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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 2, MAY 2005
A Novel Time-Domain Current-Detection Algorithm
for Shunt Active Power Filters
Hongyu Li, Fang Zhuo, Zhaoan Wang, Senior Member, IEEE, Wanjun Lei, and Longhui Wu
Abstract—A novel current-detection algorithm based on the
time-domain approach for three-phase shunt active power filters
(APFs) to eliminate harmonics, and/or correct power factor,
and/or balance asymmetrical loads is analyzed in this paper. A
basic overview and evaluation of the performance of existing
current-detection algorithms for active power filters are presented. According to different complicated power quality issues
and various compensation purposes, a novel current-detection
algorithm is then proposed. Comparing with existing algorithms,
this algorithm has shorter response time delay and clearer physical meaning. Different compensating current references can,
thus, be accurately and easily obtained by adopting the proposed
algorithm. It ensures that the shunt APF can very well achieve
different compensation purposes. Moreover, it is very easy to
implement this algorithm in a digital signal processor (DSP).
Simulation results obtained with MATLAB and testing results on
an experimental shunt APF are presented to validate the proposed
algorithm.
Index Terms—Active power filter (APF), current-detection algorithm, harmonic compensation, reactive power compensation, time
domain.
Fig. 1.
SAPF control system.
to some situation but not to all situation. A novel current-detection algorithm of SAPF for harmonic elimination, power factor
correction, and balancing of nonlinear loads is proposed in this
paper.
II. TRADITIONAL AND PROPOSED CURRENT DETECTION
ALGORITHMS
There are many existing methods of current-detection algorithms.
I. INTRODUCTION
W
ITH the proliferation of nonlinear loads such as
diode/thyristor rectifiers, nonsinusoidal currents degrade power quality in power transmission/distribution systems
[1]. Traditionally, passive filters have been used to attenuate
the harmonic distortion and compensate the reactive power, but
passive filters are bulky, detune with age, and can resonate with
the supply impedance. As active power filters are powerful tools
for the compensation not only of current harmonics produced
by distorting loads but also of reactive power and unbalance of
nonlinear and fluctuating loads [2], and they can be smaller,
more versatile, better damped, more selective, and less prone
to failure for component drift than its passive counterpart, they
are studied widely, and great developments have taken place in
theory and application of active power filters (APFs) [3].
The shunt APFs (SAPFs) are used most widely [4]. Fig. 1
shows the topology of SAPF, which is used to cancel the current distortion. The performance of SAPF strictly depends on
the features of the current-detection algorithms and controllers.
Many papers on current-detection algorithms have been published [5]–[17], and some algorithms have been applied in practice. However, usually one algorithm is only more appropriate
Manuscript received March 1, 2004; revised July 2, 2004. This work was
supported by a grant from the National Natural Science Foundation of China
(Key Program no. 59737140). Paper no. TPWRS-00110-2004.
The authors are with the Department of Electrical Engineering, Xi’an
Jiaotong University, Xi’an, China (e-mail: lihy@mailst.xjtu.edu.cn;
zffz@mail.xjtu.edu.cn).
Digital Object Identifier 10.1109/TPWRS.2005.846215
A. Analogue Methods
Analog filter has been used to detect the harmonics [5], [6],
such as the band-pass filter and low-pass filter. The main disadvantage with this method is that the derived component has
magnitude and phase errors; in other words, the precision is not
satisfactory.
B. Instantaneous Reactive Power Theory-Based Methods
Instantaneous Reactive Power Theory (IRPT) (i.e., p-q
theory), which was proposed by H. Akagi in 1983, promoted
the use of APF [4]. This approach inspired the development of
many other - theory-based methods for realizing the SAPF
[7]–[9]. However, the IRPT-based method requires coordinate
coordinates and the
transformations between the
coordinates, which increases the complexity of designing the
SAPF controller. In 1998, Peng et al. proposed a theory that
gave a general definition of the instantaneous reactive power in
coordinate [10]. Although Peng’s approach does not
the
need the coordinate transformation, it requires an additional
function for instantaneous reactive power vector calculation
in the SAPF controller. Moreover, all of the above algorithms
based on IRPT cannot be used to detect the selective order
harmonics.
