An Active Power Filter Implemented With Pwm

8/9/2019 An Active Power Filter Implemented With Pwm

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A N ACTIVE POWER FILTER IMPLEME NTED WITH PWMVOLTAGE-SOURCE INVERTERS IN CASCADELuis Mori" Juan Dixon"

* Dept. of Elechical Engg.Universidad de ConcepcionConcepcibn - CHILEP.O. OX53-C

A B S T R A C TA three-phase active power filter implemented with two P W Mvoltage-source inverters Connected in cascade is presented andanalyzed in this paper. The active power filter is connected in parallelto the system and can Compensate the reactive power and theharmonic current compon ents of high power nonlinear loads. By usingtwo P W M voltage-source inverters in cascade, the compensationcharacteristics of the active powe r filter are significantly improved.The voltage-sour1.e inverter connected closer to the nonlinear loadcompensates the tactive power and the low frequency currentcomponents requi. '-v the nonlinear load, while the second inverter;ompensates only the high frequency current components. For thisreason the first PWh.1 inverter can be implemented with GTO'soperating at lower switching frequency while the second inverter canused IGBTs since it has to operate at higher switching frequency. In

panicular, this paper discusses the proposed scheme in terms ofprinciples of operation, and the analysis under transient and steadystate operating conditions. The computer simulation for the proposedactive power filter has been d one and the results show excellent staticand dynamic performances.I.- INTRODUCTION

With the proliferation of nonlinear loads, including the increasingnumber of static power converters and electric furnaces, fast actingpower filters will have to be considered as an essential component of apower distribution installation In recent years, active power filtershave been researched and developed to suppress harmonics generatedby static power conveners and large capacity nonlinear powerapparatus [I] Various power circuit configurations have beenproposed, and gradually beiny recognized as a viable solution to theproblems created by harm onic compon ents [2 ]The topology of the three-phase active power filter presented inthis paper is shown in Fig 1 It can compensate for displacement anddistortion power factor The proposed configuration is based on twothree-phase force-commutated pulse-width modulation voltage-sourceinverters (FWM-VSI) connected in parallel to the nonlinear load. Thetwo inverters are connected in cascade and operate with independentdc voltage and current control schemes The control system of eachPWh4-VSI consists of four modules, the current generalor circuit, thedc voltage control, the inverter output current control, and the gatingsignal generator. The current generator circuits uses the concept ofInstantaneous Reactive Power [3 ] to create the required referencesignals. The gating signals of each inverter are generated by using avector control techniques The proposed vector control techniqueallows to con trol the maximum switching frequency of each conve rter.Although there are a number of articles which deal with theanalysis of active power filters using force-commutated voltage-sourceinverters connected in parallel [ I ] - [ 6 ] . he three-phase active powerfilter proposed in this paper ditkrs from previously discussedapproaches in the following ways.Each PWh4 voltage-source invener operates with differentswitching frequency allowing the generation of specific currenta)

Sergio Muller' Rogel Wallace'* * Dept. of Elech ica l Engg.

Universidiid Catblica de ChileP.O. ox 306 Correo 22Santiago - Chileharmonic component of the load. In that way, the converterconnected closer to the load operates at lower switchingfrequency (650 Hz) and compensate the reactive power andthe low frequency current components required by the load.The second inverter operates at higher switching frequency (2kHz) and compensates the high frequency current harmoniccomponents that can not be generated by the first converter.Since the converter connected closer to the load will generatea higher rms cuiient and will operate at lower switchingfrequency, it can be implem ented with GTOs or fast thyristors,which can stand highest rms current. The second inverter canbe implemented Nith bipolar transistors or IGBT's since it willoperate at higher switching frequency bu t will generate a lowerrms current.Current control in each P W M nverter is achieved with almostconstant switching frequencyCurrent control is done in time domain allowing instantaneous

