424 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 1, JANUARY 2009

Development of Hybrid Active Power FilterBased on the Adaptive Fuzzy Dividing

Frequency-Control MethodAn Luo, Zhikang Shuai, Wenji Zhu, Ruixiang Fan, and Chunming Tu

AbstractThis paper deals with a hybrid active power filter withinjection circuit (IHAPF). It shows great promise in reducing har-monics and improving the power factor with a relatively low ca-pacity active power filter. This paper concluded that the stabilityof the IHAPF based on detection supply current is superior to thatof others. To minimize the capacity of IHAPF, an adaptive fuzzydividing frequency-control method is proposed by analyzing thebode diagram, which consists of two control units: a generalizedintegrator control unit and fuzzy adjustor unit. The generalizedintegrator is used for dividing frequency integral control, whilefuzzy arithmetic is used for adjusting proportional-integral coef-ficients timely. And the control method is generally useful and ap-plicable to any other active filters. Compared to other IHAPF con-trol methods, the adaptive fuzzy dividing frequency control showsthe advantages of shorter response time and higher control preci-sion. It is implemented in an IHAPF with a 100-kVA APF installedin a copper mill in Northern China. The simulation and experi-mental results show that the new control method is not only easy tobe calculated and implemented, but also very effective in reducingharmonics.

Index TermsDividing frequency control, fuzzy adjustor, gen-eralized integrator, hybrid active power filter (HAPF).

I. INTRODUCTION

I N order to solve more serious harmonic problems of thegrid, the passive power filter (PPF) is often used at thepoint of common coupling (PCC) conventionally. However,it has many disadvantages (mistuning, resonance, instability,etc.), which discourages its implementation [1][5]. The useof the active power filter (APF) to mitigate harmonic problemshas drawn much attention since the 1970s [1], [2]. APFs seemto be a feasible solution for eliminating harmonic currents andvoltages. They are usually in parallel to harmonic loads and,therefore, are called shunt APFs. In recent years, there hasbeen a trend to develop the shunt APF that can be used undernonsinusoidal supply voltages, where the voltages at the PCCof the APF are harmonics-contaminated and caused by other

Manuscript received October 11, 2007; revised June 04, 2008. Currentversion published December 24, 2008. This work was supported in part byThe National Natural Science Foundation of China (No. 60474041) and in partby The National High Technology Research and Development of China (No.2008AA05Z211). Paper no. TPWRD-00642-2007.

A. Luo, Z. Shuai, W. Zhu, and C. Tu are with the Electrical and Informa-tion Engineering College, Hunan University, Changsha, Hunan 410082, China(e-mail: an_luo@hnu.cn; zhikangshuai@hotmail.com).

R. Fan is with the Jiangxi Electric Power Research Institute, Nanchang,Jiangxi 330096, China.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2008.2005877

connecting nonlinear loads in the APF application environment[6], [7]. However, they are limited by high cost, low-powercapacity, and are difficult to use in high-voltage grids. Anothersolution for the harmonic problem is to adopt a hybrid activepower filter (HAPF) [4]. The HAPF is the combination ofactive and passive power filters. The aim in the HAPF design isto complement or enhance the performance of the active powerfilter or passive power filter by adding passive or active com-ponents to its structure. HAPF is categorized in parallel hybridactive power filters (PHAPFs) and series hybrid active powerfilters (SHAPFs) based on the used active filter type. A seriesof PHAPFs was proposed after the 1990s [8][10]. Cheng etal. proposed a new hybrid active power filter to achieve thepower-rating reduction of the active filter [10]. But the activepower filter still bears the fundamental voltage in this design. Inthis paper, a novel HAPF with injection circuit was proposed.The novel topology has great promise in reducing harmonicswith a relatively low capacity APF.

For harmonic current tracking controls, there are two schemes[11][15]: One is the linear current control, such as ramp compar-ison control, deadbeat control, sinusoidal internal model control,generalized integrators control, etc.; the other is nonlinear currentcontrol, such as hysteresis control, predictive control, etc.

Hysteresis control has the advantage of simplicity, but leads toa widely varying switching frequency. This limitation has beenimproved with variable hysteresis band switching strategies butit requires a complex controller to achieve satisfactory perfor-mance. Predictive current control offers the best potential forprecise current control, but the implementation of a practicalsystem can be difficult and complex.