C. Fourier Transform-Based Methods
With the wide use of digital signal processor (DSP) and microcomputer, digital algorithms such as fast Fourier transform
0885-8950/$20.00 © 2005 IEEE
LI et al.: A NOVEL TIME-DOMAIN CURRENT-DETECTION ALGORITHM FOR SHUNT APFs
645
(FFT) and discrete Fourier transform (DFT) began to be studied
and used [11], which has good precision and can be used to detect the selective order harmonic, but one complete mains cycle
delay is unavoidable for the algorithm and the physical meaning
is not clear by the transformations between the time domain
and the frequency domain. Although the modified Fourier transform-based methods adopting the sliding window can improve
the dynamic response [12], [13], one main cycle is also required
to track the load change completely. Therefore, it is suitable
for slowly varying load conditions. Moreover, Fourier transform-based methods cannot be used to split the fundamental
current up into the positive-sequence/negative-sequence component and active/reactive power component of the positive-sequence fundamental current.
D. Other Methods
Some other algorithms such as fuzzy control [14], adaptive
[15], [16], and the wavelet and neural network [17], [18] algorithm have also been applied, which are quite accurate and,
of course, have a much better dynamic response than FFT, but
these algorithms require a large amount of calculation. Software implementations of signal filters as finite impulse response
(FIR) or (IIR) filters can replace the analogue techniques outlined above, but the disadvantage of analog filters is also inherent.
Fig. 2. Diagram of the symmetric weigh law.
cared, and it is not necessary to decompose the harmonic. Then,
the fundamental current component is expressed as follows:
III. OPERATION PRINCIPLE OF THE PROPOSED ALGORITHM
Based on IRPT and DFT, this paper presents a novel method
based on time domain for determining the SAPF reference compensating currents. The operation principle of the proposed algorithm is introduced, and the physical meaning is analyzed in
the following section.
In the three-phase three-wire system, the instantaneous load
, and ) can be disassemcurrents of phase “a,” “b,” “c” (
bled into positive-sequence and negative-sequence components
according to the symmetrical weigh law, which was proposed
by Fortescue separately.
(1)
where
The subscripts 1 and 2 represent the positive-sequence and negative-sequence, respectively. represents harmonic order. represents the peak value of the current and is the initial phase
( is determined as the initial phase between the positive-sequence fundamental voltage of phase “a” in order to explain
is the number of sampling point in
the physical meaning).
one fundamental cycle, and is the count value of sampling
.
Commonly, only the positive-sequence, negative-sequence,
active power, and reactive power of the fundamental current are
(2)
where, as shown in Fig. 2, the first item of (2) corresponds
to the positive-sequence component in phase with the phase
voltage, which is called the active power component of the positive-sequence fundamental current; the second item of (2) corresponds to the positive-sequence component orthogonal with the
line voltage, which is called the reactive power component of
the positive-sequence fundamental current; the third item of (2)
corresponds to the negative-sequence component in phase with
the line voltage, which is called the active power component
of the negative-sequence fundamental current; the forth item of
(2) corresponds to the negative-sequence component orthogonal
with the line voltage, which is called the reactive power component of the negative e-sequence fundamental current.
Fig. 3 shows the block diagram of the proposed current-deis synchronous with the
tection algorithm, where
positive-sequence fundamental voltage of phase “a,” which determines the calculation precision of active and reactive power
components. The low-pass filter used determines the performance of the system [20]. According to different compensation
purposes, different components will be obtained by the segregator expediently, which is superior to the algorithm based on
the instantaneous reactive power theory.
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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 2, MAY 2005
to the total power delivered from source to load). The second
item of the equation corresponds to the instantaneous reactive
power component of the positive-sequence fundamental (the
sum of three phases is zero, which circulates between the phases
and can be compensated by a compensator without an energystorage element). The third item corresponds to the instantaneous active power component of the negative-sequence fundamental (the three-phase sum of the previous part of this item is
zero, which circulates between the phases and can also be compensated by a compensator without an energy-storage element).
The three-phase sum of the rest (including the posterior part of
the third and fourth items, which is equal to
and the same for each phase) is not zero, and its frequency
is twice the fundamental, which can be compensated by a compensator with an energy-storage element). Therefore, the negative-sequence fundamental currents do not contribute to the
power delivered to the load.
Similarly, the instantaneous power of harmonics can be obtained by multiplying current by
Fig. 3. Block diagram of the proposed current-detection algorithm.
Fig. 4. Control diagram of the phase locked loop.
