the design and implementation of a shu nt active …the design and implementation of a shu nt active...

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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/4260300 The Design and Implementation of a Shunt Active Power Filter based on Source Current Measurement Conference Paper · June 2007 DOI: 10.1109/IEMDC.2007.382736 · Source: IEEE Xplore CITATIONS 24 READS 1,243 4 authors: Some of the authors of this publication are also working on these related projects: Çok Seviyeli Evirici Kullanarak 3-faz Şebeke Destekli Aktif Filtreleme Yeteneğine Sahip Fotovoltaik Elektrik Enerjisi Üretim Sisteminin Tasarımı ve Uygulanması (KOU BAP 2010/077) View project Design and Implementation of Hybrid Energy Storage System Integrated Fast Charge Station Providing Reactive Power Support to Network for Electric Vehicles View project Engin Ozdemir Kocaeli University 74 PUBLICATIONS 1,214 CITATIONS SEE PROFILE Mehmet Ucar Kocaeli University 6 PUBLICATIONS 72 CITATIONS SEE PROFILE Metin Kesler Bilecik Seyh Edebali Üniversitesi 34 PUBLICATIONS 545 CITATIONS SEE PROFILE Murat Kale London College of Fashion 19 PUBLICATIONS 460 CITATIONS SEE PROFILE All content following this page was uploaded by Metin Kesler on 09 August 2015. The user has requested enhancement of the downloaded file.

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Page 1: The Design and Implementation of a Shu nt Active …The Design and Implementation of a Shu nt Active Power Filter based on Sou rce Current Measu rement Conference Paper · June 2007

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/4260300

The Design and Implementation of a Shunt Active Power Filter based on Source

Current Measurement

Conference Paper · June 2007

DOI: 10.1109/IEMDC.2007.382736 · Source: IEEE Xplore

CITATIONS

24READS

1,243

4 authors:

Some of the authors of this publication are also working on these related projects:

Çok Seviyeli Evirici Kullanarak 3-faz Şebeke Destekli Aktif Filtreleme Yeteneğine Sahip Fotovoltaik Elektrik Enerjisi Üretim Sisteminin Tasarımı ve Uygulanması (KOU BAP

2010/077) View project

Design and Implementation of Hybrid Energy Storage System Integrated Fast Charge Station Providing Reactive Power Support to Network for Electric Vehicles View project

Engin Ozdemir

Kocaeli University

74 PUBLICATIONS   1,214 CITATIONS   

SEE PROFILE

Mehmet Ucar

Kocaeli University

6 PUBLICATIONS   72 CITATIONS   

SEE PROFILE

Metin Kesler

Bilecik Seyh Edebali Üniversitesi

34 PUBLICATIONS   545 CITATIONS   

SEE PROFILE

Murat Kale

London College of Fashion

19 PUBLICATIONS   460 CITATIONS   

SEE PROFILE

All content following this page was uploaded by Metin Kesler on 09 August 2015.

The user has requested enhancement of the downloaded file.

Page 2: The Design and Implementation of a Shu nt Active …The Design and Implementation of a Shu nt Active Power Filter based on Sou rce Current Measu rement Conference Paper · June 2007

The Design and Implementation of a ShuntActive Power Filter based on Source

Current MeasurementEngin Ozdemir Mehmet Ucar Metin Kesler Murat KaleKocaeli University Kocaeli University Kocaeli University Kocaeli University

Technical Education Faculty Technical Education Faculty Technical Education Faculty Technical Education FacultyElectrical Education Electrical Education Electrical Education Electrical Education

Department Department Department DepartmentKocaeli, TURKEY Kocaeli, TURKEY Kocaeli, TURKEY Kocaeli, TURKEY

Email: eozdemir@kou. edu. tr mucar@kou. edu. tr metinkesler@kou. edu. tr muratkale @gmail.com

