1.a three-phase active power filter for harmonic

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A Three-phase Active Power Filter for Harmonicand Reactive Power CompensationBhim SinghDepar tmen t of Electrical Engg.Indian Ins t itute of Technology, Delhi

HanzKhas, N e w D e l h iAmbrish Chandra and Kainal Al-HaddadD e p a F m e n t of Electr ica l Engg. , GREPCIE cole de technologie s iupkieure4750, av. Henri-Julien, Monltrkal (Qukbec )110016 INDIA H2T2C8 CANADA

ABSTRACT - n this paper, a 3-phase active powerfilter ('AP F) s presented to eliminate harmonics and tocomp ensate the reactive power of an uncontrolled rectifierwith mpa citive loading taken as non-linear load. Ai? APFis realized using 3 -phase voltage source inverter (VSI)withdc bu s capacitor. Reference source currents are estimatedusing P-I control over ak bu s voltage and 3-phase riourcevoltages. Command currents of he APF are obtained withreference source currents and load currents. A hysteresisbased c arrierless PWM current control over the conzmandcurrents of the APF is used to derive gating signals to thedevice s of APF . Mod eling and perforrioancecharacteristics of an I 8 kW AP F to meet the IEEE-SI9standards are presented.I. Introduction

Solid state control of ac pow er using diodes, thyristorsand traics is widely used to feed controlled ac power tovariety of electrical loads such as adjustable speed drives(ASD ) and static power supplies. These electrical loadsemploying solid state controllers draw harmonic andreactive power components of current along with activepower component of current from ac mains and thus callednon-linear loads. These injected harmonics and reactivepower burden on ac source cause low efficiency, lowpower factor, poor utilization of distribution system,reduced life of other equipments, disturbance to otherconsumers and interference to communication networks.Conventionally passive L-C filters were employed toreduce harmonics and capacitors were used to improve thepowe r factor of the loads. But passive filters have thedemeiits of fixed compensation, large size and resonance.In last two d ecades, extensive efforts are made [l-IO] onthe development of active power filter (APF) to give aneffective solution for elimination of harmonics and reactivepower compensation of the ac mains.Many configurations of APF [l-101 have appeared inlast two decades such as hybrid filter [3,7, 91, multi PWMconverters based APF [2], shunt APF [SI and unifiedpower quality conditioners [6, 101. Many control conceptsare reported such as notch filter [lo], synchronousreference frame d-q theory [S-91 and theolry ofinstantaneous powers [4].This paper is also aimed to investigate a simple 3-phase shunt APF for react ive power and haimoniccompensation of the non-linear loads. The proposed APFshown in Figure 1 consists of 3-phase voltage sourceinverter (VSI) with dc bus capacitor. Reference source

currents are generated in phase with source voltage toprovide unity power factor of the source using P-Icontroller over voltage of ithe dc bus. APF commandcurrents are derived using estimated source currents andsensed load currents. A hysteresis carrierless PWM currentcontroller [SI is used to generate gating signals to th edevices of the APF using command currents and sensedcurrents of the APF. In response to these gating signals,APF impresses 3-phase PWM voltages to meet harmonicand reactive power components of load currents locallyand it results in unity power factor of the mains.H. System Description and Control Scheme

Figure 1shows the fundamental building block of theAPF. The APFconsists of standard 3-phase voltage sourceinverter (VSI) with a capacitor c d c on the dc bus. Thenon-linear load is a 3-phase diode bridge rectifier with aninput impedance (L, an d R:;)apacitive-resistive CL, Lload. It draws pulsating current from ac source rich inharmonic and reactive components along with activepower. The main objective of the use of A P F is toeliminate harmonics and 10 meet the reactive powerrequirements of the load. Thu s ac source feeds onlyfundamental active component balanced currents.

t2 I Loadq $ v ' o w e r Activeilter

Vd cDC bus

Figure 1 Fundamental Building Block of theActive Power Filter

Figure 2shows the control scheme of the APF. Peakmagnitude of source current (Iim) s estimated employingP-I (proportional-integral) vo ltage control using averagevoltage of the APF dc bus and its desired reference value.T he ins tan taneous re f fe rence s ource cu r ren t s(isa,isb and izc) are com puted using their peak value*

C C E C E ' 9 6 0-7803-3143 5 /96/$4.00 0 1996 IEEE

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(I:m) and unit curre nt temp lates (U,,,currents of the APF (ia,.izb

instantenous referenceused over referencethe gating pulses of the devices.

I I 1IIIIIII II II II II II II II II II II II II II II II II II IL--------- as,

' d c d AP F I,ACSourceACSource

Non-Linear Loadaigure 2 Control Schemeof the 4PFIII. Analysis and Modeling I

the behavior of the system.3.1 Control Scheme

~

sequence.

