experimental design of a nonlinear control technique for three-phase shunt active power filter

7/31/2019 Experimental Design of a Nonlinear Control Technique for Three-Phase Shunt Active Power Filter

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3364 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 10, OCTOBER

Experimental Design of a Nonlinear ControlTechnique for Three-Phase Shunt Active Power Fi

Salem Rahmani,Member, IEEE , Nassar Mendalek,Member, IEEE , and Kamal Al-Haddad,Fellow, IEEE

Abstract This paper presents a nonlinear control techniquefor a three-phase shunt active power lter (SAPF). The methodprovides compensation for reactive, unbalanced, and harmonicload current components. A proportionalintegral (PI) control lawis derived through linearization of the inherently nonlinear SAPFsystem model, so that the tasks of current control dynamics anddc capacitor voltage dynamics become decoupled. This decouplingallows us to control the SAPF output currents and the dc bus volt-age independently of each other, thereby providing either one of these decoupled subsystems a dynamic response that signicantlyslower than that of the other. To overcome the drawbacks of theconventional method, a computational control delay compensation

method, which delaylessly and accurately generates the SAPFreference currents, is proposed. The rst step is to extract theSAPF reference currents from the sensed nonlinear load currentsby applying the synchronous reference frame method, where athree-phase diode bridge rectier with R L load is taken as thenonlinear load, and then, the reference currents are modied,so that the delay will be compensated. The converter, which iscontrolled by the described control strategy, guarantees balancedoverall supply currents, unity displacement power factor, andreduced harmonic load currents in the common coupling point.Various simulation and experimental results demonstrate the highperformance of the nonlinear controller.

Index Terms Active power lter, control delay compensa-tion, modeling, nonactive load current compensation, nonlinearcontrol, power quality.

I. INTRODUCTION

H ARMONICS are typically caused by the use of non-linear loads, such as switch-mode power converters,power-electronics-operated adjustable-speed drives, uorescentlamps, arc furnaces, welding equipment, and other nonlinearloads used in both domestic and industrial applications. Thepresence of harmonics in the system results in several effects(including increased heating losses in transformers, motors,and lines; low power factor; torque pulsation in motors; andpoor utilization of distribution wiring and plant). In responseto the power quality concerns of typical power distribution sys-tems in terms of harmonic current distortion and power factor,

Manuscript received April 28, 2008; revised January 28, 2009, May 29,2009, and September 2, 2009; acccepted December 2, 2009. Date of publicationJanuary 8, 2010; date of current version September 10, 2010. This workwas supported by Canada Research Chair in Energy Conversion and PowerElectronics at the cole de Technologie Suprieure.

S. Rahmani and K. Al-Haddad are with the cole de TechnologieSuprieure, University of Qubec, Montreal, QC H3C 1K3, Canada (e-mail:[email protected]; [email protected]).

N. Mendalek is with the Department of Electrical, Computer and Com-munication Engineering, Notre Dame University, Louaize, Lebanon (e-mail:[email protected]).

Color versions of one or more of the gures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identier 10.1109/TIE.2009.2038945

IEEE 519 and IEC EN 61000-3 standards specify regulatiogoverning harmonic compliance. A passive lter has beenviable approach because of low cost and high efciency. However, the performance of the passive scheme has a limitatiosince the addition of the passive lter interfaces with thsystem impedance and causes resonance with other networ[1], [2]. Numerous active solutions, which are becoming a moeffective means to meet the harmonic standards by overcomithe drawback of the passive lter, have been proposed [3][1The SAPF operates by injecting the reactive, unbalanced, an

harmonic load current components into the utility system wthe same magnitudes as the nonactive load currents demandby a given nonlinear load but with opposite phases [11][15Among the subjects related to the active lters design anapplications, the methods for extraction of the harmonic locurrents and determination of the lter reference current plan important and crucial role. Indeed, the accuracy and speof the SAPF response are related to this point [16], [17The methods of reference current generation are categorizinto two main elds: 1) time-domain and 2) frequencdomain methods [11][17]. Time-domain methods such adq transformation (or synchronous rotating reference frame pq transformation (or instantaneous reactive power), symmerical components transformation, etc., are based on the mesurements and transformation of three-phase quantities [12The main advantage of these time-domain control methodcompared with the frequency-domain methods, based on tfast Fourier transformation is the fast response obtained. On tother side, frequency-domain methods provide accurate indvidual and multiple harmonic load current detection. The compensation method presented in this paper is the time-domacontrol type of compensation, where all harmonic load currecomponents are targeted and compensated. An SAPF offers dferent options of compensation, such as harmonic attenuatioload balancing, resonance elimination, and displacement pow

factor improvement [1], [9]. Thus, the control strategy and tmethod for extracting the nonactive load current references wdepend on the compensation objectives [11][17].