Ramp comparison control using a proportional-integral (PI)regulator has a long history of use. When the reference currentis a direct signal, as in the dc motor drive, zero steady-state errorcan be secured by using a conventional PI controller. When thereference current is a sinusoidal signal, as in the ac motor drive,however, straightforward use of the conventional PI controllerwould lead to steady-state error due to the finite gain at theoperating frequency. This drawback can be solved if the cur-rent control is executed in a synchronous-coordinate referenceframe. However, it is more complex and requires more hardwareor software for implementation because it demands transferringthe measured currents to a synchronous frame, and subsequentlytransforming the output of the PI regulator back to a stationaryframe to drive the ramp comparison controller. Sinusoidal in-ternal model control also requires more hardware or softwarefor implementation.

0885-8977/$25.00 2008 IEEE

LUO et al.: DEVELOPMENT OF HYBRID APF 425

Fig. 1. Topology of the shunt hybrid APF.

In this paper, an adaptive fuzzy dividing frequency-controlmethod composed of a generalized PI control unit and fuzzyadjustor unit was proposed. In the new control scheme, the gen-eralized PI control unit is used to achieve dividing frequencycontrol; the fuzzy adjustor unit is used to adjusted parametersof the PI control unit to produce better adaptive ability and dy-namic response. At the same time, the control strategy is gen-erally useful and applicable to other active filters. It is imple-mented in an IHAPF with a 100-kVA APF installed in a coppermill in Northern China. Simulation and application results haveshown that the new dividing frequency-control method is notonly easy to be calculated and implemented, but also very ef-fective in reducing harmonics.

II. SYSTEM CONFIGURATION AND CONTROL STRATEGY

A. Topology of the Novel HAPFThe parallel HAPF has the advantages of easy installation and

maintenance and can also be made just by transformation on thePPF installed in the grid. Fig. 1 shows a PHAPF that is in use now[3]. To reduce the power of APFs, a PPF has been designed forsome certain orders of harmonics. As in Fig. 1, , ; , ,and and make up a PPF to compensate the second, fifth,and seventh harmonic current, while the APF is just used to im-prove the performance of PPF and get rid of the resonance thatmay occur. So the power of the filter can be reduced sharply, usu-ally one-tenth of the power of the nonlinear load, which enablesthe APFto be used in a high-poweroccasion. HAPFisexpected tocompensate for reactive power as well as damp harmonics in thegrid, and all of the reactive power current will go through APF.

To further decrease the power of APF, a novel configurationof the hybrid APF is proposed as shown in Fig. 2 [16]. and

tune at the fundamental frequency, and then compose the in-jection branch with . The APF, shunted to the fundamentalresonance circuit, is directly connected in series with a matchingtransformer. Therefore, the novel HAPF (IHAPF) is formed.The PPF sustains the main grid voltage and compensates for theconstant reactive power, while the fundamental resonance cir-cuit only sustains the harmonic voltage, which greatly reducesthe APF power and minimizes the voltage rating of the semi-conductor switching device. So it is effective to be used in the6-kV/10-kV medium-voltage grid.

In order to clarify the compensation principle of IHAPF, asingle-phase equivalent circuit is shown in Fig. 3, where APFis considered a controlled current source , and the nonlinearload is considered to be a harmonic current source . In Fig. 3,

and are the supply voltage and equivalent inductor ofthe grid , and , , , and are the injection capac-

Fig. 2. Topology of the novel HAPF.

Fig. 3. Single-phase equivalent circuit. (a) Single-phase equivalent circuit.(b) Single-phase equivalent circuit with the effect of a harmonic source.

itor, fundamental resonance capacitor, fundamental resonanceinductor, and the PPF capacitor and inductor, respectively.

Fig. 3(b) is the equivalent circuit of the IHAPF only con-sidering the harmonic component of the system. , ,

, and represent system impedance, PPF impedance, theimpedance of the injection capacitor, and the fundamental res-onance impedance. From Fig. 3(b), we can see that

(1)

B. Control Strategy of IHAPFThere are two types of harmonic detection methods which

play important roles in the control strategy of HAPF.Load current detection: This method detects the load cur-rent , which flows downstream of the point of installa-tion, and then extracts the harmonic current from .

