The 7th International Conference on Power ElectronicsOctober 22-26, 2007 / EXCO, Daegu, Korea

TUE1-3

A Multiband Shunt Hybrid Active Filter WithSensorless Control

Surendra Kumar SSamsung India Software Operations Pvt. Ltd.

No. 66/1, Bagmane Tech ParkC.V. Raman Nagar, Byrasandra

Bangalore 560 093, INDIA.Email: ks.surendra@siso.com

Partha Sarathi SensannaDepartment of Electrical Engineering

Indian Institute of TechnologyKanpur 208016, INDIA.

Email: sensarma@iitk.ac.in

I. INTRODUCTION

Shunt Hybrid Active Filters (SHAF), consisting of an ac­tive filter and passive filters in series have been extensivelyreported in literature [1] [2]. This combination is placed inshunt with a non-linear load, as shown in fig. 1. This topologyovercomes the disadvantages of filter overload and systemresonance with a passive filter. Also, it results in significantreduction in the active filter rating. In its basic form, one SHAF

Abstract-This paper proposes a Mutiband Shunt HybridActive Filter(SHAF) with sensorless control. The plant is modeledin the discrete- time domain and a controller is designed usingPole shifting law in the polynomial domain. This control approachis very useful for filtering the load harmonics with reduced sensorcounts where low cost solution like SHAF. Multiple SynchronousReference Frames (MSRF) and low pass filters are used to mea­sure 5th and 7th harmonic components separately from load aswell as filter currents. Individual current controllers are designedfor the 5th and 7th harmonic currents. Control is realized in thestationary, three-phase (abc) reference frame. Performance of thecontroller is validated through simulation, using realistic plantand controller models, as well as experimentally on a full-scaledistribution system.Index Terms Multiband Shunt Hybrid Active Filter, Harmonicextraction, Multiple Synchronous Reference Frames, Poleshiftcontroller.

Fig. 2. Ideal Series Resonant Circuit

(P-I) controller, which requires measurement of the filter ca­pacitor voltages for feedforward compensation of disturbanceand cross-coupling terms in the control law. This requiresadditional complexity and adds to the cost of an otherwiselow-cost solution.

In this paper, a multiband SHAF is considered, in whichtwo passive filter branches, tuned at 5th and 7th harmonicfrequencies, are connected in series with the active filter.Switching harmonics of the active filter output are filteredby the passive filter impedance, which is inductive at theswitching frequency. The plant is modeled in the discrete­time domain and a discrete-time control law is derived. Thecontroller is designed using pole shifting law in the polynomialdomain to radially shift the open loop system poles towards theorigin i.e., more stable locations. With this Poleshift controller[5], sensing of capacitor voltages in the passive filter sectionsis not required. In order to damp filter resonances duringtransient changes in load harmonics, an active damping is in­troduced to greatly improve dynamic performance. Analyticalcontrol design is validated using simulation and experimentalresults on full-scale hardware. Multi-rate sampling is used tomodel the plant (fast sample-rate) and the controller (slowsample-rate). Switching of active filter devices is consideredthough device losses are neglected.

II. DESIGN OF PASSIVE FILTER

Non-linealLoad

Rj7 Cp

PCC

DigitalController

(2)

(1)

Fig. 1. Shunt Hybrid Active Filter

branch can compensate for only one harmonic frequency. Thisrequires multiple branches for each harmonic component in theload current. The possibility of using a single active filter inseries with multiple passive filter branches have been reported[4]. The general circuit schematic of this approach is shownin fig. 1. However, this approach uses a Proportional Integral

A series resonant filter circuit, is shown in Fig. 2. The filterimpedance is given by,

Z () -(L) (_1_)_s2LfmCfm+lfm s - S fm + - ---:;",...-~--sCfm sCfm

Resonant frequency W m of the filter is given by

Wm = JLfm1Cfm

978-1-4244-1872-5/08/$25.00 © 2008 IEEE 666

The 7th International Conference on Power ElectronicsOctober 22-26, 2007 / Exeo, Daegu, Korea

In this paper, as the 5th and 7th hannonic currents are to becompensated, m=5,7 and j=50Hz (fundamental frequency).

