requires the supply of reactive power, harmonics power, and power losses pertaining to the former two [1 ]. Different solutions to minimize the effects of nonlinear loads in electric power systems (nonsinusoidal voltages, harmonic currents, nonbalanced conditions) have been proposed. As a mater of fact, there is various types of compensators proposed to increase the power system quality,[2 ,3 ,4 ]. One of those compensators is the active power filter. Usually, the voltage-source is preferred to implement the parallel active power filter since it has some advantages [2 ]. The operational process of the active filter can be divided into two stages, one dedicated to the identifying current harmonics and the other one to the compensation of identified current with injection it into power network. Up to now, different algorithms emerged for the harmonic detection, which consider the detection accuracy, the speed, the filter stability, easy and inexpensive implementation, etc. T he classification of these methods can be done relative to the domain where the mathematical model is developed. Therefore three major directions are based on analysis of time, frequency and time-frequency domain [5 ]. Traditionally, electrical power quantities are calculated using tim e and frequency domain approaches. Power quantities in the frequency domain are obtained using Fourier Transforms yielding amplitudes and phase angles of voltages and currents involved. The voltage and current signals have become less stationary and the periodicity is often lost completely. This fact poses a problem for the correct application of Fourier-based frequency domain power quantities. Practical measurements use the FFTalgorithm, implicitly assuming the infinite periodicity of the signal to be transformed. Therefore, the registered frequency domain quantities are often meaningless and too unreliable to be used in power conditioner control [6 ]. The time-domain methods are mainly used to gain more speed or fewer calculations compared to the frequency-domain methods [5 ]. One of the most popular methods based on time domain analysis is synchronous fundamental dq-frame. As shown in Fig. 1, one drawback is the slow time response of the traditional low pass filter versus steady state error. Among the many methods that have been developed in the field of harmonic detection and generating reference current in Frequency-domain (Such as: Fast Fourier Transform, Discrete Fourier Transform, Recursive Discrete Fourier Transform) and Corresponding Author: K.G. Firouzjah, Nushirvani University of Technology, P. O. Box 47135-484, Babol, Iran E-mail: [email protected], Tel: +98 111 323 9214, Fax: +98 111 323 9214 1561 J. Appl. Sci. Res., 4(11): 1561-1568, 2008 Time-domain (Such as: Synchronous fundamental dqframe, Synchronous individual harmonic dq-frame, Instantaneous power pq-theory, Generalized integrators) some new methods are proposed based on TimeFrequency domain. The fundamental restriction in obtaining the timefrequency information, especially for short time records, is that we can not localize both time and frequency to arbitrary precision. Recent approaches are based on expressing signals in terms of wavelets (much like the Fourier series) [7 ]. W avelet transform (W T) has the advantage of using a variable window size for different frequency components. This allows the use of long time intervals to obtain more precise low frequency information and shorter intervals for high frequency information [8 ]. W avelet transform is a powerful signal processing tool for computing time-frequency representation of power signals [9 ]. The paper that proceeded to investigate W T on power system harmonic and noise detection are listed in [6 ,9 ,1 5 ]. Yalazan et al. [1 1 ] proposed a discrete WT based on fundamental positive sequence in order to obtain the reference currents for APF. This paper uses symmetrical component of any u n b a l a n c e d c u r r e n ts a n d s ix - l e v e l w a v e l e t decomposition. Among these methods, Gupta et al.[1 2 ] proposed a W T based controller of APF with using synchronous fundamental dq-frame. In this paper, the HPF shown in Fig. 1 is replaced by a wavelet based filter. Due to more advantage of the synchronous fundamental dq-frame an accurate method with fast transient in harmonic detection will be proposed in this paper. As a matter of fact, the response to sudden changes over a few periods is an effect similar to what is visible in other compensation methods where some kind of signal filtering is required: there is a trade-off to be made between accuracy and fast transient response. Among all methods mentioned above, the proposed W T method will be discussed and accompanied with synchronous fundamental dq-frame in order to make reference current of converter (shunt active filter). The reference current made in the first stage (harmonic term of nonlinear load current) will be injected by using predictive current control of the voltage source inverter. To verify the theoretical analysis, computer simulation in MATLAB-SIMULINK has been used and tested with a rectifier load. The obtained result indicates that the method is accurate and computationally efficient and therefore suitable for real time applications. Furthermore, the transient response in terms of steady state error is reasonable. M ATERIALS AND M ETHODS Synchronous Fundamental dq-frame M ethod: The concept of dq-frame method is based on the fact that