An active filter has been proposed to compensate for harmonic distortion, line neutral current and reactive power in three-phase four-wire systems. The focus is concentrated on current control in order to achieve optimum current tracking by means of fixed frequency driving signals. The effectiveness of proposed control was proved in simulations where the harmonic pollution and imbalance caused by a highly distorting load have been drastically reduced.Opisan je aktivni filtar za kompenzaciju harmonijskog izobličenja, struje nultog sustava i jalove snage u trofaznim sustavima s četiri vodiča. Pozornost je usmjerena na upravljanje strujom da se postigne optimalno slijeđenje struje s pomoću konstantne frekvencije pobudnog signala. Djelotvornost predloženog upravljanja ispitana je simulacijom, gdje su harmonijsko zagađenje i neravnoteža, uzrokovani jakom distorzijom tereta, drastično reducirani

Agostino Lecci

Antonio Dell\u27Aquila

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1 INTRODUCTIONShunt active filters are designed to compensatefor harmonic currents, reactive power and neutralcurrent by injecting filtering currents into the elec-tric grid. These can be considered as a controlledcurrent source and prove to be particularly effectivewhen their control system provides a good referen-ce tracking [1–17]. The simplest control techniquefor current controlled PWM inverters, used as anAPF, is hysteresis control. However, at criticalpoints, where changes of reference waveform slopeare unpredictable, hysteresis control causes a dan-gerous increase in switching frequency which can-not be justified, even if it has the advantage of notexceeding the designed error band.The proposed current control, on the other hand,aims to reduce tracking error, by means of a fixedfrequency driving signal. During the switching periodin each inverter leg, the control allows the properstate for a longer interval resulting in the quickestpossible error reduction. Furthermore, the frequencyof the driving signal remains fixed. Active filter re-gulation is achieved by means of a fuzzy controllerwhich corrects the amplitude of mains fundamentalcurrent reference in order to move the power ba-lance. In transients and at start up the supply isasked to feed an amount of power different fromthat absorbed by the load, in order to compensated.c. side voltage error.The effectiveness of the proposed active filtercontrol was proved in a simulation, where the com-pensation of the harmonic pollution caused by ahard distorting and unbalanced load is carried out,and is evaluated by means of a performance index.Harmonic compensation as well as reactive powerreduction and line neutral current reduction areachieved by using 10 kHz inverter switching signals.2 ACTIVE FILTER TOPOLOGY AND REFERENCE COMPUTINGThe proposed three-phase four-wire shunt activefilter is shown in Figure 1.Antonio Dell'Aquila, Agostino LecciA Current Control for Three-Phase Four-Wire Shunt Active FiltersUDK 621.311.1.072IFAC IA 5.5.4Professional paperAn active filter has been proposed to compensate for harmonic distortion, line neutral current and reactivepower in three-phase four-wire systems.The focus is concentrated on current control in order to achieve optimum current tracking by means of fixedfrequency driving signals. The effectiveness of proposed control was proved in simulations where the harmonic pol-lution and imbalance caused by a highly distorting load have been drastically reduced.Key words: active filters, fuzzy logic, harmonics, power qualityAUTOMATIKA 44(2003) 3–4, 129–135              129ISSN 0005–1144ATKAAF 44(3–4),129–135 (2003)Fig. 1 Proposed three-phase four wire active power filterThe active power filter (APF) is made up of athree-phase inverter which is connected to themains by passive output filters. The