A. Selection of Cfm

The choice of Cfm is decided by the following factors.A high value reduces impedance at fundamental frequencyresulting in passage of fundamental current, which is highlyundesirable. Also a low value results in a bulky inductor in theresonant branch, which in tum increases its cost. The optimalvalue of the filter capacitor is found to be 10 J..LF. Other filterparameters are mentioned in Table I.

where, m == 5, 7. From (4) transfer function between filtercurrents and control voltage is

G () - Ifm(s) _ -s/Lfmpm S - -

Vcm(s) s2 + (Rfm/Lfm)s + l/(LfmCfm)(5)

III. SYSTEM MODEL

State space model of the SHAF system for the 5th and 7th

hannonic currents is given by

(4)

1- L

fm

o~ [~~:] [-3:= -t~m ][ ~~: ]+[

y == [1 0] [ifm Vfm]T

(3)W m == m.21fjwhere,

TABLE IFILTER PARAMETERS

L.f5 40.5 mHR.f5 1 nC.f5 10.0 J.LFLf7 20.7 mH,Rf7 0.41 nCf7 10.0 J.LF

Rf5 and Rf7 are the internal resistances of L f5 and L f7.

B. Impedance Characteristic of Passive Filter Circuit

System: sys --.-r-T""'O'""T"""_B_o-.-d_e--.--Di_ag_ra~m~~ ~~,.......,Frequency (Hz): 50.1 System: sys~nitude (dB): 43.8 ::::: :: Frequency (Hz): 9.96e+003i 40 ~J••••• Magnitude (dB): 58.7

120 Frequen~:(~~i~~/~,21:~ys ."~ 0 ..... Magnitude (dB): -0.01 .J .:. Frequency (Hz): 350

. . . . . . . . . .: Magnitude (dB): -7.75

90 : : :::: :~: (: : : ::::.... : System: sys ..:. System: sys ..i 45 : Frequency (Hz): 250 . Frequency (Hz): 350i_4:pr[(deg).O.3Jnhase(deg): 0.35

-90 "==========-...........==oi=:oio=..........=~~..............................~"-'-'-'-"" ...................................................,.".10

110

2103 10

4

Frequency (Hz)

Fig. 3. Bode magnitude plot for (Zf(s))

Fig. 3 shows the Bode plot (magnitude and phase) ofthe passive branch. It shows the fundamental componentand the switching hannonics (10 kHz or more) are blockedby the passive filter, whereas at other desired 5th and7th hannonic frequencies the filter offers low impedance.Switching hannonics of the active filter output are filtered bythe passive filter impedance, which gives more than 55dBattenuation at 10kHz. Hence only the required load hannonicswill pass through these branches, fundamental and switchinghannonics will be blocked. This results in a great reductionof the required rating of the Active filter.

IV. HARMONIC EXTRACTION

In this paper, only 5th and 7th hannonic componentsare sought to be compensated. These are extracted from ameasurement of the load current using Multiple SynchronousReference Frames (MSRF) and low pass filters [3], [4]. Phaselocking with the fundamental component of the PCC voltage isachieved through a PLL [6]. Denoting the fundamental phaseangle as (), transfonnations for each of the rotating referenceframes are carried out as shown in fig. 4.

iZailb

ilc

Fig. 4. Block diagram showing reference current generation using MSRF.

V. CURRENT CONTROLLER DESIGN

Individual current controllers are designed for the 5th

and 7th hannonic currents. The hannonic currents, extractedabove, are used as reference commands for the individualcurrent control loops. Control is realized in the stationary,three-phase (abc) reference frame.

A. Controller for 5th harmonic current

The closed-loop model of the system is shown in fig 5.Gpm(z) is the discrete-time (z-domain) transfer function of

Fig. 5. Closed loop current controller schematic.

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The 7th International Conference on Power ElectronicsOctober 22-26, 2007 I Exeo, Daegu, Korea

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System num poly b71 =-0.0048, b72= 0.004System den poly a71 =-1.95, a72 = 0.998Controller num poly 870=-184.06, 871 = 162.42Controller den poly TS1 =0.789Closed loop poles 0.974+0.193i, 0.974-0.l93i, -0.792

System num poly bS1 =-0.0025, bS2 - 0.0025System den poly aS1 --1.9729, aS2 - 0.997Controller num poly 8S0 =-374.2825, 8S1 -320.7645Controller den poly TS1 =0.7892Closed loop poles 0.981+0.l37i, 0.981-0.137i, -0.803

TABLE III5th HARMONIC CURRENT CONTROLLER

TABLE IV7th HARMONIC CURRENT CONTROLLER

where K m is the virtual resistance and U is the control input.

