design of apf 3

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Design and I mplementationof aNew T hree-phase Four-Wire Active PowerFilter with M inimum ComponentsA. Dastfan,D.Platt,V. J . Gosbell

School of Electrical, Computer and Telecommunication EngineeringUniversity of Wollongong, Northfields Ave., Wollongong

NSW 2500, AustraliaAbstract- This paper reports the development of a new three-phase four -wire active power fi lter which has no passive elementsand only has four bidi rectional switches. A new switchingtechnique based on three-dimensional vector treatment ofunbalanced three phase cir cuits is used for the control of theAPF. Experimental results from a prototype APF confirm thesuitabilityof the proposed approach not on ly for the removal ofharmonics, but also for the compensation of fundamentalunbalance currents and reactive power consumed by the load.The experimental results show that current Total Harmonic

Distortion(TH D) in each phase is reduced from 58% to less than5% which is acceptable by most harmonics standards. Theneutral current, including fundamental and harmonics, isreduced by a factor of 15.I. INTRODUCTION

In three-phase, four-wire systems, significant use ofelectronic equipment with diode rectifier and capacitor filterfront ends, such as Pc's, TV 's, high effici ency lighting and airconditioning, gives a high level of harmonic currents in boththe three line conductors and more significantly, in the neutralconductor [l , 21. Two major approaches to theimplementation of active filtering have been proposed in thepast. T he first uses three single-phase Active Power Fi lters(A PF ) and the second uses one three-phase, four wire inverter[3, 41. All of these proposed APF require substantial energystorage components and in the first case it requires a highnumber of switches.This paper presents a new A PF, not requiring any addedlarge passive elements. The switches alone are sufficient forAPF performance whenever there is sufficient upstreaminductance (eg from a supply transformer) and downstreamdiode rectifiers with capacitance, as is the case with the mostcommon type of nonlinear load. A new control algorithmbased on three-dimensional vector control has been used tocontrol the APF. Hardware implementation of a benchtopdesign of the A PF is described. This example has been chosento represent a scaled commercial building installation.Experimental results from the prototype A PF f or a balancedand unbalanced nonlinear load are presented to illustrate thecapabil ity of this system.

11. PROPOSED A PF TOPOLOGYND A SUMMA RY OFITSSWITCHING STATES OF OPERATIONS

Fig. 1 shows the basic circuit of a newly developed three-phase four-wire A PF [7]. The four switches are allbidirectional type, which can block or conduct in bothdirections. These switches can be implemented as shown inFig. 2. The nonlinear load includes single and three phasediode rectifiers with capacitor filter on the DC side. From Fig.1,the source voltage can be written as:

d .V =L, --I +vdtwhere L, is the upstream inductance which is mainly leakageinductance of the distribution transformer and:

In the three-phase four-wire system, the instantaneous a, p,and 0 transformation has been defined by Akagi et a1 [5] asfollows:

Fig. 1: Proposed three-phase four-wire APF schematic

P R

A b-'Fig. 2: Implementation of bidirectional switch

0-7803-4943-1/98/$10.000 1998 IEEE 1369


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-9V =T V

S =

where T , theap0 transformation matrix, is as follows:

- A - y -* J T( B - C )2

a=

In balanced three-phase systems, the trajectory of thevoltage vector in the ap plane is a circle. Therefore, if thesource current in c lPO coordinates is forced to follow a setcurrent which is in phase with source voltage defined in (2),the negative and zero sequence components wil l be removedfrom the source current [6].

By premultiplying both sides of (1) by the ~$0transformation matrix, T, the voltage vector can be found asfollows:d[ T V ] =L , -[TI]+ [ TV ' ]dt

Thus:-A

3 d i 2V =L ,-+vdtThe voltage vector across theAPF is equal to:1,-(V,+V)/2(v' , +v'h+v'm/ J z-(6 v -VIm )2

(4)

where v ' ~ , t,,,, and vIcnare the instantaneous phase voltagesacross the APF and have PWM waveforms. By consideringthe equivalent single-phase circuit of the system as shown inFig. 3, it can be seen that these voltages can have only threevalues:

Tt_lo* o. ! I .Fig. 3: Equivalent singlephasecircuit

ee vd c when the phase current is positive and thecorresponding switch is off,e -Vdc when the phase current is negative and thecorresponding switch isoff.

zero when the phase is switched to the neutral,

Therefore, v,=AV,(dc), v'bn=BVb(dc),nd V'cn=CVc(dc),,whereA , B, and C indicate the polarity of the load voltage ( v a n , V'bn,v'~,,) nd can be 0, 1, or -1. For the analysis presented here,equation (6) can be simplified by assuming that the DCvoltages (Va(dc),Vb(dc)rnd Vc(dc)) re equal. All componentsarealso assumed to be ideal. T hus (6)can be re-written as:

(7 )

-+us introduce the switching vector S as follows:

Furthermore it is assumed that the a,p, and 0 componentsare in the X, Y , and Z axis directions respectively. Thereforeswitching vector, s can be re-written as:3

( 9 )j=+(A--)+


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switching states, where one switch is on and three otherswitches are off, are equivalent to state 0 (no switching) andhave not been shown in this table. The following subsectionsshow a summary of the switching vectors for differentswitching states.

