This article was downloaded by: [Memorial University of Newfoundland]On: 01 August 2014, At: 14:53Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Electric Power Components and SystemsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/uemp20

Current Tracking Error Analysis for Shunt Active PowerFiltersGui-Ping Yi a & Ren-Jie Hu aa Department of Electrical Engineering , Southeast University , Nanjing , ChinaPublished online: 10 Dec 2013.

To cite this article: Gui-Ping Yi & Ren-Jie Hu (2014) Current Tracking Error Analysis for Shunt Active Power Filters, ElectricPower Components and Systems, 42:1, 35-44, DOI: 10.1080/15325008.2013.843103

To link to this article: http://dx.doi.org/10.1080/15325008.2013.843103

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Electric Power Components and Systems, 42(1):35–44, 2014Copyright C© Taylor & Francis Group, LLCISSN: 1532-5008 print / 1532-5016 onlineDOI: 10.1080/15325008.2013.843103

Current Tracking Error Analysis for Shunt ActivePower FiltersGui-Ping Yi and Ren-Jie HuDepartment of Electrical Engineering, Southeast University, Nanjing, China

CONTENTS

1. Introduction

2. System Configuration

3. Analysis of Current Tracking Error

4. Influence of Current Tracking Error

5. Experimental Results and Discussion

6. Conclusion

References

Keywords: active power filter, direct current control, current tracking error,reference current

Received 9 December 2012; accepted 7 September 2013

Address correspondence to Dr. Gui-Ping Yi, Department of ElectricalEngineering, Southeast University, No. 2, Sipailou Road, Xuanwu District,Nanjing City, 210096, China. E-mail: ygp326@163.com

Abstract—Direct current control has been used in many voltagesource converters connected to the grid, such as shunt active powerfilters. In their stationary coordinates control systems, there are twoclosed control loops, one is the current loop and the other is the voltageloop. In practical applications, because the voltage source convertersare connected to the grid, the output current will be affected, a quitesignificant tracking error exists in the current control loop while theactual output current of the converter is still satisfactory. Analysesand design considerations are carried out to investigate this confusingissue. The tracking error is caused by the source voltage; it is an activecurrent and does not affect the compensation results of reactive andharmonic current. The variables that affect the current tracking errorare identified, then the influence of tracking error is proposed to guidepractical applications. Experimental results verify the analyses anddesign considerations.

1. INTRODUCTION

Harmonic effects on power systems have received recognitionand attention. Under the background of serious harmonic pol-lution and high demands on power quality for users, applica-tion of the advanced dynamic compensation device to controlpower quality for industrial enterprises will bring considerableeconomic and social benefits [1]. The shunt active power filter(APF) has a voltage source grid-connected converter; directcurrent control and indirect current control are two commonlyused methods in the current control system of voltage sourceconverter.

In the direct current control system, there are usually twoclosed control loops; one is the current loop and the other is thevoltage loop. There is a proportional integral (PI) controller ineach closed loop. In the APF system, the command-trackingerror is the error of output current and reference current. Usu-ally, the larger the PI parameters are, the less the tracking errorwill be. However, in many control systems, the PI parametersof the current loop cannot be adjusted to approximate infinitydue to the requirements of system stability and engineeringrealization. In this article, an APF is applied to compensate thereactive and harmonic current produced by the non-linear load

35

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014

36 Electric Power Components and Systems, Vol. 42 (2014), No. 1

[2, 3]; the compensation result is good, and the output is thereactive and harmonic current of the load, but a considerabletracking error exists in the current control loop. This articlemakes detailed analyses of this phenomenon.

A feed-forward control method of source voltage harmonicdetecting is available in the literature [3, 4] to suppress theharmonic influence. This control method, which improves thecompensation characteristics and reduces the current trackingerror, is applied in the condition of source voltage distortion.The current control error in this study is different from that ofthe literature [3, 4] due to the source voltage without distor-tion in this article. The source voltage has been used directlyas feed-forward to eliminate the influence of source voltageharmonic in the literature [5, 6]; this method does not producea current tracking error, but it needs to add a source voltagedetection segment.

