A hybrid compensation system comprising hybrid

Electrical Power and Energy Systems 28 (2006) 448–458
www.elsevier.com/locate/ijepes
A hybrid compensation system comprising hybrid
power ﬁlter and AC power capacitor
Hurng-Liahng Jou a,*, Jinn-Chang Wu b, Kuen-Der Wu a,
Min-Sheng Huang a, Chih-An Lin a
a
Department of Electrical Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 80782, Taiwan, ROC
b
Department of Electrical Engineering, Kun Shan University of Technology, Tainan Hsien 710, Taiwan, ROC
Received 9 July 2004; received in revised form 15 December 2005; accepted 24 February 2006
Abstract
In this paper, a hybrid compensation system for harmonic suppression and power factor correction is developed and analyzed. This
compensation system consists of a hybrid power ﬁlter and an AC power capacitor. A small capacity power converter and a passive power
ﬁlter is serially connected to have the function of hybrid power ﬁlter, and then the hybrid power ﬁlter is connected in parallel to the AC
power capacitor to form a hybrid compensation system. The major function of the hybrid power ﬁlter is the harmonic suppression, and
the AC power capacitor performs the power factor correction. Furthermore, a method, inserting an inductor in series with the AC power
capacitor, is proposed in this paper for avoiding high frequency resonance ampliﬁcation between the hybrid power ﬁlter and the AC
power capacitor. To demonstrate the performance of this hybrid compensation system, a three-phase prototype is developed and tested.
The tested results show that the insertion of an inductor in series with the AC power capacitor can prevent high frequency resonance
ampliﬁcation between the hybrid power ﬁlter and the AC power capacitor.
Ó 2006 Elsevier Ltd. All rights reserved.
Keywords: Power ﬁlter; Harmonic; Reactive power
1. Introduction
Power quality improvement is very important in today’s
power system. The power factor correction and the harmonic suppression are very important topics in the issue
of power quality improvement. Because the AC power
capacitor is very cheap as compared with other solutions,
this is the most popular solution to correct the power factor. The harmonic pollution has become more serious due
to the wide use of nonlinear load recently, and it may result
in the degradation of the power quality [1]. The eﬀect of
harmonic pollution to the power capacitor is very serious
*
Corresponding author. Tel.: +886 7 3814526x5519; fax: +886 7
3921073.
E-mail address: [email protected] (H.-L. Jou).
0142-0615/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijepes.2006.02.008
because it may result in the power resonance. The power
resonance will amplify the harmonic current and harmonic
voltage of the AC power capacitor and then damage the
AC power capacitor and disturb the operation of neighboring equipment. The passive power ﬁlter is still the most
popular solution for suppressing the harmonic current till
now [2,3]. However, the power resonance caused by harmonics is a hidden risk.
Some power electronic based active power facilities have
been developed to replace the role of passive power facilities in the distribution power system, recently. The static
VAR compensator (SVC) is used for compensating the
reactive power, and the active power ﬁlter is used for suppressing the harmonic current [4–6]. Comparing with the
passive power facilities, the active power facilities have
the better performance and can avoid most of problems
in the passive power facilities. However, the spread of
active power facilities cannot compete with that of the
H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
passive power facilities due to the high cost. Hence, the
technology combining the passive power facilities and
active power facilities is attractive. The hybrid power ﬁlter,
comprising the passive power ﬁlter and active power ﬁlter,
was developed for harmonic suppression and power factor
correction [7–10]. The power capacity of active power facilities used in the hybrid power ﬁlter is smaller than that used
in the active power ﬁlter, and it still can solve the problems
caused by the passive power facilities. For performing reactive power compensation, a large reactive current will be
injected into the hybrid power ﬁlter due to a large AC
power capacitor used in the passive power ﬁlter. However,
the cheapest solution for power factor correction is still the
power capacitor. Hence, a hybrid compensation system,
comprising a hybrid power ﬁlter and an AC power capacitor set, is developed and analyzed in this paper for harmonic suppression and power factor correction. Because
most of reactive power is compensated by the AC power
capacitor, the major function of hybrid power ﬁlter is to
suppress the harmonic current. Hence, the power capacity
of the power converter in the hybrid power ﬁlter can be further reduced. Besides, the operation of hybrid power ﬁlter
can protect the power capacitor from the damage of power
resonance. Unfortunately, the analysis result in this paper
shows that the hybrid compensation system will result in
high frequency resonance ampliﬁcation. This phenomenon
will also occur in the parallel operation of an active power
ﬁlter and an AC power capacitor set. For avoiding the high
frequency resonance ampliﬁcation between the hybrid
power ﬁlter and the AC power capacitor, a method, inserting an inductor in series with the AC power capacitor, is
proposed in this paper. To demonstrate the performance
of this hybrid compensation system, a scale down prototype is developed and tested.