Abstract- In this study, design and implementation of a shunt mactive power filter (APF) based on a simplified control method isgiven without load and filter current measurement. The proposed vsimplified control method is based on instantaneous reactive ZLoadpower theory (IRP) and requires only measuring the source P Non-linearRLoaLcurrents to reduce the number of current sensors (CSs) required Source-- Non-linear-Loadin the conventional control approach. The source currents are - RCexactly in phase with the line voltages and approximately in 4 Lcsinusoidal waveform after reactive power and harmonic . _C

compensation. The proposed control technique has been testedunder different load conditions using Matlab/Simulink Shunt Active Power Filtersimulations and validated with a 10 kVA/380 V experimentalprototype based on digital signal processor (DSP) TMS320F2812. Fig. 1. The basic compensation principle of the three-phase shunt APF.Both simulation and experimental test results demonstrate thatthe proposed method is feasible in meeting the IEEE 519-1992 In recent years, several methods based on the IRP theoryrecommended harmonic standard limits. [4]-[6], also known as p-q theory, have been used to obtain the

current reference in the APFs. Although several improvedI. INTRODUCTION algorithms are proposed [7]-[10], most control circuits are

Harmonic current pollution of three-phase electrical power complicated and it is not easy to implement them. In

systems is becoming a serious problem due to the wide use of conventional p-q theory based control approach for the shunt

non-linear loads, such as diode or thyristor rectifiers and a vast APF, the compensation current references are generated basedvariety of power electronics basedapplianceson the measurement of load currents as shown in Fig. 2.variety of power electronics based appliances. Traditonally, However, the current feedback from the shunt APF output

passive inductance-capacitance (LC) filters have been used to current is also required, and therefore, minimum four CSs areeliminate the current harmonics and to improve the power desired. In the proposed method, the number of requiredfactor. However, passive LC filters are bulky, load dependent CSs is minimized as shown in Fig. 3.and inflexible. They can also cause resonance to the system.

In order to solve these problems, APFs have been reported _ _ C. LL[1]-[3] and considered as a possible solution for reducing ErAA0J Non-linear

9 ~~~~~~~~~~~~~~~~~~~~~~~~loadcurrent harmonics and improving the power factor. -i, II -Fig. 1 shows the basic compensation principle of the three- AcSource PTphase shunt APF. It is designed to be connected in parallel with csthe non-linear load to detect its harmonic and reactive currentand then to inject a compensating current into the system. cTherefore, the current drawn from the power system at thecoupling point of the shunt APF will result in sinusoidal 6waveform. The source current (is) is the result of summing the DSP Control Unit Active Power Filterload current (iL) and the compensating current (ic) as in (1).

iS=iL+iC ~~~~~~(1l) Fig. 2. Schematic diagram of the conventional shunt APF configuration.

1-4244-0743-5/07/$20.00 ©2007 IEEE 608

Page 3: The Design and Implementation of a Shu nt Active …The Design and Implementation of a Shu nt Active Power Filter based on Sou rce Current Measu rement Conference Paper · June 2007

RW iL5 CS RL LLThus, the sums of both the instantaneous source voltageso + 7 load

Non-linear and currents of the three phases are zero. As a result,.II I measuring only two source voltages and currents are adequate

Ac Surce PT for the reference current calculations. Therefore, theconventional Clarke Transformation of the source voltages andcurrents are calculated as shown in (2) and (3) [11].

<,<,<,Rc

<.c FVa 1 la O 1 FV5" 1 ~~~~~~~~~~~~~~(2)DSP ContrlUnit 6 Active Power Filter LVP ]L1/2 ]L2 v:i(2

C|().... Vd Fial=F32 °0 1Fa1a (3)Fig. 3. Schematic diagram of the proposed shunt APF configuration. Lj 1/ 2 42 Sb

In addition, the reference current calculation algorithm is In this paper, in order to perform easily implementation ofsimplified and easily implemented on the experimental the u-P transformations in the DSP software, (2) and (3) areprototype. In the proposed control technique, sensing only two- multiplied with 2/ and the simplified Clarkephase source voltages and currents along with a dc-link voltage transformati are otn an (4) andf(5).is adequate to compute reference currents of the three-phaseshunt APF. In this way, the overall system design can be easilyapplied, and the total implementation cost is reduced. The val 1 0] VSa (waveform of the source current in the proposed control method Lvfi L/,3 2/I3j Lvsbican be approximated as a sinusoidal waveform aftercompensation. Simulations and experimental tests areperformed in a laboratory prototype to confirm the validity of F 1 0 Sa (5)the proposed control algorithm. The proposed method is found L Iii ,L/3 2/I3j Lisbiquite satisfactory to compensate the reactive power and currentharmonics under different load parameters. In the conventional p-q theory based control algorithm with