Estimation of Peak Source CurrentPeak value of the source current (I:,) is estimatedusing P-I voltage controller of the APF dc bus. The dcvoltage is sensed using a voltage sensor and averaged over

the one sixth period of ac source frequency. Th e averageddc bus voltage (vdc) is compared with its set referencevalue (v:,). The resu ltin g volt age erro r v ~ ( ~ )t nthsample instant is expressed as :

*'e(n) = Vdc(n)-Vdc(n)The output of the P-I voltage controller v ~ ( ~ )t the nthsampling instant is expressed as :

Vo(n) = vo(n-1)+ Kp {ve(n)- Ve(n- I ) 1+ KiVe(n) ( 2 )Where K, and Ki are proportional and integral gainconstants of the voltage controller. v0+1) a nd ~ ~ ( ~ - 1 )rethe output of voltage controller and voltage error at (n-1) thsampling instant. This output v ~ ( ~ )f the voltagecontroller is taken as peak value of source current (I;,).Estimation of Instantaneous Reference Source Currents

Harmonic free unity power factor, 3-phase sourcecurrents may be estimated using unit current templates inphase with source voltages and their peak values. The unitcurrent templates are derived as :

The 3-phase source voltages may be expressed as :vsa = V,, sin wtVsb = V,, sin (wt - 2 x/3)vs c =V,, sin (wt + 2 d 3 ) (4)

Where V,, is the peak value of source voltage and w is theac source frequency. The instantaneous reference sourcecurrents may be computed as :(5).* * . * * .* *'sa = Ism %a; 'sb = Is m %b; ls c = Ism

Computation of Reference APF CurrentsThe 3-Phase APF reference currents may be computed

and izc) and. *using reference source currents (isa,isbsensed load currents as :

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Hysteresis Current Co ntrollerThe current controller contributes the switchingpattenns to the devices of the APF. The switching logic isformulated as :- if ica c ii, - b) upper switch is OFF nd lower- if iCa7 (ir, +hb) upper switch is ON and lowerswitch is ON of the phase "a" leg of the AP F,

switch is OFF of phase "a" leg of the APF.Similarly other two-phases ("b" and "c" ) switches aremade ON and OF F based on current control. Where hb isthe width of the hysteresis band around the referencecurrents. In this fashion, the AP F currents (i,,, icb and icc)are regulated in close hysteresis band of their referencevalues (iEa,iEb and i;,).

3.2 State Space Equations of the APFTh e A P F is a 3-phase VSI having 3-phase ac sourcevoltages impressed through inductances on ac side (input)and a dc bus capacitor on its output. The APF is operatedin cunent controlled mode and modeled by the followingstate space equations :

Where p is the differential operator (d/dt). SA , SB and SCare the switching functions stating ON/OFF positions ofthe 3-phase legs of the APF devices. The vca, Vcb itnd vccare the 3-phase PWM voltages reflected on ac input side ofthe AP F may be expressed in terms of instantaneous dc busvoltage (Vdc) and switching function s of the APF as :

3.3 Non-Linear LoadA 3-phase diode bridge with input impedance andcapacitive-resistive loading on d c bus is a non-linear loadcommonly used in practice. It has two operating modesi.e. when diodes are in conducting or nonconducting states.When diodes are conducting, the ac source (line-linevoltage) is connected to the load and basic circuit

equations are as :2 R, id + 2 Lsp & i- VL = V,I

which may be m odified as :p id = (vsl - VL - 2 R, i&2 L,) (12)

The capacitive load charging; discharging equation is :p V L = (id - iR) /C L (13)

Where R, and Ls are the resistance and inductance of theinput impedance of diode rectifier. CL is the loadcapacitance on dc s ide and VL is the instantaneous voltageacross it. Current i d is the charging current flowing fromac source through diod e pair to the capacitor CL nd iR inthe resistive load current (VLR L).The vsl is the ac source line voltage segments (Vsab,.Vsbc, VSca, vsba Vscb and V depending upon which diodepair is conducting. The load currents in 3-phases off acsource (iLa, Lb and iLc) are achieved using the magnitudeof id and their signs are decided by the respectiveconducting diode pair. Mor eover, the angle of overlap(commutation mode) is also considered if id is continuousand accordingly segments of source voltages and loadcurrents are modified. When none of diode pair isconducting then id and its derivative are zero. However , thecharged capacitor CL will be discharged through loadresistor R L and equation (1 3) is m odified accordingly.The set of first order differential equations (7)-(10)and (12), (13) along with 'other expressions defines thedynamic model of the APF system. These equations aresolved using fourth order Runge-Kutta method to analyzethe transient and steady statle behavior of the APF system.A standard FFT package is used to compute harmonicspectrum and THD of the ac load and ac source currents.IV. Performance Characteristicsof the APF

Performance of the APF system is demonstratedthrough Figures 3-4. The essential parameters of thesystem are given in the Appendix. From these results, thefollowing observations a re made.