2. Operation theory
Fig. 1 shows the system conﬁguration of the hybrid
compensation system for the power factor correction and
the harmonic suppression. This system comprises a hybrid
power ﬁlter and an AC power capacitor. The AC power
capacitor may consist of several sets of AC power capacitor
conﬁgured as an automatic power factor regulator (APFR)
to match the variation of load. The capacity of AC power
capacitor switched into the power feeder depends on the
instantaneous reactive power demanded by the loads.
The hybrid power ﬁlter, conﬁgured by a power converter
and a passive power ﬁlter, is expected to suppress the harmonic current of nonlinear loads. The passive power ﬁlter
of hybrid power ﬁlter is used to reduce the capacity of
power converter, and it may contain only one set or several
sets of tuned ﬁlter. A DC capacitor is located at DC side of
power converter, and the power converter is a voltagesource power converter. The control algorithm of power
converter is consisted of two control loops, a harmonic
suppression loop and a DC voltage regulation loop. It is
stated in the following.
449
Fig. 1. The system conﬁguration of the hybrid compensation system.
2.1. Harmonic suppression
The power converter of hybrid power ﬁlter is expected
to suppress the harmonic current ﬂowing between the utility and the load. The conventional control algorithm of
power converter for hybrid power ﬁlter [7,10] is used in this
paper, and output voltage va(t) of power converter for harmonic suppression is represented as
va1 ðtÞ ¼ k 1 ish ðtÞ
ð1Þ
where ish(t) is the harmonic component of the utility current, and k1 is a constant. The power converter used in
the hybrid power ﬁlter is to improve the problems of passive power ﬁlter, such as poor ﬁlter performance and power
resonance. The power converter generates a voltage proportional to the harmonic component of the utility current
shown in (1), and it acts as a virtual harmonic resistor serially connected to the utility impedance at the harmonic frequency [7,10]. Hence, the power converter can suppress the
harmonic current ﬂow between the load and the utility due
to the virtual harmonic resistor inserted in the utility side.
Therefore, the power converter can improve the ﬁlter performance because the equivalent system impedance is enlarged. The harmonic current of loads is forced to ﬂow
into the hybrid power ﬁlter and AC power capacitor to ensure the utility current with low total harmonic distortion
(THD). Moreover, it can avoid the power resonance between the system impedance and passive power ﬁlter
including in the hybrid power ﬁlter due to the existence
of a virtual harmonic resistor. Hence this control algorithm
of power converter can solve the problems of passive power
ﬁlter. Besides, the virtual harmonic resistor can also protect
the AC power capacitor from the over-current damage due
to the harmonic current injecting from the neighboring
facilities of the utility side.
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H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
2.2. DC voltage regulation
In Section 2.1, the power converter acts like a virtual
harmonic resistor, and it will consume real power. This real
power is absorbed into the DC capacitor of the power converter, and then the DC capacitor voltage increases. To
maintain the constant DC capacitor voltage, the energy
stored in the DC capacitor must be regenerated back to
the utility via the power converter. Hence, the role of the
DC capacitor in the power converter performs as an energy
buﬀer that is used to absorb the harmonic real power and
regenerate a fundamental real power to the utility. To
obtain this function, the power converter must generate a
voltage represented as
va2 ðtÞ ¼ k 2 ih1 ðtÞ
ð2Þ
where ih1(t) is the fundamental current of the hybrid power
ﬁlter. If the power converter can generate a voltage shown
in (2), the power converter acts as a virtual fundamental
resistor with k2X. The value k2 may be positive or negative
to absorb or regenerate the fundamental real power to
maintain the constant DC capacitor voltage.