4 y

/ :-1 j v : I \ A 2 x7J r *(=T)A. Single Phase to Neutral Switching (States I , 2, and 5)There are 12 vectors corresponding to the single phaseswitching states. These vectors are of length and form two

hexagons in theX -Y plane as shown in Fig. 4. The numbers in4(a) shows the switching vectors when the load voltage in twoother phases have the same polarity. At any time only onevector from this group is available being the closest one to thevoltage vector, v . The second group, shown in Fig. 4(b),demonstrates the switching vectors in a single phase switchingwhen the load voltage in two other phases have oppositepolarity. From this group, at any time, only the two vectors

brackets show the value of components in the Z direction. Fig. - _ -Fig.5: Switching vectors for phase to phase switching (Z valuesgiven in brackets)+ closest to the voltage vector are available.

B. Phase to Phase Switching (States3,6,and8)There are six possible switching vectors of length 2t y

(0) ......................................... (0)@ x*_ -(0) ........................ 2 .............. (0)

(b)Fig.4: Single phase 3D switching vectors diagram with Zvaluesgiven In brackets: (a)twootherphase voltages have thesamepolanty (b) twoother phase voltages have opposite

polarity

corresponding to these three switching States, forming ahexagon in theX-Y plane as shown in Fig. 5 . At each momentthe three switching vectors available are those closest to thevoltage vector, v .By examination of equation (9) for State0, it can be shown that this State will reduce to one of thevectors shown in Fig. 5. Therefore, State 0 isnot consideredin any further analysis.

-+

C. Double Phase to Neutral Switching (States 4, 7,and9)There are six switching vectors corresponding to a doublephase to neutral switching. These vectors have the same

magnitude of 3 and form a hexagon in the X -Y plane asshown in Fig. 6. At any time, the three vectors closest to thesupply voltage vector areavailable.L

Fig.6: Switching vectors for doublephase to neutral switching( 2 alues given in brackets)

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Finally for the State10,three phases are connected to eachother (or to the neutral). Therefore, A= B= C= 0 and S isequal to zero and is located at the origin.

+

111. CONTROLLABILITY OF THE SOURCE CURRENTControl of the three-phase source currents can be achievedwhen the current vector follows the supply voltage vector,which in a balanced system is a circle ina@lane. In order tohave a full control, the current vector should be able to movein any direction which may be done by selecting acombination of the available switching vectors. From (5), the

current vector changes, df , s:--f +-+ dtd i = ( v - S Vdc)-L ,

where Vdc, dt and L , are average dc voltage, sampling timeand supply inductance respectively. Fig. 7 shows an exampleof ten possible current change vectors, d i , where voltagevector is in the Region 3. These vectors are calculated from(lo), and by applying ten possible switching vectors whichhave been explained in the previous section. The direction ofthe d t n the zero axisaregiven in the brackets.

+

T ,It isclear from this figure that d 1 can be constructed in alldirections by selecting a proper combination of switchingvectors. Therefore full control of the source current vector isachievable. However, if the DC voltage in nonlinear load isless than the maximum phase voltage, in some part of thecycle d i cannot be constructed in all directions. Thus thecondition for full controllabil ity of the source current vector isthat the DC voltage of the single-phase diode rectifiers, shouldbe at leat equal to the maximum of the phase voltage (eg340V in Australia), and the DC voltage of the three phase diode

--f

-?Fig. 7: Possible current vector changes (d 1 ) for 10available switching vectors (Z direction shown inbrackets)

rectifier should be at least equal to the maximum of the line-to-line voltage (eg 586V in Australia).IV. CONTROL ETHODOLOGY

The function of the controller is to force the current vectorto follow, as closely as possible, the reference current vector.The proposed control algorithm isbased on a switching vectorselection procedure.After sampling three source currents and by using theas0

transformation, the current vector ( i ) can be calculated. Inorder to find the voltage vector ( v ), it is assumed that theload is supplied by a three-phase balanced sinusoidal voltage.Thus:

++

V," +Vb" +v,, =0 ( 1 1)By measuring two phase voltages and using (2) the sourcevoltage vector components can be found:

1v - - (va" + V b " +v,,)=O."&The basic structure of the three-phase four-wire APFcontroller is shown in Fig. 8. The DC voltage on the dioderectifier loads is controlled by the amplitude of reference

current vector, i' . Detail of the DC voltage controller isshown in Fig. 9.

