lcl filter

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 3, MARCH 2012 1443

Generalized Design of High Performance ShuntActive Power Filter With Output LCL Filter

Yi Tang, Student Member, IEEE, Poh Chiang Loh, Member, IEEE, Peng Wang, Member, IEEE, Fook Hoong Choo,Feng Gao, Member, IEEE, and Frede Blaabjerg, Fellow, IEEE

AbstractThis paper concentrates on the design, control, andimplementation of an LCL-filter-based shunt active power filter(SAPF), which can effectively compensate for harmonic currentsproduced by nonlinear loads in a three-phase three-wire powersystem. With an LCL filter added at its output, the proposedSAPF offers superior switching harmonic suppression using muchreduced passive filtering elements. Its output currents thus havehigh slew rate for tracking the targeted reference closely. Smallerinductance of the LCL filter also means smaller harmonic voltagedrop across the passive output filter, which in turn minimizesthe possibility of overmodulation, particularly for cases wherehigh modulation index is desired. These advantages, togetherwith overall system stability, are guaranteed only through properconsideration of critical design and control issues, like the selec-tion of LCL parameters, interactions between resonance dampingand harmonic compensation, bandwidth design of the closed-loopsystem, and active damping implementation with fewer currentsensors. These described design concerns, together with theirgeneralized design procedure, are applied to an analytical exam-ple, and eventually verified by both simulation and experimentalresults.

Index TermsActive power filter, current control, LCL filter,resonance damping.

I. INTRODUCTION

THE higher order LCL filter has commonly been usedin place of the conventional L-filter to give a bettersmoothing of output currents from a voltage source converter[1], [2]. Its applications to grid-connected inverters and pulse-width modulated active rectifiers have recently attracted a lotof research attentions [1][8], mainly due to its ability tominimize the amount of current distortion injected into theutility grid. Power quality of the grid is hence enhanced, whichis particularly important for small-scale distributed generationsystems, where the ac bus is not strong [6]. Despite having theseadvantages, there are some challenges faced by the LCL filterin practical implementations, whose common concern is the

Manuscript received March 29, 2011; revised July 12, 2011; acceptedAugust 16, 2011. Date of publication September 6, 2011; date of current versionOctober 25, 2011.

Y. Tang, P. C. Loh, P. Wang, and F. H. Choo are with the School of Electricaland Electronic Engineering, Nanyang Technological University, Singapore639798 (e-mail: [email protected]; [email protected]; [email protected];[email protected]).

F. Gao is with the School of Electrical Engineering, Shandong University,Jinan 250061, China (e-mail: [email protected]).

F. Blaabjerg is with the Institute of Energy Technology, Aalborg University,9220 Aalborg East, Denmark (e-mail: [email protected]).

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

Digital Object Identifier 10.1109/TIE.2011.2167117

possibility of exciting serious resonance at certain frequency.The overall system might therefore be unstable, but fortunatelycan be resolved by applying existing damping techniques, likeadding a real resistor in series with the filter capacitor [1],actively feeding back some measured or estimated electricalvariables for control purposes [7][12], and splitting the filtercapacitor to reduce the system order [13], [14]. These tech-niques have no doubt contributed prominently to the wide-spread adoption of LCL filter by the industry [1].

Although extensive, most investigations on LCL filter nowhave focused on topics like fundamental current tracking andresonance damping for mostly simple grid-tied dc-ac invertersand ac-dc rectifiers. For these applications, the LCL resonancefrequency is usually tuned to be at least ten times of thefundamental line frequency [1]. It is therefore not difficult tosimultaneously achieve the desired control objectives at fun-damental frequency using existing control techniques. In [15],a slightly more complicated design scenario was consideredfor a three-phase inverter driven by direct power control andconnected to an ac grid with fifth harmonic voltages. A similarstudy was conducted in [16], where the low-order grid harmonicproblem was solved by feeding forward the grid voltages.The highest harmonic orders considered in these studies were,however, quite small and hence far away from the resonancefrequencies of their respectively designed LCL filters. Theireffectiveness in compensating harmonics was, therefore, quiteexpected since interactions with system damping and stabilitywere not significant.