compensation characteristics.By connecting the two inverters in cascade a significantimprovement in the active power filter compensationcharacteristics is achieved since the second inverter willgenerate all the current harmonic that the first converter is notable to provide.Moreover, compared with active power filters using quad seriesPWh4 inverters [4]-[SI, the proposed topology requires less number ofconverters, a simple and conventional transformer, and a simplercontrol circuit and compared with active power filters implementedwith parallel converters [ 6 ] , he active power filter proposed in thispaper presents a be tter Com pensation performance since, by using anindependent control scheme. the second converter compensates thecurrent harmonics introduced by the low frequency PW M switchingpattern used in the first converter.The treatment presented in this paper includes a comprehensivesteady state and transient analysis of the proposed system. Specialemphasis is given tci the transient behavior of the active filter while it iscompensating a fluctuating non linear load Finally, the validity of theproposed schem e is confirmed by com puter simulation.

3 + WIM-VSI 0 1hee-Phasen o n h e a r L oad

L

Fig 1 The proposed active power filter configuration108

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II.- PRINCIPLESOF OPERATIONIt is well known that active power filters compensate currentsyste m distortion caused by non linear load s by injecting equa l-but-opposite current harmonic components at specific points of a powerdistribution system [2]. The active power filter compensationchrvrcteristics depend mainly on the control strategy. The controlsystem of each PWM inverter has to be able to generate the currentreference waveform, maintain the dc voltage constant, and has to8CIlente the inverter gating signals. The principle of operation of theactive power filter control system proposed in this paper is presented

in the next subsections.C a r l n ~ ignalaGenerator........................

r--.- . . . . . . . . . . . . . . . . . . . . . . . . . .I

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Dc Volrap ControlUnlturm( Refe- Generator

Fig. 2. The block diagram of the a ctive power filter control system.7he current reference generator circuit defines the compensationcharacteristics and accuracy of the active power filter. The referen cesignals are generated by using the Instantaneous Reactive PowerConcept (31 which allows a more flexibility in the active power filtercompensation performance. Depending upon the reference signalsused the active power fitter can compensate only the displacementpower factor, only current harmonics or both at the same time. Theinstantaneous reactive power concept also allows the generation of thereference signals required to control the d c voltage. Ac cording withthe Instantaneous Reactive Power Theory, the reference currentsexpressed in aq fl reference fiame are defined by the followingqua t i ons 131:

-v +*q+-4--q ,f v 1 Pac Va l + VB 1 dc Va l + V$Ic = $

where paf is the ac component of the active power p(t), q k and Q~are the dc and the ac com ponents of the reactive power q(t). The dccomponents are associated with the displacement power factorgenerated by the fundamental components, while the ac compo nentsof p(t) and q(t) are associated with the reactive power generated byharmonics. Since the proposed active power filter will compensate fordisplacement power factor and harmonic current distortionsimultaneously, the current reference waveforms must include theta m s multiplied by pm 9aCand qdc If

(3 )(4)

By replacing (3 ) and (4) in ( I ) and (2) and by changing fiom 04 fl to U.b. c, reference frame, the active power filter reference currents aredefined by:/ 1 O \

Equation ( 5 ) shows that in order to obtain the reference currents it isnecessary to calculate p' and 9'. The ac component of the activepower, pa,-, ca n be obtained by substracting the dc component, p bfrom the ins tantan eous activ e pow er p(t). This can be easily achievedby using a low pass second order filter. In order to reduce the timeresponse of this filter, normally it is tuned at 150 Hz.However, if lowfrequency power va riations are generated by the nonlinear load, thelow pass filter used t o gen erated p' do es not allow their compensation,thus the voltage source inverters will experience low frequency dcvoltag e fluctuatio n. This problem can be solved by using a low p mfilter tuned at a frequency lower than the fundam ental (see Fig. 3).