B. Active Damping

Quality factor for 5th hannonic filter is

Qfs = wsLfs = 63.5Rf5

In order to damp filter resonances during transient changesin load hannonics, Qf5 has to be reduced. For this, seriesresistance of the 5th hannonic filter has to be increased. Butadding physical resistance would increase losses. Instead, a"virtual resistance" [8] is added which is essentially an activedamping tenn introduced in the control law and is given as

U1 Hm(Z-l)ifrefm - ifm (13)

U U1 + Kmifm

C. Composite Controller

Using the above design procedure for the two controllers,analytical predictions of the closed-loop perfonnance is re­ported here. The w-plane plots are analyzed to obtain the phaseerror (between reference command and output) for 5th and 7th

hannonic currents. Fig. 6 shows the magnitude and phase plotin w-plane for the 5th hannonic controller, after transfonnation[7] of (9) to the w-plane, using

2 z-1w == ---. (14)

Ts z + 1

From fig.6, the predicted phase error for 5th hannoniccurrent is negligible (~ 1.7°). Corresponding plot for the 7th

hannonic controller is also obtained in a similar fashion. Fig.7 shows the magnitude and phase plot in w-plane for the7th hannonic controller. From fig.7, the predicted phase errorfor the 7th hannonic current is also found to be negligible(~ 2.0°).

(8)

Sampling interval(Ts ) 100 J-LsSwitching frequency (Ie) 10 kHzLoad inductance (Ld) 10.0 mHLoad resistance (Rd ) 30 nPCC voltage (I-I, rms) 415 VVde 80 V

TABLE IISYSTEM PARAMETERS

Am(Z-l )Rm(z-l) + Bm(Z-l )Sm(z-l) == Tm(Z-l). (10)

In (10), Tm(z-l) is the closed loop system characteristicequation obtained after shifting the open loop poles. It ischosen to be of the following fonn.

Tm(z-l) == Am(,~Z-l) == I+Aam1Z-1+A2am2Z-2, 0 < A < 1(11)

where,A is the pole shift factor and determines the proximity of theclosed-loop poles to the origin. A larger value of A impliesthe closed loop poles are close to the open-loop pole locations.As smaller values of A require a larger control effort, for theSHAF system, this implies a higher output voltage demandfrom the active fi Iter. However, this would increase the VArating of the active filter and would therefore undennine thecost advantage of SHAF. So, this pole shift factor is chosenhere to be 0.6. Using this advanced control method, sourcehannonic currents are reduced below limits prescribed in IEEE519-1992, even with distorted PCC voltages.

System parameters are mentioned in Table III. Solving

the plant and H (z) denotes the Poleshift controller. Sincecontrol is realized using a digital processor, it is appropriateto transfonn the plant transfer function in to its discrete-timeequivalent. Zero-order-hold equivalent of the plant is obtainedusing the following transfonnation [7].

Gpm(z) = (z - l)Z {Gp:(s) } . (6)

Consequently, the discrete-time plant transfer function is de­termined as

-1 Bm(z-1) bm1 z-1+ bm2z-2 (7)Gpm(z ) = Am(Z-1) = 1 + am1Z-1 + am2z-2'

Expressing the controller transfer function H (z) as

(-1) Sm(z-l) SmO + Sm1 Z -

1

H Z == == ------=--m Rm(z-l) 1 + Tm1Z-1

from fig. 5 the closed loop system transfer function is

. Bm(z-l)Sm(z-l). [k]zfm[k] = Am(z-1)Rm(z-1) + Bm(Z-1)Sm(Z-1)Zfref m (9~

The controller parameters are obtained from the solution ofthe following Diophantine equation.

(10) and (11), the numerator and denominator polynomialsof the 5th and 7th hannonic current controllers are obtainedas mentioned in Tables III and IV.

VI. SIMULATION RESULTS

Perfonnance of closed loop system is simulated for bothpure sinusoidal and distorted PCC voltage cases. The activefilter is simulated using ideal switches so as to include

668

~ 20 ';'" : : T" ..< 0 ..~.... ..:.... ..;.... ..~.... .

