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 . 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 , and flux based controllers  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. 134 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 ii_tiJLi_^tisg_s Fig. 2 Control Scheme of the AF 135 PL = vsa 'La + vsb *Lb + v s (1) The total peak source current from equations (3) and (5) is: 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. u 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 sc 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 : ONforleg'a'(SA=l). 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) 136 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. v 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 137 SO 100 200 I 0| VwVwVw -200 VVVWSv -200 100 100 so 100 I -100 50 100 100 -100 50 100 500 £450 vwwwwwii Mmmmmim 400 400 50 50 100 100 Time (mSec) Time (mSec) 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  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 "20 340 Trans, on Power Apparatus and Systems, Vol. PAS-90, No 5,1971, pp. 2009-2019. '20  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 30 OrderK  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.  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 40 168-174. 10 20 30 40 Order K Order K  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. 138  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  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  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  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.  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-  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  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  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.  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  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  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.