Other more challenging studies on LCL filter can certainly befound in the literature, but only a few has discussed about meritsand design challenges faced when applied to shunt active powerfilter (SAPF) [17], [18]. In [19], a repetitive control schemecoupled to a one-beat-delay current controller was proposed forLCL-filter-based SAPF. Although the system exhibited goodperformance under both dynamic and steady-state conditions,the design of LCL filter and resonance damping control wasnot specifically addressed. A design procedure for determiningthe parameters of the LCL filter was subsequently discussed in[20] for SAPF controlled by a hysteresis scheme with variableswitching frequency. The provided methodology, however, ledto very different grid- and converter-side inductors, which weretherefore not yet optimized, based on concepts discussed in[21], [22]. Moreover, only passive damping technique wasconsidered in [20], meaning real resistors were added in serieswith the filter capacitors, leading to unnecessary power losses.These earlier studies on SAPF also included only simulationresults with their practicalities left unverified.

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1444 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 3, MARCH 2012

Fig. 1. Circuit diagram of proposed SAPF with output LCL filter.

A comparative study can also be found in [23], where theLCL-filter-based and L-filter-based SAPFs were compared ex-perimentally. Conceptual explanation for that study was, how-ever, lacking, hence making it hard to appreciate improvementcontributed by the LCL filter. These shortfalls, together witha number of other issues identified in the literature, lead tothe general belief that LCL filter for the more complex SAPFhas not been fully understood. Its real advantages over theL-filter-based SAPF are, therefore, not yet well-defined andare investigated here by addressing a few control objectivesrelated to the LCL-filter-based SAPF. As a start, a frequencydomain model of LCL filters, which takes into account thephase lag introduced by the LCL resonance, is established.Analysis of this model reveals that the maximum achievablesystem bandwidth is closely linked to the resonance frequencyof the LCL filter. A general design guideline is then proposed toensure proper placement of the resonance frequency within anappropriate chosen range, so as to simultaneously achieve accu-rate harmonic compensation and optimum resonance dampingwithout any tradeoff noted between them.

Active damping, being more efficient, is also explicitlyconsidered here for embedding within the control loop, soas to alter the plant transfer function to get a more well-damped system. A design example then follows, whoseobjective is to compensate for harmonic currents up to the25th order in a 50-Hz three-phase three-wire power system.

The designed system is next compared with its L-filter-basedcorrespondence, designed to have similar ripple filtering.Through the comparison, an attractive advantage of the LCL-filter-based SAPF is identified for cases where high modulationindex (e.g., 0.9) is demanded, which so far has not been pre-viously discussed. Simulation and experimental results forverifying this advantage, together with other performanceimprovements, are subsequently provided, before concludingon the effectiveness of the proposed SAPF design and controlmethodology.

II. MODEL OF LCL FILTER

Fig. 1 shows the typical circuit diagram of a SAPF imple-mented as a three-phase three-wire system. Between the SAPFand utility grid is an LCL filter added for current smoothing,whose model is formulated by first making a few assumptionsfor simplifying the analysis. Foremost would be to assume thatthe three-phase voltages at the point of common coupling aresinusoidal and balanced. That then means the grid can rea-sonably be treated as a short-circuit when performing stabilityanalysis in the high frequency range. In addition, all equivalentseries resistances (ESRs) of passive components, including theconverter-side inductor Lff , grid-side inductor Lgf , and filtercapacitor Cf , are neglected, since they provide some degreesof resonance damping, and would thus raise the overall systemstability. Ignoring ESRs therefore represents the worst case

TANG et al.: GENERALIZED DESIGN OF HIGH PERFORMANCE SHUNT ACTIVE POWER FILTER WITH OUTPUT LCL FILTER 1445

Fig. 2. Plant models of (a) undamped and (b) actively damped SAPFs.

scenario in terms of damping, even though it represents the bestcase in terms of loss reduction. Applying these assumptionsthen leads to the model shown in Fig. 2(a) for representingthe power stage of the SAPF, whose converter bridge has beenrepresented by a gain of Vdc/2, as per previous practice.

Fig. 2(a) can further be written as a set of transfer functionsin the frequency domain, as demonstrated by

Gp(s) =Igf (s)Vm(s)

=Vdc/2

LffLgfCfs3 + (Lff + Lgf )s(1)

Icf (s)Igf (s)

=LgfCfs2 (2)

where Vm is the normalized modulating signal, Vdc is thedc-link voltage, Igf and Icf are the currents injected into thegrid and absorbed by the filter capacitor, respectively. Applyingunity feedback control to (1) then results in a characteristicpolynomial without the s2 term. The overall closed-loopsystem is thus unstable or marginally stable according to theRouths stability criterion and would need additional dampingto stabilize it.