426 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 1, JANUARY 2009

Supply current detection: This method detects the supplycurrent , which escapes upstream of the point of instal-lation, and then extracts harmonic current from .

1) Control Strategy Based on Load Current Detection: Thismethod detects the load harmonic current , and the APF iscontrolled as

(2)From (1) and (2) and when only harmonic current is consid-

ered, the supply harmonic current should be

(3)

Equation (3) can be written as

(4)

It can be seen that the characteristic of PPFs is optimizedand the harmonic impedance of the grid is increased, which im-proves the performance of harmonic elimination. However, thepossibility of resonance between the IHAPF and the grid cannotbe avoided, and it increases the difficulty of parameter design.Moreover, it is not suitable to be used in the situation where theimpedance of the grid changes at high frequency.

2) Control Strategy Based on the Supply-Current Detection:This method detects the supply harmonic current , and theAPF is considered as a controlled current source

(5)where is the controlled gain of . From (1) and (5), thesupply current should be

(6)Equation (6) indicates that it is possible to eliminate the influ-

ence of the load harmonic current and supply harmonic voltageas low as possible if is large enough. Moreover, if the supplyharmonic voltage is not considered, that is

(7)Equation (7) shows that Figs. 4 and 3(b) are equivalent, where

. According to Fig. 4, theAPF of the IHAPF tends to be a harmonic resistance, which isin series with the . When is large enough, the harmoniccurrent flowing into the grid is nearly zero. Thus, it has a goodperformance in harmonic elimination. At the same time, it can

Fig. 4. Single equivalent circuit by just considering .

restrain the possibility of parallel resonance between the IHAPFand the grid.

As stated before, it can be found that for the sake of com-pensating harmonic current, the control strategy based on thedetection of load harmonic current is a good choice. But the pos-sibility of resonance between the IHAPF and the grid cannot beavoided, and it increases the difficulty of the IHAPF parameterdesign. If the control strategy based on supply current detectionis used, IHAPF can eliminate not only the harmonic current, butalso the possibility of parallel resonance between IHAPF andthe grid will be restrained. So the control strategy based on thesupply current detection is applied in this paper.

III. NECESSITY ANALYSES OF DIVIDING FREQUENCY CONTROLBased on the detected harmonic current in the grid, the

APF can compensate harmonics by making the inverter generateharmonics whose magnitude is equal to but the phase is theopposite of it. However, as parallel HAPFs in Figs. 1 and 2, ifAPF generates harmonics as the same order as PPF, the per-formance of the PPF may be counteracted, even if an accidentoccurs for the overcurrent of PPF. That is to say, just for HAPF,there is no need to control some order harmonics, as it can wastethe compensation capacity easily [16]. This is one reason whywe need to adopt the dividing frequency-control method.

Taking the IHAPF, for example, as for the sake of simplicity,the influence of PPF and the equivalent impedance of the gridhave not been considered. Therefore, the single-phase equiva-lent circuit can be received as shown in Fig. 6, where is theoutput voltage of the inverter equivalent to the primary side ofthe coupling transformer; and are the inductor and ca-pacitor of output filter, respectively; and is the harmoniccurrent injected to the grid.

Loop current , , and in Fig. 5 can be ex-pressed as shown in (8), at the bottom of the page.

(8)

LUO et al.: DEVELOPMENT OF HYBRID APF 427

Fig. 5. Single-phase equivalent circuits.

Fig. 6. Bode diagram of .

From (8), we can get obtain (9), shown at the bottom of thepage.

When , , , and are 116.84 , 350.52 ,29.77 mH, 30 and 1 mH, the bode diagram of can beshown in Fig. 6

From Fig. 6, it can be seen that the amplitude-frequency char-acteristic of the transfer function just has one resonance point be-yond the fundamental frequency, and the phase-frequency char-acteristic is divided by this resonance pulsations and the phaseposition is changed from 90 to 90 . Obviously, when the har-monic of both sides of needs to be compensated, it is hard toobtain ideal performance if the single control strategy is adoptedwithout considering the influence of phase. For different kindsof HAPF, the differences of structure and parameters will lead tothe discrepancy of . Moreover, the rule of phase change maybe different. Therefore, in order to achieve good performance,the phase and amplitude should be considered at the same time.And, thus, dividing frequency control must be adopted.