The control method in this article, which adopts direct cur-rent control that merely detects voltage synchronous signal,is different from that of the literature [5, 6]. The direct cur-rent control without a voltage feed-forward link for savingcosts is usually applied to the situation of undistorted sourcevoltage. In this article, based on the obtained current looptransfer function and the system block diagram, analytical ex-pressions of the current control error are derived. The variablesaffecting the tracking error are then obtained. If the system pa-rameters are not chosen correctly, the tracking error will behigh enough. The reasons why a control error exists togetherwith satisfactory output current are subsequently revealed. Thetracking error affects the peak value of the modulation wave.If the peak value of the modulation wave is higher than thatof the carrier wave, the system will work abnormally. Accord-ing to the choice of variables that affect the tracking error, themethod to design a voltage source converter with direct currentcontrol is presented. Finally, the influence of control error oncurrent compensation characteristics is proposed. The experi-mental results verify the validity of analyses and conclusions[7].

2. SYSTEM CONFIGURATION

The main circuit of shunt APF is shown in Figure 1(a), andthere is a voltage source converter in the system. Figure 1(b)shows the single-phase equivalent circuit. In Figure 1(c), theblock diagram of reference current calculation is also shown;the instantaneous reactive power theory is utilized to calculatethe reference current in this system [3, 8], where PLL is aphase-locked loop, LPF is a low-pass filter, iLk (k = a, b, c)is the load current, i∗

ck is the reference current, and ick is theoutput current. �ick is the difference between i∗

ck and ick; afteramplification by the PI controller, it is compared with the trian-

FIGURE 1. Shunt APF: (a) main circuit, (b) single-phaseequivalent circuit, (c) block diagram of reference current cal-culation, and (d) diagram of direct current control.

gular wave generated by the pulse-width modulation (PWM)signal wave. uk is the source voltage, U ∗

dc is the reference of theDC-side voltage, and Udc is the DC-side voltage, respectively.The current control system is shown in Figure 1(d), where the

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014

Yi and Hu: Current Tracking Error Analysis for Shunt Active Power Filters 37

cki*cki

iPK

FBK

ku

1

Ls RPWM

s1

K

T sFBK

*ck0i

dci

(a)

*ck0i

dci

cki ckiiPKFBK

ku*cki

PWM

s1

K

T s

1

Ls R

(b)

FIGURE 2. Direct current control system: (a) block diagramof current loop and (b) unit feedback block diagram of currentloop.

direct current control of bipolar triangular wave modulation isused [7, 9]. The impedance value of the reactor connected tothe converter is ωL + R. Together with the voltage control cur-rent of DC side, the reactive and harmonic currents detectedthrough the circuit of reference current calculation are used asthe reference current. The APF produces compensation cur-rent to suppress the reactive and harmonic current of the sourcethrough the current closed-loop control and PWM control. Asa result, the source current no longer contains harmonic andreactive current.

3. ANALYSIS OF CURRENT TRACKING ERROR

3.1. Current Loop Control Diagram

Figure 2(a) shows the block diagram of direct current controlsystem [10–12], and Figure 2(b) shows the unit feedback blockdiagram. The main circuit loss determined basically by theresistor R value is equivalent to resistor R loss [7, 13].

Here, i∗ck0 (k = a, b, c) is the reference current in the

form of a digital signal, idc is the loss current of converter,i∗ck = i∗

ck0 + idc is the reference current in the form of analogsignal, and KiP is the proportional parameter value in thecurrent loop. The integral parameter value is too small to beconsidered. KFB is the proportional coefficient of alternating-current/direct-current (AD) conversion, �ick is the trackingerror and ick is the output current, respectively. Ts is the switchperiod, Ts/2 is the delay time of PWM [9]; signal samplingtime of current loop, and operation delay time are alsoTs/2. KPWM is the proportional parameter of the converter,KPWM = Udc/2UT ; UT is the peak value of the triangularwave. To ensure steady operation, KiP is as big as possible.