-+

A traditional integrator controller isused in order to controlthe DC voltage. The DC voltage is kept constant by adjustingthe amplitudeof the reference current vector ( i* ). In order to+

"dCAP F

Fig. 8: The basic structure of the controller

Fig. 9: The DC voltage controller details

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have unity power factor, and with the assumption that thesource voltages are balanced and sinusoidal, the referencecurrent vector is:T ? +1 =pv

A. Power CircuitThe power circuit is composed of a three phase four wirepower source, three series inductances, the nonlinear load andthe APF circuit. T he nonlinear load isa combination of single

and three phase diode rectifiers with capacitors on the DCside. A 220 Q resistor bank is connected as a DC load forcapacitors have been used which limit the maximum ripple ofvoltage on the DC si de to less than 5%.

(13)where is Once each Of the DC each rectifier, single and three-phase. 1100 pF electrolytic-+voltage controller. The desired switching vector ( s ,, can becalculated from equations (5)as follows:

1 1 JA P F

-+-+ 4 d idt,J ( v -L , - )I V ,

v t l JVoltage V ector currentector SwitchingSta teCalculation Calculation

-3 #V

Optimum CvrrentVector SetpointCalculationA

The power source has an impedance dominated by itsinductive components. The greatest contribution comes fromthe distribution transformers leakage inductance which is(14)

~, dc

-+. typically 510% in per unit system for a 50Hz power system.For the prototype circuit the following parameters have beenused:where Vdc is the measured DC voltage and d i is a smallchange in the current vector which is desired to be equal to:

(15) 1pu VA =2500 VA-+where i is the measured source current vector. The nextstep is to choose the available switching vector closest to thedesired switching vector, S d . Then this switching vector isapplied for the time interval dt, after which the process isrepeated. The operational principle of the proposed three-dimensional vector control scheme is illustrated by the blockdiagram shown in Fig. 10.

-+

V. HARDWAREESIGNIn this section a detailed design of a 2.5 kW laboratoryprototype of the proposed three-phase four wire APF ispresented. The load is acombination of single and three phasenonlinear loads.

1pu voltage=415V (li ne to line voltage)1pu current =3.48 A1pu impedance =69R1 pu inductance=220 mHDue to some software and hardware limitations, themaximum switching frequency which could be achieved forthe present set-up is7.5 kHz. To limit the source current THDto approximately 5%and by referring to [8], the value of thesource inductance should be at least 0.125 pu. Therefore thevalue of the line inductance should be at least:Ls=12.5% of 220 mH =27.5 mHThree 30 mH inductances have been used in thisexperimental set-up.

1 Nonlinear B. DSP controller and Associated Hardware1 Load ITo achieve real time operation of the proposed APF, aDigital Signal Processor (DSP) board has been used. Threephase source currents, two source voltages and aDC voltageare the six analogue signals which are fed into the DSP board.

VI. EXPERIMENTALESULTSThis section presents the experimental results of theproposed three-phase four-wi re APF with different loadcombinations. All tests have been done with the switchingfrequency of 7.5 kHz and DC voltage reference of 330V. Ineach subsection, experimental and simulation results arecompared.

Fig. 10: Proposed3-D vector control scheme

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A. Balanced Nonlinear Load * TIn this part a load which is a combination of a three-phaseand three single-phase diode rectifiers is considered as abalanced nonlinear load. Fig. 11 shows the phase and neutralcurrent waveforms before and after using the APF. Fig. 12shows the harmonic spectrum of the 'a' phase current beforeand after using the APF. The average THCD for the phasecurrents before using the APF is 63% for the first 50harmonics, while after using the A PF i t has been reduced to4.75%.The RMS neutral current is also reduced from 6.2 Ato 0.4 A after using the APF which means a reduction by afactor of 15.5. These values confirm the great reduction ofphase and neutral current harmonics due to the use of theAPF.A lthough it was expected that the fundamental componentof the phase current would reduce as a result of power factorcorrection, it is slightly increased after using the APF. T hedif ference is mainly due to the increase of the DC voltage and

also to losses related to the APF switches and power diodes.Fig. 13 shows source voltages and currents in a and pcoordinates which are drawn by using data downloaded bymeans of the DSP. From these figures it is clear that thesource voltages are not purely sinusoidal. T he current vector

PM3384.FLUKE8 PHIUPS

(b)Fig. 11: Phase andneutral currents for balanced load (a) beforeand ( b) after using theAPF (10A/div &5 ms/dlv)

.-4LL---,S T(b)

Fig. 12: Harmonic spectrums of 'a' phase current (a) before and(b)after using the APFis also in phase with the voltage vector after using the APF ,showing that unity power factor has been achieved.

