IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 3, JULY 2007
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Study on the Influence of Supply-Voltage Fluctuation
on Shunt Active Power Filter
Wu Longhui, Student Member, IEEE, Zhuo Fang, Zhang Pengbo, Li Hongyu, and
Wang Zhaoan, Senior Member, IEEE
Abstract—Is there any influence of supply-voltage fluctuation
on the shunt active power filter? Few papers have discussed this
problem. In this paper, based on the instantaneous power balance
of shunt active power filter ac-side and dc-side, a small-signal
model of dc-link voltage control is derived. According to this
small-signal model, the influence of supply-voltage fluctuation on
the dc-link voltage of shunt active power filter is analyzed in detail.
The conclusion is that the supply-voltage fluctuation has influence
on the dc-link voltage of shunt active power filter. Then a feedforward control method of supply-voltage and compensation current
is proposed to eliminate the influence. The proposed feedforward
control method can be easily implemented in practical. In this
paper, the influence of supply-voltage fluctuation on compensation
performance of shunt active power filter is also analyzed when the
dc-link voltage is constant. From the analysis, it can be concluded
that current controller with PI regulator has better performance
to suppress the influence of the supply-voltage fluctuation. Finally,
the experimental results are given to demonstrate the conclusions.
Index Terms—Feedforward control, PI current regulator, shunt
active power filter, supply-voltage fluctuation.
Fig. 1. Topology of SAPF.
I. INTRODUCTION
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 eliminate the
harmonic distortion and compensate the reactive power, but
passive filters are bulky, de-tune with age and can resonate
with the supply impedance. As active power filters (APF)
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 APF can be smaller, more versatile, better damped, they
are studied widely, and great developments have taken place in
theory and application of APF [3].
The shunt APF (SAPF) is used most widely to eliminate the
current distortion [4]. Fig. 1 shows the topology of load-current
denotes the dc-link voltage
detection type SAPF. Here,
regulator, and represents the equivalent resistance of the inverter loss, the inductance loss, and the circuit loss.
is
In Fig. 1, the harmonic component of load current
obtained through the reference identifier using the current-detection algorithm mentioned in literature [5], and the dc-link
W
Manuscript received March 28, 2006; revised August 11, 2006. Paper no.
TPWRD-00162-2006.
The authors are with the State Key Laboratory of Electrical Insulation and
Power Equipment, Xi’an Jiaotong University, Xi’an, China (e-mail: wlh@mail.
xjtu.edu.cn; zffz@mail.xjtu.edu.cn).
Digital Object Identifier 10.1109/TPWRD.2007.899786
voltage regulator is usually a PI regulator. The output of the regulator is multiplied by phase-lock-loop output
to produce
for dc-link voltage
fundamental active current reference
regulation. The reference of the current controller
can be
to , which controls the voltage source
obtained by adding
power converter to generate the compensation current using
pulse-width modulation (PWM) with symmetrical triangular
carriers.
Lots of studies have been pursued on SAPF. But in most
studies, the supply voltage is considered as a sinusoidal variable with constant amplitude. However, in some system such as
small rating stand-alone power system, the supply-voltage fluctuation is very serious. Is there any influence of supply-voltage
fluctuation on the SAPF? By now, few papers have discussed
this problem. In this paper, influence of supply-voltage fluctuation on dc-link voltage of SAPF and on performance of SAPF is
discussed in detail. Then an easily implemented method of eliminating the fluctuation is proposed. Experiments are also carried
out to demonstrate the proposed method.
II. INFLUENCE OF SUPPLY-VOLTAGE FLUCTUATION
ON DC-LINK VOLTAGE OF SAPF
The power converter used in the SAPF is usually a voltagesource PWM converter. Therefore, to get better performance of
SAPF, the dc-link voltage should be maintained at a constant
0885-8977/$25.00 © 2007 IEEE
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 3, JULY 2007
where
Fig. 2. Dc-link voltage control of SAPF.
value [6]. It is completed by controlling the SAPF to absorb/regenerate the active component of fundamental current. Traditional closed-loop control of the dc-link voltage is shown in
Fig. 2.