Passive damping is certainly a simple and straightforwardmethod for consideration but would introduce high losses,particularly for SAPF, where high switching harmonic currentwill flow through the added damping resistor per phase. Passivedamping is therefore not considered further. Instead, activedamping is focused, which when applied, leads to the activelydamped system shown in Fig. 2(b). In that figure, the filtercapacitor current is sensed and added to the modulating signalthrough a damping gain Kd. The new transfer function is thenwritten as

Igf (s)Vm(s) Icf (s)Kd =

Vdc/2LffLgfCfs3 + (Lff + Lgf )s

. (3)

Upon substituting (2) for Icf (s), the new plant model Gpd(s)is derived as

Gpd(s)

=Igf (s)Vm(s)

=Vdc/2

LffLgfCfs3+(Vdc/2)KdLgfCfs2+(Lff+Lgf )s. (4)

Fig. 3. Bode plot of (6) obtained using the parameters listed in Table I.

TABLE ISYSTEM PARAMETERS USED FOR SIMULATION AND EXPERIMENT

With a finite s2 term now introduced to its denominator,closed-loop stability of (4) can easily be tuned by varying thefeedback gain Kd appropriately. Damping factor , represent-ing the extent of resonance damping, can also be tuned as

2res =VdcKd2Lff

= 2

Lff + LgfLffLgfCf

(5)

where res represents the LCL resonance frequency, deter-mined solely by the passive component values. Substituting (5)into (4) then results in the following simplified damped systemmodel:

Gpd(s) =Vdc

2LffLgfCf 1s (s2 + 2ress + 2res)

. (6)

Bode diagrams of (6) under various damping factors cannow be plotted as in Fig. 3, using parameters listed inTable I. Also drawn are the first-order curves associated witha simple L-filter, whose inductance is set to Lt = Lff + Lgf .


Comparing the curves then leads to the general observationthat the magnitude response of the LCL filter approaches thatof the L-filter in the low frequency range (below resonancefrequency), regardless of the damping factor chosen. Theirphase responses can, however, be quite different, which maysignificantly impact the system stability. Moreover, it is sensedthat the control bandwidth cannot exceed or even be close tothe resonance frequency, since it will create a 180 phase lag,whose resulting influence is an insufficient phase margin forclosed-loop control. Non-negligible delays caused by samplingand modulation would also constrain the system crossoverfrequency c, limiting it to be less than 0.3 times the resonancefrequency res, based on the region suggested in Fig. 3.

Defining as c/res 0.3 then leads to a phase lag ofLCL radians for the LCL filter at c, calculated as

LCL={Gpd(jc)}

={

Vdc2LffLgfCf

1(jc)3+2res(jc)2+2resjc

}

={

Vdc2LffLgfCf

1(jres)3+2res(jres)2+2resjres

}

={

Vdc2LffLgfCf

1223res+(3)j3res

}

=arctan 12

2. (7)

When the damping factor of LCL resonance is chosen tobe 0.707 (a very typical value used for second-order system),LCL is calculated as 0.64 or 115, which is not a very severedegradation, as compared to the value of 0.5 or 90 of anL-filter. Parameter c or 0.3res should, moreover, be chosenmuch higher than the highest harmonic current compensatedby the SAPF, so as to completely eliminate its interactionwith the LCL resonance. The desired switching frequency caneventually be set, which according to [24], should be set atleast two times of res, so as to provide sufficient harmonicattenuation around the switching frequency.

III. CONTROL OF SAPF

Upon figuring out the relationships among system band-width, LCL resonance frequency, and converter switchingfrequency, development of control algorithms for the LCL-filter-based SAPF can proceed. The resulting control blockdiagram is shown in Fig. 1, where active damping, harmoniccurrent compensation, and dc-link voltage control are all con-sidered. Regarding active damping, it has earlier been demon-strated on LCL-filter-based SAPF in [25], where the filtercapacitor current was measured and fed to the inner currentfeedback control loop to imitate a virtual damping resistor.Although the controlled system can eventually be stabilizedin the steady state, its damping gain at resonance frequencywas not analytically determined, but rather obtained throughtrial and error. Proper guide on how to choose the damping

Fig. 4. Root locus of (6) showing trajectories of closed-loop poles.

gain is, therefore, absent, implying that optimal damping of theLCL filter cannot be guaranteed. This is clearly confirmed bythe dynamic results presented in [25], where obvious currentoscillations and overshoots can be seen. Proper sizing of thedamping gain is, therefore, important and is precisely deter-mined here by using the plant model in (4) and (5) to arrive at

Kd =4Vdc

Lff (Lff + Lgf )

LgfCf(8)

where Kd is shown to be proportional to the damping factor, whose value can freely be tuned to arrive at the desireddamping response.