The purpose of designing the control system is to make ick

equal i∗ck . The system is a two-input and one-output system.

One of the inputs is source voltage, and it will affect the outputcurrent; the tracking error then exists. The influence of eachinput on output will be discussed in what follows, and themethod to design the control system is presented.

3.2. Influence of Reference Current i∗ck on

Tracking Error

Assuming the source voltage input is zero, the output currentis ick1. The open-loop transfer function of output current toinput reference current can be obtained as

G(s) = (KFB Kip KPWM)/[(LTss2 + (L + RTs)s + R]. (1)

The closed-loop transfer function is expressed as

�1(s) = G(s)

1 + G(s)= (KFB Kip KPWM)/[(LTss2 + (L + RTs)s

+ R + KFB Kip KPWM]. (2)

Lettin s = jω, the frequency characteristics can be derived asfollows:

�1( jω) ={

1, ω << ωc

G( jω), ω >> ωc. (3)

The Bode plot is shown in Figure 3, and Bode plots withchanging parameters are shown in Figure 4. The Bode plotsshow that parameters Ts, R, and L do not influence the transferfunction at low frequency, so these parameters can be ne-glected. In addition, in practical applications, the cut-off fre-quency is ωc ≈ 104 rad/s, and the value is bigger than the com-pensation harmonic frequency. Thus, the closed-loop transferfunction can be represented as

�1(s) ≈ 1. (4)

According to Eq. (4), the gain of reference current to the outputcurrent is 1, the proportional control error of current loop is

FIGURE 3. Bode plot of transfer function of Eq. (2) (colorfigure available online).

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014

38 Electric Power Components and Systems, Vol. 42 (2014), No. 1

-80

-60

-40

-20

0

20

Mag

nitu

de (d

B)

102

103

104

105

-180

-135

-90

-45

0

Pha

se (d

eg)

Bode Diagram

Frequency (rad/sec)

L=2mH

L=4mH

L=2mH

L=4mH

L=0.4mH

L=0.4mH

(a)

-80

-60

-40

-20

0

20

Mag

nitu

de (d

B)

102

103

104

105

-180

-135

-90

-45

0

Pha

se (d

eg)

Bode Diagram

Frequency (rad/sec)

R=10�

R=1�

R=1�

R=10�

R=0.1�

R=0.1�

(b)

-80

-60

-40

-20

0

20

Mag

nitu

de (d

B)

101

102

103

104

105

-180

-135

-90

-45

0

Pha

se (d

eg)

Bode Diagram

Frequency (rad/sec)

Ts=1TTs=0.5T

Ts=4T

Ts=1T

Ts=0.5T

Ts=4T

(c)

-100

-80

-60

-40

-20

0

20

Mag

nitu

de (d

B)

101

102

103

104

105

-180

-135

-90

-45

0

Pha

se (d

eg)

Bode Diagram

Frequency (rad/sec)

Kip=0.5

Kip=0.5

Kip=1

Kip=4

Kip=4

Kip=1

(d)

FIGURE 4. Bode plots with changing parameters: (a) withchanging L, (b) with changing R, (c) with changing Ts, and (d)with changing KiP (color figure available online).