Although conventional linear controllers may fulll certacompromises between steady-state performance, and harmonload current compensation and dc bus voltage regulation, thremain unable to compensate the inherent nonlinearity of sucircuits, which is generated by the switching process. Thmanifests with important overshoots and long settling timeduring transients from both the ac or dc side [2], [11], [12[15]. On the other hand, most of the techniques mentioned the literature assume sinusoidal supply voltages when compesating unbalanced nonlinear load currents [3], [12]. Howeve

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RAHMANIet al. : EXPERIMENTAL DESIGN OF NONLINEAR CONTROL TECHNIQUE FOR THREE-PHASE SAPF

in reality, the utility voltage available at the downstream end isnonsinusoidal due to the harmonic load currents. A thoroughinvestigation of the experimental results reported in [2], [8],and [16], reveals that the total harmonic distortion (THD) in thesupply currents cannot be brought down below 5% to satisfythe IEEE-519 standard. This is due to the presence of notches in

the supply currents, whereas feedforward control methods areused. The drawbacks can be eliminated by using the nonlinearcontrol theory, ideally without exaggerating computational andimplementation complexities. In addition, Youssef et al. [18]and Yacoubiet al. [19], [20] implemented very useful advancednonlinear control techniques to active rectiers with activeltering function. These control techniques can be applied toactive ltering technology. In [21], a nonlinear control strategyof an SAPF based on the internal model principle is proposed.The stabilization of the dc-link voltage dynamics is addressed,along with the fulllment of the harmonic load current com-pensation objective. The two-time scale behavior of the SAF is

exploited to apply the averaging theory in the control design.In [22], a nonlinear control strategy for an active lter isproposed. It is based on the inputoutput linearization methodimplemented on adq 0 rotating current reference frame. Thestructure balances the load currents, obtains unity displace-ment power factor, and reduces the harmonic load currents inarbitrary loads. In [23], the current loop dynamics in thesynchronousdq frame are controlled using multiple-inputmultiple-output optimal control based on the predictive controlapproach.Thenonlinearcontrol strategy does not require onlineoptimization and overcomes the aforementioned difcultiesby ensuring fast current tracking, current loop stability, andcompensation robustness under nonideal load and/or supplyconditions.

In this paper, the theoretical development of the SAPF isbased on the work done in [24]. However, no experimental vali-dation for the proposed control was conducted. It was shown bysimulations that the nonlinear control technique enhances thedynamic performance of the SAPF modeled in the synchronousorthogonal dq frame. The exact feedback linearization theorywas applied in the design of the controller. This control strategyallowed the decoupling of the currents, enhanced their trackingbehavior, and improved the dc voltage regulation. The referencesignals were obtained by extracting the harmonic currents fromthe measured load currents. In the orthogonal frame, the funda-

mental current component can be seen as a dc component, andas a consequence, the harmonic load currents can be extractedwith high-pass lters (HPFs). The HPFs were based on fourth-order Butterworth low-pass lters. The main problem withthis method is the delay that occurs when the control systemis digitally implemented. Even if the HPF would perfectlyperform, not all the harmonic load currents could be ltered.In addition, the system cannot completely compensate loadcurrent unbalance because of the phase shift caused by the lter.

The studies on active power lters, which appeared in theliterature [1][17], [24], all ignore the delay time such as thecurrent response delay generated by the boost inductors and dc-link voltage feedback delay due to the detection circuits.