In literature [7], a small-signal model of dc-link voltage
control is presented; this model is based on the instantaneous
power balance of SAPF ac-side and dc-side. However, the
supply-voltage fluctuation is not taken into account in this
model. In this section, influence of supply-voltage fluctuation
on the SAPF dc-link voltage will be discussed in detail.
of the SAPF is
In Fig. 1, ac-side instantaneous power
Then, ac-side instantaneous power of SAPF can be divided
into the following items.
1) Three-phase instantaneous active power of fundamental
component can be calculated as
(4)
2) Three-phase instantaneous reactive power of fundamental
component can be calculated as
(5)
The dc-side instantaneous power
of SAPF is
3) Three-phase instantaneous power of harmonics can be expressed as (6). Here, assuming that the load is a three-phase
diode with a resistor on dc-side, the harmonic current can
be written as
According to the instantaneous power balance of SAPF ac-side
and dc-side
, the following equation can be obtained:
(1)
(6)
In this paper, the influence of amplitude fluctuation of supplyvoltage is discussed, so the supply voltage can be represented as
(2)
It can be seen that instantaneous power of harmonics fluctimes of fundamental frequency. However,
tuates with
the average value in one fundamental cycle is zero. To simplify the analysis, it can be neglected.
4) Three-phase instantaneous power consumed on is
(7)
The output current of SAPF includes the compensation current
and the active component of fundamental current for
dc-link voltage regulation, and the compensation current can
be written as the sum of the reactive component of fundamental
current and the harmonic current . Then the output current
of SAPF can be represented as follows:
5) Three-phase instantaneous power consumed on
is
(8)
From the items 1) 5), the instantaneous power balance of
SAPF in (1) can be obtained as follows:
(3)
(9)
LONGHUI et al.: STUDY ON THE INFLUENCE OF SUPPLY-VOLTAGE FLUCTUATION ON SHUNT APF
Fig. 3. Small-signal model of the closed-loop control of SAPF dc-link voltage.
Assuming the parameters under some steady state are , ,
, , when added small-signal, they can be represented as
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Fig. 4. Feedforward control for dc-link voltage regulation.
The output of Fig. 3 can be written as
(10)
(16)
Then (9) can be written as
(11)
In the steady state, the real power injected into the SAPF is
equal to the power loss of SAPF. Then in steady state, the equation of system power balance can be expressed as
(12)
If the items above the second order are neglected in (11), the
small-signal equation can be obtained as
(13)
After Laplace transforming, the small-signal model at some
balance point can be obtained, as (14) shows
(14)
The small-signal model of dc-link control loop in Fig. 2 can
be written as
(15)
where is the value of
in the small-signal model.
Then the small-signal model of the closed-loop control of
SAPF dc-link voltage can be obtained as Fig. 3 shows, where
,
,
,
. In most cases,
is a PI
.
controller, then
In (16), it can be seen that both the amplitude fluctuation of
the supply voltage
and the fluctuation of the compensation
can cause the fluctuation of SAPF dc-link voltage.
current
If the dc-link voltage is too low, the output voltage of PWM
converter will not be high enough to ensure the current tracking
result. If the dc-link voltage is too high, it will threaten the safe
operation of the system considering the safe voltage limitation of
semiconductor. At the same time if dc-link voltage is too high, it
will cause the ripple of SAPF output current increase, and then
EMI problem will become serious. So the fluctuation of dc-link
voltage caused by supply-voltage fluctuation or the compensation current fluctuation will depress the performance of SAPF.
Take the 50 kVA SAPF as an example, the dc-link capacitor
, the dc-link voltage reference is set at 750 V and
is 3900
the system efficiency is 95%. When the amplitude of the supply
voltage rises by 30%, within one fundamental cycle the dc-link
voltage may rise by 611 V. In this case, to ensure the safe operation
of the system, the protecting cell of SAPF will cut off the SAPF.
Moreover, the fluctuation of supply voltage will make an impact on the load current. Therefore, the compensation current of
SAPF will fluctuate.