IV. ADAPTIVE FUZZY DIVIDINGFREQUENCY-CONTROL METHOD

The conventional linear feedback controller (PI controller,state feedback control, etc.) is utilized to improve the dynamic

Fig. 7. Configuration of the adaptive fuzzy dividing frequency controller.

response and/or to increase the stability margin of the closed-loop system. However, these controllers may present a poorsteady-state error for the harmonic reference signal. An adaptivefuzzy dividing frequency control method is presented in Fig. 7,which consists of two control units: 1) a generalized integratorcontrol unit and 2) a fuzzy adjustor unit. The generalized inte-grator, which can ignore the influence of magnitude and phase,is used for dividing frequency integral control, while fuzzy arith-metic is used to timely adjust the PI coefficients.

Since the purpose of the control scheme is to receive a min-imum steady-state error, the harmonic reference signal is setto zero. First, supply harmonic current is detected. Then, the ex-pectation control signal of the inverter is revealed by the adap-tive fuzzy dividing frequency controller. The stability of thesystem is achieved by a proportional controller, and the perfectdynamic state is received by the generalized integral controller.The fuzzy adjustor is set to adjust the parameters of propor-tional control and generalized integral control. Therefore, theproposed harmonic current tracking controller can decrease thetracking error of the harmonic compensation current, and havebetter dynamic response and robustness.

A. Generalized Integral Controller

The generalized integral PI controller carries out the dividingfrequency control of the sinusoidal signal. Similar to the directsignal case, the generalized integrator just works on the ampli-tude of a sinusoidal signal , but has noeffect on its frequency and phase. So the amplitude integrationof this signal can be written as . Furtherdefining an auxiliary signal , the Laplacetransforms of the three signals are

(10)

(11)

(12)

(9)

428 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 1, JANUARY 2009

So

(13)

When the frequency of the sinusoidal signal has a deviation

(14)

The auxiliary signal and integration signal can be shown as

(15)(16)

And then

(17)

where is the Laplace transform of the signal .When the frequency deviation is small, there is

(18)

So (17) can be written as

(19)

From (19), it can be seen that (13) comes into existence allthe same even when the frequency of the sinusoidal signal hasa small deviation .

When is far bigger than 1, there is

(20)

As for

(21)

So when the frequency deviation is large, the amplitude inte-gration will be zero.

And so, for the three sinusoidal signals

(22)

(23)

(24)

where

(25)(26)

Fig. 8. Configuration of the generalized integrator PI controller.

According to the previous analyses, when ,their Laplace transforms can be written as

(27)

From (27), it can be seen that (13) has a selectivity of fre-quency. It indicates that the integration signal of a sinu-soidal signal with the frequency can be obtained basedon (27).

At the same time, we can see that

(28)

According to (28) and (13), then

(29)

Relative to , is negligible; thus, thetransfer function of the generalized integrator, which has afunction of dividing frequency, is

(30)

In terms of the analysis from before, the block diagram ofthe generalized integrator PI controller can be obtained by thecharacteristic of the generalized integrator, shown in Fig. 8.

To reduce count quantity and improve the real time, the in-cremental iteration algorithm is applied. On the principle of thecontrol quantity of the previous two-control cycle, the output ofthe generalized integrator is expressed as

(31)

The generalized integrator PI controller law is

(32)

LUO et al.: DEVELOPMENT OF HYBRID APF 429

Fig. 9. Block diagram of the fuzzy adjustor unit.

where is the sampling value of the current time, isthe sampling value of the previous cycle, and and arethe proportional coefficient and integrator coefficient of the PIcontroller, respectively, and is a set of harmonic orders thatneed to be eliminated. In order to eliminate disturb efficiently,the discrete differential coefficient can be obtained byadopting (15)

(33)

B. Fuzzy AdjustorThe fuzzy adjustor is used to adjust the parameters of propor-

tional control gain and integral control gain , based onthe error and the change of error

(34)

where and are reference values of the fuzzy-gener-alized integrator PI controller. In this paper, and arecalculated offline based on the ZieglerNichols method. In afuzzy-logic controller, the control action is determined from theevaluation of a set of simple linguistic rules. The developmentof the rules requires a thorough understanding of the process tobe controlled, but it does not require a mathematical model ofthe system. A block diagram fuzzy-logic adjustor is shown inFig. 9. In this way, system stability and a fast dynamic responsewith small overshoot can be achieved with proper handing ofthe fuzzy-logic adjustor.