Considering the function of harmonic suppression and
DC voltage regulation, the output voltage of power converter is expected to be
va ðtÞ ¼ k 1 ish ðtÞ þ k 2 ih1 ðtÞ
the DC capacitor voltage is compared with a set value and
then sent to a PI controller. The output of PI controller is
the fundamental resistor k2X. The output current of power
converter is fed to a band-pass ﬁlter to extract its fundamental component. The output signals of PI controller
and band-pass ﬁlter are sent to a multiplier to obtain the
output of the DC voltage regulation block. After summing
the outputs of harmonic suppression block and DC voltage
regulation block, the desired voltage of the power converter is obtained. This desired voltage is sent to a PWM
modulator to generate the driver signals for the power
switches of power converter.
The DC capacitor in the dc side of power converter acts
as an energy buﬀer and oﬀers a stable DC voltage for the
power converter in the steady-state condition. However,
the DC capacitor will absorb or supply real power in the
transient state. Due to the response time of band-rejection
ﬁlter in the harmonic suppression block, it will result in a
signiﬁcant variation of DC capacitor voltage. However,
the DC voltage regulation block will adjust the DC capacitor voltage automatically to its set value. The variation of
DC capacitor voltage is dependent on the response of the
band-rejection ﬁlter, the PI controller and the capacity of
DC capacitor. Hence the value of DC capacitor is determined by the parameters of control circuit.
ð3Þ
4. System analysis
3. Control block diagram of power converter
Fig. 2 shows the control block diagram of the hybrid
power ﬁlter. The control block is divided into two parts,
a harmonic suppression block and a DC voltage regulation
block. The harmonic suppression block is used to ﬁlter out
the harmonic current of nonlinear loads. The DC voltage
regulation block is used to maintain the DC bus voltage
at a constant value. The harmonic suppression block contains a band-rejection ﬁlter, consisting of a band-pass ﬁlter
and a subtractor, and an ampliﬁer. The band-rejection ﬁlter is used to ﬁlter out the fundamental component of the
utility current. The output of band-rejection ﬁlter is sent
to an ampliﬁer, and then the output of harmonic suppression block is obtained. In the DC voltage regulation block,
The harmonic equivalent circuit of hybrid compensation
system, consisting of an AC power capacitor and a hybrid
power ﬁlter, is shown in Fig. 3. Since the voltage-source
power converter, generates a voltage shown in (3), is used,
the power converter is regarded as a dependent voltage
source dependent on the harmonic component of the utility
current. The nonlinear load in the load side is simpliﬁed as
a current source.
Before the power converter of hybrid power ﬁlter is
applied (that is k1 = 0), the equivalent impedance from
the viewpoint of the harmonic current source in the load
side can be derived as
Z eq ¼
Z ch Z hh Z sh
Z ch Z hh þ Z sh Z hh þ Z sh Z ch
Fig. 2. The control block diagram of the power converter.
ð4Þ
H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
451
(5)–(7), it can be found that the parallel resonance will result in the harmonic current ampliﬁcation. After applying
the power converter of hybrid power ﬁlter, the harmonic
current feedback to the utility can be rewritten as
Z ch Z hh
I Lh
Z ch Z hh þ Z sh Z hh þ Z sh Z ch þ k 1 Z ch
1
1
1
1
¼
þ
I Lh
Z sh Z eq Z sh Z hh =k 1
I sh ¼
ð8Þ
The harmonic current ﬂows into the AC power capacitor is
rewritten as
Fig. 3. The equivalent circuit of the hybrid compensation system.
The harmonic current feedback to the utility can be derived
as
I sh ¼
Z eq
I Lh
Z sh
ð5Þ
The harmonic current ﬂows into the AC power capacitor is
derived as
I ch ¼
Z eq
I Lh
Z ch
ð6Þ
The harmonic current ﬂows into the hybrid power ﬁlter is
derived as
I hh ¼
Z eq
I Lh
Z hh
ð7Þ
From (4), it can be found that the equivalent impedance
Zeq will be ampliﬁed if the parallel resonance occurs. From
Z sh Z hh
I Lh
Z ch Z hh þ Z sh Z hh þ Z sh Z ch þ k 1 Z ch
1
1
1
1
¼
þ
I Lh
Z ch Z eq Z sh Z hh =k 1
I ch ¼
ð9Þ
The harmonic current ﬂowing into the hybrid power ﬁlter
is rewritten as
Z sh Z ch þ k 1 Z ch
I Lh
Z ph Z hh þ Z sh Z hh þ Z sh Z ch þ k 1 Z ch
1
1
k1
1
1
¼
1þ
þ
I Lh
Z hh
Z eq Z sh Z hh =k 1
Z sh
I hh ¼
ð10Þ
From (8)–(10), it can be found that the term k1Zch is added
in the denominator of the above equations due to the use of
power converter.