The synchronous signal can be obtained by soft phase loop
lock (SPLL) [19]. The control diagram of the SPLL is shown
is set to zero, the
calcuin Fig. 4. When the reference
lated is synchronous with the positive-sequence component of
is not set to zero, a fixed phase
fundamental voltage. When
and the positive-sequence comdifference is between the
ponent of fundamental voltage, which make the control of the
displacement factor easy. Moreover, this phase difference will
not affect the validity of the selected harmonics detection. The
can be obtained as
. A “table look-up”
scheme is employed to get
, and
for
calculation, which has been calculated and stored in a data table
to reduce processing time.
The phase voltage is expressed by per-unit; the base quantities for per-unit value is the peak value of positive-sequence
fundamental phase voltage. Then, three phase voltages can be
, respectively. The instantaexpressed as
neous power of the fundamental current can be obtained by multiplying current by phase voltage
(4)
It can be seen that either the negative-sequence or positive-sequence component has one part of which the three-phase sum up
to zero, which can be compensated by a compensator without
energy storage, and the rest can be compensated by a compensator with energy storage.
In (4) and (5), the lowest frequency component is twice the
fundamental frequency; the dc component can be obtained by a
low-pass filter with a cutoff frequency lower than twice the funsamples.
damental frequency or by a sliding-window with
Then, multiplying by 2, the following equation can be obtained:
(5)
Multiplying (1) by
tion can be obtained:
, the following equa-
(3)
where the first item of the equation corresponds to the instantaneous active power component of the positive-sequence fundamental (the sum of three phases is constant, which contributes
Using the same method, the following equations can also be
obtained:
(6)
LI et al.: A NOVEL TIME-DOMAIN CURRENT-DETECTION ALGORITHM FOR SHUNT APFs
647
Here, define
(7)
where
and
are the peak values of the reactive power
component and active power component of positive-sequence
and
are the peak
fundamental current, respectively.
values of the reactive power component and active power component of negative-sequence fundamental current of phase “a,”
respectively. According to phase “b” and “c,” the peak values
and
are
, respectively.
and
Similarly, multiplying (1) by
, respectively, and going through the
low-pass filter,
and
can be obtained:
Then, define
(8)
(9)
(10)
(11)
Equations (7)–(10) compose the segregator shown in Fig. 1,
by which various results can be achieved according to different
compensation purposes. If the SAPF is used to compensate
harmonics and the negative-sequence component of the fundamental current, the positive-sequence component of the
can be obtained from (8), and the
fundamental current
current reference can be obtained as
by subtracting
from the load current. If the line current
after compensation is expected to be a symmetrical three-phase
fundamental current, and the power factor is 1, the active power
component of the positive-sequence fundamental current
can be obtained by assuming
in (8), and the current
by subreference can be obtained as
from the load current. Similarly, by setting
tracting
to zero, the reactive power component of the positive-sequence
fundamental current can be obtained. The negative-sequence
Fig. 5. Simulated three-phase voltage and load current.
Fig. 6. Estimated fundamental current by IRPT and the proposed algorithm.
component of the fundamental current can be obtained by (9).
If the APF is used to compensate the selected order harmonics,
the compensating reference can be obtained by (11). In fact,
the “active power” component and “reactive power” component of harmonics do not need to be divided, so the factors
and
can be
and
, separately.
replaced with
Then, the programming can be greatly simplified. Based on
the detection methods, different compensation aims can be
achieved by using specific combinations.
It can be seen from the above analysis that the delay resulting
from the proposed algorithm is less than half of the main cycle,
which is half of that of DFT and the same as that of the algorithm
based on IRPT. Besides, the algorithm proposed could detect
the positive/negative-sequence fundamental current, active/reactive power component of positive-sequence fundamental current, and selective harmonics expediently, which is more flexible
than the algorithm based on IRPT and DFT. Moreover, the proposed algorithm has clear physical meaning and does not need
the coordinate transformation.
IV. SIMULATION RESULTS
In order to test the operation of the novel current-detection algorithm, the simulation model has been built. The
simulation was performed by MATLAB dynamic simulation
tool—Simulink.
A. Steady-State Conditions Simulation
The test system for steady-state conditions consisted of a
three-phase diode rectifier with a 4 ohm dc-side resistor and a
1.8 mH ac-side inductor in phase “b” branch.
Fig. 5 shows waveforms of three-phase voltage, which is symmetrical, and load current, which is nonsinusoidal and unbalanced. Figs. 6–9 show waveforms of the derived fundamental
current, which include both the positive-sequence and negative-sequence components; the derived positive-sequence fundamental current, where both active-power and reactive-power
components exist; the derived active-power component of the
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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 2, MAY 2005
Fig. 7. Estimated positive-sequence fundamental current by IRPT and the
proposed algorithm.