The delay time caused by the lter control algorithm is dueto the low-pass lter used for reference current calculation and

the active lter natural response determined by boost inductorand dc-link voltage capacitors [25]. To simplify the currencontrol plant to be of rst-order delay type, voltage decouplerrotating frame transformation, and pole-zero cancellation techniques were used in current regulators. In [26], the concepof delay time was discussed. The method considered the in

stantaneous power delay caused by the current regulators andc-link voltage feedback circuit and presented the load poweestimation method to improve the dynamic response of inpupower regulation.

A computational control delay compensation method wasalso presented in [27], where only the feedforward controof the load current was used. The method is very effectivefor decreasing the magnitudes of the lower order harmoniload currents but cannot fully compensate the fast load currentransients. The HPF time constant is about 8 ms. It is reportethat, in the case of load current step changes, the system takeabout 19 ms to reach steady state. In addition, a multistagadaptive lter was discussed in [28]. This method combinea low-pass lter and an adaptive predictive lter, making ipossible to extract the sinusoidal active current componenfrom the distorted waveform without harmful phase shift, evewhen the frequency and amplitude simultaneously altered. Thdrawback of this technique is the difculty to design the dc-linvoltage and the current regulators.

In this paper, the authors propose a detailed nonlinear controtechnique, as previously introduced in [24], that uses a computational control delay compensation method to overcome thconventional method drawbacks. The rst step is to extract thSAPF reference current. Then, the phase shift of the referenccurrent is modied, so that the delay will be compensated

In addition, the nonlinear control is theoretically establishedand experimentally validated using both simulations and experiments. Consequently, the currents very closely track theireferences. The SAPF compensates for unwanted reactive, unbalanced, and harmonic load current components under nonsinusoidal supply voltage conditions. The SAPF performanceduring both nominal and severe operating conditions, is thenevaluated in real time using the dSPACE DS1104 controllerboard, which is supported by a Matlab/Simulink Real-TimWorkshop environment.

II. THREE-PHASESHUNTACTIVEFILTERTOPOLOGY

An SAPF conguration is considered in this paper in ordeto avoid harmonic pollution along the power line caused by three-phase diode bridge rectier load, followed by an inductoLL in series with a resistorRL . The SAPF acts as a controlledcurrent source connected in parallel with the nonlinear loadIt has the structure illustrated in Fig. 1. It consists of a fullbridge voltage source pulsewidth-modulation inverter, a dc-sidcapacitorC dc , and ac-side high-frequency inductorsLc that arerequired to shape the compensator input currentsi1 , i2 , andi3 .

A. Modeling of Shunt Active Filter

Kirchoffs rules for voltages and currents, as applied to thisystem, provide us with the three differential equations in th


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Fig. 1. Basic circuit of SAPF.

stationaryabc frame

v1 = v1N = Lcdi1dt

+ Rc i1 + v1M + vMN

v2 = v2N = Lcdi2dt

+ Rc i2 + v2M + vMN

v3 = v3N = Lcdi3dt

+ Rc i3 + v3M + vMN (1)

wherev1 , v2 , andv3 denote the line-to-ground voltages of thethree-phase balanced system measured at the point of commoncoupling (PCC).

Using the following assumptions:

v1 + v2 + v3 = 0 , i1 + i2 + i3 = 0

the following relation is obtained:

vMN = 133

m =1vmM . (2)

The switching functionck of thekth leg of the converter (fork = 1 , 2, 3) is dened as

ck =1, if S k is On andS k is Off 0, if S k is Off andS k is On.

(3)

Thus, vkM

= ckv

dc. The phase-k dynamic equation of the

lters model is given by the following equation:

dikdt

= R cLc

ik 1

Lcck

13

3

m =1cm vdc +

vkLc

. (4)

A switching state functiondnk is dened as

dnk = ck 13

3

m =1cm

n

. (5)

The value of dnk depends on the switching staten and thephasek. In other words,dnk simultaneously depends on theswitching functions of the three legs of the SAPF. This showthe interaction between the three phases.


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The resulting transformed model in the synchronous orthog-onal rotating frame is given as follows [24]:

ddt

idiq

vdc

=

R cL c

d ndL c

R cL c

d nqL c

d ndC dc

d nqC dc 0

idiq

vdc

+1

Lc

vdvq0

.