Fig. 4 shows the frequency response of the utility current
to the load harmonic current before and after applying the
power converter. Table 1 is the major parameters used in
Fig. 4. The spectrum of the utility current under diﬀerent k1: (a) k1 = 0, (b) k1 = 1, (c) k1 = 8.
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H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
Table 1
The major parameters of the hybrid compensation system
System impedance
AC power capacitor
Fifth tuned ﬁlter
Seventh tuned ﬁlter
DC capacitor of power converter
2 mH
20 lF
L = 5 mH, C = 25 lf
L = 15 mH, C = 20 lf
2200 lF
the simulation. The passive power ﬁlter contains two sets of
tuned ﬁlter tuned at ﬁfth and seventh order frequency.
Fig. 4 indicates that the high frequency resonance ampliﬁcation of the utility current caused by the AC power capacitor after applying the power converter is very serious, and
the larger k1 is the more serious of the high frequency resonance ampliﬁcation will be. The total harmonic distortions (THDs) of utility current shown in Fig. 4 are 15%,
26% and 35% under k1 of 0, 1 and 8, respectively. In practical distribution power system, the system impedance Zsh
is inductive. The term ZshZhh/k1 may be a positive or negative resistor depends on Zhh. If Zhh is capacitive, the term
ZshZhh/k1 acts as a positive resistor. On the contrary, the
term ZshZhh/k1 acts as a negative resistor for Zhh with
the characteristic of inductive. If the term ZshZhh/k1 has
the characteristic of a positive resistor, it acts as a damper
to suppress the parallel resonance caused by the AC power
capacitor. However, the parallel resonance becomes more
serious as the term ZshZhh/k1 has the characteristic of a
negative resistor.
In the hybrid compensation system shown in Fig. 1, the
resonant frequency caused by the AC power capacitor is
higher than the tuned frequency of passive power ﬁlter.
Hence Zhh is inductive and the term ZshZhh/k1 is a negative
resistor at the resonance frequency caused by the AC
power capacitor. This implies that the parallel resonance
caused by the AC power capacitor in the hybrid compensation system shown in Fig. 1 will be further serious. This is
the reason why the larger k1 is the more serious of resonance problem will be in Fig. 4. Hence, the hybrid compensation system, shown in Fig. 1, must be improved and
modiﬁed. The resonant frequency caused by AC power
capacitor must be decreased to be lower than the tuned frequency of passive power ﬁlter used in the hybrid power ﬁlter, and the term ZshZhh/k1 must act as a positive resistor.
The proposed method to decrease the resonant frequency
caused by the AC power capacitor is to insert an inductor
serially connected to the AC power capacitor.
Fig. 5 shows the frequency response of the utility current
after applying the power converter (k1 = 8) and with diﬀerent ZSL/ZPC, where ZSL and ZPC are the impedance of
inserted inductor and the AC power capacitor, respectively.
The values of ZSL/ZPC in Fig. 5(a)–(c) are 1.4%, 4.2% and
7%, respectively. Compared to Fig. 4, it can be found that
an inductor serially connected to the AC power capacitor
can suppress the high frequency ampliﬁcation caused by
the AC power capacitor eﬀectively. The THDs of utility
currents shown in Fig. 5(a)–(c) are 22%, 4.2% and 7%,
respectively. The simulation results show that the proper
serial inductor is near 4.2%. Hence, the hybrid compensation system can suppress the harmonic current and correct
the power factor of nonlinear load eﬀectively if an adequate
Fig. 5. The spectrum of the utility current under diﬀerent ZSL/ZPC: (a) ZSL/ZPC = 1.4%, (b) ZSL/ZPC = 4.2%, (c) ZSL/ZPC = 7%.