The average measured DC voltages of the single phasediode rectifiers before using the APF was 318V and for thethree-phase diode rectif iers it was 548 V. The A PF hasincreased these DC voltages have been increased to 330V forthe single phase diode rectifiers and 570V for the three-phasediode rectifier.B. Unbalanced Nonlinear Load

For this part, the 'b' phase diode rectif ier has been

0 001 002 003T im 1Sec.l(a)

0 001 002 003TimetSn )(b)

Fig. 13: a and p components of the source voltage and currentvectors (a)beforeand (b) after using the APF

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disconnected to make the nonlinear load unbalanced. Fig. 14(a) presents the source phase and neutral currents and Fig. 15(a) is the frequency spectrum of these currents. As can be seenfrom this figure the neutral current consists of the fundamentaland triplen harmonics, with the 31dbeing dominant.Fig. 14(b) shows the APF performance for this unbalancedload where three phase currents are well balanced and theneutral current has been significantly reduced which can beseen in Fig. 15(b). The average current THD of the threephase currents has been reduced from 71% before using theAPF to 5.4% after using the APF. The neutral current RM Svalue is also reduced from 4.9 A to 250 mA which is areduction factor of about 20 times. Due to the boost action ofthis circuit and the voltage set point being 330 V, the averageDC voltage has been increased from 320 to 330 V which isabout a3% increases. This results in a7% increase in outputpower, since the load is resistive.The average fundamental current for the three phases after

using the APF is slightly higher than the average fundamentalcurrents before compensation. T his is consistent with anincrease in the real power drawn to account for the higheroutput power and also some losses in theAPF.

. . : L~ ; ,e ; ; ; I."L; I ~

00 500 1000 1500 2000 2500

00 500 1000 1500 2000 2500

00 500 1000 I S00 2000 2500

* T

0 so0 1000 1500 2000 2500Frequency ( Hz)(a)

* T

0 500 1000 1500 2000 2500

0 050 0 1000 1500 2000 2500

8 1

0 500 1000 1500 2000 2500.q,-- ; - ; -~ ; 'I0

0 500 1000 1500 2000 2500Frequency (Hz)(b)

Fig. 15: Harmonic spectrums of the phase and neutral currents inunbalanced load condition (a)before and (b) after using the APF( b)

Fig. 14: Three phase and neutral currents for unbalanced loadcondition (a)before and (b) after using the APF (10Ndiv & 5msldiv)

VII. CONCLUSIONSThe work presented in this chapter describes theimplementation of a 2.5 kVA, 415V three-phase four-wire

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A PF controlled by three-dimensional control methodology.Hardware requirement of the benchtop design are explainedand the experimental results of the proposed APF for differentnonlinear load conditions are presented.

[4]

151he results show that the proposed APF and its controlsystem is able to reduce the harmonic contents of the sourcecurrent and reduce the current TH D to around 5% whichmeets IEEE-5 19 standard requirement. The experimentalresults for unbalanced nonlinear load also showed that thisAPF can compensate the unbalanced current and reduce theneutral current by a factor of 20. It is also shown that the APFcan achieve unity power factor. [6]

VIII. REFERENCES[71Gruzs T. M ., A Survey of Neutral Current in Three-Phase Power Systems, IEEE Transaction on IndustryApplications, Vol. 26, No. 4, 1990, pp. 719-725.

L iew A ., Excessive Neutral Current in Three-phaseFluorescent L ighting Circuits, IEEE Transactions onIndustry Applications, V ol. 25, No. 4, pp. 776-782,1989.Quinn C. A., Mohan N., Mehta H., A Four-Wire,Current-Controlled Converter Provides HarmonicNeutralisation in Three-phase, Four-Wire Systems,IEEE APEC93, pp. 841-846, 1993.

P

Sutanto D., Bou-Rabee M., Tam K . S., Chang C. S.,Harmonic Filters for Industrial Power Systems, IEEInternational Conference on advances power systemcontrol, operation and management, Hong K ong, pp.Akagi H., K anazawa Y ., Nabae A., I nstantaneousReactive Power Compensator Comprising SwitchingDevices Without Energy Storage Components, IEEETransaction on Industry Applications, Vol. IA -20, No. 3,Watanabe E. H., and Stephan R. M., New Concept ofInstantaneous Active and Reactive Power in E lectricalSystems with Generic Loads, I EEE Transactions OnPower Delivery, Vol. 8, No. 2, pp. 697-703, 1993.Dastfan A., Platt D., V . J. Gosbell, Control of Three-Phase, Four-Wire Active Power Fil ter Using Three-Dimensional Vector Control, in Proc. of A ustralianUniversities Power Engineering Conference(AUPEC96), Melbourne, Australia, p. 223-228, 1996.Dastfan A., Active power fil ter with minimumcomponents, PhD Thesis, University of Wollongong,1998.

594-598, 1991.

1984, pp. 625-630.

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