Fig. 12.
Estimated fundamental current by DFT and the error.
Fig. 8. Estimated active power component of positive-sequence fundamental
current by IRPT and the proposed algorithm.
Fig. 13. Estimated fundamental current by instantaneous reactive power
theory and the error.
Fig. 9. Estimated negative-sequence fundamental current by IRPT and the
proposed algorithm.
Fig. 14.
error.
Estimated fundamental current by the proposed algorithm and the
Fig. 10. Estimated fifth-order harmonics by DFT and the proposed algorithm.
Fig. 15. Difference of the estimated fundamental current between the
instantaneous reactive power theory and proposed algorithm.
Fig. 11.
Simulated load current and the fundamental component.
positive-sequence fundamental current; the derived negative-sequence fundamental current, which when obtained by the proposed algorithm is the same as that obtained by the IRPT-based
algorithm [4]. As shown in Fig. 10, the firth-order harmonics
obtained by the proposed algorithm and DFT [11] are also the
same. Therefore, the proposed algorithm has the functions of
both IRPT and DFT, which is more flexible.
B. Dynamic Response Simulation
In order to compare the dynamic response of the DFT, IRPT,
and the proposed algorithm, a different test system for transient experiments is built, which consists of a three-phase diode
bridge rectifier with a 20–10 ohm varying dc-side resistor; negative-sequence fundamental voltage that is 10% of the positive-sequence fundamental voltage is added.
Fig. 11 shows the load current and the fundamental component. Figs. 12–15 show estimated the fundamental current and
the error by adopting different algorithms. The sliding-window
average is adopted to obtain the dc component in IRPT and the
proposed algorithm. As shown in Fig. 9, there is one main cycle
delay in the estimated fundamental current by adopting DFT.
This leads to a residual fundamental component in the reference current, which, in turn, causes a large real power flow in
the APF. However, the delay by adopting the algorithm based
on IRPT and proposed algorithm is half of one main cycle, and
the estimated fundamental current error is smaller than adopting
DFT.
As shown in Fig. 15, the response time and precision of the
proposed algorithm and the algorithm based on IRPT are almost
the same.
Fig. 16 shows the firth-order harmonics of the load current.
Figs. 17 and 18 show estimated fifth-order harmonics and the
detection error by adopting DFT and the proposed algorithm,
respectively. As shown in these two figures, the precision in
steady state by adopting both algorithms are the same; however,
the proposed algorithm has better character of dynamic response
than DFT, whose response time is half of that of DFT, as pointed
out in the analysis in Section III.
LI et al.: A NOVEL TIME-DOMAIN CURRENT-DETECTION ALGORITHM FOR SHUNT APFs
Fig. 16.
Fig. 17.
649
Fifth-order harmonics.
Fig. 20.
Phase voltage and line current before compensation.
Fig. 21.
Phase voltage and line current after harmonics is compensated.
Estimated fifth-order harmonics by adopting the DFT and the error.
Fig. 18. Estimated fifth-order harmonics by adopting the proposed algorithm
and the error.
Fig. 22. Phase voltage and line current after compensation, where only the
active-power component of positive-sequence fundamental current remains.
Fig. 19.
Configuration of experimental system.
V. EXPERIMENTAL VERIFICATIONS
An experimental system was constructed in order to demonstrate the operation of the proposed algorithm. Fig. 19 shows
the configuration of the experimental system. The objectives
are to show that the proposed algorithm has better performance
than conventional algorithms, such as the instantaneous reactive
power theory-based algorithm and the DFT-based algorithm,
and can be implemented well in real time.
mented by analog circuit instead of digital circuit to avoid using
too many A/D converters. In the presented control system, the
number of D/A converters is always three, no matter how many
models exist in the APF system, because the current instructions of the models are the same. So, it is easier to expand the
power rating of APF through the digital-analog hybrid control
method. The load current is sampled 500 times in a fundamental
cycle by three rapid 12-bit parallel A/D converters (AD7892).
The current references calculated by DSP are given to the analog
tracking circuit via a rapid parallel DAC- MAX547, which is 13
bits and has eight channels. The tri-carrying current tracking is
adopted in current control in order to achieve the high performance of multiplex well.