Referring next to (6), the general observation noted is that thedamped LCL network has a pair of conjugate complex poles inthe left half plane and another pole at the origin. The locationsof these poles, and hence the system response and performance,can be varied by applying unity feedback, and then tuning theproportional gain Kpc of the current controller. Theoretically, alarge proportional gain would force the real closed-loop pole tomove further away from the imaginary axis, hence attenuatingits impact, and causing the two conjugate poles to dominate.The conjugate poles would also move closer toward the righthalf plane, causing the system to gradually become unstable.The described pole trajectories are shown by the root locusof (6) plotted in Fig. 4, which also shows the closeness ofthe poles, even though they are gradually moving apart, asKpc increases. The impact of the real pole, therefore, cannotbe neglected, but should be understood by comparing the stepresponse of the closed-loop system with the following second-order system Gs(s) at different damping factors:

Gs(s) =2res

s2 + 2ress + 2res. (9)

The results are plotted in Fig. 5, where a feature notedwith the real pole is its slowing down of the overall stepresponse, hence leading to a longer settling time. It, however,damps transient oscillations more forcefully, leading to smallerovershoots at all damping factors. Based on these observations,a recommended value for with active damping incorporatedis 0.7, since it leads to a smooth system recovery with no


Fig. 5. Step responses of Gs(s) and closed-loop of Gpd(s).

noticeable overshoot and an acceptably short response time.At times, can also be chosen slightly smaller, like 0.5, tointroduce a safer phase margin (see Fig. 3), but slightly higherovershoot. Further reduction of is, however, not recom-mended, since it will not improve the phase response too much,but only lead to even serious oscillations, as seen in Fig. 5. Upondeciding on the value of , Kd can follow up be determinedusing (8) without much difficulty.

Proceeding on to the inner current control loop, its respon-sibilities are clarified as power flow regulation and harmoniccurrent compensation. Unlike those methods proposed in [19],[23], [25], where both nonlinear load and SAPF currents weresensed, only the line currents are measured here, and controlledto be balanced and sinusoidal. One set of current sensors, to-gether with the load harmonic extraction module for generatingthe SAPF reference currents, are therefore eliminated, leadingto a simpler control implementation. For unity power factoroperation, the reactive grid current reference should further beset to zero, while using the following proportional-integral (PI)controller in the synchronous dq frame for forcing the gridcurrent to track an active reference per phase:

Gcf (s) = Kpc

(1 +

1cs

)(10)

where Kpc and c are, respectively, the proportional gain andintegral time constant. As Kpc dominates the bandwidth of theinner current control loop, its value must properly be chosen toensure that c falls well within the frequency range discussedin Section II, and indicated in Fig. 3. For that, the followingequation can be used for calculating Kpc [26], after decidingon the value of c (= 0.3res, as explained earlier):

Kpc cLtVdc/2

=c(Lff + Lgf )

Vdc/2. (11)

The value of c, on the other hand, mainly determines thefundamental steady-state tracking error and should therefore besmall. A conservative value recommended for it to avoid im-pacting on system stability, like the reduction of phase margin,is given in

{Gcf (jc)} =90 arctancc 2and c 30/c. (12)

It should also be noted that adding this PI controller in thecurrent control loop will introduce an additional pair of zeroand pole to the closed-loop response. These added terms are,

however, close to each other, allowing their effects to cancelout. The overall system response would, therefore, still bedominated by those three poles indicated in Fig. 4.

Adding on to the fundamental current regulation is the com-pensation for harmonic currents, which can be implemented inthe synchronous dq frame by using multiple paralleled resonantcontrollers, expressed as

Gch(s) =k

n=1

Kihs

s2 + (6nn)2(13)

where n, Kih, and k represent the nominal angular frequency,respective resonant gain, and highest harmonic order that canbe compensated. Rather than (13), resonant controllers placedin the stationary frame can also be used, but would result inmore terms for summation. This is explained in [27], where itis shown that a resonant controller in the synchronous frame ismore effective, since it represents two equivalent resonant termsin the stationary frame for compensating two harmonics. Otherdetails on the discretization and optimization of the resonantcontrollers can be found in [27], [28], and are therefore notexplicitly elaborated here.