-80

-60

-40

-20

0

20

Mag

nitu

de (d

B)

10 10 10 10 100

45

90

135

180

225

Pha

se (

deg)

Bode Diagram

Frequency (rad/sec)

FIGURE 5. Bode plot of transfer function of Eq. (6) (colorfigure available online).

very low, and a high tracking error existing in the experimentis not the proportional control error of current loop. The outputcurrent and input reference current are equal when consideringonly the influence of reference current i∗

ck on the tracking error;i.e., this influence is negligible, so it can be deduced as

ick1 ≈ i∗ck . (5)

3.3. Influence of Source Voltage uk on Tracking Error

Assuming the value of input current reference is zero, theoutput current is ick2. The closed-loop transfer function ofsource voltage uk to output current ick2 is shown as follows:

�2(s) = −(Tss + 1)/[LTss2 + (L + RTs)s + R

+ KFB Kip KPWM]. (6)

Lettin s = jω, frequency characteristics can be derived as

�2( jω) = −( jωTs + 1)/[LTs( jω)2 + jω(L + RTs) + R

+ KFB Kip KPWM]. (7)

The Bode plot is shown in Figure 5, and Bode plots withchanging parameters are shown in Figure 6. The Bode plotsshow that the parameters Ts, R, and L do not influence thetransfer function at low frequency, so these parameters can beneglected. In addition, assuming the source voltage is a 50-Hzsinusoidal wave without harmonics, s = jω = j50 × 2π . Inpractical applications, R, L, ωTs , ω(RTs + L), and LTsω

2 aremuch smaller than KFB KiP KPWM, so Eq. (7) can be expressedas [7, 15]

�2(s) ≈ − 1

KFB Kip KPWM, (8)

where KFB KiP KPWM ≈ 4.5. When considering only the influ-ence of source voltage uk on the current tracking error, theoutput current ick2 can be denoted as follows:

ick2 = − 1

KFB KiP KPWMuk . (9)

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014

Yi and Hu: Current Tracking Error Analysis for Shunt Active Power Filters 39

-50

0

50

100

150

Mag

nitu

de

(dB

)

101

102

103

104

105

-270

-180

-90

0

Pha

se (

deg)

Bode Diagram

Frequency (rad/sec)

L=0.5mH

L=2mH

L=4mH

L=2mH

L=4mH

L=0.5mH

(a)

-50

0

50

100

150

Mag

nitu

de (d

B)

101

102

103

104

105

-270

-180

-90

0

Pha

se (d

eg)

Bode Diagram

Frequency (rad/sec)

R=1�

R=0.1�

R=10�

R=0.1�

R=1�

R=10�

(b)

-150

-100

-50

0

50

100

150

Mag

nit

ud

e (d

B)

100

101

102

103

104

105

106

-270

-180

-90

0

Pha

se (

deg

)

Bode Diagram

Frequency (rad/sec)

Ts=0.5T

Ts=1T

Ts=2T

Ts=1T

Ts=2TTs=0.5T

(c)

-100

-50

0

50

100

150

Mag

nitu

de (d

B)

101

102

103

104

105

-270

-180

-90

0

Pha

se (d

eg)

Bode Diagram

Frequency (rad/sec)

Kip=0.5

Kip=1

Kip=2

Kip=2 Kip=0.5

Kip=1

(d)

FIGURE 6. Bode plots with changing parameters: (a) withchanging L, (b) with changing R, (c) with changing Ts,(d) with changing KiP (color figure available online).

It can be obtained from Eq. (9) that the source voltageaffects the output current. When the proportional parametervalue is infinite, the output current is not affected by the sourcevoltage. But because the proportional parameter value cannotreach infinity in a practical application system, this influenceand current tracking error exist universally, and the error isquite significant.

3.4. Influence of Two-input Co-action on Tracking Error

As expressed in Eq. (9), output current produces a currenttracking error under the influence of source voltage uk, and thetotal output current is

ick = ick1 + ick2 = i∗ck − 1

KFB KiP KPWMuk . (10)

The current tracking error is

�ick = i∗ck − ick = 1

KFB KiP KPWMuk = 2UT

KFB KiPUdcuk . (11)

In Eq. (11), KiP can be a different regulator, such as a PIcontroller or a proportional resonant (PR) regulator.

The current tracking error ick2 caused by source voltage uk

lags the source voltage 180◦, so it is an active power current,and the compensation results of harmonics and reactive powerare not affected.

