A New Control Approach to Three Phase Active Filter for Harmonics

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					IEEE Transactions on Power Systems, Vol. 13, No. 1, February 1998                                                                        133

                        A New Control Approach to Three-Phase Active Filter for
                            Harmonics and Reactive Power Compensation
                                  Bhim Singh                   Kamal Al-Haddad and Ambrish Chandra
                            Electrical Engg. Dept.                    GREPCI, Electrical Engg. Dept.
                        Indian Institute of Technology                Ecole de technologie supeiieure
                           Hauz Khas, New Delhi                   4750, av. Henri-Julien, Montreal (Quebec)
                                110016 INDIA                                H2T2C8 CANADA

  ABSTRACT — This paper deals with a new control scheme for                    The results of simulation study of the new AF control
  a parallel 3-phase active filter to eliminate harmonics and to          strategy are presented in this paper. The study is based on a
  compensate the reactive power of the non-linear loads. A 3-phase        3-wire 3-phase system. The familiar 3-phase uncontrolled
  voltage source inverter bridge with a dc bus capacitor is used as       rectifier with capacitive loading is taken as a non-linear load.
  an active filter (AF). A hysteresis based carrierless PWM               The steady state and transient performance of the proposed
  current control is employed to derive the switching signals to the      control scheme is found quite satisfactory to eliminate the
  AF. Source reference currents are derived using load currents,          harmonics and reactive power components from utility
  dc bus voltage and source voltage. The command currents of the
  AF are derived using source reference and load currents. A 3-           currents.
  phase diode rectifier with capacitive loading is employed as the
  non-linear load. The AF is found effective to meet IEEE-519                           II. SYSTEM CONFIGURATION AND
  standard recommendations on harmonics level.                                                  CONTROL SCHEME

                       I. INTRODUCTION                                         The basic building blocks of the conventional parallel AF
                                                                          are shown in Fig. 1. The AF is composed of a standard
       Solid state power converters are widely used in                    3-phase voltage source inverter bridge with a dc bus capacitor
  applications such as adjustable speed drives (ASD), static              to provide an effective current control. A hysteresis based
  power supplies and asynchronous ac-dc links in wind and                 carrierless PWM current control is employed to give fast
  wave generating systems. These power converters behave as               response of the AF. The non-linear load is a dc resistive load
  non-linear loads to ac mains and inject harmonics and result            supplied by 3-phase uncontrolled bridge rectifier with an
  in lower power-factor and efficiency of the power system.               input impedance and dc capacitor on the output. Due to
  Conventionally, passive filters were the choice for the                 capacitive loading the uncontrolled bridge rectifier draws non
  elimination of harmonics and to improve power-factor. These             sinusoidal pulsating currents from ac source. Depending upon
  passive filters have the disadvantages of large size, resonance,        the load magnitude and its parameters it also draws reactive
  and fixed compensation. In the last couple of decades, the              power from the mains. The basic function of the proposed
  concept of active filters (AF) has been introduced and many             parallel AF is to eliminate harmonics and meet the reactive
  publications have appeared on this subject [1-16]. Several              power requirements of the load locally so that the ac supply
  approaches, such as, hybrid filters and multistep inverters are         feeds only the sinusoidal balanced unity power factor
  reported to reduce the size of active filters [16]. Many control        currents. The desired AF currents are estimated by sensing
  concepts, such as instantaneous power theory [5, 10, 11, 16],           the load current, dc bus voltage, and source voltage. The
  notch filters [14], and flux based controllers [15] have also           hysteresis current controller generates the switching signals to
  been introduced. Most of these control schemes require                  AF devices to force the desired currents into the AF phases.
  various transformations and are difficult to implement. This            With this control feature, the AF meets harmonic and reactive
  paper presents a simple algorithm to achieve the control for            current requirements of the load. The AF connected in shunt
  AF. In AF, the main objective is to maintain sinusoidal unity           with the load, also enhances the system efficiency as the
  power-factor supply currents (by shunt AF) to feed active               source does not process harmonic and reactive power.
  power to the load and to meet the losses in the AF. These two
  components of active power can be computed from load                                                 R S ,L S
  currents, dc bus voltage and supply voltages.                                  s