output filterconsists of a link reactor, which limits the ampli-tude and frequency of the switching ripple.Reference computation is achieved aiming atthree different compensating tasks. Line neutralcurrent reduction remains the main goal, but bymeans of a proper reference waveform, reactivepower and harmonics compensation can also beachieved.As shown in Figures 7 and 8, the proposed algo-rithm proved to be effective in reducing mains har-monic content as well as neutral current. It is im-portant to point out that the polluting load was de-signed in order to drain a large current on phase»b« and therefore create a notable imbalance be-tween the three phases. Reference waveform gene-ration distributes active power among the phases,thus causing a line current on »a« and »c« phaseswhich has a larger fundamental component com-pared to »a« and »c« uncompensated line currents,as shown in Figure 7. In phase »b« the oppositehappens.A switching frequency of 10 kHz gives the follo-wing results: THDR index exceeded 90 % and, aboveall, the peak neutral current was reduced from 15 Ato less than 3 A.This compensation result was made possible byan optimum regulation of d.c. bus voltage, whichmaintained its reference of 800 V by means of afuzzy controller. Figure 9 shows this result.6 CONCLUSIONSA shunt active filter was proposed. Its controlstrategy is the result of an analytical developmentwhich supplies a design equation for switching sig-nal generation and effective current tracking. Simu-lations were carried out to show active filter perfor-mance under highly polluting load operation; theeffectiveness of proposed filter is shown by numeri-cal results.7 APPENDIXA complete development of control design equa-tion (3) is given in this section. The analysis of cur-rent waveforms is carried out for one phase only,since the same considerations are valid in everyphase.Figure 10 shows reference and filtering currentsin one phase during the switching period. In thesame diagram, four time subintervals are shown, de-termined by the switching instants, and the changesof filtering current during each subinterval are la-belled.132                                   AUTOMATIKA 44(2003) 3–4, 129–135A. Dell'Aquila, A. LecciA Current Control for Three-Phase ...Fig. 9 Neutral current reduction: load and mains neutral currentsFig. 8 Fuzzy regulation on active filter d.c. side: d.c. bus voltageFig. 10 Reference and filtering current during switching period TSIn order to achieve a error by the end of theswitching period, the sum of changes in filteringcurrents, diminished by initial tracking error ε,should be equal to reference current change.Thus the following calculation is used:AF =  AB + BC + CD + DE + EF (5)that is:s*TS = −ε + s1T1 + s2T2 + s3T3 + s4T4          (6)where s* is the reference current derivative in TS,(s1, s2, s3, s4) are the derivatives of compensatingcurrent in the four intervals T1, T2, T3, T4, and T1 + T2 + T3 + T4 = TS                     (7)while ε is the tracking error at the beginning of theswitching period:ε = iF–ref − iF.                 (8)Equation (6) is valid for all the inverter legs:sa*TS = −εa + sa1T1 + sa2T2 + sa3T3 + sa4T4 sb*TS = −εb + sb1T1 + sb2T2 + sb3T3 + sb4T4       (9)sc*TS = −εc + sc1T1 + sc2T2 + sc3T3 + sc4T4.The dependency of the intervals Ti on the valuesof the duty cycle D can be seen as follows. If Dminis the duty cycle on the inverter leg which switchesfirst, Dmean is the duty cycle on the inverter legwhich is the next to change and Dmax is the largerduty cycle which is the last to change on the in-verter leg, the following calculations can be made:T1 = DminTST2 = (Dmean − Dmin)TS    (10) T3 = (Dmax − Dmean)TST4 = (1 − Dmax)TS. By substituting (10) for (9) the result is:By following the path in Figure 11 the result is:vLFa + van − vC1 = 0             (13)and in the hypothesis that a complete d.c. voltageregulation is achieved:(14)resulting in:(15)where i = a, b, c, and gi = +1 if upper switch is closesand gi = −1 if lower switch is closed in ith inverterleg.Considering the term:(si1 − si2),                  (16)by substituting (12) and (15) for (16), we obtain thefollowing results:(17)where the first index is i = a, b, c while the secondone refers to the time interval T1, T2, T3, T4, whereg is computed.Generally each leg changes its status only onceduring the switching period. The three switching in-stants are different. The switching order of thethree inverter legs may be: (a, b, c) or (a, c, b), (b,a, c), (b, c, a), (c, a, b), or the last case (c, b, a).The following table may be useful in findingswitching variable g values in the different cases:1 2 1 22( ) ( )dci i i iFvs s g gL− = −2dcLFi in ivv v g= − +1 2 2dcC Cvv v= =AUTOMATIKA 44(2003) 3–4, 129–135       133A. Dell'Aquila, A. Lecci A Current Control for Three-Phase ...41 2 mean 2 3 3 441 2 mean 2 3 3 441 2 mean 2 3 3 4min maxmin maxmin max( ) ( ) ( ),( ) ( ) ( ),( ) ( ) ( ).aa aSa a a a a abb bSb b b b b bcc cSc c c c c cs sTD s s D s s D s ss sTD s s D s s D s ss sTD s s D s s D s sεεε∗∗∗+ − == − + − + −+ − == − + − + −+ − == − + − + −(11)It is possible to point out the dependence of sion voltage drop across coupling inductances LFi.The following equation can be used:(12)The voltage drop across coupling inductancesmay be computed by following the path shown inFigure 11..LfiiFivsL=Fig. 11 Close path for inductance voltage drop computingIf switching sequence is (a, b,c) the following cal-culation are used:Dmin = DaDmean = Db (18)Dmax = Dcand by substituting (18) and (17) for (11) the fol-lowing results are obtained:(19)If switching sequence is a,c,b the following calcu-lation are used:Dmin = DaDmean = Db (20)Dmax = DcTherefore it is possible to obtain the followingthree equations which relate D values to other elec-trical parameters:(21)4 min4 max4 mean,,.dcaa aS Fdcbb bS Fc dcc cS Fvs s DT Lvs s DT Lvs s DT Lεεε∗∗∗+ − =+ − =+ − =4 min4 mean4 max,,.dcaa aS Fdcbb bS Fc dcc cS Fvs s DT Lvs s DT Lvs s DT Lεεε∗∗∗+ − =+ − =+ − =It is possible to analyse the other four situationsin the same way. By solving equations with respectto D, the result is a design equation which may beapplied to each inverter leg:(22)REFERENCES[1] H. Akagi, New Trends in Active Filters for Power Conditi-oning. IEEE Trans. on Ind. Applicat., vol. 32, Nov./Dec.1996, pp. 1312–1322.[2] H. Akagi, Control Strategy and Site Selection of a ShuntActive Filter for Damping of Harmonic Propagation in Po-wer Distribution Systems. IEEE Trans. on Power Delivery,vol. 12, No. 1, January 1997, pp. 354–363.[3] S. Jeong, M.Woo, DSP-Based Active Power Filter with Pre-dictive Current Control. IEEE Trans. on Industrial Electro-nics, vol. 44, no. 3, June 1997, pp. 329–336.[4] F. Z. Peng, Application Issues of Active Power Filters. IEEEIndustry Application Magazine, September/October 1998,pp. 21–37.[5] S. Buso, L. Malesani, P. Mattavelli, Comparison of CurrentControl Techniques for Active Filter Applications. IEEETrans. on Ind. Electronics, vol. 45, no. 5, October 1998, pp.722–729.[6] T. Thomas, K. Haddad, G. Joos, A. Jaafari, Design and Per-formance of Active Power Filters. IEEE Industry Applica-tion Magazine, September/October 1998, pp. 38–46.[7] A. Dell'Aquila, M. Liserre, F. Loiudice, M. Marinelli, P.Zanchetta, Performance Evaluation of Active Filters forCompensation of Distorted Line Currents Produced by In-duction Motor Drives. Proc. of ELECTRIMACS '99 Con-ference, Lisbona (Portugal), September 1999, vol. III, pp.63–68.