control of a shunt active power filter

8/11/2019 Control of a Shunt Active Power Filter

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AbstractThis paper presents a control method of a NPC three-level four-wire inverter of a shunt active power filter (SAPF) byswitching functions. The switching functions of the inverter areextracted by equations of the inverter averaged model to compensate

load harmonic currents. The averaged model of the inverter isaccording to allowable switching states of the inverters switches(IGBTs). In this paper, the control system of SAPF based onswitching functions employs THD calculation block diagram to

generate signal-gates of the inverter switches. The proposed controlmethod is applicable under asymmetrical and non-sinusoidal three-

phase source. The principles of the presented control method areanalyzed in this paper. Also, the control method is modeled and

simulated in MATLAB/Simulink to validate effectiveness of theproposed control method.

KeywordsShunt active power filter, Multi-level inverter,averaged model, switching function, THD

I.

INTRODUCTION

dvent of non-linear electrical loads, such as diode

rectifiers, uninterruptable power supplies and adjustable

speed drive systems causes harmonic current injection in to

the electrical grids and degrades the power quality. Low

power quality may cause other problems, such as additional

losses in the transmission lines, overheating of electricalequipment, EMI problems and some undesirable effects.

Limitation of the harmonic currents and the harmonic voltages

are specified by the international standards (IEEE519,

IEC61000-3-2 and EN50160). These standards determine

allowable amount of harmonic injection of electrical

equipment and the facilities. There are several methods to

improve the power quality and to decrease the harmonic

currents injected to the grid. The simplest solution is parallel

passive filter (PPF). The PPFs are widely used for decreasing

of the harmonic currents in the utilities due to their low cost

and high efficiency, but they have some drawbacks, such as

the effects of the source impedances on their characteristics,

series and parallel resonance with the source and the loads and

over-voltage under no-load or light load conditions. [1, 2, 3]

Shunt active power filters (SAPFs) is a suitable solution

method without disadvantages of the PPFs. Since the SAPFs

are adapted to the load currents, no over voltage, no under

M. Asadi is with Dept of Elec. Eng., Iran University of Science and

Technology, Tehran, Iran (e-mail: [email protected]).A. Jalilian is with the Dept of Elec. Eng., and Center of Excellence for

Power System Automation and Operation, Iran University of Science and

Technology, Tehran, Iran (Corresponding author, e-mail: [email protected]).

voltage and no resonance are occurred [3, 4].

Control system of the SAPF consists of two main unit,

reference signal extraction unit and controller and modulation

unit. Reference signals extraction of the SAPF is the first step

for design of the control system. Reference signals are

extracted in two domains of time and frequency. The time

domain techniques are p-q, d-q, SRF 1, DPC2, DC BEB3

theories [5, 6 and 7] and the others are expressed in frequency

domain such as Fourier transformer [5, 7]. For control design,

modeling of SAPF is necessary. The inverter model based on

the state-space model or the transfer function model is done byaveraged model in papers of [8-10].

In the recent years, multi-level inverters are widely used

in power quality conditioners such as shunt active power

filters, hybrid active power filters and STATCOMs. Not only

in high voltage applications, the multi-level inverters are good

ideas, but also they are suitable for decrease of output current

ripples, reduction of electrical strain such as dV/dt on IGBTs

and small size of output passive filter of the inverter [11-12].

In this paper, a NPC three-level inverter is used in SAPF.

Due to using of three-level inverter in configuration of the

SAPF, it is suitable for high voltage applications. The current

control of the inverter is based on switching function extracted

by averaged model of NPC three-level inverter. A blockdiagram of THD calculation is used to extract switching

functions too. Whereas, system voltages and output current of

the inverter are considered as parameters to extract switching

functions, the harmonic currents are effectively compensated

under asymmetrical and non-sinusoidal source voltages

conditions.

II.

AVERAGED MODEL AND SWITCHING FUNCTIONS

Figure (1) shows the configuration of the SAPF comprising

a NPC three-level inverter and control circuit of DC-link. The

inverter is connected in parallel with the source and the loads

through three inductors at the points of common coupling

(PCC). The PCC voltages are shown by VAFa,b,c in figure (1).

Some parameters of the circuit shown in figure (1) are listed in

table I.

1Synchronous Reference Frame

2 Direct Power Control3 DC Bus Energy Balance

Control of a Shunt Active Power Filter based on

THD Tracking under Unbalanced Condition

Mehdi Asadi, and Alireza Jalilian

A

2nd International Conference on Advances in Electrical and Electronics Engineering (ICAEEE'2013) Dec. 20-21, 2013 Bali (Indonesia)

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Control System

LAFb

Lsa

Lsb

Lsc

Vsa

Vsb

Vsc

Acti ve Part

(4-Wire 3-Leg inverter)

Linear

and

Non-

Linear

Loads

LLa

LLb

LLc

C1

C2

LAFa LAFc

iAFa iAFb iAFc

iLa

iLb

iLc

isa

isb

isc

VAFa

VAFb

VAFc

RAFa RAFb RAFa

RDC-link

RDC-link

DC Cont.