: : : :

~ -20

0.4 0.42 0.44 0.46 0.48 0.5

! 1:

-18.4 0.42 0.44 0.46 0.48 0.5

!-:~

The 7th International Conference on Power ElectronicsOctober 22-26, 2007 I Exeo, Daegu, Korea

Bode Diagram10 . (Hi 249

~ F\: Ma~'nitude [dB' -0.0682aJ 0 / \...: _: :/~ -10~·····.. ·,····················· .. ········, ········· , / ;-;-~: ~ 0.1

Q)

~ -20~" ..:.. -:...:.: -:.:-::-:.:- .... :...:. -:..:-:.:::: .....:...:.. '...'.:.:.:.:.: ..... ,.. ,..:..:.:., :::.......:- ..... ,.~ ,.:.:.'-1

"c ,/~ -30 ~ :. .. :.. ::.; .:.:.:0:.: ; ...:. .:..:. :.;;;;/./... .:.. ; .:..:.:.:.:.: ; .. ; ..:..:.:.;;;: :. .. ;..;.~; .:.:.;.1

~ -40 1- " .•.:.:.:.:.: ; .. ;. ~.; ;;; : :.. ;.; ;.:.:.:.: ; .. ; ..:. ;.:.; ;;; : :.. ; .~; ..:.:.:.j

I------~tIO~~~ ............................+++-~ .................................................~...........~1oNoI

.............:_ 135~'" ·.... ·0· ".; .:.:.:.:.: ....."'-.; .. :..:.;;;;; ......: ... :.. ;.; ;.:.:.:.: ..... ; .. ; ..:. ;.:.; ;;; .....: ... :.. ;.~ ;.:.:.:.1

0>~ 90~ ....:···:··;;·;·:·:·:·:·:·····; .. ;··:··:·:·;;;;~~~~:-,.", .. ;.. ;..:.;.:.;;;:......:...:.. ;.l; ..:.JQ) \ System: sys~ 45~ ....:···;·;·;·:·:·:·:·:·····; .. ;··:··:·;;;;;·····:···:.. ;.:.;.:.:.:.:.....,. Frequency (Hz): 250if 0 \ Phase (deg): 1.94

~.I-45~...............................;.;.L........................O""""O""'~ .....................;"..",;..;..,;,.;.;.;.L....................................~...............~~

10-1 10° 101 102 103

Frequency (Hz)0.4 0.42 0.44 0.46

Time(sec)0.48 0.5

351

Fig. 6. Magnitude bode plot (w-plane) of closed loop system

. System: sys.----.--..--.-T"'"T""T'"1~--.-----.---B.......,O-.-de.,...,..DTT'"I_ag_ra..-m-.- Frequency (Hz): 351

m 0,:.,~-0.137~ -20 ..... ,....... ,....... ,... :-- .... ~ ... ~ .. >:..:.»Q) : ::: ::::::~ .~ .~ -40 :::: : :.. :..:.:.::.:.: ..0> : : : : : ::::

~::~ffiW:135r ..... ;....:.. :..:..:.;.:.;;_...... ;_... ;_~~-:-::-;:.:- ;·~.. \ .. :..:.;.:.;.:.:.......:.... :.. :.j.:.;:.:.f

-0 901---.....;--.-~~~····;·.. ·:- ..:·.:··:.;·:-:-:·· :.. ·,··;··:.·:-:·:.:-:····· .. :.. ··; .. ;·1·;-:·;.:-1

CD 45r ·; .. ··:···:··:-·:·;·:-:·:···· .. ·:·· ..:· ..:··:··:·:·:·:·:·· ·:· .. :I··:··:··:·:·:·:·:····· .. :· .. ·: .. :·j·;-:·:·:-I

~ O~ ·· .. ·......·· ..··· .. ·.... ·.. ·· ..···.... ·· ......·.. ·.. ·· .. ··\..,~ -45 System:~ -90 Frequencya.. -135 Phase

-180 r ·: ~ .. :..:..:. :.:.:: : : :..:. ~.: .:.:.: : :.. :..:.:.: :.:.: : :.. :.',. :.::~_225b..........". ~ ~~""-'-'-'-".i............. ..........................L.....:...~~..L....i...,.;......,

10° 101

102

103

104

Frequency (Hz)

Fig. 7. Magnitude bode plot (w-plane) of closed loop system

switching action without considering switch losses. Multi­rate simulation is carried out using 2J-ts sampling intervalfor the continuous time plant and 100J-ts for the discrete­time controller. System parameters used are as indicated inTables I and III. Performance of the MSHAF is tested undervarious operating conditions. Specifically, the performanceunder distorted PCC voltages and de-tuning of passive filteris investigated and reported.