Returning back to k in (13), its value should rightfully bemuch smaller than the specified resonance frequency. Thatthen corresponds to the low frequency range shown in Fig. 3,whereas mentioned earlier, would cause the LCL filter tobehave like a small inductance. Output current produced bythe SAPF in this range can, therefore, be of high slew ratefor tracking the harmonic reference accurately. A first-orderL-filter, designed to produce the same switching ripple filtering,would not be able to respond that fast because of its largerinductance. A possible solution for it is to tune up its controllerproportional gain to maximize the system bandwidth. This,however, is quite hard to achieve in reality, since it can leadto unwanted noise amplification, and hence instability.

Moving next to the outer voltage control loop of the SAPF,its responsibility is to keep the dc-link capacitor voltage con-stant by compensating for active power losses in the system.Its realization can, therefore, be just the stationary-frame PIcontroller Gv(s) written in (14), whose high dc gain wouldforce the tracking error to zero

Gv(s) = Kpv

(1 +

1vs

)(14)

where Kpv is the proportional gain, and v is the time constantof the integral term. Gv(s) here must rightfully be designed tobe much slower than the current controller Gc(s)(= Gcf (s) +Gch(s)), so as to avoid interference between them.

Another feature exhibited by the dc-link control loop is itslower dc voltage requirement. This is possible for the LCLfilter, since its total inductance is much smaller, and hencethe unfiltered converter output needs to compensate for onlya much smaller voltage drop across it. The dc-link voltagecan, therefore, be reduced, while yet maintaining the samehigh modulation index that is less prone to overmodulation.This is, however, not true for the L-filter-based SAPF, whichalways requires a larger inductance, and hence a larger voltagedrop across it. Consequently, its output current would run


Fig. 6. Simulated results of LCL-filter-based SAPF when subjected to a 33%to 100% step-up load change.

into saturation way earlier than that of an LCL-filter-basedSAPF system. Being applied to SAPF also leads to a moreprominent voltage drop, since it deals with sizable harmoniccurrents flowing through sizable inductive impedance that is ktimes larger than the fundamental. In contrast, similar effectsexperienced by grid-tied inverters and rectifiers would likelybe less obvious, since they deal with fundamental currents andinductive impedances only.

IV. GENERALIZED DESIGN PROCEDURE AND EXAMPLE

Based on reasons discussed earlier about parameter sizing,the generalized design procedure for LCL-filter-based SAPFis now presented in per-unit terms for easier future systemscalability. The procedure would quite expectedly begin bydefining the highest order harmonic current k that needs tobe compensated. According to Section II, the cutoff frequencyc and resonance frequency res should then be larger thankn and kn/0.3, respectively (n being earlier defined as thenominal fundamental frequency). To be slightly more conserv-ative so as to fully avoid interference between harmonic currentcompensation and resonance damping, the resonance frequencycan instead be set to

res = kn/0.25 = 4kn. (15)

To next cater for sufficient switching harmonic suppression,the desired switching frequency of the converter can be set twotimes larger than the LCL resonance frequency. Even higherswitching frequency can of course be used for better harmonicattenuation, but would incur additional losses, and thereforenot firmly recommended. With res now decided, the filtercomponent values can follow up be determined, but beforeprogressing ahead, some base inductance Lb and capacitanceCb values need to be defined for per-unit representation. Thesebases are written as

Lb =Zb/n

Cb =1/nZb (16)

Fig. 7. Simulated results of L-filter-based SAPF when subjected to a 33% to100% step-up load change.

Fig. 8. Experimental steady-state results of LCL-filter-based SAPF.

where Zb is the base impedance calculated by dividing thesystem rated power from the square of its rated voltage.

Noting also that the grid and converter-side inductancesshould be set equal to produce the lowest resonance frequency,and hence the maximum switching harmonic attenuation, theset of filter parameters recommended should be

Lff =Lgf = xLb = xZb/n

Cf = yCb = y/nZb (17)

where x and y are the per unit inductance and capacitance,respectively, which are usually chosen below 5% to bring downthe system cost. Substituting (17) to (5), followed by somesimple manipulation, then leads to

xy = 2(n/res)2 = 2(1/4k)2. (18)

Apparently, (18) has infinite solutions, but it is recommendedhere that the total per unit value of the two inductors should bechosen equal to that of the filter capacitor, hence yielding

Lff =Lgf = (1/4k)Lb

Cf =(1/2k)Cb. (19)


Fig. 9. Experimental results of LCL-filter-based SAPF when subjected to a 33% to 100% step-up load change.