III. PROPOSED FEEDFORWARD CONTROL METHOD
From the analysis above, to achieve high and stable performance of SAPF, the fluctuation of the dc-link voltage caused by
supply-voltage fluctuation should be eliminated. In traditional
design of the dc-link voltage regulator as mentioned in literature [7], the supply-voltage fluctuation is not taken into account. Under the condition of supply-voltage fluctuation, the
regulator should be redesigned. This makes many troubles in
practice. In this paper, an easily implemented feedforward control method of supply-voltage and compensation current is presented, with which redesign of traditional dc-link voltage regulator is needless.
The proposed control method is shown in Fig. 4, where
and
are the supply-voltage feedforward controller and the compensation current feedforward controller,
respectively.
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 3, JULY 2007
Fig. 5. Current control block diagram of APF.
The output of Fig. 4 can be expressed as
(17)
,
When
, (17) can be written as:
(18)
Fig. 6. Comparison of the closed-loop transfer functions with P and PI current
regulator.
From above analysis, it can be seen that after reasonable designing of the feedforward controller
and
, the
influence of the supply-voltage fluctuation
and the comon the dc-link voltage can be
pensation current fluctuation
eliminated.
In most control systems of SAPF, the supply voltage is detected for phase lock loop [8], [9], so it is easy to obtain the
fluctuation of supply voltage. And the compensation current
fluctuation can be easily obtained by calculated harmonic current reference. Then the proposed feedforward control method
is easy to be implemented in practical SAPF system.
IV. INFLUENCE OF SUPPLY-VOLTAGE FLUCTUATION ON
COMPENSATION PERFORMANCE OF SAPF
In this section the influence of supply-voltage fluctuation on
compensation performance of SAPF will be discussed. In the
following discussion, the dc-link voltage of SAPF is assumed
to be constant.
Fig. 5 shows the block diagram of the SAPF current control
is the gain of PWM converter which is
system. Here,
is the current
considered as a proportional component [10],
regulator, which is usually a P or a PI regulator. In Fig. 5, the
supply voltage is a disturbance of the current loop. Neglecting
of the dc-link voltage controller and the
the output current
harmonic current , the closed-loop transfer function using the
supply voltage as input can be deduced.
is a P regulator, the closedWhen the current regulator
loop transfer function can be deduced as follows:
(19)
Fig. 7. Comparison of the closed-loop transfer functions which reflects the current tracing performance.
When the current regulator
is a PI regulator, the closedloop transfer function can be deduced as follows:
(20)
Fig. 6 shows the comparison of the closed-loop transfer functions with P and PI current regulator when other parameters in
the system are all the same.
It can be seen that, in high-frequency band, the P and PI controllers have the same characteristics both in the amplitude-frequency response and in the phase-frequency response. However,
in low-frequency band, the response of P controller to supply
LONGHUI et al.: STUDY ON THE INFLUENCE OF SUPPLY-VOLTAGE FLUCTUATION ON SHUNT APF
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Fig. 8. Control diagram of SAPF.
voltage is approximately a constant value 40 dB, while PI controller has much smaller gain than the P controller. It means that
PI controller has better performance to suppress the influence of
the supply-voltage fluctuation.
of dc-link voltage
If neglecting the output current
controller and the source voltage , the closed-loop transfer
function which reflects the current tracing performance can be
deduced.
is a P regulator, the closedWhen the current regulator
loop transfer function of the whole system can be written as
follows:
(21)
is a PI regulator, the closedWhen the current regulator
loop transfer function of the whole system can be written as
follows:
(22)
Fig. 7 shows bode plots of the closed-loop transfer functions
with P and PI current regulator when other system parameters
are the same. From Fig. 7, it can be seen that, the system has
good performance in current tracing both using the P and PI
current regulator in current controller.
From above analysis, if the dc-link voltage of SAPF is maintained at a constant value, the current controller with PI regulator has better performance to suppress the influence of the
supply-voltage fluctuation. Therefore, in this paper, the PI regulator is adopted in the current controller.