(6)

B. Harmonic Current Control

A PI control law was derived through linearization of theinherently nonlinear SAPF system model, thereby decouplingthe tasks of harmonic load currents tracking and dc capacitorvoltage regulation. This decoupling allows the SAPF to com-pensate for the ac currents and the dc-bus voltage independentlyof each other but results in either one of these decoupledsubsystems having a dynamic response that is signicantlyslower than that of the other. In order to obtain a fast dynamic

response of harmonic load currents compensation, the structureof a fast inner loop (current tracking loop) and a slow outer loop(dc voltage regulation loop) is adopted. The dynamics of the accurrents in (6) can be rewritten as follows:

Lcdiddt

+ Rc id = Lc iq vdc dnd + vd

Lcdiqdt

+ Rc iq = Lc id vdc dnq + vq . (7)

Let us dene the equivalent inputs as

ud = Lc iq vdc dnd + vduq = Lc id vdc dnq + vq . (8)

Thus, through the input transformation (8), the coupled dynam-ics of the currents tracking problem have been transformedinto decoupled dynamics. Hence, the currentsid and iq canindependently be controlled by acting upon inputsud and uq ,respectively. By using the error signalsid = id id and iq =iq iq , and applying proportional integral compensation, onecan choosednd anddnq such that

ud = k p id + ki id dtuq = k p iq + ki iq dt. (9)The transfer function of the PI compensator is

G i (s) =U q (s)I q (s)

=U d (s)I d (s)

= k ps + k ik p

s(10)

and the closed-loop transfer function of the current loop is

I q (s)I q (s)

=I d (s)I d (s)

=k pLc

s + k ik ps2 + (R c + k p )L c s +

k iL c

. (11)

For the optimal value of the damping factor = 2/ 2, thetheoretical overshoot is 20.79%. Nevertheless, in order to elim-

Fig. 2. Inner control loop of the currenti q .

Fig. 3. DC-bus voltage control loop.

inate the zero in the closed-loop transfer function, a prelteG p (s) is added, as shown in Fig. 2, i.e.,

G p (s) =1

1 + ( k p /k i )s. (12)

The response of the current loops becomes that of a secondorder transfer function with no zero; hence, the followingdesign relations can easily be derived:k p = 2 ni Lc R c andki = Lc 2ni .

The control law is given by the following:

dnd =vd + Lc iq ud

vdc(13)

dnq =vq Lc id uq

vdc. (14)

The inner control loop of the currentiq

is shown in Fig. 2.

C. DC Voltage Regulation

The instantaneous active and reactive powers exchangedbetween the SAPF and the ac mains are given byp = vd idandq = vd iq (becausevq = 0 under ideal supply conditions,as shown here). To maintain somevdc level across the dccapacitor of the SAPF, the losses through the active powelters resistiveinductive branches can be compensated byacting on the supply current. Ideally, it must act on the activcurrent componentid

C dcdv

dcdt = dnd id + dnq iq . (15)

An equivalent inputudc is dened as

udc = dnd id + dnq iq . (16)

To regulate the dc voltagevdc , the errorvdc = vdc vdc ispassed through a PI-type controller given byudc = k1 vdc + k2 vdc dt. (17)

The transfer function of the PI compensator is

Gv (s) = U dc (s)V dc (s)

= k1 s +k 2k 1

s. (18)


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Fig. 4. Nonlinear control scheme of the SAPF.

The resulting closed-loop transfer function is

V dc (s)V dc (s)

= 2 nvs + nv2

s2 + 2 nv s + 2nv(19)

where the proportional and integral gains are

k1 = 2 nv C dc and k2 = 2nv C dc .

Fig. 3 illustrates the outer control loop of the dc voltage.

The control effort of this outer loop is given by the following [24]:

ido = 23 vdcV udc . (20)The reference current in (20) is added to the harmon

reference current of id loop, as shown in Fig. 4.ido is a dccomponent, and it will force the SAPF to generate or to dra


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Fig. 5. Delays generated by the system.

a small current at the fundamental frequency. Furthermore,by designing the dc voltage loop to be much slower than thecurrent loops, there would not be any interaction between thetwo loops. Fig. 4 represents the nonlinear control of the SAPF.