4-7Ziz-pilter (30Hz)Fig. 3. The block diagram of the power reference generator

J3) Dc Voltaee Control U uFigure I shows that each PWM voltage source inverter isconnected to a dc capacitor in the dc bus. Voltage control in the dcbu s isperformed by adjusting the small amount of real power a bsorbedby each con verte r. The real powe r flowing into each PWM voltage-source inverter depe nds on the amplitude of the fundamental currentcomponent in phase with t he respective phase to neutral voltage. From

( 5 ) t is found that the reference current of each phase contains a termin phase w ith the res pectiv e phase to neutral voltage, and with anamplitude proportional to Pavewhich is obtained from the Dc VoltageControl Unit (Fig 2) . By adjusting Pave. each inverter will abso rb thereal power required to cover the switching losses and to maintain thesteady state dc capacitor voltage constant.

s G e n e r m rThe generation of the converter gating signals depends on thecurrent control technique used in the P W M oltage-source inverter.The current control strategy plays an important role in active powerfilters. since it defines the converter switching frequency, the convertertime response, and the accuracy to follow the current references. Alsofor high powe r applications t is very important to operate the inverterwith a c ontro lled switching frequency, and with a high voltage gain.In this paper, current control is achieved by using a vector controltechn ique. The c urren t control used in this paper was proposed iq [7],and is not a predictive control but a feedback control, which hasproved to present a better performance for active power filter

applications.CurrentControl Techtiique

Cur rent contr ol is achieved by selecting the inverter outp ut voltag ethat will minimized the current error signal. This control techniq uedivides the or, fl reference frame in six regions (Fig. 4), and then109



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(6 )identifies in which region the current error ve ctor, Ai, is located andselec ts the inverter output volta ge that will fo rce the curr ent erro r tochange in an opposite direction, keeping the inverter output currentclose r to the reference signal. By selecting the inv erter outp ut Voltagethat presents the largest opposite direction compon ent to the currenterror a faster time respo nse in the current control loop is achieved.

diV(k) == L r Eowhere V(k) is the inverter output voltage, Eo is the phase to neutralsource voltage, L is the sy nchronou s inductor, and igen is the inverteroutput current. The current error vector, Ai is defined by theexpression:

Scni = i * - iBy replacing (7 ) in (6)

V(k) k=O k=l k= 2 k=3 k 4 k =5

dA i di*L--= L x EO - V(k)dtIf E = Ldi*/dt + Eo' then (8) becomes:

k=6 k=7

(9 )dA iFig. 4 . Hexagon for different region of inverter output voltage . L-;i ;= E - V(k)

7 1

Figure 5 shows the inverter equivalent circuit connected to loadarid the power system

3 5 0

RS Ls

Power System Lb 1T 2Vdc

a b cPW M VSIFig.5 The P\i'h,l voltage-source nverter equivalent circuit.

I n Table I, al l the possible switching comb inations of the inverteraie shown One or zero of the switching hn ctio ns Sa, Sb, and S,corresponds to the mode in which the upper side device or the lowerside device is on respectively For each switching combination theinverter output v oltage is defined in Table 11.Table 1

(Sa, Sb. S,) I 000 I 100 I 110 I010 I o 1 1 IO01 I 101 I 1 1 1 1Table I1 e

Equation (9) represents the active power filter state equation andshows that the wror current vector variations, dAildt, can becontrolled by selecting the appropiate inverter outp ut voltage vectorV(k).

The selection of the switch ing mode is defined by the reg ion inwhich the current error vecto r is located Figure 6 shows the sixregions defined by the inverter outp ut vo ltage vecto r, while Fig. 7illustrates the six regions defined by the in verte r outp ut cur rent vector.The tw o hexagones are phase-shifted by 30 degrees.a-?

Fig.6 . The hexagone defined by the inve rter outp ut voltage vector .a"

/ 4 \Fig 7 The hexagone defined by the inverter output current vector.

The selection of the inverters switching mode can be explainedassuming that E is located in Region I (Fig. 6) nd A i in Region 6 (Fig.7) The voltage vectors located closer to E are V , and V,. The vectorsE-V, and E-V, define two vectors L dAi/dt, located in regions 111 andIV respectively In order to reduce the error c urrent vector Ai, LdAddtmust be located in region I11 thus V(k) has to be equd to V ,. If thesame analysis is done for all the possible combinations, the inverterswitching modes for each location of Ai and E can be defined (Table111).