       From the measured active power required by the system,
                                                                            AC Source     u                          onlinear
                                                                                                                                %3 K
  reference unity power-factor supply currents are derived. By                                                       Load
  subtracting load currents from these reference supply
  currents, compensating currents of the AF phases are
  obtained.                                                                                          Active Filter

  PE-155-PWRS-0-04-1997 A paper recommended and approved by                                     dc
  the IEEE Power System Engineering Committee of the IEEE Power                           DC bus
  Engineering Society for publication in the IEEE Transactions on Power
  Systems. Manuscript submitted July 10, 1SS6; made available for              Fig. I Basic Building Block of the Active Filter
  printing April 11,1997.

       Fig. 2 shows the proposed control scheme of the shunt            and i cc ) to obtain the gating signals to the devices of the AF.
  AF. The ac source feeds fundamental active power                      The devices of the AF are considered ideal. The value of AF
  component of load currents and another fundamental                    inductance (Lc) is selected on the basis of proper shaping of
  component of current to maintain the average capacitor                compensating currents.            With higher value of L c ,
  voltage to a desired value. This later component of source            compensating currents do not track reference currents and if a
  current is to feed the losses in the converter such as switching      lower value of Lc is chosen, there are large ripple in
  loss, ohmic loss, capacitor leakage loss, etc. in the steady state    compensating currents. The AF meets the requirements of
  and to maintain the stored energy on the dc bus during                harmonic and reactive components of load currents locally,
  transients conditions such as sudden fluctuations of load etc.        resulting in sinusoidal unity power factor source currents
  This component of source current (I sm d) is computed using           under varying operating conditions of the system.
  dc bus capacitor value (Cdc)> average voltage on dc bus (V(jca)
                                                                                    i n . ANALYSIS AND MODELING
  and a chosen reference voltage of the dc bus (V(jc). The
  fundamental active power component of the load currents                    The system comprises of ac source, non-linear load, the
   (I s m p ) is computed using sensed load currents and voltages.      AF and the new control scheme. The components of the
                                                                        system are analyzed separately and integrated to develop the
  The total reference source peak current (I s m ) is computed          complete model for the simulation.
                         *            *
  using components Ismcj and I s m p.           The reference           A. Control Scheme
  instantaneous source currents (i sa , i s b and i s c ) are
                                                                        The operation of the control scheme has been explained in the
  computed using their peak value (I sm )and unit current               previous section. The governing equations for the different
  templates (u sa , usb and u sc ) derived from sensed source           blocks are deduced in sequence.
  voltages. The command currents of the AF
                                                                        Peak Source Current Estimation
   (i c a , i c b and i c c ) are computed by taking the difference
  between instantaneous source reference currents
                                                                            The peak source current (I s m ) has two components
   (i sa , i s b and i s c )     and   sensed    load     currents
                                                                        estimated as follows. The source active component
   (iLa> ^Lb a n d ijLc)- The hysteresis rule based carrierless
                                                                        corresponding to the load (I s m p ) is computed from the
  PWM current controller is employed over the reference AF
                                                                        average load power (ps). The instantaneous power PL is,
  currents (i c a , i^ and i c c ) and sensed AF currents (i ca , iCD

                                                                                                 v        v
                                                                                   I         >       sb   sc

                               Compute Source Current                                     Compute Source
                             Component to Recover Energy                                 Reference Currents
                                  Storage on dc Bus

                                                                                         Compute Command
                              Compute Source Active Component                              AF Currents
                                 of Current using Averaged of
                               Instantaneous Active Load Power .
                                  over Regular Pulse Interval
                                                                                         Hysteresis Based

                        L .
                                           I,, t.
                                    ._Isi_Isi_Jsi                            1
                                                                                         Current Controller

