Download A New Harmonic Detection Method for Shunt Active

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
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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:
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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.
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(
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
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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.
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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.
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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.
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