The closest commercially available capacitance value shouldthen be chosen, while the inductance value can be woundaccordingly. If desired, the actual realized resonance frequencycan be calculated using these final chosen reactive values andshould roughly match the value recommended in (15) for thedesign. The reactive values, together with the chosen damp-ing factor (0.5 0.7), cutoff frequency c, and dc-linkvoltage Vdc, can next be substituted to (8), (11), and (12) todetermine the important control parameters of Kd, Kpc, andc, respectively. Other control parameters like Kih in (13) forharmonic current compensation, and Kpv and v in (14) for dc-link voltage regulation, can be tuned based on classical outerloop control and zero tracking error operating principles. Theseare well-established and, therefore, not explicitly shown here.

The above design procedure can now be applied to anexample SAPF, whose objective is to compensate up to the25th harmonic current (k = 25) in a 173-V (line-to-line RMS),2-kVA, 50-Hz three-phase three-wire system. From (15),the resonance frequency should rightfully be chosen as1250/0.25 = 5000 Hz or a value between 1250/0.3 = 4167 Hzand 5000 Hz. Since the desired switching frequency shouldbe at least two times larger than the resonance frequency, itsvalue should be fixed to 10 kHz or more. Using (16), the baseinductance and capacitance values can next be calculated as47.8 mH and 212 F, respectively. Substituting these bases andk = 25 to (19) then leads to the calculated values of 0.478 mHand 4.24 F for the LCL filter. Based on available commercialvalues, the final LCL parameters are chosen as Cf = 5 Fand Lff = Lgf = 0.5 mH, giving a recalculated resonancefrequency of fres = res/2 = 4504 Hz, which indeed fallswithin the range from 4167 Hz to 5000 Hz that has earlier beenidentified. Using these reactive parameters, together with =0.5, c = 8485 rad/s, and Vdc = 300 V, the corresponding con-trol parameters are eventually determined as Kd = 0.09, Kpc =0.05, c = 0.0035 s, Kih = 20, Kpv = 0.2, and v = 0.04 s.

V. SIMULATION RESULTS

Simulation was conducted with Matlab/Simulink andPLECS, based on the system shown in Fig. 1. The aim wasto examine the performance of the proposed SAPF system

Fig. 10. Grid current spectrum versus IEEE 519-1992 standard.

Fig. 11. Experimental steady-state results of L-filter-based SAPF.

and to compare it with the conventional L-filter-based SAPF.The specifications of the designed SAPF and other systemparameters were based on those derived in Section IV andsummarized in Table I for comprehensiveness. The ac lineand dc-link voltages stated in Table I were found to givean approximate modulation index of 141/150 = 0.94 for theSAPF converter, which indeed was a reasonably high value.Such a high value was used for proving the lower likelihoodof entering overmodulation by the LCL-filter-based SAPF.

Beginning with Fig. 6 where the proposed SAPF was sub-jected to a 33% to 100% step-up nonlinear load change, theresults show a smooth compensation of harmonic currents upto the 25th order. Total harmonic distortion (THD, calculated


Fig. 12. Experimental results of L-filter-based SAPF when subjected to a 33% to 100% step-up load change.

Fig. 13. Harmonic spectrum of grid current in high frequency range.

up to the 100th order) of the full load grid current is in factonly 2.91%, even though the load THD is 44.20%. Modulatingreferences in the last plot of Fig. 6 are also noted to vary belowunity without entering overmodulation, even with a detected dipin dc-link voltage during the transient.

For comparison, the LCL network was next replaced by a5 mH inductor, followed by a retuning of the current controllergains to produce the same dynamic response, as per the previ-ous simulation. Subjecting the L-filter-based SAPF to the sameload transient then results in Fig. 7, where a prominent increasein modulation index is observed with larger power flow. Theincrease is for compensating the larger voltage drop acrossthe L-filter and transient dip in dc-link voltage. That pushes thesystem into overmodulation like the example illustrated here,whose eventual effect is a set of distorted grid currents withTHD as high as 7.79%.

VI. EXPERIMENTAL RESULT

To validate the proposed SAPF practically, a prototype wasbuilt in the laboratory, based on the same parameter valueslisted in Table I and circuit connection shown in Fig. 1, as perearlier used for simulation. The developed control algorithmwas executed on a dSPACE1103 real-time platform, and thedigital signal processor TMS240F2812 was employed with itssampling frequency being set as 20 kHz in the controller board,which is twice of the switching frequency. The first set ofexperimental results obtained is shown in Fig. 8, during whichthe proposed SAPF is supplying 100% nominal load power

in the steady state. As anticipated, the SAPF compensates theload harmonic currents well, giving rise to smooth sinusoidalcurrents drawn from the grid with a THD of only 3.49%. This isdespite the load currents being heavily distorted with a THD of40.37%. Also shown in the last plot of Fig. 8 is the modulatingreference for one phase of the SAPF, being fully within theshaded linear modulation range.