[8] B. Singh, K. Al-Haddad, A. Chandra, A Review of ActiveFilters for Power Quality Improvement. IEEE Trans. onIndustrial Electronics, vol. 46, no. 5, October 1999, pp.960–971.1 12.ii in F idc SD v L sv Tε∗  = + + +    134                                   AUTOMATIKA 44(2003) 3–4, 129–135A. Dell'Aquila, A. LecciA Current Control for Three-Phase ...Table 2. Switching function g during TS in the six different casesSwitching sequence (a, b, c)ga 1 −1 −1 −1gb 1 1 −1 −1gc 1 1 1 −1T1 T2 T3 T4Switching sequence (a, c, b)ga 1 −1 −1 −1gb 1 1 1 −1gc 1 1 −1 −1T1 T2 T3 T4Switching sequence (b, c, a)ga 1 1 1 −1gb 1 −1 −1 −1gc 1 1 −1 −1T1 T2 T3 T4Switching sequence (b, a, c)ga 1 1 −1 −1gb 1 −1 −1 −1gc 1 1 1 −1T1 T2 T3 T4Switching sequence (c, b, a)ga 1 1 1 −1gb 1 1 −1 −1gc 1 −1 −1 −1T1 T2 T3 T4Switching sequence (c, a, b)ga 1 1 −1 −1gb 1 1 1 −1gc 1 −1 −1 −1T1 T2 T3 T4[9] P. Mattavelli, A. M. Stankovic, Energy-based CompensationStrategy for Active Filters. Proc. of the 38th Conference onDecision & Control, Phoenix Arizona (USA), December1999, pp. 4656–4661.[10] K. Wada, T. Shimizu, Mitigation Method of 3rd-harmonicVoltage for a Three-phase Four-wire Distribution SystemBased on a Series Active Filter for the Neutral Conductor.In Proc. of IAS 2000, vol. 1, 2002, pp. 64–69.[11] B. Dobrucky, H. Kim, V. Racek, M. Roch, M. Pokorny, Sin-gle-phase Power Active Filter and Compensator Using In-stantaneous Reactive Power Method. In Proc. of PCC2000, Osaka 2002, pp. 167–171.[12] J. Mossoba, P. W. Lehn, A Controller Architecture for HighBandwidth Active Power Filters. IEEE Trans. on PowerElect., vol 18, no 1, Jan. 2003.[13] A. Dell'Aquila, A. Lecci, M. Liserre, P. Zanchetta, Design ofthe Optimum Duty Cycle for a Fuzzy Controlled ActiveFilter, Proc. of ISIE 2000 Conference, Puebla (Mexico),December 2000.[14] S.Tnani, J. Bosche, J. Gaubert, G. Champenois, Sliding Mo-de Control of Parallel Hybrid Filters. Proc. of 9th Euro-pean Conference on Power Electronics and Applications,Graz (Austria), August 2001.[15] A. Abeillan, J. Benavent, E. Figueres, I. Miro, A New Com-bined Control Method for Shunt Active Filters Applied toFour-Wire Power Systems. Proc. of 9th European Conferen-ce on Power Electronics and Applications, Graz (Austria),August 2001.[16] B. Lin, S.Tsay, M. Liao, Integrated Power Quality Compen-sator Based on Sliding Mode Controller. Proc. of 9th Eu-ropean Conference on Power Electronics and Applications,Graz (Austria), August 2001.[17] A. Dell'Aquila, A. Lecci, P. Zanchetta, M. Liserre, FuzzyActive Filter Performance in Transient Conditions. Proc. of9th European Conference on Power Electronics and Appli-cations, Graz (Austria), August 2001.[18] A. Dell'Aquila, A. Lecci, M, Liserre, Microcontroller-BasedFuzzy Logic Active Filter for Selective Harmonic Compen-sation, Proc. of IEEE IAS Annual Meeting, Salt Lake City(USA), October 2003.AUTOMATIKA 44(2003) 3–4, 129–135       135A. Dell'Aquila, A. Lecci A Current Control for Three-Phase ...Upravljanje strujom trofaznih paralelno spojenih aktivnih filtara s ~etiri vodi~a. Opisan je aktivni filtar zakompenzaciju harmonijskog izobli~enja, struje nultog sustava i jalove snage u trofaznim sustavima s ~etiri vodi~a.Pozornost je usmjerena na upravljanje strujom da se postigne optimalno slije|enje struje s pomo}u konstantnefrekvencije pobudnog signala. Djelotvornost predlo`enog upravljanja ispitana je simulacijom, gdje su harmonijskozaga|enje i neravnote`a, uzrokovani jakom distorzijom tereta, drasti~no reducirani. Klju~ne rije~i: aktivni filtri, neizrazita logika, harmonici, kvaliteta snageAUTHORS’ ADDRESSES:Antonio Dell'Aquila, ProfessorAgostino Lecci, PhD studentDipartimento di Elettrotecnica ed ElettronicaPolitecnico di BariVia E. Orabona 4, 70125 Bari, ItalyPhone: +39-080-5963.366/433 Fax: +39-080-5963.410dellaqui@poliba.it lecci@ieee.orghttp://dee.poliba.itReceived: 2003−11−14

Upravljanje strujom trofaznih paralelno spojenih aktivnih filtara s četiri vodiča

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