According to Eq. (11), there is a big active power currentflowing into the converter. Because there is a voltage controlloop in the control system, the reference current contains a bigactive power current that is used to control the DC-side volt-age as a constant; the influence of source voltage on outputcurrent is suppressed by changing idc, and the system oper-ates steadily. The block diagram of fundamental active currenttracking control is illustrated in Figure 7.

To sum up, in the current control of an APF, the currenttracking error is caused by the source voltage. The current loopproportional parameter cannot reach infinity, so a significantcurrent tracking error related to frequency exists universally.Source voltage affects the active power part of the output cur-rent; the tracking error is an active power current and has thesame phase as source voltage. Changing the current referenceto eliminate the influence of source voltage by the voltageloop control makes the output current expected, but the output

ck1I*dcU

iPKFBK

ku

dcU

1

Ls RPWM

s1

K

T siP2K 1.5

sC

*ck1I

FIGURE 7. Block diagram of fundamental active currenttracking control with voltage loop.

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014

40 Electric Power Components and Systems, Vol. 42 (2014), No. 1

reactive and harmonic current are not affected, which is whythe tracking error is very large, but the compensation result isgood.

4. INFLUENCE OF CURRENT TRACKING ERROR

As expressed in Eq. (9), the converter absorbs a large activepower current, and DC-side voltage rises. In Figure 8, theDC-side voltage control loop provides a current reference tosuppress the influence of source voltage on output current, thereference is added to the harmonic and reactive reference cur-rent to be compensated, and the system can finally run steadily[7, 14–16]. Although the fundamental current tracking errorexists, the output current is expected. The current tracking er-ror �ick = i∗

ck − ick is related to the source voltage but is notrelated to the voltage-loop PI regulator. The input uk can beconsidered as a voltage closed-loop disturbance; as the valueof voltage-loop PI regulator increases, the values of i∗

ck and ick

will decrease, but the current tracking error �ick is invariable,so the current tracking error is a visual error caused by thesource voltage. The bigger the value of the voltage loop PIregulator is, the smaller the visual error is.

The influence of current tracking error includes steady-stateand dynamic influence. In steady state, the modulation wave isexpressed in as Eq. (12). In practical applications, the variablesUT, Udc, and uk must be chosen correctly. Although a currenttracking error exists, the peak value of the modulation waveu∗

mk is smaller than that of the carrier wave; i.e., the modulationratio is less than 1, as shown in Figure 9. The output currentwill be not affected, and the infuence of the current trackingerror on the steady-state run will be suppressed [5, 7, 17, 18].Source voltage and load current of the experiment system areshown in Figure 10, and the compensation result is illustratedin Figure 11:

u∗mk = Kip KFB(i∗

ck1 − ick) + 2UT

Udcuk . (12)

The modulation ratio is

m = u∗mk

UT= KiP KFB(i∗

ck1 − ick)

UT+ 2uk

Udc. (13)

di*

dcU

ku

dcUiP2K

ckidcG (s)

abcdq

T

FB iP dc

2U

K K U

*cki

cG (s)dq

abc0

FIGURE 8. Block diagram of voltage loop control.

FIGURE 9. Modulation wave with low peak value.

FIGURE 10. Source voltage and load current before compen-sation.

FIGURE 11. Source voltage and load current after compen-sation.

FIGURE 12. Output current and reference current.

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014

Yi and Hu: Current Tracking Error Analysis for Shunt Active Power Filters 41

FIGURE 13. Modulation wave with high peak value.

If variables KiP, Udc, KFB, and UT are chosen incorrectly,the current tracking error will be high enough, as shown inFigure 12. The peak value of the modulation wave(referencecurrent) affected by the error can reach the limitation valueof PWM, as shown in Figure 13, The output current will beaffected [19–21].