V. EXPERIMENT VERIFICATION
In order to demonstrate the operation of the PI current regulator used in the current controller and the proposed feedforward control method, an experimental system was constructed
as shown in Fig. 1. To simulate the voltage fluctuation, a programmable AC source is used. The load is three-phase diode
bridge rectifier with resistor in dc-side. The SAPF and load are
parallel connected to the programmable AC source.
A. Control of SAPF
is the
The control diagram of SAPF is shown in Fig. 8.
is the RMS of the calculated load harsupply voltage and
monic current which can represent the compensation current of
SAPF. The proposed feedforward control method and the current detection algorithm are complemented by a 32-bit floating
point DSP—TMS320VC33, by which the precision of calculation can be ensured. The PI current regulator is used in the
current controller which is implemented by analogy circuit.
is added to
Output of proposed feedforward controller
to control the funthe traditional dc-link voltage regulator
damental active current of SAPF. The current controller, which
uses the current error filtered by a PI regulator as the modulating
signal, performs a sine-triangle PWM voltage modulation of the
power converter.
B. Experimental Results
Fig. 9 is the experimental results without the proposed feedis the dc-link voltage,
is
forward control method, where
is the current reference, and
is output
the supply voltage,
current of the SAPF. In Fig. 9(a), the supply voltage was suddenly decreased from 60 to 30 V, and in Fig. 9(b) the supply
voltage was suddenly increased from 30 to 60 V. It can be seen
that both the decrease and increase of the supply voltage can
cause the fluctuation of SAPF dc-link voltage.
Fig. 10 is the experimental results with the feedforward
control method under the same fluctuation condition of supply
is the dc-link voltage of SAPF,
voltage in Fig. 9. Where
is the supply voltage,
is the current reference, and
is
output current of the SAPF. It can be seen that the proposed
feedforward control method can eliminate the fluctuation of
dc-link voltage effectively when the supply voltage is increased
or decreased suddenly.
Fig. 11 shows the performance of SAPF when the supplyis the dc-link voltage,
is the
voltage fluctuates, where
is the load current, and is the source cursupply voltage,
rent after compensation. It can be seen that the proposed feedforward control method can eliminated the influence of the supplyvoltage fluctuation on SAPF dc-link voltage. SAPF with the PI
current regulator and proposed feedforward control has good
and stable performance when the supply-voltage fluctuates.
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 3, JULY 2007
Fig. 9. Experiment result without feedforward control (1:U 100 V/div; 2:I
1 V/div; 3:U 75 V/div; 4:I 50 A/div; t: 20 ms/div). (a) Sudden decrease of
supply voltage. (b) Sudden increase of supply voltage.
Fig. 10. Experiment result with feedforward control (1:U 100 V/div; 2:I
1 V/div; 3:U 75 V/div; 4:I 50 A/div; t: 20 ms/div). (a) Sudden decrease of
supply voltage. (b) Sudden increase of supply voltage.
It should be noticed that in the experiment, the load is constant; therefore, with the fluctuation of supply voltage the load
current in Fig. 11 is also changed, so does the current reference
in Fig. 9 and Fig. 10.
VI. CONCLUSION
In traditional studies on SAPF, the supply voltage is considered as a sinusoidal variable with constant amplitude. In this
paper, the influence of supply-voltage fluctuation on SAPF is
discussed. Experiments are also carried out. From the analysis
and the experimental results, the following can be concluded.
1) Both the amplitude fluctuation of the supply voltage and
the fluctuation of the compensation current can cause the
fluctuation of SAPF dc-link voltage, and then depress the
performance of SAPF. The proposed feedforward control
method of supply voltage and compensation current can
eliminate this influence. The proposed method can be implemented easily in practice, and redesign of traditional
dc-link voltage regulator is needless.
2) When the dc-link voltage is maintained at a constant value,
the PI current regulator used in current controller has better
performance to suppress the influence of supply voltage
fluctuation on compensation performance of SAPF.