The same demanded performance is shown in Fig. 9, wherea step load transient from 33.3% to 100% of nominal loadis intentionally triggered. This sudden increase in harmoniccurrents causes the dc-link voltage Vdc to drop to 279.2 V,which, due to limited channels available on the digital scope,is not explicitly shown here. This drop under an undisturbed acgrid would cause the modulation index to rise to approximately141/139.6 1.01, which, although is slightly greater unity,would still not lead to overmodulation problem. The reason ispartly due to the low series impedance of the LCL filter andpartly due to the presence of triplen offset that can clearly beseen added to the modulating reference of each phase. Transientevents are therefore mostly ridden through smoothly with noobvious harmonic distortion sensed from the line current. Forfurther demonstrating that the proposed SAPF meets interna-tional standard, low-order harmonic spectrum of the resultinggrid current under nominal load condition is plotted in Fig. 10,which undeniably shows that the IEEE 519-1992 standard hasbeen met comfortably.

The output filter of the SAPF was subsequently replaced bya 5-mH inductor, and retested under the same experimentalconditions. Fig. 11 shows the steady-state experimental results,where slight overmodulation is observed under nominal loadoperating condition. This overmodulation is caused by the needto compensate for a larger voltage drop across the filter im-pedance, while yet keeping the same low dc-link voltage. Its ex-tent can in fact worsen under transient conditions, like the 33%to 100% load step change shown in Fig. 12. The correspondingeffect is of course a distorted grid current, whose low-orderspectrum under nominal load condition is shown in Fig. 10.The spectrum undoubtedly shows poorer performance than theIEEE standard with its THD of 7.86% in excess of the normal5% limit. Adding on to these inferiorities is its poorer switching


ripple filtering, even after increasing its filter inductance to befive times larger than that of the LCL filter. The correspondingresults are shown in Fig. 13, where the switching and associatedsideband harmonics are plotted for both L-filtered and LCL-filtered SAPFs. The results indeed show the former havingpoorer filtering performance, particularly at high frequency.

VII. CONCLUSION

This paper proposes an LCL-filter-based SAPF for three-phase three-wire power system, together with its generalizeddesign and control procedure. Being of higher order, the pro-posed SAPF provides better filtering without using large pas-sive components. Its resulting output currents therefore havehigh slew rate for accurate harmonic compensation withoutunnecessarily entering overmodulation mode during transient.Stability concerns are, however, more involved but can beresolved by the proposed design and control tuning method-ology. Experimental testing of the methodology has proven itseffectiveness in ensuring proper damping, overall stability, andsmooth transient response achieved through a more comprehen-sive and generalized design procedure.

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Yi Tang (S10) received the B.Eng. degree in elec-trical engineering from Wuhan University, Wuhan,China, in 2007 and the M.Sc. degree from NanyangTechnological University, Singapore, in 2009, wherehe is currently working toward the Ph.D. degree inthe School of Electrical and Electronic Engineering.

During the summer of 2007, he was a visitingscholar with the Institute of Energy Technology,Aalborg University, Aalborg East, Denmark, wherehe worked on the control of grid-interfaced invertersand uninterruptible power supplies.


Poh Chiang Loh (S01M04) received the B.Eng.(Hons.) and M.Eng. degrees in electrical engineer-ing from the National University of Singapore,Singapore, in 1998 and 2000, respectively, and thePh.D. degree in electrical engineering from MonashUniversity, Clayton, Vic., Australia, in 2002.

During the summer of 2001, he was a visit-ing scholar with the Wisconsin Electric Machineand Power Electronics Consortium, University ofWisconsin-Madison, Madison, where he worked onthe synchronized implementation of cascaded multi-

level inverters and reduced common mode carrier-based and hysteresis controlstrategies for multilevel inverters. From 2002 to 2003, he was a projectengineer with the Defence Science and Technology Agency, Singapore, man-aging major defense infrastructure projects and exploring new technology fordefense applications. From 2003 to 2009, he was an assistant professor withthe Nanyang Technological University, Singapore, and since 2009, he is anassociate professor at the same university. In 2005, he has been a visitingstaff first at the University of Hong Kong, Hong Kong, and then at AalborgUniversity, Aalborg East, Denmark. In 2007 and 2009, he again returned toAalborg University, first as a visiting staff working on matrix converters and thecontrol of grid-interfaced inverters, and then as a guest member of the VestasPower Program.

