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. 450 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. 452 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. 454 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. 456 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. 458 H.-L. Jou et al. / Electrical Power and Energy Systems 28 (2006) 448–458 References [1] Henderson RD, Rose PJ. Harmonics: the eﬀects on power quality and transformers. IEEE Trans Ind Appl 1994;30(3):528–32. [2] Gonzalez DA, Mccall JC. Design of ﬁlters to reduce harmonic distortion in industrial power systems. IEEE Trans Ind Appl 1987;23(3):504–11. [3] Wu CJ, Chiang JC, Yen SS, Liao CJ, Yang JS, Guo TY. Investigation and mitigation of harmonic ampliﬁcation problems caused by single-tuned ﬁlters. IEEE Trans Power Deliver 1998;13(3):800–6. [4] Grady WM, Samotyj MJ, Noyola AH. Survey of active power line conditioning method. IEEE Trans Power Deliver 1990;5(3): 1536–42. [5] Singh B, Haddad KA, Chandra A. A review of active ﬁlter for power quality improvement. IEEE Trans Ind Electron 1999;46(5):960–71. [6] Wu JC, Jou HL. A simpliﬁed control method for single-phase active power ﬁlter. IEE Proc—Electric Power Appl 1996; 143(3):219–24. [7] Peng FZ, Akagi H, Nabae A. Compensation characteristics of the ﬁlter system of shunt passive and series active power ﬁlter. IEEE Trans Ind Appl 1993;29(1):732–47. [8] Jung GH, Cho GH. New active power ﬁlter with simple low cost structure without tuned ﬁlter. IEEE PESC 1998:217–22. [9] Bhattacharya S, Cheng PT, Divan DM. Hybrid solutions for improving passive ﬁlter performance in high power applications. IEEE Trans Ind Appl 1997;33(3):732–47. [10] Fujita H, Akagi H. A practical approach to harmonic compensation in power system, series connection of passive and active ﬁlters. IEEE Trans Ind Appl 1991;27:1020–5.

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