II. THE PROPOSED SIMPLIFIED CONTROL METHOD load current measurement, the instantaneous imaginary power(q) is calculated and its negative is used in the control

The block diagram of the proposed simplified control technique for reactive power compensation. The calculation ofmethod for the three-phase shunt APF is shown in Fig. 4 It the q is not required in the proposed method, since it is notconsists of p calculation including simplified Clarke desired to draw the q from the source for power factorTransformation, a low pass filter (LPF), one proportional- correction. The calculation of the instantaneous real power (p)integral (PI) controller for dc voltage regulator, reference is adequate as shown in (6). The complicated calculations incurrent calculation including simplified inverse Clarke the conventional instantaneous reactive power theory are notTransformation and hysteresis-band current controller. required in the proposed algorithm. Therefore, the proposed

control scheme has been simplified in the calculations of DSPp calculation ref. current calc. software.

Vs, * 4 4__1 _ AHVSb lInstant. a-fl a-fl HysteresisQALis*.s~~ ~ ~ ~ ~ ~ ~~~p=VSalS+V (6)Power Current Inverse I Band |_H P Sa SaICalcul. IX IReferen. is8 Transf. IiSb Current I

B

iS, (Eq. 6) | (Eq. 8) (Eq. 9) |'L otolrg£BlSb --,* (q.L5) IQI I,CLThe instantaneous real power includes ac and dc values, can

||L--------- ------------_ Vdc L A___ _ _ _ __ _ _, + + +

A- l Vd*c PIoss llSc be expressed as+ dc voltage regulator-

p = p + (7)

Fig. 4. The block diagram of the proposed simplified control method. In the proposed control algorithm, instantaneous imaginarypower is set to zero (q=0) in order to compensate reactive

It can be seen in Fig. 4 that only source voltage and current power. Therefore, a single dc component of the real power ( p )signals are utilized in the control circuit of the proposed shunt p

is selected as a reference for harmonic and reactive powerAPF to calculate the reference currents of the voltage sourceinverter (VSI). Thus, the proposed control method is simplercopnai.Th cmeston urntefecsaethan~~~thto h ovninlAFagrtm. Inti.tuy h calculated by (8). In order to produce the dc component of the

shunt APF is connected to a three-phase three-wire system, ntnaeu elpwr(7) ntnaeu elpwriwhich has balanced source voltages and loading conditions. filtered using 1st order LPF with a cut-off frequency at 50 Hz.

609

Page 4: The Design and Implementation of a Shu nt Active …The Design and Implementation of a Shu nt Active Power Filter based on Sou rce Current Measu rement Conference Paper · June 2007

The additional average real power ( is added to the dc A A 0.A A 0

component of the instantaneous real power ()to cover the 3-phase sab Rc L R

VSI losses of the shunt APF. - source i~~~~~~~~~~~~~~~~~~~~~~b s~~~bc ~ ~~~P~~~1~~sohyristorbcthy bridgeidgVSI losses oftheshuntAPF. ~~~~~~~~~~~~~~~~~v-i measur v-i measure J*1hd rectifier

A B C step pulse generator

lSa ~ I Va ABC+Plss-4vb vbeta vbeta isla isla isb iab

Sflv + vpLV 0Vdcsimp. clarke current ref.ci simp. Inverse hyst.-bandtrans.p calc. dc voltage reg clarke Trans. cur. control

In this study, the compensation current references in the a-/5 (Fig. 4)coordinates (i*a is*) aetetrnfmdbckiotha-b-c Th rooe SmlfidCoto Mto

coordiates (i* i* throuh the inversesmlfdCare Ts=le-00 73-Leg VSI Blockcoordinates (~~~~~~~Sj Sb ) 06ipiid lre DsceesseTransformation as given below.

Fig. 5. Schematic block diagram of three-phase shunt APF system.1 0FLSa - 1 0 1Ca (9) In this study, the load considered was a three-phase half-

_-1/2 -,~FI2_ j*'Sb L cjP controlled thyristor bridge rectifier feeding an RL load. Fig. 6and 7 demonstrate the simulation results for the current

The phase "C" current reference (i*) is calculated by harmonic filtration and the reactive power compensationSC performance of the shunt APF.

tSc+ta+s) 1)4Without+41 WithAPAPF 4 -~Load Variation------

These reference currents should be supplied to the power 200system by switching of the insulated-gate-bipolar-transistor VSab, [V] 0-