                                                    Fig. 2 Control Scheme of the AF

               PL = vsa 'La + vsb *Lb + v s                 (1)             The total peak source current from equations (3) and (5)
     Here, iL a , i n , and iLc a r e three phase sensed load
currents and v sa , vsb and v sc are the sensed 3-phase source                                           ~ Ismp                        (6)
voltages and under ideal conditions these can be expressed as
                                                                     Source Reference Currents Generation
                             v sa = V sm sin cot
                    vsb = V s m sin (cot - 2TI/3)           (2)          Harmonic free unity power-factor, 3-phase source
                      vSc = V sm sin (cot + 271/3)                   currents may be estimated using unit current templates in
                                                                     phase with source voltages and the computed peak values.
     In Eq. (2), V s m is the peak of source voltage and CO is the   The unit current templates are derived from equation (2) as :
frequency of the ac mains in rad/sec.
                                                                         sa=v S a/ v sm;   u S b=v s b/V s m ;    usc=vsc/Vsm          (7)
     If PL is averaged over one sixth the period of supply
frequency it results in ps which may be expressed as :                     The reference 3-phase source currents are estimated as :

                         P s =(3/2)V s m I s m p            (3)                               'sb    =                     u

    The peak fundamental unity power-factor source current           Reference AF Currents Generation
component II sm pj can be estimated using ps and V s m from               The 3-phase AF reference currents are estimated using
Eq. (3).                                                             the reference source currents in Eq. (8) and the sensed load
                                                                     currents as:
    The second component of source current (I sm d) is to
maintain the average voltage on the dc bus at a constant                                                             ice = isc ~ *Lc
value, overcoming the switching, ohmic and capacitor losses
                                                                     Hysteresis Based Current Controller
in the AF. The computation of I s m d is based on the
following logic. A reference dc bus average voltage (v dc ) is            The current controller decides the switching pattern of
assumed. By sampling the actual dc bus voltage the average           the AF devices. The switching logic is formulated as
(vdca) is computed over the one sixth period of supply               follows:
frequency (Tx). The energy difference corresponding to v d c ,
                                                                     If i c a < (i ca - hb) upper switch is OFF and lower switch is
and Vdca o v e r the Tx, is :
                                                                     If i c a > (i ca + hb) upper switch is ON and lower switch is
                = e dc - e dc = C dc [jv dc ) 2 -           (4)      OFF for leg 'a' (SA = 0).

                                                                         The switching functions SB and SC for phases b and c
     The AF attempts to draw this energy difference Aedcfrom         are determined similarly, using the corresponding reference
ac mains through unity power-factor current with a peak              and measured currents and the hysteresis band hb.
value of I s m d , over the same interval T x . This energy
relationship can be expressed as                                           The AF currents i ca , icb and icC are regulated to be in
                                                                     good agreement with the reference values iCa>icb and i c c .
                    Ae             V                        (5)
                         dc = I - sm "*                              B. Active Filter (AF)

                                                                          Three-phase ac source through the source inductances is
    From Eq. (5), I s m d is obtained. When V dc well
                                                                     the input to the AF (3-phase VSI bridge) and dc bus with a
chosen, under steady state operation v d c a will never become       capacitor (Cdc) is its output. The AF operating in the current
equal to v d c but I sm( j will established to a fixed value as      controlled mode is modeled by the following differential
demanded by the losses in the AF. Under transient condition,         equations:
I s m d will take either positive or negative value as demanded                       ! = - (Rc / Lc) i c a + (vSa - Vca^c   (10)
by the energy exchange between the AF and the load.                                        = - (Rc                  - vcb)/T-c      (11)

                    p i cc = - (Re / LG) i c c + (v sc - vcc)/Lc   (12)            IV. PERFORMANCE OF AF SYSTEM