B. Steady-State Conditions Experiments
A. Configuration of APF
A 100-kVA SAPF is developed [21], which is multiplex and
composed of two models. The detection algorithm proposed in
this paper is adopted in the APF system and complemented by
a 32-bit floating point DSP—TMS320C32, by which the precision of calculation can be ensured. The current control is imple-
The test system for steady-state experiments consisted of a
three-phase diode bridge rectifier with a 2 ohm dc-side resistor
and a 1.8 mH ac-side inductor in phase “b” branch. Fig. 20
shows the phase voltage and the line current before compensation, which is nonsinusoidal and unbalanced and has a reactive power component. Figs. 21–24 show experimental re-
650
Fig. 23. Phase voltage and line current after compensation, where only the
positive-sequence fundamental current remains.
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 2, MAY 2005
Fig. 26. Dynamic response of APF adopting the proposed algorithm when all
harmonics below 25th are compensated (time base 40 ms/div).
dynamic response, and the THD of the line current after compensation is lower than 4% in the transient process.
VI. CONCLUSION
Fig. 24. Phase voltage and line current after fifth-order harmonics is
compensated.
A novel current-detection algorithm based on time domain
is proposed in this paper. The algorithm is realized by DSP.
From the analysis, simulation, and experiment, we can see that
the algorithm presented in this paper has some advantages: 1)
clear physical meaning, 2) flexible, 3) rapid, 4) accurate, and
5) easy to implement. On this basis, a 100-kVA APF is developed, and the research of simulation and experiment is also
done. The results of the simulation indicate that this algorithm
can detect the active power, reactive power, positive-sequence,
negative-sequence, active component of positive-sequence current, and each selected harmonics below 25th expediently and
quickly. The experimental results indicate that the APF adopting
the new algorithm performs well and can be used in practice.
REFERENCES
Fig. 25. Dynamic response of SAPF adopting DFT when all harmonics below
25th are compensated (time base 40 ms/div).
sults according to different compensation purposes, where is
phase voltage, is line current, and time base is 10 ms/div. As
shown in these waveforms, the steady-state performance of APF
adopting the proposed algorithm is perfect.
C. Dynamic Response Experiments
In Figs. 25 and 26, the dynamic response of the APF adopting
the DFT or the proposed algorithm are shown, respectively,
is the load
where is the line current after compensation,
current, and
is the reference for compensating (amount of
fundamental component is composed in the reference in order
to control the dc voltage of the APF, and this part does not
change with the load current varying). As shown in Fig. 25,
there is one main cycle delay in the reference identifying.
Therefore, the THD of the line current after compensation is
higher than 10% in the transient process. However, as shown
in Fig. 26, the APF adopting the proposed algorithm has good
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Fang Zhuo was born in Shanghai, China, on May
20, 1962. He received the B.S., M.S., and Ph.D. degrees from Xi’an Jiaotong University, Xi’an, China,
in 1984, 1989, and 2001, respectively.
Beginning in 1984, he was a Lecturer with Xi’an
Jiaotong University, where he now is an Associate
Professor. He is engaged in research on power electronics, motor driver control, active power filters, and
power quality.
Zhaoan Wang (SM’98) was born in Xi’an, China,
on June 9, 1945. He received the B.S. and M.S. degrees from Xi’an Jiaotong University, Xi’an, China,
in 1970 and 1982, respectively, and the Ph.D. degree
from Osaka University, Osaka, Japan, in 1989.
From 1970 to 1979, he was an Engineer at Xi’an
Rectifier Factory. He was an Associate Professor at
Xi’an Jiaotong University, where he is currently a
Professor. He is engaged in research on power conversion system, harmonics suppression and reactive
power compensation, and active power filters.
Wanjun Lei was born in Shannxi, China, in 1978.
He received the B.S. and M.S. degrees from Xi’an
Jiaotong University, Xi’an, China, in 2000 and 2004,
respectively. He is currently working toward the
Ph.D. degree from the Department of Electrical
Engineering, Xi’an Jiaotong University.
His research interests are active power filter and
power quality improvement.
Hongyu Li was born in Shandong province, China, in
1978. He received the B.Sc. and M.Sc. degrees from
Xi’an Jiaotong University, Xi’an, China, in 1999 and
2002, respectively. Since 2002, he has been pursuing
the Ph.D. degree in the Department of Electrical Engineering, Xi’an Jiaotong University.
His research interests are active power filters and
power quality improvement.
返
651
Longhui Wu was born in Shandong, China, in
1981. He received the B.S. and M.S. degrees from
Xi’an Jiaotong University, Xi’an, China, in 2002 and
2005, respectively. He is currently working toward
the Ph.D. degree in the Department of Electrical
Engineering, Xi’an Jiaotong University.
His research interests are active power filter and
power quality improvement.
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