Therefore, the parameters should be chosen reasonablywhen designing the control system. The DC-side voltage Udc

was first chosen, as needed; Udc must be larger than twicethe output voltage, and KiP must take the maximum value inthe steady-state operation condition. If the modulation waveamplitude can reach the limitation value of PWM, the trian-gular wave amplitude UT and feedback coefficient KFB willbe adjusted to reasonable values. This can also eliminate theinfluence of current tracking error on the compensation char-acteristics.

In the dynamic process shown in Figure 8, when the con-verter starts to work, the difference of the DC-side voltageand reference current is negative, and the charging referencecurrent i∗

ck is generated. The error signal caused by uk alsogenerates charging current, as shown in Eq. (9). The charg-ing current produced by the current tracking error and thecharging reference current i∗

ck charges the DC-side capacitorsimultaneously, and the charging current produced by the cur-rent tracking error is very large, so that the output currentreaches the peak value 45 A, as shown in Figure 14. In orderto prevent the start over-shoot current caused by the currenttracking error, the system gives a discharge signal at the startmoment and switches to the voltage loop when steady statearrives, as shown in Figure 15 [7, 22–24].

It can be inferred from the above analyses that the currenttracking error has little influence on steady-state operation buthas a large influence on the dynamic process.

5. EXPERIMENTAL RESULTS AND DISCUSSION

In order to verify the validity of the analyses, the experimentalresults based on the APF are shown in Figures 16(a) and 16(b).

FIGURE 14. Over-shoot start current.

i

i

i

i

ua

iLaiLbiLc LPF

iaf

ibf

icfc

sincos

iq ip

c c23c32

PLL

PI Udc

Udc

ip

0

Ap

-

+InitialState

FIGURE 15. Start process.

FIGURE 16. Experimental results: (a) reference current, out-put current, load reactive, and harmonic current and (b) sourcevoltage, load current, and source current after compensation(color figure available online).

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014

42 Electric Power Components and Systems, Vol. 42 (2014), No. 1

FIGURE 17. DC voltage.

FIGURE 18. THD of output current: (a) before compensationand (b) after compensation.

FIGURE 19. Experimental results of output current and refer-ence current when parameters change: (a) increasing KiP, (b)increasing Udc, (c) increasing UT, and (d) increasing KFB (colorfigure available online).

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014

Yi and Hu: Current Tracking Error Analysis for Shunt Active Power Filters 43

ckiΔ

FBK

iPK

dcU

FBKiPK dcU

(a)

ckiΔ

ku

TU

kuTU

(b)

FIGURE 20. Relationship between error and parameterschange: (a) when KiP, KFB, Udc change and (b) when uk and UT

change.

The fully digital and direct current control strategy is used,where KiP = 2, Udc = 800 V, KFB = 45, UT = 5859, andua = 311coωt.

In Figure 16(a), because of the influence of the source volt-age, a quite significant tracking error exists in the current con-trol loop between output current ick and reference current i∗

ck;however, output current ick is nearly equivalent to the reactiveand harmonic current iq of the load because of the very smallloss current of compensation converter. In Figure 16(b), thewaveforms of source voltage, load current, and source currentare shown after compensation. The DC-side voltage wave-form is shown in Figure 17, which nearly maintains 800 V.Figure 18 shows the total harmonic distortion (THD) of theoutput current, which is 24.3% before compensation and 5.5%after compensation. It can be seen that the compensation resultis still satisfactory.

The experimental waveforms of Eq. (11) are illustrated inFigure 19. When variables KiP, Udc, and KFB increase, thecurrent control error decreases; when variables UT and uk de-crease, the current control error decreases, and reference cur-rent i∗

ck1 switches to i∗ck2. The relationship between the error

and parameters change is shown in Figure 20. In practical ap-plications, because the peak value change of source voltageis very small, the experiment of uk change is neglected. Theexperiment verifies the influence of the variable changes ontracking error and the above analyses.