System

IGBT1

IGBT2

Q1a

Q2a

Q3a

Q4a

Q1b

Q2b

Q3b

Q4b

Q1c

Q2c

Q3c

Q4c

Fig. 1 The shunt active power filter

TABLE I. SOME SYSTEM PARAMETERS

The source inductances Lsa=L sb=Lsc=0.1mH

The line inductances

LLa,b,c=0.1mHThe capacitance of DC-Link

capacitorsC1,2=2350 F

The inductance of the inverter LAFa,b,c=10mH

RAFa,b,c=1

Rdc-Link1 , Rdc-Link2 2000

A. The averaged model based on switching functions

Since the four-wire three-level inverter is employed in the

SAPF topology, each phase of the inverter shown in figure (1)

is independent of the others. For switching functions

extraction, all of the possible switching states must be

investigated. Each phase of NPC three-level inverter has four

states as shown in table (II). Assuming that parameters dKa,b,c

are defined as switching functions phases a, b and c, they canbe expressed as:

=

stateoffareQif

stateonareQifd

cbKa

cbKa

cbKa

,,

,,

,, ,0

,1 (1)

Where, index K is 1 or 2. The switches Q3a,b,c and Q4a,b,c are

complement of switches Q1a,b,cand Q2a,b,crespectively.

TABLE II. SWICHING TABLE OF THE SAPF

d1 d2 VF iC1 iC2

Phase-a

0 0 -VC 0 - iAF

0 1 0 0 0

1 0 0 0 0

1 1 +VC iAF 0

Phase-b

0 0 -VC 0 - iAF0 1 0 0 0

1 0 0 0 0

1 1 +VC iAF 0

Phase-c

0 0 -VC 0 - iAF

0 1 0 0 0

1 0 0 0 0

1 1 +VC iAF 0

The inverter output voltages and the DC-link capacitors

currents are shown in table (II). Considering equation (1) and

table (II), the output voltage of the inverter and the capacitors

currents can be written based on the switching functions as

follows:

C

cc

bb

aa

Fc

Fb

Fa

V

dd

dd

dd

V

V

V

+

+

+

=

1

1

1

21

21

21 (2)

[ ]

=

AFc

AFb

AFa

ccbbaaC

i

i

i

ddddddi 2121211

(3)

[ ]

=

AFc

AFb

AFa

ccbbaaC

i

i

i

ddddddi )1)(1()1)(1()1)(1( 2121212

(4)

Therefore, the NPC three-level inverter can be modeled as

shown in figure (2).

C1

C2

vC

vC

+

-

+

-

LSa

LSb

LSciSc

iSb

iSaVSa

VSb

VSc

VAFa

VAFb

VAFc

iC1

iC2+ _

+ _

+ _

LAFc

LAFb

iAFb

LAFa

iAFa

vFc

vFb

vFa

iAFc

Linear and

Non-Linear

Loads

LLa

LLb

LLc

iLb

iLc

iLa

RAFa

RAFb

RAFc

Fig. 2 The averaged model of the SAPF

Figure (3) shows the averaged model of the SAPF, where

the inverter is considered as two controlled current sources

(iC1 and iC2) and three controlled voltage sources (V Fa, VFb

and VFc). Considering that, the output voltages of the inverter

are dependent on the switching functions; the output currentsof the inverter are controllable. In this paper, capacitors

voltages of inverter are controlled by separated control system

based on hysteresis controllers. Therefore, the DC-link of the

inverter can be considered as two constant voltage sources.

B.Switching function ratios

The NPC three-level inverter of the SAPF consists of three

legs. Each leg has four gate-signals which the gate-signals of

the lower switches (Q3a,b,c and Q4a,b,c) are complement of the

upper switches (Q1a,b,c and Q2a,b,c).

=

)(

)(

)(

)(

)(

)(

1

2

1

2

1

2

c

c

b

b

a

a

QON

QON

QON

QON

QON

QON

c

b

a

T

T

T

T

T

T

MR

MR

MR (5)

In this paper, switching function ratio is used for gate

signals generation. The switching function ratio is a good

approach to extraction of gate-signals of Q 1a,b,cand Q2a,b,c . The

ratios of on-state times of Q 1a,b,c to on-state times of Q2a,b,c


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are defined as MRa,b,c4 respectively. Therefore, the switching

functions can be written as:

=

c

b

a

c

b

a

c

b

a

d

d

d

MR

MR

MR

d

d

d

1

1

1

2

2

2

00

00

00 (6)

The switching function ratios are determined based on THD

Tracking of the source current specified by internationalstandard, in this paper.