3) SAPF with the PI current regulator and proposed feedforward control has good performance when the supply
voltage fluctuates.
Fig. 11. Performance of SAPF with the proposed feedforward control (1:U
200 V/div; 2:I 50 A/div; 3:U 150 V/div; 4:I 25 A/div; t: 40 ms/div).
Maybe there are other influences of supply voltage fluctuation
on SAPF. This will be studied in future works.
REFERENCES
[1] P. Jintakosonwit, H. Fujita, and H. Akagi, “Control and performance of
a fully-digital-controlled shunt active filter for installation on a power
distribution system,” IEEE Trans. Power Electron., vol. 17, no. 1, pp.
132–140, Jan. 2002.
[2] P. Mattavelli, “A closed-loop selective harmonic compensation for active filters,” IEEE Trans. Ind. Appl., vol. 37, no. 1, pp. 81–89, Jan. 2001.
[3] Z. Wang, J. Yang, and J. Liu, Harmonics Elimination and Reactive
Power Compensation. Beijing, China: China Machine Press, 1998.
[4] H. Akagi, “New trends in active filters for power conditioning,” IEEE
Trans. Ind. Appl., vol. 32, no. 3, pp. 1312–1322, Jun. 1996.
LONGHUI et al.: STUDY ON THE INFLUENCE OF SUPPLY-VOLTAGE FLUCTUATION ON SHUNT APF
[5] L. Hongyu, Z. Fang, W. Zhaoan, L. Wanjun, and W. Longhui, “A novel
time-domain current-detection algorithm for shunt active power filters,” IEEE Trans. Power Syst., vol. 20, no. 2, pp. 644–651, May 2005.
[6] Y. Jun, W. Zhaoan, and Q. Guanyuan, “DC-side voltage control of
shunt active power filter,” Power Electron., no. 4, pp. 48–50, Apr. 1996.
[7] L. Shiguo and H. Zhencheng, “Stability research on DC voltage close
loop control for an active power filter,” J. Chongqing Univ., vol. 17, no.
3, pp. 60–68, May 1994.
[8] H. Akagi, Y. Kanazawa, and A. Nabae, “Instantaneous reactive power
compensating comprising switching devices without energy storage
components,” IEEE Trans. Ind. Appl., vol. IA-20, pp. 625–630, May/
Jun. 1984.
[9] J. S. Tepper, J. W. Dixon, G. Venegas, and L. Moran, “A simple frequency-independent method for calculating the reactive and harmonic
current in a nonlinear load,” IEEE Trans. Ind. Elect., vol. 43, no. 6, pp.
647–654, Dec. 1996.
[10] R. Parikh and R. Krishnan, “Modeling, simulation and analysis of an
uninterruptible power supply,” in Proc. IEEE-IECON’94, Bologna,
Italy, Sep. 1994, vol. 1, pp. 485–490.
Wu Longhui (S’05) wan born in Shandong Province,
China, in 1981. He received the B.Sc. and M.Sc.
degrees in 2002 and 2005, respectively, from Xi’an
Jiaotong University, Xi’an, China, where he is currently pursuing the Ph.D. degree in the Department
of Electrical Engineering.
His research interests are power quality improvement and renewable energy.
Zhuo Fang 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 is now a Professor. His
areas of research include power electronics, motor
driver control, active power filters, and power quality.
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Zhang Pengbo wan born in Hebei Province, China,
in 1982. She received the B.S. degree in 2004 from
Xi’an Jiaotong University, Xi’an, China, where she is
currently pursuing the M.S. degrees in the School of
Electrical Engineering.
Her areas of research are power quality control and
applications of power electronics in power systems.
Li Hongyu was born in Shandong Province, China,
in 1978. He received the B.S., M.S., and Ph.D. degrees from Xi’an Jiaotong University, Xi’an, China,
in 1999 and 2002 and 2005, respectively.
Wang Zhaoan (SM’98) was born in Xi’an, China,
in 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 is now a Professor at Xi’an Jiaotong University. He is engaged in research on power
conversion system, harmonics suppression and reactive power compensation, and active power filters.