6. CONCLUSION

In this article, detailed analyses and design considerations arecarried out to look into the current tracking error issue inshunt APFs. The reasons why a current tracking error existstogether with satisfactory compensation results are revealed.The variables that affect the current control error are clearlyidentified. The quantitative relationship between the variablesaffecting the control error and the current tracking error isdeduced. The influence of current control error on currentcompensation characteristics is proposed. All these analysescan guide practical applications so a reliable compensator canbe designed. The experimental results verify the validity of theabove analyses and conclusions.

REFERENCES

[1] Henderson, R. D., and Rose, P. J., “Harmonics: The effectson power quality and transformers,” IEEE Trans. Ind. Appl.,Vol. 30, No. 3, pp. 528–532, May/June 1994.

[2] Akagi, H., “Active harmonic filters,” Proc. IEEE, Vol. 93,No. 12, pp. 2128–2141, December 2005.

[3] Bhattacharya, S., Frank, T. M., Divan, D. M., and Banerjee, B.,“Active filter system implementation,” IEEE Trans. Ind. Appl.,Vol. 4, No. 5, pp. 47–63, September/October 1998.

[4] Jain, S. K., Agarwal, P., and Gupta, H. O., “A control algo-rithm for compensation of customer-generated harmonics andreactive power,” IEEE Trans. Power Delivery, Vol. 19, No. 1,pp. 357–366, January 2004.

[5] Fu, Q., and Yang, G., “A novel control method for active powerfilter considering harmonic voltage in power source,” Proceed-ings of the IEEE 37th Annual Power Electronics SpecialistsConference 2006 (PESC 06), pp. 1–6, Jeju, Korea, 18–22 June2006.

[6] Tzou, Y. Y., “DSP-based fully digital control of a PWM DC-AC converter for AC voltage regulation,” Proceedings of theIEEE 26th Annual Power Electronics Specialists Conference1995 (PESC 95), Vol. 1, pp. 138–144, Atlanta, GA, 18–22 June1995.

[7] Zhao, G. P., Liu, J. J., Li, K., and Wang, Z. A., “Analysis and de-sign of fully digital and direct current controlled voltage sourceconverters connected to the grid,” Proceedings of the IEEE 37th

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014

44 Electric Power Components and Systems, Vol. 42 (2014), No. 1

Annual Power Electronics Specialists Conference 2006 (PESC06), pp. 1–5, Jeju, Korea, 18–22 June 2006.

[8] Czarnecki, L.S., “Instantaneous reactive power p-q theory andpower properties of three-phase systems,” IEEE Trans. PowerDelivery, Vol. 21, No. 1, pp. 362–367, January 2006.

[9] Lin, B.-R., and Yang, T.-Y., “Three-level voltage-source inverterfor shunt active filter,” IEE Proc. Electron. Power Appl., Vol.151, No. 6, pp. 744–751, November 2004.

[10] Douangsyla, S., Indarack, P., Kanthee, A., Kando, M., Kittirat-satcha, S., and Kinnares, V., “Modeling for PWM voltage sourceconverter controlled power transfer,” Proceedings of IEEE In-ternational Symposium on Communications and InformationTechnology 2004 (ISCIT 04), pp. 875–878, Sapporo, Japan,26–29 October 2004.

[11] Le, J. Y., Xie, Y. X., Zhang, Z., and Chen, L., “State feedbackexact linearization control for APF,” Elect. Power Automat.Equip., Vol. 30, No. 2, pp. 81–85, February 2010.

[12] Zhou, K., Wang, D., and Low, K.-S., “Periodic errors elimi-nation in CVCF PWM DC/AC converter systems: Repetitivecontrol approach,” IEE Proc. Control Theory Appl., Vol. 147,No. 6, pp. 694–700, November 2000.

[13] Casanellas, F., “Losses in PWM inverters using IGBTs,” IEEProc. Electron. Power Appl., Vol. 141, No. 5, pp. 235–239,September 1994.