III. CONTROLDELAYCOMPENSATION

In this paper, the analytical model and design methods are de-scribed in continuous time. In practice, a dc-link voltage regu-lator, current regulators, and low-pass lter are implemented bya personal-computer-based discrete system. A computationalcontrol delay compensation method is used. Fig. 5 illustrates

the total delay resulting from the chain of acquisition and thereal-time controller, which uses the sampling period namedT s .The delay timeT sens caused by boost inductors and dc-linkcapacitor is approximated to 100s, which corresponds to adephasing anglesens of 2 at 60 Hz. Moreover, the interfacecommunication and computing time of the algorithms x theminimum sampling period of the DSP. The delayT circ broughtby the digital circuit is thus equal toT s . The delivered signalby the numerical system has pace in stairs of widthT s . Bycarrying out the average over each sampling period, one obtainsthe signals3 . The delayT samp resulting from this average overone sampling period is equal toT s / 2. The delayT comp due to

the discretization and the computing time is equal to3T s / 2.Thesampling period for program execution isT s = 52 s. Thus, thetotal delayT d is approximately equal to 178s.

While s1 is the signal without delay,s2 is the signal atthe output of the sensor, ands3 is the signal at the output of the DSP.

The delayT d involves a dephasing angled 1 = 3 .8 at60 Hz between the reference current and the current injected bythe SAPF. The proposed strategy consists of creating a phaselead at 60 Hz on the reference currents to compensate for thetotal delay. Therefore, from the measured voltagesvs () at thePCC, the phase-locked loop rebuilds the voltages by integratingthe desired dephasings (sens and comp ). Consequently, thereference currents are corrected, and the lter currents behaveas desired.

Fig. 6. Current controller performance without control delay compensation.

Fig. 7. Waveforms showing the tracking performances of the inner loop.

Wheresens is the delay caused by boost inductors and dc-link capacitor,comp is the delay caused by discrete digitalimplementation and the computing time.

A. Current Controller Performance

Fig. 6 shows test results of the current controller withoucontrol delay compensation. Thed-axis id , the q -axis iq , andthe phase 1 active lter current in steady-state operation superposed with their respective references are shown. The resulshow the appearance of a time delay between the referenccurrents and the sensed currents.

Fig. 7 shows the test results of the nonlinear control withthe proposed control delay compensation method. The resultclearly show that the oscillating current harmonics injected bthe lter track their reference templates with high accuracy. Idemonstrates that the computational control delay compensation method performs very well.


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TABLE ISPECIFICATIONPARAMETERS

IV. SIMULATIONRESULTS

The nonlinear control scheme and compensation by SAPF issimulated under MATLAB/Simulink and power system block-set environment to estimate its performance. The nonlinear loadconsists of one three-phase and one single-phase diode rectier,so that the effectiveness of the nonlinear control scheme tocompensate for unbalanced load can be tested. The rectiersare feedingRL-type circuits. The source current waveformsof the simulation results have been analyzed to obtain theirTHD under varying load conditions. The main purpose of thesimulation is set to study three different aspects: 1) reactive andharmonic load currents compensation; 2) dynamic response of the SAPF to load variations; and 3) compensation of nonactiveload currents.

The system parameters used in these simulations are given inTable I.

One can read, for the case of a balanced load, the following

main power magnitudes (active power, reactive power, dis-tortion power, and apparent power) and power factor:P L =818.6 W;QL = 162 VAR;D L = 207 .4 VAR;S L = 859 .9 VA;andP F = 95 .2%.

The SAPF power magnitudes (active power, reactive power,distortion power, and apparent power) are given as follows:P c = 6 .6 W, Qc = 159 VAR, D c = 226 .6 VAR, andS c =276.9 VA.

The source power magnitudes (active power, reactive power,and apparent power) and power factor are given as follows:P s = 825 .2 W, Qs = 3 VAR, S s = 826 .2 VA, and P F =99.88%.

One can deduce that the SAPF power rating to compensatereactive and harmonic load current components is 32.2%(S c =32.2%S L ) of the load nominal power.

For the case of unbalanced nonlinear loads, the fundamentalpositive-sequence active power, reactive power, and appar-ent power are given as follows:P L 1+ = 503 .8 W, QL 1+ =65.55 VAR, andS L = 532 .1 VA.