-400(IGBT). The method for the generation of the switching pattern 4028 03 02 034 06 038 04 02

is achieved by the instantaneous current control of the shunt 20APF line currents. The actual suc currents (iSa iSb) are bjA]0

-40measured instantaneously and actual phase C' current ( i )002 0.3 0.32 0.34 0.36 0.38 0.4 0.42

is obtained from Fig. 4. Then they are compared with the iILb, A] 0.-20.

reference currents (iP P* P ) generated by the control -40Sa Sb SC 0.28 0.3 0.32 0.34 0.36 0.38 0.40.42

40

algorithm in the hysteresis-band current controller. Three ------[-------0-hysteresis-band current controllers generate the switching -20.--pattern of the VSI. The switching logic is formulated as 0e.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42

follows tm s

Fig. 6. Simulation results for the current harmonic filtration performance ofIf iSa < ( i a - HB) higher switch is OFF and lower switch is the shunt APF.

ON for leg "A" (QA=1)4-Without - ~ With APFIf iSa > ( i a + HB) higher switch is ON and lower switch isAPs +~~~~~~~~~~~~~~~~~~~~AF4 Load Variation - 0

OFF for leg "A" (QA = 0). 0 ----i\---- 1~---VSa [V] 200"400

-400 sa 5hyTereswis-band currnctiontrol is the fases ontrols methond 025 03 035 0.4 0.45 0.5

400witharminimumihardwrsiiandy usoftwa orebtvrepniablerswitchin vV]200-------------- \--------frequencyris itsrmant adrawbackr[12] Thendc-inkh volTage -200hysteresis-band current control is the fastest control method ~0.25 0.3 0.35 0.4 0.45 0.5regulator is designed to give both good compensation and an~~~~~~~4

rgltrisII sgedtSIMUATIO oANEXERoETARomensULtSo n a 0.25 0.3 0.35 0.4 0.45 0.5

lime [s]A. Simulation Results

wasfirstFig. 7. Simulation results for the reactive power compensation performance ofThe- performancei of the- proposezd control nalgrithm theZicz shn APF.

Page 5: The Design and Implementation of a Shu nt Active …The Design and Implementation of a Shu nt Active Power Filter based on Sou rce Current Measu rement Conference Paper · June 2007

proposed method, in 0.36 s thyristor rectifier firing angle (a) using C programming language in TIs C2000 code composerare increased from 15° to 45°. The source current waveforms studio (CCS) integrated development environment (IDE).reveal that the shunt APF is effective in compensating for the Moreover, it was verified by implementing an algorithmload harmonic current and reducing the total harmonic programmed by C language using floating-point arithmetic (IQdistortion (THD) of the source current from 24.5% to about math) in the DSP. F2812 eZdsp has an internal 36 kB RAM, 23.4% in 0.3<t<0.36 s, and from 40.8% to about 4.7% after load kB OTP ROM, 256 kB flash, 16 channels pulse widthhas changed in 0.36 s. In thyristor bridge rectifier, the power modulation (PWM), 12-bit 16 channels analog-to-digital (A/D)factor decreases as the firing angle increases. The system converters and an external 128 kB SRAM, expansionpower factor is also compensated as shown in Fig. 7. The shunt interfaces and parallel port JTAG interface. It can performAPF forces the mains current to be sinusoidal and in phase parallel multiply and arithmetic logic unit (ALU) on integer orwith the mains voltage in the proposed control algorithm. The floating point data (using IQ math floating point engine) in asimulation results have clearly shown that the shunt APF 6.67 ns single cycle instruction time with a peak computationperformance is quite similar to that of conventional solutions. rate of 150 million instruction per second (MIPS).Moreover, as the proposed circuit needs only source current The source voltage and current signals are measured byfeedback signals where the load CSs are not required, thereby potential transformers (PTs) and LEM hall-effect CSs,simplifying the circuit design significantly. respectively. The dc-link voltage is sensed using an AD210

B. Design and Implementation of the Three Phase Shunt APF isolation amplifier from Analog Devices. These signals weresent to the interface boards for calibration before applying toprototype. A/D inputs of DSP.