[14] Ujita, H., and Agaki, H., “The unified power quality conditionerof series and shunt active filters,” IEEE Trans. Power Electron.,Vol. 13, No. 2, pp. 315–322, March 1998.

[15] Rastogi, M., Mohan, N., and Edris, A.-A., “Hybrid-active filter-ing of harmonic currents in power systems,” IEEE Trans. PowerDelivery, Vol. 10, No. 4, pp. 1994–2000, October 1995.

[16] Blasko, V., and Kaura, V., “A novel control to actively dampresonance in input LC filter of a three-phase voltage sourceconverter,” IEEE Trans. Ind. Appl., Vol. 33, No. 2, pp. 542–550,March/April 1997.

[17] Lascu, C., Asiminoaei, L., Boldea, I., and Blaabjerg, F., “Highperformance current controller for selective harmonic compen-sation in active power filters,” IEEE Trans. Power Electron.,Vol. 22, No. 5, pp. 1826–1835, September 2007.

[18] Moran, L., Ziogas, P. D., and Joos, G., “A solid-state high-performance reactive-power compensator,” IEEE Trans. Ind.Appl., Vol. 29, No. 5, pp. 969–978, September/October 1993.

[19] Patidar, R. D., and Singh, S. P., “Digital signal processor basedshunt active filter controller for customer-generated harmonics

and reactive power compensation,” Elect. Power Compon. Syst.,Vol. 38, No. 8, pp. 937–959, May 2010.

[20] Ghamri, A., Benchouia, M. T., and Golea, A., “Sliding-modecontrol based three-phase shunt active power filter: Simulationand experimentation,” Elect. Power Compon. Syst., Vol. 40,No. 4, pp. 383–398, January 2012.

[21] Gupta, N., Singh, S. P., and Bansal, R. C., “A digital signalprocessor based performance evaluation of three-phase four-wire shunt active filter for harmonic elimination, reactive powercompensation, and balancing of non-linear loads under non-ideal mains voltages,” Elect. Power Compon. Syst., Vol. 40,No. 10, pp. 1119–1148, July 2012.

[22] Allmeling, J. H., “A control structure for fast harmonicscompensation in active filters,” IEEE Trans. Power Electron.,Vol. 19, No. 12, pp. 508–514, March 2004.

[23] Zargari, N. R., and Joos, G., “Performance investigation of acurrent-controlled voltage-regulated PWM rectifier in rotatingand stationary frames,” IEEE Trans. Ind. Electron., Vol. 42,No. 4, pp. 396–401, August 1995.

[24] Rivas, D., Moran, L., Dixon, J., and Espinoza, J., “A simplecontrol scheme for hybrid active power filter,” Proceedings ofthe IEEE 31th Annual Power Electronics Specialists Conference2000 (PESC 00), Vol. 2, pp. 991–996, Galway, Ireland, 18–23June 2000.

BIOGRAPHIES

Gui-Ping Yi received the B.S. degree from the College ofElectrical and Information Engineering, Nanchang Universityin 2004, and the M.S. degree from the College of ElectricPower and Automation Engineering, Shanghai University ofElectric Power in 2010, respectively. He is presently a Ph.D.student in Southteast University, Nanjing, China. His researchinterests include micro-grid power quality, electric power sav-ing, reactive power compensation, and active power filters.

Ren-Jie Hu was born in Jiangsu, China, on May 12, 1962. Hereceived the B.S., M.S. and Ph.D. degrees in electrical engi-neering from Southteast University, in 1985, 1990 and 2002,respectively. He has been with the Department of ElectricalEngineering, Southteast University, where he is currently aProfessor and serves as the chief of Electrical and ElectronicExperiment Center. His research interests are power electron-ics and power delivery, distributed generation, power qualitymanagement and super capacitor energy storage.

Dow

nloa

ded

by [

Mem

oria

l Uni

vers

ity o

f N

ewfo

undl

and]

at 1

4:53

01

Aug

ust 2

014