A. PCC voltage without distortion

Fig. 8, shows the simulated results for pure sinusoidal PCCvoltage. Fig. 9 shows the FFT analysis of source and loadcurrents. In this 5th and 7th source harmonic currents arereduced with in IEEE 519-1992 limits and 11 th and 13th

source harmonic currents are not affected.

B. PCC voltage with distortion

Fig. 10, shows the simulated results for distorted PCCvoltage having 5% of 5th and 4% 7th harmonics. Fig. 11shows the FFT analysis of source and load currents. In this5th and 7th source harmonic currents are reduced with in IEEE

Fig. 8. Case A: (a) Load current; (b) Filter current; (c)Source current

100

90

80

70~c:

60E~

'T:l 50r::tE'E 40

~30

20fiedby

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Hannonic number

Fig. 9. Case A: FFf Comparison of Load and Source currents

IS. 40

~-:g~~ -48.5 0.52 0.54 0.56 0.58 0.6tr.l Time(sec)

!-:~e 0.5 0.52 0.54 0.56 0.58 0.6

tr.l Time(sec)p. 40

~-:g~~ -48.5 0.52 0.54 0.56 0.58 0.6

Time(sec)

Fig. 10. Case B: (a) Load current; (b) Filter current; (c)Source current

519-1992 limits and 11 th and 13th source harmonic currentsare not affected.

C. De-tuned passive filter

Fig. 12 shows the simulated results for +5% De-tuned 5th

and 7th harmonics LC components. This has shifted comer

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The 7th International Conference on Power ElectronicsOctober 22-26, 2007 / EXCO, Daegu, Korea

Fig. 11. Case B: FFf Comparison of Load and Source currents

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Harmonic number

VII. EXPERIMENTAL RESULTS

Fig. 14. MSHAF Experimental test setup

The Poleshift control strategy has been experimentallytested on a 415 V, 3-phase, 50 Hz distribution line. The loadcomprised a diode rectifier feeding a resistive load throughan inductive filter. A two-level, low power (400 VA) inverter(active filter) was used. Passive filter parameters used were asmentioned in Table I. The entire control algorithm includingharmonic extraction and PLL was realized on a DSP platform,using TMS320F240 processor. Hall effect current sensors wereused to sense the filter and load currents. As a three-wiresystem has been considered, only two line currents have beeensensed. The active filter was designed along with all associatedprotection and gate triggering circuitry. Sensed signals wassent to on board ADC and the PWM signals having carrierfrequency of 10kHz are generated using Simple compareunit of DSP. In the experiment, inverter DC bus voltage wasmaintained constant with help of a diode bridge rectifier. The

1

0 Load Current, THD=19.28% l_ Source Current, THD=3.05%

100

90

80

70cad

60C)

S(;l

"t:l 50c::.z...... 400

~30

20

10

Maximum Individual Harmonic Cur ent

~ n / linjits Sp.ci~ed ~y tgEE 519-199

l..o ..

!-::0.5 0.52 0.54 0.56 0.58 0.6

10til0.. : :E : : :i 0

-18.5 0.52 0.54 0.56 0.58 0.6

~ 20:•.::" ::.::.. ' ...........••.•:•............... :••.•:...............•< a ,. .

~-20 : : .

0.5 0.52 0.54 0.56 0.58 0.6Time(sec)

frequency of the 5th harmonic filter from 250 Hz to 238 Hz.For the 7th harmonic filter the shift is from 350 Hz to 332 Hz.Fig. 13 shows the FFT analysis of source and load currents.

100

Fig. 13. Case C: FFf Comparison of Load and Source currents

Fig. 12. Case C: (a) Filter current; (b) Load current;(c)Source current

120 ~r---t-----.----.--r----.---,-~::=c:=:x:::;=c:::=c=~=c==:::c::::::;l

1

0 Load Current, THD=19.96% 1

_ Source Current, THD=5.32%

experimental test setup is shown in Fig. 14.

Using this set-up, the performance of the MSHAF wastested under different rectifier loading conditions. For prac­tical constraints, neither arbitrary distortion in the availablePCC voltage nor de-tuning of the passive filter could not becreated. Fig. 15 shows a particular case where the fundamentalcomponent of the load current is 6 A (rms). The filter current,load current and source current waveforms are shown. Thesource current waveforms are seen to be practically sinusoidal.Fig. 16 shows the FFT analysis of source and load currents.