The SAPF fundamental positive-sequence active power,positive-sequence reactive power, and apparent power are givenas follows:P c1+ = 8 .22 W, Qc1+ = 60 .8 VAR, andS c =197 VA.

The source fundamental positive-sequence active power,positive-sequence reactive power, and apparent power are givenas follows:P s 1+ = 512 W, Qs 1+ = 4 .75 VAR, andS s =513 VA.

Fig. 8. Steady-state response of the SAPF.

Therefore, the maximum rating of the SAPF to achievnonactive load current compensation represents 37% of the loanominal power.

A. Reactive and Harmonic Currents Compensation of a Nonlinear Load

The simulation results of the SAPF system are presente

in Fig. 8. The supply voltagevs 1, load currentsiL 123 , supplycurrentsis 123 , SAPF currents (ic123 ), and dc voltagevdc aredepicted there. The THD of the current generated by the nolinear load is observed to be approximately 25.8%, wherethe compensated supply current has a THD of approximate2.62% at steady state. A graphical representation of the loacurrent (top plot) and the supply current (bottom plot) aftSAPF connection appears in Fig. 9(a) and (b). The resulpresented in Figs. 8 and 9 coincide with those included Figs. 13 and 14 of Section V-A.

B. Response of the SAPF to Nonlinear Load Variation

In practice, nonlinear loads are usually time varying nature. Therefore, it is necessary to study the dynamic peformance of the SAPF when variations in the nonlinear loaare considered. The nonlinear load current was subjected 100% step decrease att = 366 .7 ms and 100% step increaseat t = 483 .3 ms. In other terms, the value of the load resistancis changed from 16 to 8 at t = 366 .7 ms and then changedfrom 8 to 16 at t = 483 .3 ms. The relevant waveforms aredepicted in Fig. 10. These results conrm the good dynamperformance of the SAPF for a rapid change in the nonlineload current. The waveforms presented in Fig. 10 coincide wthose included in Section V-B. As shown in Fig. 15, the settlitimes of dc-link voltagevdc and line currentis are less than3 ms. Nevertheless, the results show that the computation


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Fig. 9. Spectrum of phase 1. (a) Load current. (b) Source current aftercompensation.

Fig. 10. Dynamic response of SAPF under varying distorted nonlinear loadconditions.

control delay compensation possesses good dynamic responsefor both harmonic current compensation and dc-link voltageregulation. It is important to note that the THD of the supplycurrents are largely reduced, which is well below the IEEE-519standard requirement.

C. Compensation of Nonactive Load Currents

With the adopted control algorithm, this test aims to evaluatethe capability of the SAPF to compensate for nonactive loadcurrents. To carry this out, the load consists of a three-phasediode rectier, followed by inductorLL = 10 mH in serieswith a resistorRL = 16 , and a single-phase diode rectier,followed by inductorLL = 10 mH in series with a resistorRL = 40 . The single-phase rectier is connected between

Fig. 11. Steady-state response of SAPF with nonlinear load unbalances.

Fig. 12. Spectrum of load currents and source currents after compensation fasymmetrical load conditions.

phases 1 and 2, as shown in Fig. 1. The supply voltagevs 1 ,unbalanced three-phase load currentsiL 123 , supply currentsis 123 , SAPF currentsic123 , and dc bus voltage of the SAPF areshown in Fig. 11. One notes that these supply currents aftecompensation are balanced. Furthermore, spectrum analysis oload and line currents depicted in Fig. 12 indicates that thSAPF can largely improve the THD of the supply currentwhile feeding unbalanced load. The THD of the source currenis 123 are reduced from 15.91%, 22.12%, and 25.76% beforecompensation to 1%, 1.27%, and 1.27% after compensation, respectively. These results conrm the capability of the algorithmto balance the line currents while simultaneously compensatinfor reactive and harmonic load current components. The waveforms presented in this section and showed in Figs. 11 and 1


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Fig. 16. Steady-state response of the SAPF for asymmetrical load conditions.