Fuzzification converts crisp data into fuzzy sets, making itcomfortable with the fuzzy set representation of the state vari-able in the rule. In the fuzzification process, normalization byreforming a scale transformation is needed at first, which mapsthe physical values of the state variable into a normalized uni-verse of discourse.

The error and change of error are used as numerical vari-ables from the real system. To convert these numerical variablesinto linguistic variables, the following seven fuzzy levels or setsare chosen as [17]: negative big (NB), negative medium (NM),negative small (NS), zero (ZE), positive small (PS), positivemedium (PM), and positive big (PB).

To ensure the sensitivity and robustness of the controller, themembership function of the fuzzy sets for , , ,and in this paper are acquired from the ranges of , ,

, and , which are obtained from project and expe-rience. And the membership functions are shown in Fig. 10,respectively.

Fig. 10. Membership functions of the fuzzy variable. (a) Membership functionof and . (b) Membership function of and .

The core of fuzzy control is the fuzzy control rule, whichis obtained mainly from the intuitive feeling for and experi-ence of the process. The fuzzy control rule design involvesdefining rules that relate the input variables to the output modelproperties.

For designing the control rule base for tuning and ,the following important factors have been taken into account.

1) For large values of , a large is required, and forsmall values of , a small is required.

2) For , a large is required, and for ,a small is required.

3) For large values of and , is set to zero, whichcan avoid control saturation.

4) For small values of , is effective, and islarger when is smaller, which is better to decreasethe steady-state error. So the tuning rules of and

can be obtained as Tables I and II.The inference method employs the MAX-MIN method. The im-

precise fuzzy control action generated from the inference mustbe transformed to a precise control action in real applications.The center of gravity method is used to defuzzify the fuzzy vari-able into physical domain

(35)

V. SIMULATION AND APPLICATION RESULTS

A. Simulation ResultsSimulation results of a 10-kV system have been carried

out with software PSIM. The system parameters are listed inTable III. The PPFs are turned at the 11th and 13th, respectively.The injection circuit is turned at the 6th. In this simulation,ideal harmonic current sources are applied. The dc-side voltageis 535 V. Simulation results with the conventional PI controllerand the proposed current controller are shown in Figs. 11 and

430 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 1, JANUARY 2009

TABLE IADJUSTING RULE OF THE PARAMETER

TABLE IIADJUSTING RULE OF THE PARAMETER

TABLE IIIPARAMETERS OF THE IHAPF

12. , , , , and the error represent the load current,supply current, current though the injection capacitor, currentthrough APF, and error of compensation.

Fig. 11 shows the dynamic response of IHAPF when differentcontrollers are adopted. At 0.3 s, the THD increases from 9.6%to 21.8%. When the conventional PI controller is used, the errorcan be reduced to 20 A in 0.06 s, but there is an obvious steady-state error at 1.0 s all the same. When the generalized integralcontroller is used, the error reduces to 10 A at 0.6 s; however,it can only be reduced to 30 A in 0.06 s. When the proposedcontroller is used, the error can be reduced to 10 A in 0.06 s.It is observed that compared to the conventional PI controllerand generalized integral controller, the proposed controller hasbetter dynamic performance.