                   P v d c = (ica SA + icb SB + i cc SC)/Cdc       (13)        Performance characteristics of the AF system with
                                                                          proposed control scheme are given in Figs. 3-5 illustrating the
      where p is the differential operator (d/dt). SA, SB and SC are      steady state and transient behavior at different loads. The
      the switching functions decided by the switching status of the      parameters of the system studied are given in the Appendix.
      AF devices. v ca , vc\, and v cc are the 3-phase PWM voltages            Fig. 3 shows the source voltage, 3-phase currents, load
      reflected on ac input side of the AF expressed in terms of the      current, AF current and dc bus voltage when an extra load of
      instantaneous dc bus voltage (V(jc) and switching functions         10 kW is added after two cycles. The source currents respond
                                                                          very quickly and settle to steady state value within a cycle.
      as:                                                                 The AF current increases almost instantaneously to feed the
                      v ca = (v d c /3)(2SA-SB-SC)
                                                                          increased load current demand by taking the energy
                     v c b-(vdc/3)(-SA + 2SB-SC)                   (14)   instantaneously from dc bus capacitor. DC bus capacitor
                                      (-SA- SB + 2SC)                     voltage recovers within a cycle. Source currents always
                                                                          remain sinusoidal and lower than the load currents. Load
      C. Nonlinear Load                                                   current changes from discontinuous to continuous from with
                                                                          increased load. The active power supplied from source
           A 3-phase uncontrolled diode bridge rectifier with input       changes from 8 kW to 18 kW. The sixth harmonic voltage
      impedance and capacitive-resistive loading is taken as a non-       ripple is observed in dc bus voltage and its magnitude varies
      linear load (Fig. 1). It has two operating modes based on the       well within 2 % of the reference value. Fig. 4 shows similar
      diode conduction state.                                             results as in Fig. 3 for sudden decrease of load. The active
                                                                          power supplied from source is decreased form 18 kW to 8
           When the diodes are conducting, the ac source (line-line       kW. Source currents settle to steady state value within a
      voltage) is connected to the load and the basic equations are :     cycle demoristrating the excellent transient response of the
                                                                          AF. DC bus voltage rises only to 481 V but reaches the
                         2 Rs id + 2 L s pid + VL = vs                    steady state value within a cycle. Load current changes from
                                                                          continuous to discontinuous form. Source currents remain
      which may be modified as :                                          always less than the load currents under all operating
                                                                          conditions. The AF meets the requirements of harmonic and
                        pid = (vs-v L -2R s i d )/(2L s )          (15)   reactive components of load current and maintains the source
                                                                          currents sinusoidal in transient and steady state conditions.
            The capacitor charging/discharging equation is :                   Fig. 5 shows the harmonic spectra of the load and the
                                                                          source currents at light (8 kW) and heavy (18 kW) load
                                                                   (16)   conditions. It may be observed from the harmonic spectra of
                                                                          Figs. 5(a) and 5(c) that the dominent harmonics in load
      where Rs and Ls are the resistance and inductance of the ac         currents are of order below 30th and the AF is found effective
      source. CL is the load capacitance on the dc side and VL is         to eliminate them. The THD of source current is reduced
      the instantaneous voltage across it. "id" is the current flowing    from 105 % to 2.07 % under light load (8 kW) and from 53 %
      from ac source through a diode pair to charge the capacitor         to 1.07 % during heavy load (18 kW). The AF is quite
      C L and IR is the resistive load current (VL/RTJ.                   effective to reduce the THD well below the specified 5 %
           "vs" is the ac source line voltage segment (vsab, vsba,        limit of standard IEEE-519.
       sbc> vscb> vsca or vsac) depending on which diode pair is               The performance of the proposed control algorithm of the
      conducting. Similarly the load currents in all the 3-phases of      AF is found to be excellent and the source current is
                                                                          practically sinusoidal and in phase with the source voltage.
      the ac source (iLa> iLb a n ( i iLc) a r e obtained using the       The fast response of the AF ensures that the AF is not
      magnitude of id and sign corresponding to conducting pairs of       overburdened during transient conditions. The voltage ripple
      diodes. When none of the pairs of diodes is conducting, id          is quite small in dc bus capacitor voltage and may be reduced
      and its derivative will be zero. However, charged capacitor         further by increasing the capacitor value. Surge in dc bus
      CL will be discharged through load resistor RL and equation         voltage is observed to be + 8 % during transients which may
      (16) will be modified accordingly.                                  be controlled by the design to a lower value but at the expense
           The set of first order differential equations (10), (11),      of increased value of source currents during transients.
      (12), (13), (15), and (16) along with other expressions define      However, this surge in dc bus voltage reduces with increased
      the dynamic model of the AF system. These equations are             value of bus capacitor.
      solved using fourth order Kunge-Kutta method in FORTRAN
      to analyze the dynamic and steady state performance of the                              V. CONCLUSIONS
      AF system. A standard FFT package is used to compute the
      harmonic spectrum and THD of the ac load and source                     This paper demonstrates the validation of a simpler
      currents.                                                           control approach for the parallel active power filter. The AF