Fig. 17. Harmonic spectra of load currents and supply currents.

operation mode, as shown in Fig. 13. These results show theeffectiveness of the SAPF to compensate harmonic currentscreated by a three-phase diode rectier type of load. In thisgure, the supply voltagevs 1 in phase 1, the load currents

iL 123 , the supply currentsis 123 , and the compensating currentsof the SAPFic123 are presented. The harmonic spectrumsof load and source currents have been given in Fig. 14(a)and (b), respectively. The compensated source current proleshows that the SAPF was effectively working, thus reducingthe source current THD from 26% to 3.1%. This signicantreduction occurred when the utility voltage measured THD is8.8%; consequently, the SAPF system is able to reduce thesource current THD (3.1%) well below the IEEE-519 standardrequirement.

B. Dynamic Performance of the Active Power Filter

Fig. 15 shows the transient response of the SAPF duringsudden variations in nonlinear load. It also shows the SAPF dc-

bus voltage, phase-1 supply, load, and lter currents. The loacurrent is abruptly decreased from 7.85 A (rms) to 3.8 A (rmsand then increased from 3.8 A (rms) to 7.85 A (rms). As viewefrom the experimental results, the changeover from one operaing condition to the other is quite smooth, therefore maintaining excellent compensation. The increase in load current wi

immediately be supplied from the SAPF, resulting in decreaseenergy storage of the dc bus capacitor. This reduction in the dbus voltage of the SAPF will activate the dc voltage controlleto increase the supply current. This increased source currentries to restore the stored energy of the capacitor in additioto increased load active power. Within one cycle, the supplycurrent settles to steady-statevalue. Similarly, the reverse actiontakes place as the load current decreases from 7.85 A (rms) t3.8 A (rms), causing the dc link to slightly increase, as showin Fig. 15. This will momentarily decrease the supply currento reduce the capacitor voltage at a set reference value. Withione cycle of ac source, the supply current settles to steady-stat

value. Since the corrective action of the voltage controller itaken within a half cycle of the ac mains, it results in fast responseof the scheme. It was observed that this dip in the dc-linkvoltage was about 7 V for 200-V dc link (3.5%). Neverthelesthe conditions previously discussed prove that the APF systemcompensates the reactive and harmonic load current components during steady state, as well as under transient operatinconditions.

C. Compensation of Reactive, Unbalanced, and Harmonic Load Current Components

The SAPF consists of six IGBTs(S 1 , S 2S 3 , S 1 , S 2 , S 3). Theload consists of three-phase and single-phase diode rectierfollowed by inductorLL in series with a resistorRL . Thesingle-phase rectier is connected between phases 1 and 2by closing the switch SW, as shown in Fig. 1. The globaload currents containing asymmetrical components are showin Fig. 16. This gure illustrates the supply voltagesvs 1 of phase 1, the unbalanced three phase load currentsiL 123 , thesupply currentsis 123 , and the SAPF currentsic123 . One cannote that supply currents after compensation are balancedThe spectral analysis of load and line currents is performedusing Fluke Model 41BPowerHarmonicsAnalyzer. Theresultsdepicted in Fig. 17 shows the ability of the SAPF to improvthe THD of the supply currents with unbalanced load. Therms source currents before compensation wasI s 1 = 4 .31 A,I s 2 = 4 .64 A, andI s 3 = 3 .23 A; therefore, after compensation,these currents become equal toI s 1 = I s 2 = I s 3 = 4 .56 A. TheTHD of the source currentsis 123 are reduced, respectively, from13.6%, 14%, and 21% before compensation to 2.9%, 3%, an2.3% after compensation. The SAPF system works as expectedThe compensated source currents, as viewed from Fig. 16, arsinusoidal and close to balanced. The lter currents suggesthat the SAPF system inject different currents to compensatnonactive load current demands in each phase. This proves thathe control approach with the SAPF system can quite effectively handle the most critical situation in a power distributiosystem.


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VI. CONCLUSION

The nonlinear control algorithm of an SAPF has been imple-mented to enhance its response for compensation of nonactiveload currents. The nonlinear control technique of the SAPF hasbeen designed, which is based on two inner current loops andan outer dc bus voltage regulator loop. It has been observedthat there is no interaction between inner and outer loops inaddition to good performance in both steady-state and transientoperations. Simulation and experimental results have validatedthe nonlinear control approach of the SAPF. It has been shownthat the system has 1.5 cycles for the outer voltage loop and0.5 cycles for the inner current loop and is able to keep the THDof the supply current below the limits specied by the IEEE-519 standard. The obtained results have demonstrated the highperformance of the SAPF.