H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
inductor is connected in series with the AC power
capacitor.
The power rating of power converter depends on the
product of its voltage and current. The desired voltage of
power converter shown in (3) contained a fundamental
component and a harmonic component is the same as that
of conventional hybrid power ﬁlter. Because the AC power
capacitor may absorb a little harmonic current, the output
harmonic component of the power converter is slight lower
than that of the load current. This means that the power
rating of the hybrid power ﬁlter in the proposed compensation system can be smaller as comparing with that of the
pure hybrid power ﬁlter from the viewpoint of harmonic
compensation. The output current of the conventional
hybrid power ﬁlter contains a large reactive fundamental
component (caused by the tuned ﬁlter) and a small real
fundamental component (caused by the regenerated fundamental real power). Because the reactive power of the load
is dominantly compensated by the AC power capacitor in
the proposed hybrid compensation system, the fundamental component of the power converter current can be
reduced signiﬁcantly. This means that the power rating of
the hybrid power ﬁlter in the proposed compensation system can be smaller as comparing with that of the pure
hybrid power ﬁlter from the viewpoint of reactive power
compensation. Therefore, the power rating of the power
converter can be further reduced compared with the conventional hybrid power ﬁlter.
5. Experimental results
To verify the performance of hybrid compensation system, a scale-down prototype is implemented due to the
limitation of power source in the laboratory. The conﬁguration of the scaled down prototype is shown in Fig. 1. The
main parameters of the prototype are shown in Table 1.
453
Fig. 6. The simulation and test result of THD% of the utility current
under k1 = 8.
Fig. 7. The test result of THD% of the utility current under
ZSL/ZPC = 4.2%.
The switching frequency of power electronic devices is
20 kHz. The inductance is larger and the capacitance is
smaller in the tuned ﬁlter of the scale-down prototype. In
the practical application, the hybrid power ﬁlter not only
can suppress the current harmonics but also can supply a
ﬁxed capacity of the reactive power. Therefore, the
required power rating of the AC power capacitor can be
Fig. 8. The test result of load current: (a) waveform, (b) spectrum.
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H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
reduced. Because an autotransformer is applied in the front
end of the utility, the system impedance is assumed to be
2 mH after considering the impedance of the autotransformer. The load used in the following experiment is a
three-phase rectiﬁer.
Fig. 6 shows the simulation and test results for THD%
of the utility current under diﬀerent ZSL/ZPC where k1 in
this simulation is 8. As seen in Fig. 6, both of the simulation and test results show that the minimum THD% occurs
under ZSL/ZPC near 4%. Since the resonant frequency of
the AC power capacitor and the inserting serial inductor
is near 300 Hz under ZSL/ZPC near 4%, and Zhh is capacitive under the resonant frequency caused by AC power
capacitor. Hence the high frequency resonance ampliﬁcation caused by AC power capacitor can be avoided when
ZSL/ZPC is larger than 4. Fig. 7 shows the test results of
THD% of the utility current under diﬀerent k1 where
ZSL/ZPC in Fig. 7 is 4.2%. As seen in Fig. 7, the larger k1
is the smaller THD% of the utility current will be.
Fig. 8 shows the waveform and spectrum of the load
current. This ﬁgure shows that the load current contains
rich harmonic current, and the THD% of the load current
is 36.1%. Figs. 9 and 10 show the waveform and spectrum
of the capacitor current under k1 = 1 and k1 = 8. It can be
found that, the capacitor current contains rich harmonic
current, and the THD% of the capacitor current is 63.2%
Fig. 9. The test result of capacitor current after applying the hybrid power ﬁlter under k1 = 1 and without a serial inductor: (a) waveform, (b) spectrum.
Fig. 10. The test result of the capacitor current after applying the hybrid power ﬁlter under k1 = 8 and without a serial inductor: (a) waveform, (b)
spectrum.