harmonics are transformed into oscillations in the synchronous reference dq-frame. In the dq-frame, if the voltage is sinusoidal with only the nominal frequency, this voltage appears as a dc voltage. In the presence of harmonics, the voltage appears as a dc component but superimposed with oscillations whose frequency depends on the order of the present harmonic and the nominal frequency. Thus, by estimating the average of the voltage in the dq-frame, the fundamental voltage can be separated [1 6 ]. The measured three phase load current is transformed by using Park transform, from ab-c to d-q-o frame: ( iLa ,iLb and iLc are load currents and ω is the angular frequency. According to the mentioned above the id and iq have DC and AC terms (illustration of the main frequency and harmonic distortion), as: (3) As shown in Fig. 1, the harmonic components of d and q axis current can be decomposed by mean of a high pass filter: 1562 J. Appl. Sci. Res., 4(11): 1561-1568, 2008 Fig. 1: Principle algorithm of fundamental dq-frame [5 ]. the synchronous Fig. 5: The spectrum of a windowed ideal filter. Fig. 2: The decomposition process of the fast W T [4]. Fig. 6: Magnitude spectrum of rectangular window. Fig. 3: S p e c t r a l c h a ra c te ristics decomposition [4 ]. fo r 3 -le v el Fig. 4: The 3-level wavelet analysis tree. Fig. 7: Magnitude spectrum of Hamming window. 1563 J. Appl. Sci. Res., 4(11): 1561-1568, 2008 ( Above currents are used as compensator reference currents. In other words, these currents are applied to filter control system by means of reference current which is produced by active filters. As a matter of fact, the detection of the harmonics becomes a matter of removing the dc-signal with a High-Pass Filter (HPF in Fig. 1 with a cutting frequency between 25 Hz - 120 Hz) [5 ,1 7 ,2 0 ] . It is clear that the reverse relationship between accuracy and fast transient response will prevent HPF to achieve these terms. Therefore, improvement of the conventional HPF or LPF with new DSP algorithms will be expedient. Fig. 8: d axis current (id). W avelet Transform Algorithm: W avelet Transform: There are numerous types of wavelets to choose from [8 ]. All of the wavelets are scaled version of the “mother wavelet”. The continuous W T is defined as: (6) Fig. 9: M ultiplication of a selected window of id and the Hamming window with length of 1000 samples. According to (4), AC terms of d-q components are caused by harmonic components of load current. Thus, injection these currents with using another source, we can prevent harmonic current flowing in system power source. To achieve this purpose, ( currents should be transformed to a-b-c components Park inverse transform. W here p and τ are real and Ψ(t) is the mother wavelet. The wavelets are contracted (p < 1) or dilated (p > 1) and moved with shift time τ over the signal to be analyzed. In the wavelet analysis, we often speak of approximations and details. The approximations are the high-scale, low-frequency components of the signal. The details are the low-scale, high-frequency components. For the discrete W T, the decomposition process is shown in Fig. 2. In this figure, the symbol 29 represents down sampling by 2. The decomposition process can be iterated with successive approximations being decomposed in turn. Fig. 3 shows the resulting spectral characteristics of the filter bank for 3-level decomposition. Fig. 4 shows a 3-level wavelet analysis. W indowing Based W T: The former proposed W T method for AF [1 2 ] has been established as a combination of synchronous fundamental dq-frame Method and W T. The d and q axis current are ) collected as a signal with length of N samples during the observation period T. The mother wavelet db4 and db20 is used for decomposition of load current. In spite 1564 J. Appl. Sci. Res., 4(11): 1561-1568, 2008 Fig. 12: The average of 200 middle samples of the approximated signal. Fig. 13: Diode rectifier load current. Fig. 10: Results of db8 analysis and decomposition at eight levels. Fig. 11: The original and approximated signals. Fig. 14: D-axis current of nonlinear load. of the reduced harmonic in the de-noised signal, this method has some drawbacks. One of the main disadvantages of this method is its usage of the whole data in an observation window. In other words, this paper used a rectangular window to generate f(t). According to the definition of convolution, if two signals are multiplied together (in time domain), the frequency response of the product corresponds to the convolution of the individual frequency responses. As a result, multiplication in one domain corresponds to convolution in the other [7 ]. According to the windowing method [7 ,2 1 ], multiplication of a hypothetical signal and a rectangular signal, changes to convolution of a SINC function and frequency response of the other one. As an ideal goal, we want to close the SINC function into impulse. 