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         Fig. 3 Performance of the AF System under Fig. 4 Performance of the AF System under
                Load Change from 8 kW to 18 kW            Load Change from 18 kW to 8 kW

is observed to eliminate the harmonic and reactive                                           VI. ACKNOWLEDGEMENTS
components of load current resulting in sinusoidal and unity
power-factor source currents. It is observed that the source                         The authors wish to thank Hydro-Quebec, the Natural
current remains below the load current even during transient                    Science and Engineering Research Council of Canada and
conditions. The AF enhances the system efficiency because                       FCAR for their financial support. The first author also wishes
the source need not process the harmonic and reactive power                     to thank to IIT, N. Delhi, India, for granting him long leave
demanded by the load. Experimental verification of the                          during the course of action of this work.
scheme based on the new concept is being performed and test
results will be reported in the future.                                                            VII. REFERENCES
                                                                                [1] H. Sasaki and T. Maichida, "A New Method to Eliminate
    30                            (a)                                    (c)
                                        60                                           AC Harmonic Currents by Magnetic Flux
                                                                                     Compensation-Considerations on Basic Design", IEEE
                                        340                                          Trans, on Power Apparatus and Systems, Vol. PAS-90,
                                                                                     No 5,1971, pp. 2009-2019.
                                        '20                                     [2] L. Gyugyi and E C . Strycula, "Active AC Power
                                                                                     Filters", IEEE-IAS Annual Meeting Record, 1976,
                                                                                     pp. 529-535.
                                   40               10     20      30     40
           10     20
                Order K
                                                         OrderK                 [3] A. Ametani, "Hamonic Reduction in Thyristor
                                                                         (d)         Converters by Harmonic Current Injection", IEEE
                                                                                     Trans, on Power Apparatus and Systems, Vol. PAS-95,
                                         40                                          No 2, March/April 1976, pp. 441-449.
                                                                                [4] N. Mohan, H.A. Peterson, W.F. Long, G.R. Dreifuerst
                                        "20                                          and J.J. Vithayathil, "Active Filters for AC Harmonic
                                                                                     Suppression", IEEE/PES Winter Meeting, 1977, pp.
                                                    10     20      30      40
           10     20       30      40
                Order K                                  Order K                 [5] H. Akagi, Y. Kanazawa and A. Nabae, "Instantaneous
                                                                                     Reactive Power Compensators Comprising Switching
Fig. 5 Harmonic Spectra of (a) Load Current; (b) Supply
       Current at 8 kW Load; (c) Load Current;                                       Devices without Energy Storage Components", IEEE
       (d) Supply current at 18 kW Load                                              Transactions on Industry Applications, Vol. IA-20, No.
                                                                                     3, May/June 1984, pp. 625-630.
      [6] C. Wong, N. Mohan, S.E. Wright and K.N. Mortensen,                            IX. BIOGRAPHIES
           "Feasibility Study of AC- and DC-Side Active Filters
           for HVDC Converter Terminals", IEEE Trans, on Power            Bhim Singh was born at Rahamapur, U.P. (India) in
           Delivery, Vol. 4, No 4, October 1989, pp. 2067-2075.      1956. He received his B.E. degree from University of
      [7] W.M. Grady, M.J. Samotyj and A.H. Noyola, "Survey          Roorkee, and M. Tech. and Ph.D. degrees from Indian
           of Active Power Line Conditioning Methodologies",         Institute of Technology, New-Delhi in 1977, 1979 and 1983,