H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
455
Fig. 11. The test result of the utility current after applying the hybrid power ﬁlter under k1 = 1 and without a serial inductor: (a) waveform, (b) spectrum.
in Fig. 9 and 146.5% in Fig. 10. Both ﬁgures indicate that
serious high frequency resonance ampliﬁcation occurs at
the frequencies higher than 11th harmonic. Figs. 11 and
12 show waveform and spectrum of the utility current
under k1 = 1 and k1 = 8. It can be found that the utility
current also contains rich harmonic current, and the
THD% of the utility current is 12.8% in Fig. 11 and
14.7% in Fig. 12. From Figs. 9–12, it can also be found that
the larger k1 is the more serious of resonance problem will
be. This result is consistent to the system analysis in Section
4.
Figs. 13 and 14 show the waveform and spectrum of the
capacitor current and the utility current after inserting a
4.2% inductor serially connected to the AC power capacitor under k1 = 8. The THD% of the capacitor current
and the utility current after inserting the serial inductor
are 20.3% and 4.5%, respectively. Comparing with Figs.
12 and 14, it can be found that the power resonance problem is avoided. This means that inserting a proper serial
inductor to the AC power capacitor can suppress the resonance caused by the AC power capacitor, and it is consistent to the system analysis in Section 4.
Fig. 15 shows the test result after inserting a 4.2% serial
inductor under k1 = 8. From Fig. 15, it can be found that
the harmonic current of load is injected into the hybrid
power ﬁlter and the AC power capacitor mainly supplies
the fundamental reactive power. Hence the hybrid compensation system is consistent to the expected function. Fig. 16
shows the transient response of the improved hybrid compensation system at the instant of applying nonlinear load
Fig. 12. The test result of the utility current after applying the hybrid power ﬁlter under k1 = 8 and without a serial inductor: (a) waveform, (b) spectrum.
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H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
Fig. 13. The test result of the capacitor current after applying the hybrid power ﬁlter under k1 = 8 and ZSL/ZPC = 4.2%: (a) waveform, (b) spectrum.
Fig. 14. The test result of the utility current after applying the hybrid power ﬁlter under k1 = 8 and ZSL/ZPC = 4.2%: (a) waveform, (b) spectrum.
under k1 = 8 and ZSL/ZPC = 4.2%. It shows that the transient performance of the proposed hybrid compensation
system is excellent.
6. Conclusions
The harmonic suppression and reactive power compensation are the very important topics in the issue of power
quality improvement. Although the AC power capacitor
and passive power ﬁlter have the risk of power resonance,
these passive devices are still the most popular solution to
compensate the reactive power and suppress the harmonic
current. Some power electronic based active power facilities have been developed to replace the above passive
power devices, recently. However, the wide use of these
active power facilities is limited due to their high cost.
For reducing the cost of pure active power facilities, the
hybrid power ﬁlter, comprising the passive power ﬁlter
and a power converter, has been developed.
In this paper, the hybrid compensation system conﬁgured by the AC power capacitor and hybrid power ﬁlter is
developed for further reducing the cost of hybrid power ﬁlter. The analysis result shows that the hybrid compensation
system has the problem of high frequency resonance ampliﬁcation. For avoiding this problem, a method, inserting an
inductor in series with the AC power capacitor, is proposed.
The test results show that the proposed method can solve
the problem of high frequency resonance ampliﬁcation
eﬀectively. From the above analysis and experiment, this
hybrid compensation system has the following advantages:
H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
457
Fig. 15. The test result of the improved hybrid compensation system under k1 = 8 and ZSL/ZPC = 4.2%: (a) the utility current, (b) the AC capacitor
current, (c) the output current of the hybrid power ﬁlter, (d) the load current.
Fig. 16. The transient response of the improved hybrid compensation system under k1 = 8 and ZSL/ZPC = 4.2%: (a) the utility current, (b) the AC
capacitor current, (c) the output current of the hybrid power ﬁlter, (d) the load current.
(1) lower cost as comparing with pure active power ﬁlter
or hybrid power ﬁlter,
(2) avoiding power resonance caused by passive power
ﬁlter or power factor correction AC power capacitor,
(3) protecting the AC power capacitor from the over-current damage due to the harmonic current injected
from the neighboring facilities of the utility side.
Acknowledgements
The authors would like to express their acknowledgement to the ﬁnancial support of National Science Council
under the contract NSC-91-2213-E-151-010 and the students of KUAS who help in the set-up of the hardware circuit for test.
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H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458
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