The feasibility of hardware experimentation for the proposed The CONCEPT 6SD106EI six-pack IGBT driver module issimplified control method was evaluated by designing and used for driving the IGBTs. It has short circuit and over-implementation of the three-phase shunt APF. A three-phase current protection functions for every IGBT and providesthyristor rectifier with the RL load is connected to ac mains to electrical isolation of all PWM signals applied to DSP. Onlydemonstrate the effectiveness of the proposed method for one input PWM signal is required for each VSI leg. It canreactive power and current harmonic compensation. Fig. 8 generate dead times and the reverse PWM signal directly.shows the configuration of the 10 kVA experimental prototype. Therefore, only three PWM signals are generated in DSP andThe current control of the shunt APF is implemented by applied to IGBT driver. Then, general purpose I/Os (GPIO) arehysteresis-band current controller on the DSP. The proposed used to generate switching signals instead of internal pulsecontrol technique is implemented on the F2812 eZdsp board width modulators of the DSP.

VS RsLXS iLa RL* i iiL

Cs Rd,0

T ~~~~~~~~~~~~~~~~~~~~~~Ld,

AC SouceC380V, 5OHz

VS. Vsb ~ ~ ~ ~ ~~~~~,Thyristor bridge rectifierVSa VSb iSa iSb Non-linear load

CS-Hall effect Current Sensor

Pre-Charging Shunt Active Power FilterResistors t t t AJ BJ CJ

Semicoductor QA QELl QOL Amplifier

QAI QA QB QBL QCH

CGBTD river lBoard Vc InpV~~ V~lt~~g~ (vs~~, VSb)~ ~ V5~~ DI VSb Dl p~B Cd,kI)>

(gate driver solationshor ci cut Islto

QAHI tA QBHItB QCHt CI

Fig. 8. The shunt APF configurationCoftheexpeorimntearot protoo611iSaAIiSb AI T al eZds

Interface I oerotgSource Voltages (VSa, VSb) Boards VSa DI, VSb DIprotection)

|Parallel nort cable

Page 6: The Design and Implementation of a Shu nt Active …The Design and Implementation of a Shu nt Active Power Filter based on Sou rce Current Measu rement Conference Paper · June 2007

C. Experimental Results Fig. 10(b). It can be shown that an improvement in theFig. 9 and Fig. 10 show experimental results with firing waveform of the source current when compared with the load

angle a=15° and a=45°, respectively. The source voltage and current waveform. The load and filter current waveforms withload current waveforms with firing angle a=15° and a=45° are firing angle a=15° and a=45° are illustrated for phase "A" inillustrated for phase "A" in Fig. 9(a) and Fig. 10(a), Fig. 9(c) and Fig. 10(c), respectively. After compensation,respectively. After start up of the shunt APF, the source source current becomes sinusoidal and in phase with the source

voltage and compensated source current waveforms with voltage. Hence, both harmonics and reactive power are

a=150 and a=450 are showed for phase "A" in Fig. 9(b) and compensated simultaneously.

AUTO CH2 DDC STOP AUTO CH1I DC STOP,,

(a) (a)

AUJTO CH2fOC STOP AUJTO CH1ifOC STOP

CHi_2V CH2 02V 5ms

,,z,i,,,,j,,,,j,,e, ,,,,i ~~~~~~~~~~~~~~~~~~~. . . . . r. i , m , ,,j,,, . l. . . . . .,,,,,,f,2-~~~ ~ ~ ~ ~ ~~~~~1

CH1 1V CH2 0.2V 5mns CH1 1V CH2 0.2V 5ms

(a) (a)

AUTO CH2 -r DC STOP AUTO CH1 I DC STOP

U.......v

2-r 2- IS

CH1 1V CH2 0.2v 5ms CH1 1V CH2 0.2V 5ms

(b) (b)

612~~~2

Page 7: The Design and Implementation of a Shu nt Active …The Design and Implementation of a Shu nt Active Power Filter based on Sou rce Current Measu rement Conference Paper · June 2007

The flow chart of the control algorithm in the DSP software IV. CONCLUSIONis shown in Fig. I11. This paper proposes a new simplified control method for the

shunt APF based on source current detection. With theproposed technique, detection of neither load current nor APF

Initialization of processor output current is necessary. Therefore, computations andcircuit implementation of the proposed control method become

Initialization of varibles quite simple compared to conventional load current detection11 techniques. In order to confirm the effectiveness of the

Input data from AD (Vs,, VSb, iS,, iSb, Vdc) proposed control algorithm, the approach has been tested, I> through the simulation and experimental validation.