1565 J. Appl. Sci. Res., 4(11): 1561-1568, 2008 Fig. 15: D-axis current of nonlinear load (zoomed). Fig. 16: D-axis current with a step change in load current of the nonlinear load whose spectra have small or positive sidelobes [7 ]. In addition to the rectangular window, there are some windows such as Hamming, Hanning, Blackman and Kaiser windows. According to the spacious issues in [7 ,2 1 ] each window will be expedient in specific terms. Figure 6 and Fig. 7 illustrate the effect of windowing in the frequency domain for two popular windows. Magnitude spectra of rectangular and Hamming windows are shown in Fig. 6 and Fig. 7 respectively. T he magnitude spectrum of each window is characterized by a large main lobe at zero frequency fallowed by a series of side lobes which decreasing amplitudes. As shown in these figures, the Hamming window is closer than rectangular window to the impulse function in frequency domain. Since the Hamming window side-lobe level is more than 40 dB down, it is often a good choice for accurate systems. Therefore, the rectangular window (used in [1 2 ]) is replaced by Hamming window. The d and q axis current (shown in Fig. 1) are sampled and collected as a signal with length of 1000 samples during the observation period T=10µs. Thereupon, sampled window is multiplied to Hamming window with same length. Figure 8 shows the d axis current (id). According to the mentioned above, a window with length of 1000 samples is selected from this signal. The selected window and Hamming window and multiplication of these windows are shown in Fig. 9. Then the achieved signal (production of id and Hamming window) is applied to the wavelet based filter to decompose the noise and main signal (in this term the main signal is the DC component of id). As mentioned above, there are numerous types of wavelets to choose from. According to the aspect of the achieved signal shown in Fig. 9, the mother wavelet db8 has been used for decomposition of load current at d and q axis. The approximate and detail signals at 8 levels are shown in Fig. 10. Another illustration of wavelet decomposition, the original signal and approximated signal are shown in Fig. 11. According to the Fig. 11, the db8 wavelet is able to approximates signal well. As final step of de-noising process, the average of 200 middle samples of the approximated signal has been used to generate existing state of d and q axis signals (Fig. 12). RESULT AND DISCUSSION Fig. 17: Filtered sinusoidal current through the supply. According to the mentioned above and the behavior of an ideal low pass filter (as shown in Fig. 5), there are overshoot and oscillations in the spectrum of the filter. To reduce the over shoot and oscillations, researcher suggest to chose windows The proposed technique is verified using a MATLAB-Simulink model. The nonsinusoidal current is generated by connecting a diode rectifier load. Figure 13 shows the load current when the system is not compensated and the source voltages are balanced and not distorted. 1566 J. Appl. Sci. Res., 4(11): 1561-1568, 2008 According to the proposed method, the three phase nonsinusoidal load current is transferred to the dqframe. It must be pointed out that the waveletwindowing based method is trying to be a low pass filter with high accuracy and fast transient response toward traditional FFT based filter. Therefore, the proposed wavelet-windowing based filter is used to pass D C component of the d and q-axis currents. As a result of this issue, Fig. 14 and Fig. 15 show the d-axis current after filtering. This figure is comparison between the traditional FFT based LPF (with cut off frequency 10 Hz) and the wavelet-windowing based low pass filter. As a consequent, the proposed method has a fast transient response and desirable accuracy. In order to validate the fast transient response of the proposed method, simulations are carried out with a step change in the load current at 0.15 sec. As shown in Fig. 16, the proposed filter has a fast transient response and desirable accuracy. In addition, by transforming of the filtered q and q-axis into abc-frame (by the inverse Park transform shown in Fig. 1) the harmonic components of the nonsinusoidal current can be decomposed well. From the simulation results (shown in Fig. 17), it can be seen that the line current is improved and becomes nearly sinusoidal. Conclusion: This paper proposes a new method for harmonic identification based on W T and synchronous fundamental dq-frame method. The present work has been incorporated with windowing technique in DSP field. In order to reduce the effect of windowing aspects (such as overshoot, oscillations and sidelobes) on the frequency domain, a Hamming window has been used in the filtering process. Simulation results are exhibited to compare the effectiveness of the Hamming window on wavelet based filtering technique. According to the results, The Hamming -W avelet method is superior in terms of harmonic elimination and transient response. The transient response of the Hamming W indowing and W T based filter is as fast as a FFT based filter (smaller than 0.5 cycles in comparison with the former wavelet based methods). Therefore, in many applications this method becomes superior to FFT based algorithms and similar works. The performance of the used wavelet types is compared in terms of their accuracy, generalization ability, and noise tolerance limits. The results show that db8 is able to have a good approximation at 8 levels. The proposed method has been verified with MATLAB-SIM ULINK model and wavelet toolbox. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. REFERENCES 1. Singh, B.N., B. Singh, A. Chandra, P. Rastgoufard and K. Al-Haddad, 2007. An Improved Control 1567 Algorithm for Active Filters.IEEE Trans. Power Delivery, 22(2): 1009-1020. Bollen, M.H., 1999. Understanding Power Quality Problems: Voltage Sags and Interruptions. W ileyIEEE Press. Hingorani, N.G. and L. Gyugyi, 1999. 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