III.

REFERENCE SIGNALS EXTRACTION AND THD

CALCULATION

Figure (3) shows equivalent single-phase circuit of the

system shown in figure (2) in harmonic domain.

LS

iS(h)VS(h)

+

_

LAF

vF(h)=(d1+d2-1)VC

iAF(h)

iD(h)

iAF(h)

VAF(h)iL(h)

Fig. 3 single-phase circuit of the SAPF

Considering current detectors locations, the source and

detected currents are expressed as [11, 12]:

[ ] [ ] cbDadqodqocbahDcbahL iTHPFTii ,,1

,,)(,,)(

== (7)

[ ] [ ] cbAFadqodqocbahAF

VTHPFTV ,,1

,,)(

= (8)

where iL,iD , VAF, Tdqo and HPF are the load current, the

detected current of the sensor S 1, the load voltage,

transformation matrix and high pass filter respectively. Also

the index (h) denotes the harmonic components. The

transformation matrix Tdqois given as:

[ ]( ) ( )( ) ( )

+

+

=

2

1

2

1

2

13

2sin3

2sinsin

32cos

32coscos

3

2

ttt

ttt

Tdqo

(9)

Considering to equations (7) and (8), extraction block

diagrams of currents and voltages are shown in figure (4).

abc

to

dqo

vAFa

HPF

dqo

to

abc

vAFb

vAFc

vAF(h)a

vAF(h)b

vAF(h)c

PLL

abc

to

dqo

iDa

iDb

iDc

HPF

iDd

iDq

iDo

dqo

to

abc

iD(h)a

iD(h)biD(h)c

two

two

two

two

Fig. 4 The extarction of currents and voltages components

The detected signals are sent to transformation matrix of

4Modulation Ratio

Tdqoand, are passed through the high pass filters to generate

harmonic components of them in d-q-o coordination system.

Finally, inverse of Tdqo is used to produce harmonic

components in a-b-c coordination system. In this paper, THDs

of currents are employed to generate modulation ratios

MRa,b,c . The equation (10) shows extraction of the source

currents.

cbAFacbDacbSa iii ,,,,,, = (10)

The extraction method of THDs of the source currents can

be implemented by block diagrams shown in figure (5). After

extraction of the fundamental and harmonic components of the

source currents, squares of them are passed through low pass

filters to produce their mean squares.

_ +

_ +

_ +

iSaiSb

iSc

iDaiDb

iDciAFa

iAFb

iAFc

abc

to

dqo

HPF

dqo

to

abc

()2

LPFiSha

()2

LPF

_

+

iSa iS(1)a ()-1

()2

LPF

()2

LPF

_

+

iSb iS(1)b ()-1

()2

LPF

()2

LPF_+

iSc iS(1)c ()-1

iShb

iShc

THDa

THDb

THDc

two

two

Fig. 5 The extarction method of the THDs of the source currents

=

)()1(

)()(

)()1(

)()(

)()1(

)()(

rmscS

rmschS

rmsbS

rmsbhS

rmsaS

rmsahS

c

b

a

i

i

i

i

i

i

THD

THD

THD (11)

Where, iSand T denote the source current and periodic time

of grid voltages.

The extracted THDs are employed to determine themodulation ratios of the three-level inverter of the SAPF.

IV. THE CONTROL STRATEGY

Whereas the SAPF compensates the harmonic components

of the loads, it should be analyzed in domains of harmonic

frequencies. Figure (3) shows equivalent circuits of the system

in harmonic domains. As shown in the figure, the three-level

inverter of the SAPF is considered as a harmonic source

voltage. Considering KVL equations in figure (3), the inverter

currents can be written as:

+

=

AFc

chAFchF

AFb

bhAFbhF

AFa

ahAFahF

chAF

bhAF

ahAF

AFc

AFc

AFb

AFb

AFa

AFa

chAF

bhAF

ahAF

L

vv

L

vv

L

vv

i

i

i

L

R

L

R

L

R

dt

didt

didt

di

)()(

)()(

)()(

)(

)(

)(

)(

)(

)(

00

00

00 (12)

In order to effective harmonic compensation, the source

currents of iSha,b,c should be near to zero, So in harmonic

domains, the inverter currents can be decided as:

cbahDcbahAF ii ,,)(,,)( = (13)


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Fig. 7 The source currents

Fig. 8 THD of the source currents

TABLE IV. FUNDAMENTAL AND THD OF THE SOURCE CURRENT

Isa Isb Isc

Before Applying of the SAPF

THD (%) 15.58 18.7 15.93

I(1)(A) 8.58 7.78 8.4

After Applying of the SAPF I(1)(A) 8.48 8.46 8.47

Figure (9) shows the modulation ratios produced by control

system under the worst condition. As shown in figure (10), the

capacitors voltages are effectively fixed around 330V.