Simplified Clarke Transform. (v vfi i,i, ) Experimental test results using a F2812 eZdsp board areCalculation of instantaneous real power (p)

given to demonstrate the performance of the proposed method.Filtration of p with LPF ( Both simulations and experimental results confirm that the

proposed control method is simple and easy to implementDC voltage regulator with PI control (Pls) compared with the conventional techniques. The resultsCalculation of current references (.~ obtained have clearly shown that, even using only sourceCalculation of cuffent references (i isSimpif. v..ClarkeTrans. ) and ca current measurement system, the APF performance is quiteSimplif. inv. Clarke Trans. ( i* ) and iSc calc

l__T_Sb SC

similar to that of conventional solutions. Moreover, as theHysteresis-band current controller (QA, QB, Qc) proposed circuit needs only supply current feedback signals

where the load CSs are not required, thus the circuit design can[Digital outputs for PWM signals (QAH QBHQBH) be simplified significantly.

ACKNOWLEDGMENTFig. 11. The flow chart of the control algorithm in the DSP software. This research was supported by TUBITAK Research Fund,

(No: 105E182-HD-08) and Kocaeli University Research Fund,The design specifications and the main parameters of the (No: 2001/13).

prototype are indicated in Table I. The photograph of the shuntAPF prototype is shown in Fig. 12. REFERENCES

[1] H. Akagi, Y. Kanazawa and A. Nabae, "Instantaneous reactive powerTABLE I compensators comprising switching devices without energy storage

MAIN PARAMETERS OF THE PROTOTYPE elements," IEEE Trans. Industrial. Applications, vol. IA-20, 1984, pp.System Parameters 625-630.

Source voltage VSabc 220 vns [2] B. Singh, K. Al-Haddad and A. A. Chandra, "A review of active powerSystemIfrequency fs 50 Hz

filters for power quality improvement," IEEE Trans. Industrialsystem frequency fs 50 Hz Electronics, vol. 46, Oct. 1999, pp. 1-12.

APF Parameters [3] A. Emadi, A. Nasiri and S. B. Bekiarov, Uninterruptible power suppliesDc-link voltage Vdc 800 V and activefilters. New York: CRC Pres, 2005, pp. 73-11 1.[4] E. H. Watanabe, R. M. Stephan and M. Aredes, "New concepts ofDc side capacitance Cdc 1100 pF instantaneous active and reactive powers in electric systems with genericAc side inductance Lc 3.75 mH loads," IEEE Trans. Power Delivery, vol. 8, 1993 pp. 697-703.

Switching frequency fs. lokHz [5] F. Z. Peng and J. S. Lai, "Generalized instantaneous reactive powertheory for three-phase power systems," IEEE Trans. Instrum. Meas., vol.

Load Parameters ~~~~~~45,Feb. 1996, pp. 293-297.Ac side inductance LLac 1 mH [6] J. Afonso, C. Couto and J. Martins, "Active filters with control based onDc side resistance RLdc T 18 Q the p-q theory," IEEE Industrial Electronics Society Newsletter, vol. 47,Dc side inductance LLdc 18 mH, no. 3, 2000, pp. 5-11.Dc side inductance LLdC j 85 mH [7] F. S. Pai and S. J. Huang, "A novel design of line-interactive

uninteffuptible power supplies without load current sensors," IEEE Trans............................Power Electronics, vol. 21, no. 1, January 2006, pp. 202-210.

3-phase thyristor Measurementbr [8] D. Casadei, G. Grandi, U. Reggiani and C. Rossi "Control methods for

rcifie mod=E *=[E 10 ; =

rectifierrShurtAPF module Prag s =active power filters with minimum measurement requirements," IEEE

App. Power Elect. Conference., APEC, Dallas, USA, March 1999, pp.14-18.

[9] L. Zhou and Z. Li, A novel active power filter based on the leastcompensation current control method," IEEE Trans. Power Electronics,

Interface boards ~~~~~~~~~~Vol.15, no. 4, July 2000, pp. 655-659.[10] G. Escobar, A. M. Stankovic and P. Mattavelli, "An Adaptive Controller

in Stationary Reference Frame for D-Statcom in Unbalanced Operation",Power IEEE Trans. Indust. Electronics, vol. 51, no. 2, Apr. 2004, pp. 401-409.

[12 . Malesani Pigh

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