Fig. 12 shows the steady-state performance of the IHAPFwhen different controllers are used. From Fig. 12, it can be seenthat after IHAPF with the conventional PI controller runs, thecurrent total harmonic distortion reduces to 3.8% from 21.8%,and the power factor increases to 0.95 from 0.55. When the

Fig. 11. Simulation results of the dynamic performance. (a) Simulation re-sults with the conventional PI controller. (b) Simulation results with the conven-tional generalized integral controller. (c) Simulation results with the proposedcontroller.

conventional generalized integral controller is used, the currentTHD reduces to 3.3% from 21.8%, while after the IHAPF withthe proposed PI controller runs, the current THD reduces to1.8% from 21.8%. So it can be observed that the proposed cur-rent controller exhibits much better performance than the con-ventional PI controller and the conventional generalized integralcontroller.

B. Application ResultsThe control method proposed in this paper is also success-

fully implemented in an IHAPF with a 100-kVA APF for com-pensating a large power rating industrial rectifier in NorthernChina. A TI 2407 DSP is used on the controller board to im-plement the adaptive fuzzy dividing frequency-control method.System parameters used for the device are listed in Table III.The IHAPF prototype, DSP-based controller, and experimental

LUO et al.: DEVELOPMENT OF HYBRID APF 431

Fig. 12. Simulation results of steady-state compensation. (a) Simulation re-sults with the conventional PI controller. (b) Simulation results with the conven-tional generalized integral controller. (c) Simulation results with the proposedcontroller.

TABLE IVCOMPARISON OF SUPPLY CURRENT THD AND POWER FACTOR

results are shown in Fig. 13. Table IV is the THD of the supplycurrent before and after the IHAPF has been used.

Application results demonstrate that after the IHAPF wasused, the supply current turns to be a nearly sinusoidal wavefrom the distortion wave, and the reactive power of the grid wascompensated effectively.

VI. CONCLUSIONA novel hybrid APF with injection circuit was proposed. Its

principle and control methods were discussed. The proposedadaptive fuzzy-dividing frequency control can decrease thetracking error and increase dynamic response and robustness.

Fig. 13. IHAPF prototype and experimental results. (a) Local equipment ofIHAPF. (b) DSP-based controller. (c) Dynamic performance when the IHAPFsudden runs. (d) Supply current before the IHAPF runs. (e) Supply current afterthe IHAPF runs.

432 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 1, JANUARY 2009

The control method is also useful and applicable to any otheractive filters. It is implemented in an IHAPF with a 100-kVAAPF system in a copper mill in Northern China, and demon-strates good performance for harmonic elimination. Simulationand application results proved the feasibility and validity of theIHAPF and the proposed control method.

ACKNOWLEDGMENTThe authors would like to thank Prof. Z. J. Shen and D. Mi

for their helpful comments and revisions.

REFERENCES[1] L. Gyugyi and E. C. Strycula, Active ac power filters, in Proc. IEEE,

Ind. Appl. Soc. Annu. Meeting, 1976, pp. 529535.[2] N. Mohan, H. A. Peterson, W. F. Long, G. R. Dreifuerst, and J. J.

Vithayathil, Active filters for AC harmonic suppression, presented atthe IEEE Power Eng. Soc. Winter Meeting, 1977.

[3] F. Peng, H. Akagi, and A. Nabae, A new approach to harmonic com-pensation in power system-a combined system of shunt passive and se-ries active filters, IEEE Trans. Ind. Appl., vol. 26, no. 6, pp. 983990,Nov. 1990.

[4] C. Madtharad and S. Premrudeepreechacharn, Active power filter forthree-phase four-wire electric systems using neural networks, Elect.Power Syst. Res., vol. 60, no. 2, pp. 179192, Apr. 2002.

[5] H. Fujita and H. Akagi, A practical approach to harmonic compen-sation in power system-series connection of passive and active filters,IEEE Trans. Ind. Appl., vol. 27, no. 6, pp. 10201025, Nov. 1991.

[6] H. Fujita and H. Agaki, The unified power quality conditioner: theintegration of series and shunt-active filters, IEEE Trans. Power Elec-tron., vol. 13, no. 2, pp. 315322, Mar. 1998.

[7] K. J. P. Macken, K. M. H. A. De Brabandere, I. J. L. Dnesen, and R. J.M. Belmans, Evaluation of control algorithms for shunt active tillersunder unbalanced and nonsinusoidal conditions, in Proc. IEEE PortaPower Tech. Conf., Porto, Portugal, Sep. 1013, 2001, pp. 16211626.