In this 5th (2.44%) and 7th (1.57%) source harmonic currentsare reduced with in IEEE 519-1992 limits and 11 th and 13th

source harmonic currents are reduced by a small amount. Thisis however purely incidental, as the control does not focus oncompensation of these harmonics.

Fig. 17 shows the results for another loading condition. Herethe load current (fundamental, rms) is 12 A. Fig. 18 showsthe FFT analysis of source and load currents. Also in this case,the 5th (2.24%) and 7th (1.07%) source harmonic currents arereduced with in IEEE 519-1992 limits.

5 6 7 8 9 10 11 12 13 14 15Harmonic number

/

MaXI•• mum Individual Harmonic Current Limit Spa ified by

• IEEE519-1992,..,. ..

1 2 3 4

20

ca 80

=~-g 60.z......o~ 40

In this 5th (3.92%) and 7th (1.93%) source harmonic currentsare reduced with in IEEE 519-1992 limits and 11 th and 13th

source harmonic currents are not affected.

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The 7th International Conference on Power ElectronicsOctober 22-26, 2007 / Exeo, Daegu, Korea

100

90

80

70~

=6011)

~"0 50dcE...... 400

~30

20

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Hannonic number

Fig. 18. Rated load perfonnance: FFf of Load and Source currents

Fig. 15. Filter perfonnance under light load conditions. (a)Filter current;(b)Load current ; (c)Source current

I0 Load Current l_ Source Current

n / 11::1:1:: r In Inn..,

II I 1 n.. • '-

100

90

80

70~I 60

] 50~'0 40

~30

20

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Hannonic number

Specifie

IEEE 519-1992. Use of reduced sensor count along with an

active damping scheme ensures a low cost solution without

sacrificing any performance advantage. The complete analyti­

cal design procedure of controller parameters is presented. It is

verified by simulation that the proposed approach is immune to

parameter variations in the passive filter and distortions in the

supply voltage. Poleshift Control algorithm for 5th and 7th

harmonics was verified experimentally on a full-scale diode

rectifier load operating in a 3-phase, 415 V, 50 Hz system. DC

bus voltage of hybrid active filter was supported by a small

rating diode rectifier. Experimental results obtained completely

validate the analytical and simulation results.

REFERENCES

Fig. 16. Light load perfonnance: FFf of Load and Source currents

Fig. 17. Filter perfonnance under rated load: (a) Filter current (b) Loadcurrent (c) Source current

VIII. CONCLUSION

A Multiband SHAF scheme with a Poleshift controller is

shown to be an attractive realization approach for harmonic

compensation. Using this advanced control method, harmonics

in the source current are controlled within limits specified by

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[2] Po-Tai Cheng; Bhattacharya, S; Divan, D. M. , "Line Hannonics Reduc­tion in High- Power Systems Using Square-Wave Inverters Based Domi­nant Hannonic Active Filter", IEEE Transactions on Power Electronics,Vol. 14, NO.2, pp 265-272, Mar. 1999.

[3] Bhattacharya,S.; Divan, D. M. ; Banerjee, B. , "Synchronous ReferenceFrame Hannonic Isolator Using series Active Filter", Proc. 4th EPE,Vol.3, pp 030-035, 1991.

[4] Sukin Park; Soo-Bin Han; Bong-Man Jung; Soo-Hyun Choi; Hak-GeunJeong. , "A Current Control Scheme Based on Multiple SynchronousReference Frame for Parallel Hybrid Active Filter", Power Electronicsand Motion control conference 2000,Proceedings PIMEC 2000. The ThridInternational, Beijing, China, Aug. 2000.

[5] Ghosh, A.; Jindal, A.K.; Joshi, A., "Inverter control using output feedbackfor power compensating devices", IEEE Region 10 Conference on Con­vergent Technologies for Asia-Pacific Region,TENCON 2003, Bangalore,India, Oct. 2003.

[6] Kaura, V ;Blasko, V., "Operation of phase locked loopsystem underdistorted utility conditions", IEEE Transactions on Industry Applications, vol.33, no. 1,pp 58-63, Jan/Feb 1997.

[7] B.C. Kuo, Digital Control Systems, Mc-Graw Hill, 1999.[8] Pekik Argo Dahono, "A Control Method to Damp Oscillation in the

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