           IEEE Trans, on Power Delivery, Vol. 5, No 3, July         respectively. In 1983 he joined as a Lecturer and
           1990, pp. 1536-1542.                                      subsequently became Reader in 1988 in Department of
      [8] W.M. Grady, M.J. Samotyj and A.H. Noyola,                  Electrical Engineering, University of Roorkee. In December,
           "Minimizing Network Harmonic Voltage Distortion           1990 he joined as an Assistant Professor in the Department of
           with an Active Power Line Conditioner", IEEE Trans.       Electrical Engineering at IIT, New-Delhi. Since February
           Power Delivery, Vol. 6, 1991, pp. 1690-1697.              1994 he is an Associate Professor at Indian Institute of
      [9] A.E. Emanuel and M. Yang, "On the Harmonic                 Technology, New-Delhi. His field of interest includes CAD,
           Compensation in Non Sinusoidal Systems", IEEE Trans,      power electronics, active filters, static VAR compensation,
           on Power Delivery, Vol. 8, No 1, January 1993, pp. 393-   analysis and digital control of electrical machines. He is a
           399.                                                      member of IE(I) and life member of ISTE, SSI and NIQR.
      [10] H. Akagi and H. Fujita, "A New Power Line conditioner
           for Harmonic Compensation in Power Systems", IEEE             Kamal Al-Haddad (S'82-M'88-SM'92) was born in
           Trans, on Power Delivery, Vol. 10, No 3, July 1995,       Beirut, Lebanon, in 1954. He received the B.Sc.A. and the
           pp. 1570-1575.                                            M.Sc.A. degrees from the Universite du Quebec a Trois-
      [11] M. Aredes and E.H. Watanabe, "New Control                 Rivieres, Canada, and the Ph.D. degree from the Institut
           Algorithms for Series and Shunt Three-Phase Four-Wire     National Polytechnique, Toulouse, France, in 1982,1984, and
           Active Power Filters", IEEE Trans, on Power Delivery,     1988, respectively.
           Vol. 10, No 3, July 1995, pp. 1649-1656.                      From June 1987 to June 1990, he has been a Professor at
      [12] N.R. Raju, S.S. Venkata, R.A. Kagawala and                the Engineering Department, University du Quebec, Trois-
           V.V. Sastry, "An Active Power Quality Conditioner for     Rivieres. In June 1990, he joined the teaching staff as a
           Reactive Power and Harmonics Compensation", IEEE-         professor of the Electrical Engineering Department of the
           PESC Conference Record, 1995, pp.209-214.                 Ecole de technologie superieure (Universite du Quebec) in
      [13] S. Saetieo, Rajech Devaraj and D.A. Torrey, "The          Montreal, Canada. His fields of interest are static power
           Design and Implementation of a Three-Phase Active         converters, harmonics and reactive power control, switch
           Power Filter Based on Sliding Mode Control", IEEE         mode and resonant converters, including the modeling,
           Transactions on Industry Applications, Vol. 31, No. 5,    control, and development of industrial prototypes for various
           September/October 1995, pp.993-1000.                      applications.
      [14] M. Rastogi, N. Mohan and, A.A. Edris, "Hybrid-Active          Dr. Al-Haddad is a member of the Order of Engineering
           Filtering of Harmonic Currents in Power Systems",         of Quebec and the Canadian Institute of Engineers.
           IEEE Transactions on Power Delivery, Vol. 10, No. 4,
           October 1995, pp. 1994-2000.                                  Ambrish Chandra was born in India in 1955. He
      [15] S. Bhattacharya, A. Veltman, D.M. Divan and R.D.          received the B.E. degree from the University of Roorkee,
           Lorenz, "Flux Based Active Filter Controller", IEEE-      India, the M. Tech. degree form I.I.T., New-Delhi, India, and
           IAS Annual Meeting Record, 1995, pp.2483-2491.            the Ph.D. degree from University of Calgary, Canada, in
      [16] H. Akagi, "New Trends in Active Filters for Improving     1977, 1980, and 1987, respectively.
           Power Quality", IEEE-PEDES Conference Record,                  He worked as a Lecturer and later as a Reader at
           January 1996, pp. 417-425.                                University of Roorkee. Presently he is working as a Professor
                                                                     in the Electrical Engineering Department at Ecole de
                          VIII. APPENDIX                             technologie superieure. His main research interests are self
                                                                     tuning control, FACTS and power systems control.
      Vs(rms/phase) = 127 V, F = 60 Hz, Rc = 0.1 ohm,
      L c = 0.3 mH, C L = 330 u.F, Rs = 0.01 ohm, L s = 0.25 mH,
      C d c = 1500 fiF.