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Salem Rahmani (M06) was born in Tunisia. Hereceived the B.Sc.A. and M.Sc.A. (electrical) de-grees and the Specialized Scientic Studies Certicate (CESS) from the High School of Sciences andTechnologies of Tunis (ESSTT), Tunis, Tunisia, in1992, 1995, and 2001, respectively, and the Ph.D.degree from the National Engineering School ofTunis (ENIT), Tunis, in 2004.

In September 2002, he was an Assistant Professorwith the Department of Electrical Engineering, HighInstitute of Medical Technologies of Tunis (ISTMT)

Tunis. Since the elaboration of his Ph.D. degree, he has been a Member of Research Group in Power Electronics and Industrial Control (GREPCI), c

de Technologie Suprieure, University of Qubec, Montreal, QC, Canada. research interests are power quality, active lters, and resonant converteincluding power converter topology, modeling, and control aspects.


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Nassar Mendalek (M00) was born in Lebanon. Hereceived the B.E. degree in electrical engineeringfrom St-Joseph University, Beirut, Lebanon, in 1983and the M.S. and Ph.D. degrees from the Ecole deTechnologie Suprieure, Montreal, QC, Canada, in1997 and 2003, respectively.

From 1983 to 1990, he was with the LebaneseTelecommunication Ministry as a Design and Sup-

port Engineer. From 1995 to 2004, he was withthe Research Group in Power Electronics and In-dustrial Control (GREPCI), Ecole de Technologie

Suprieure, where he was involved in teaching and research activities relatedto power electronics. Since 2004, he has been an Assistant Professor with theDepartment of Electrical, Computer and Communication Engineering, NotreDame University, Louaize, Lebanon. He teaches courses in power electronics,energy conversion, and analog and digital electronics. His research interestsinclude power quality, renewable energy, and the modeling and control aspectsof power converter topologies.

Kamal Al-Haddad (S82M88SM92F07) wasborn in Beirut, Lebanon, in 1954. He receivedthe B.Sc.A. and M.Sc.A. degrees from the Uni-versity of Qubec Trois-Rivires, Trois-Rivires,QC, Canada, in 1982 and 1984, respectively,and the Ph.D. degree from the Institut NationalPolythechnique, Toulouse, France, in 1988.

From June 1987 to June 1990, he was a Pro-

fessor with the Engineering Department, Universitdu Qubec Trois Rivires. Since June 1990, hehas been a Professor with the Electrical Engineering

Department, cole de Technologie Suprieure (ETS), Montreal, QC, wherhe has been the holder of the Canada Research Chair in Electric EnergConversion and Power Electronics since 2002. He has supervised more tha60 Ph.D. and M.Sc.A. students working in the eld of power electronicsFrom 1992 to 2003, he was the Director of the graduate study programat the ETS. He is a Consultant and has established a very solid link witmany Canadian industries working in the eld of power electronics, electritransportation, aeronautics, and telecommunications. He is the Chief of thETSBombardier Transportation North America division, which is a joinindustrial research laboratory on electric traction system and power electronicHe is also a coauthor of the Power System Blockset software of Matlab. Hhas coauthored more than 250 transactions and conference proceeding paperHis research interests are highly efcient static power converters; harmonicand reactive power control using hybrid lters; and switch-mode and resonanconverters, including the modeling, control, and development of prototypefor various industrial applications in electric traction, power supply for drivetelecommunication, etc.

Dr. Al-Haddadis a Fellow Memberof theCanadianAcademy of Engineeringand a Life Member of the Circle of Excellence of the University of QuebeHe is active in the IEEE Industrial Electronics Society, where he is the VicPresidentfor Publication, an AdCommember, andserves as anAssociateEditofor the IEEE TRANSACTIONS ONINDUSTRIALELECTRONICS. He was therecipient of the Outstanding Researcher Award from ETS in 2000.

experimental design of a nonlinear control technique for three-phase shunt active power filter

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