Figure 1. Modulation ratios of the inverter

Fig. 9 DC-link voltages of the inverter

VI. CONCLUSIONS

In this paper, a control method of an active power filter is

discussed based on averaged model to produce switching

functions. The switching functions are employed to

compensate the source current harmonic components. The

extraction of switching functions is based on allowable THDs(within 5% limits) of the source currents specified by

international standards such as IEEE 519. Based on

MATLAB-Simulink, simulations were carried out under non-

sinusoidal and asymmetrical three-phase system. Whereas the

voltages of the HAPF are used in the control method, the

switching functions can effectively compensate the harmonic

components of the source currents under non-sinusoidal and

asymmetrical three-phase grid.

REFERENCES

[1] Hurng-Liahng Jou, Kuen-Der Wu, Jinn-Chang Wu, and Wen-JungChiang,'' A Three-Phase Four-Wire Power Filter Comprising a Three-Phase Three-Wire Active Power Filter and a ZigZag Transformer'',

IEEE Transactions on Power Electronics, Vol. 23, No. 1, Jan. 2008.

[2]

G. K. Singh,Power system harmonics research: a survey, EuropeanTransactions on Electrical Power (ETEP) , Vol. 19, 29 August 2007, pp.151-172

[3]

M.Asadi, A.Jalilian, Using Magnetizing Reactances of Transformer inHybrid Active Power Filter, In Proc.of 2ndPower Electronics & DriveSystems and Technology Conference, 16-17 Feb. 2011, Tehran, Iran, pp268 - 273

[4]

B. Singh, K. Al-Haddad, A. Chandra, Active Power Filter forHarmonic and Reactive Power Compensation in Three-Phase, Four-Wire Systems Supplying Non-Linear Loads, European TransactionsOn Electrical Power (ETEP), Vol. 8, No. 2, MarcMApril 1998, pp. 139-145

[5]

G.Tsengense, G.Adamidis,'' An Improved Current Control Techniquefor the Investigation of a Power System with a Shunt Active Filter'', InProc. Of International Symposium on Power Electronics, ElectricalDrives, Automation and Motion Conference, 2010,

[6]

Mara Isabel Milans Montero, Enrique Romero Cadaval and FermnBarrero Gonzlez,'' Comparison of Control Strategies for Shunt ActivePower Filters in Three-Phase Four-Wire Systems'' , IEEE Transactionson Power Electronics , Vol. 22, No. 1, Jan. 2007,pp 22

[7] T.C. Green and J.H. Marks, Control techniques for active powerfilters, IEE Procceding on Electric Power Application, Vol. 152, No. 2,March 2005.

[8]

N.Kroutikova, C.A.Hernandez and T.C.Green,'' State-Space Model ofGrid-Connected inverters Under Current Control Mode'', IETTransactions on Electr. Power Appl. Vol.1, No.3, May 2007, pp 329-338


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[9]

Guijun Yao, Lars Norum,'' New Transfer Function Model for PWMPower Converter'', In Proc. Of 16th Annual Conference of IndustrialElectronics Society (IECON), 27-30 Nov. 1990, pp 1135 - 1142

[10]

H.Y.Kanaan, A.Hayek and K.Al-Haddad,'' Averaged Model-BasedNonlinear Control of a PWM Three-Phase Four-Leg Shunt ActivePower Filter'', In Proc. of Canadian Conference on Electrical andComputer Engineering (CCECE), 22-26 April 2007, pp 1002 1005

[11]

Cheng-Che Chen and Yuan-Yih Hsu, A Novel Approach to the Designof a Shunt Active Filter for an Unbalanced Three-Phase Four-WireSystem under Nonsinusoidal Conditions, IEEE Treansactions on

Power Delivery, Vol. 15, No. 4, Oct. 2000, pp 1258 1264[12]

M. Asadi, A. Jalilian,An Improved Current Control Method of ShuntActive Power Filter Based on State-Space Variables UnderAsymmetrical and Non-Sinusiodal Conditions, In Proc.of the 5thInternational Power Engineering and Optimization Conference(PEOCO2011), Shah Alam, Selangor, Malaysia, June 2011.


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control of a shunt active power filter

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