Peng Wang (M00) received the B.Sc. degree fromXian Jiaotong University, Xian, China, in 1978, theM.Sc. degree from Taiyuan University of Technol-ogy, Taiyuan, China, in 1987, and the M.Sc. andPh.D. degrees from the University of Saskatchewan,Saskatoon, SK, Canada, in 1995 and 1998,respectively.

Currently, he is an associate professor of NanyangTechnological University, Singapore.

Fook Hoong Choo received the B.Sc. degree fromUniversity of Leeds, Leeds, U.K., in 1977, and theM.Sc. degree from the University of Manchester,Manchester, U.K., in 1979.

He was employed as a Design Engineer with GECat Rugby, U.K. from 1979 to 1983 and Project Engi-neer with Lucas Research at Birmingham, U.K. from1983 to 1984. He joined Nanyang TechnologicalUniversity, Singapore, (formerly Nanyang Techno-logical Institute), in 1984 where he is currently anAssociate Professor with the School of Electrical and

Electronic Engineering. His current research interests include power electron-ics, ac drives, magnetics, renewable energy generation and control, and energy,water and environmental research.

Feng Gao (S07M09) received the B.Eng. andM.Eng. degrees in electrical engineering fromShandong University, Jinan, China, in 2002 and2005, respectively, and the Ph.D. degree from theSchool of Electrical and Electronic Engineering,Nanyang Technological University, Singapore, in2009.

From 2008 to 2009, he was a Research Fellowin Nanyang Technological University. Since 2010,he joined the School of Electrical Engineering,Shandong University, where he is currently a Profes-

sor. From September 2006 to February 2007, he was a visiting scholar at theInstitute of Energy Technology, Aalborg University, Aalborg, Denmark.

Dr. Gao was the recipient of the IEEE Industry Applications Society Indus-trial Power Converter Committee Prize for a paper published in 2006.

Frede Blaabjerg (S86M88SM97F03) re-ceived the M.Sc. degree in electrical engineeringfrom Aalborg University, Aalborg, Denmark, in 1987and the Ph.D. degree from the Institute of EnergyTechnology, Aalborg University, in 1995.

From 1987 to 1988, he was with ABB-Scandia,Randers, Denmark. In 1992, he became an AssistantProfessor with Aalborg University, where in 1996,he became an Associate Professor and, in 1998, aFull Professor of power electronics and drives. In theperiod of 20062010, he was the Dean of the faculty

of Engineering, Science, and Medicine at Aalborg University, Denmark. Duringthe last years, he has held a number of Chairman positions in research policyand research funding bodies in Denmark. In 2007, he was appointed to theboard of the Danish High Technology Foundation. He is the author or coauthorof more than 600 publications in his research fields, including the book Controlin Power Electronics (Eds. M. P. Kazmierkowski, R. Krishnan, F. Blaabjerg)(Academic Press, 2002). His research areas are in power electronics, staticpower converters, ac drives, switched reluctance drives, modeling, character-ization of power semiconductor devices and simulation, power quality, windturbines, custom power systems, and green power inverter.

Dr. Blaabjerg has been an Associate Editor of the IEEE TRANSACTIONSON INDUSTRY APPLICATIONS, IEEE TRANSACTIONS ON POWER ELEC-TRONICS, Journal of Power Electronics, and of the Danish journal Elteknik.In 2006, he was the Editor-in-Chief of the IEEE TRANSACTIONS ON POWERELECTRONICS. He was the recipient of the 1995 Angelos Award for hiscontribution in modulation technique and control of electric drives and anAnnual Teacher prize from Aalborg University in 1995. In 1998, he was therecipient of the Outstanding Young Power Electronics Engineer Award fromthe IEEE Power Electronics Society. He was also the recipient of nine IEEEPrize Paper Awards during the last ten years, the C. Y. OConnor Fellowshipin 2002 from Perth, Australia, the Statoil Prize in 2003 for his contributions inpower electronics, and the Grundfos Prize in 2004 for his contributions in powerelectronics and drives. From 2005 to 2007, he was a Distinguished Lecturer forthe IEEE Power Electronics Society. It is followed up as Distinguished Lecturerfor the IEEE Industry Applications Society from 2010 to 2011.

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