[8] F. Ruixiang, L. An, and L. Xinran, Parameter design and applicationresearch of shunt hybrid active power filter, Proc. CSEE, vol. 26, no.2, pp. 106111, Jun. 2006.

[9] S. Kim and P. N. Enjeti, A new hybrid active power filter (APF)topology, IEEE Trans. Power Electronics, vol. 17, no. 1, pp. 4854,Jan. 2002.

[10] S. Bhattachaya, P.-T. Cheng, Deep, and M. Divan, Hybrid solutionsfor improving passive filter performance in high power applications,IEEE Trans Ind. Appl., vol. 33, no. 3, pp. 732747, May 1997.

[11] L. Malesani, P. Mattavelli, and P. Tomasin, High performancehysteresis modulation technique for active filters, IEEE Trans. PowerElectron., vol. 12, no. 5, pp. 876884, Sep. 1997.

[12] S. Fukuda and R. Imamura, Application of a sinusoidal internalmodel to current control of three-phase utility-interface converters,IEEE Trans. Ind. Electron., vol. 52, no. 2, pp. 420426, Apr. 2005.

[13] X. Yuan, W. Merk, H. Stemmler, and J. Allmeling, Stationary-framegeneralized integrators for current control of active power filters withzero steady-state error for current harmonics of concern under unbal-anced and distorted operating conditions, IEEE Trans. Ind. Appl., vol.38, no. 2, pp. 523532, Mar. 2002.

[14] K. Nishida, Y. Konishi, and M. Nakaoka, Current control implemen-tation with deadbeat algorithm for three-phase current-source activepower filter, Proc. Inst. Elect. Eng., Electr. Power Appl., vol. 149, no.4, pp. 275282, Jul. 2002.

[15] J. H. Marks and T. C. Green, Predictive transient-following controlof shunt and series active power filters, IEEE Trans. Power Electron.,vol. 17, no. 4, pp. 574584, Jul. 2002.

[16] A. Nakajima, K. Oku, J. Nishidai, T. Shiraishi, Y. Ogihara, K. Mizuki,and M. Kumazawa, Development of active filter with series resonantcircuit, in Proc 19th IEEE Annu. Power Electronics Specialists Conf.Rec., Apr. 1114, 1988, vol. 2, pp. 11681173.

[17] B. K. Bose, Expert systems, fuzzy logic, and neural network appli-cation in power electronics and motion control, in Proc. IEEE, Aug.1994, vol. 82, no. 8, pp. 13031323.

An Luo was born in Hunan, China, on July 21,1957. He received the B.S. and M.S. degrees fromHunan University, Changsha, in 1982 and 1986,respectively, and the Ph.D. degree from ZhejiangUniversity, Hangzhou, in 1993.

From 1986 to 2003, he was a Lecturer at CentralSouth University, Changsha, where he became a Pro-fessor. In 2003, he became a Professor at Hunan Uni-versity. He is engaged in research on power conver-sion systems, harmonics suppression, reactive powercompensation, and electric power savings.

Zhikang Shuai was born in Shandong, China, onDecember 19, 1982. He received the B.S. degreefrom the College of Electrical and Information En-gineering at Hunan University, Changsha, in 2001.

He has been a graduate student at the College ofElectrical and Information Engineering at HunanUniversity, where he has been since 2005. Hisresearch interests include electric power savings,reactive power compensation, and active powerfilters.

Wenji Zhu was born in Guangxi, China, on October17, 1983. She received the B.S. degree from theCollege of Electrical and Information Engineering,Hunan University, Changsha, in 2001, where she iscurrently pursuing the Ph.D. degree.

Her research interests include neural networks,analog fault diagnosis, and active power filters.

Ruixiang Fan was born in Hunan, Changsha, China,on December 21, 1978. He received the M.S. andPh.D. degrees from Hunan University, Changsha, in2004 and 2007, respectively.

He is engaged in research on the harmonics sup-pression and reactive power compensation for power-electronic devices.

Chunming Tu was born in Jiangxi, Nanchang,China, on February 16, 1976. He received the M.S.and Ph.D. degrees from Central South University,Changsha, in 2001 and 2004, respectively.

His research interests include electric power sav-ings and active power filters