-200 - - - . - - A0 50 100 150 200IO 0h- 0

-1uu- ~0 50 I00 150 200

-1ooL----5000 50 100 150 200

1 ' -4000' 50 100 150 200Time (mSec)Figure 3 Performance of the APF System underLoad Change from 8 kW to 18 kWand 18 kW to 8 kW

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3 2 0240L0 10 20 30 40OrderK

0 10 20 30 40Order K

Figure4 Harmonic Spectrum of (a) Load Current;(b) Source Current at 18kW LoadFigure 3 shows source voltage (v,), load current (Il),3-phase supply current (Is), AP F current (I,) and d c busvoltage (v & ) for the addition of 10kW load (from 8 kW to18 kW) after two cycles and removal of part load (same 10kW) after seventh cycle. Three p hase source currents settle

to steady state values very quickly well within a cycleunder both conditions of load addition and removal. Loadcurrent increases and becomes continuous at addition ofload while it remains discontinuous at low values of load.AP F current is more p eaky at light load com pared to heavyload condition. It is because that it filters spikes of th eload current which are more pronounce at light load. DCbu s capacitor voltage dips to 405 V at load addition andrises to 495 V at load removal and settled down within acycle. These changes in dc bu s voltage are due to suddenexchange of energy by the APF current to meet abruptchange in load without m uch distorting the source currents.Source currents always remain less than load current in alloperating conditions.Figure 4 shows the harmonic spectrum of load andsource currents at heavy load (1 8 kW). It may be observedthat the harmonics are d rastically reduced in source currentcompared to load current. The THD of source is reducedto 3.62 % from 63.08 % of the load current which is wellbelow the specific limit of 5 % of standard IEEE-519.V. Conclusions

Performance of th e APF is observed quite satisfactoryand it reduces harmonics and reactive power componentsof load current resulting in sinusoidal and unity powerfactor source currents under transient and steady stateconditions. It is also observed that the source currentsremain always below load currents even during transientconditions. The APF is able to reduce THD of supplycurrent we ll below 5 % and meets IEEE-5 19 standard.

VI. AcknowledgementsThe authors wish to thank H ydro-Qukbec, the NaturalSciences and Engineering Research Council of C anada andFCAR for their financial support. The first author also

wishes to thank to IIT, . elhi, India, for granting himlong leave during the course of action of this work.VII. References

H. Akag i , Y . K a n a z a w a a n d A . N a b a e ,"Ins tantaneous React ive Power CompensatorsComprising Switching Devices without EnergyStorage Components", IEEE Transactions on IndustryApplications, Vol. IA-20, No. 3 , May-June 1984,H. Akagi, A. Nabae and S. Atoh, "Co ntrol Strategy ofActive Power Filters using Multiple Voltage-SourcePWM Converters", IEEE Transactions on IndustryApplications, Vol. 22, No. 3, May-June 1986,pp. 460-465.F.Z. Peng, H. Akagi and A. Nabae, "CompensationCharacteristics of the Combined System of ShuntPassive and Series Active Filters", IEEE T ransactionson Industry Applications, Vol. LA-29, No. 1, Jan.-Feb. 1993, pp. 144-152.T. Furuhashi, S . Okuma and Y. Uchikawa, "A Studyon the Theory of Instantaneous Reactive Power",IEEE Transactions on Industrial Electronics, Vol. 37,No. 1, February 199 0, pp. 86-90.W.M. Grady, M.J. Samotyj and A.H.Noyola, "Surveyof Active Power Line Conditioning Methodologies",IEEE Transactions on Power Delivery, Vol. 5, No . 3,A. Van Zyl, J.H.R. Enslin, W.H. Steyn and R. Spee,"A New Unified Approach to Power Qual i tyManagem ent", IEEE-PESC C onference Record 1995,M . Rastogi, N. Mohan and A.A. Edris, "Hydrid-Active Filtering of Harmonic Currents in PowerSystems", IEEE Transactions on Power Delivery,Vol. 10,No. 4, October 1995 , pp. 1994-200 0.S. Bhattacharya, A. Veltman, D.M. Divan and R.D.Lorenz, "Flux Based A ctive Filter C ontroller", IEEE-IAS Ann ual Meeting Record, 1995, pp. 2483-2491.S. Bhattacharya and D. Divan, "Synchronous FrameBased Controller Implementation for a Hybrid SeriesActive Filter System", IEEE-IAS Annual MeetingRecord, 1995, pp. 2531-2540.

pp. 625-630.

July 1990 , pp. 1536- 1542.

pp. 183-188.

[IO] H. Akagi, * * N i w T rends in Active Filters forImproving Power Quality", EEE-P EDE S ConferenceRecord, 1996, pp. 417-425.VIII. AppendixV,(rms/phase) = 127 V, F = 60 Hz, R, = 0.1 ohms,L, = 0.3 mH, CL = 33 0 pF, Rs = 0.01 ohms, L, = 0.25 mH,Cdc= 3000 pF, K, = 0.76, Ki = 0.0067, RL = 5.0 ohms and15.0ohms.

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1.a three-phase active power filter for harmonic

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