The equation that relates the active power filter voltages and currentsis :110



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Table Il lInverter Switching ModeE Ai Region I

VI v, v, v,-v, v,-v, v, V,Table 111 shows that the switching hnction is determined by theregion in which Ai and E are located. It is important to note that it isnot necessary to know the magnitude of the error current vector, thussimplifying the curr ent contro l circuit implementation. In case Ai needsto be changed faster it is necessary to determine which vector E-V(k )presents the higher component in the oppositve direction to Ai For theexample shown previously, E-V, repres ents the best solution (Fig. 8)

E.V,4

YV

Fig. 8. Representation of all possible E-V(k) vectorsTable IV shows the switching mode in case Ai becomes large intransient state and needs to be changed faster.

Table 1VSwitch M o d hrnges en Ai

Table 111shows the inverter switchiny modes when Ai experimentssmall changes and in Table IV the switching modes required when Aibecomes large in transient state are defined The control circuit mustbe able to identify the switching modes that will apply. For that arelationship is defined between the two references; that is h = a + 6,where a s some marginSwitching Frequency Co ntrol

Th e tw o hexagon that defines the switching modes characteristicsare shown in Fig. 9.

-

111

Fig. 9. Hexagons that defin es he switching criteriaIf Ai is located below the 6 region no commutation is applied tothe inverter. If Ai is located between 6 and h, the switching modesshown in Table 111 must be applied, and if Ai passes through the hhexagon, then the control system is switc:hed over to the faster loopand appli es the switching modes defined in Table IV . Once the currentcontr ol circuit has selected the region where V(k) must commutated, tverifies the time t h a t has passed since the last commutation, and then itcom pares with the switching frequency selected for the inv erter. If thetime is higher o r equal to 1/2fc a new switching function is applied tothe inverter semiconductors.Figure IO shows the block diagram o f theinverter current control schemeI ref

Evaluation of EI . . V Io commui~ i ionV(W Table IV

V(k)Fig. 11 . The block diagram of the current control scheme111.- SIMULATED RESULTS

The steady state and transient performance of the active powerfilter presented in this paper is proved by computer simulation. Thesteady state compensation characteristics of the active power filterwhile com pens ates a six step controlled rectifier are shown in Fig. 12.Specifically, Fig. 1 2 4 0 and 12-(g) show the line current and itsfrequency spectrum. The frequency spectrum is low and the linecurrent is in phase with the respective phase-to-neutral voltage. Thisproves the effectiveness for steady state compensation. Transientbehavior of the ac tive power filter is proved for the comp ensation of astep change in the gating signals of the controlled rectifier Simulatedwaveform s are illustrated in Fig 13 Figure 13-( c) shows that th e linecurrent is almost sinusoidal and remains in phase with the respectivephase to neutral voltage. Finally, in Fig. 14 the good compensationperformance of the active power filter while compensating a lowfrequ ency pow er load fluctuation is demonstrated. This figures showthe influence o f the low pass filter implemented to obtain the referencesignals Figu res 14-(b ) show that if the second order low pass filter istuned at 150 Hz the active powe r filter is not.able to compensate thispower fluctuation. This problem is solved by decreasing the resonantfrequency of the filter as shown in Fig. 14-(d)



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0.80. 6

p.uP.J0.2

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-' I- -____

- A A A ,'\ r., , . , , ~

10.8

. 0.6?0.40.2

0.40.2

p.u 04 2-0.4

__--n ,?0 6 r .j - - , \ I- I-,

0 0.02 0.04 006 0.09 0.1 0.12 0.14(4

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-1

0 0.02 0.W 0.06 0.08 0.1 0.12 0.14(b)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14(c )

Fig. 13. Simulated results for transient operating conditions. (a) Theload current. (b) The line current after the first inverter and therespective phase to neutral voltage. (c) Th e power system line currentand the phase t o neulral voltage.

-1.5 10 0.02 0.04 0.06 0.08 0.1 0.12 0.14(9

112



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An Active Power Filter Implemented With Pwm