THREE-PHASE ACTIVE POWER FILTER CONTROLLER FOR BALANCED AND UNBALANCED NON-LINEAR LOAD

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Vol. 2(9), 2010, 4072-4082

THREE-PHASE ACTIVE POWER FILTER

CONTROLLER FOR BALANCED AND

UNBALANCED NON-LINEAR LOAD

G.NAGESWARA RAO 1

Vijaya Institute of Technology for Women Electrical & Electronics Eng Dept Enikepadu, Vijayawada, A.P, India

Dr.K. CHANDRA SEKHAR 2

R.V.R & J.C College of Eng Electrical & Electronics Eng Dept

Guntur, A.P, India

Dr.P. SANGAMESWARA RAJU 3

S.V.University, Tirupathi Electrical & Electronics Eng Dept

Tirupathi, A.P, India

Abstract:

The active power filter produces equal but opposite harmonic currents to the point of connection with the nonlinear load. This results in a reduction of the original distortion and correction of the power factor. A three-phase insulated gate bipolar transistor based current controlled voltage source inverter with a dc bus capacitor is used as an active filter. The firing pulses to the shunt active filter will be generated by using sine PWM method. The models for three-phase active power filter controller for balanced and unbalanced non-linear load is made and is simulated using Matlab/simulink software.

Keywords: Active power filter, Harmonics, PWM

1. Introduction

Power electronic equipment usually introduces current harmonics. These current harmonics result in problems such as a low power factor, low efficiency, power system voltage fluctuations and communications interference. Traditional solutions for these problems are based on passive filters due to their easy design, simple structure, low cost and high efficiency. These usually consist of a bank of tuned LC filters to suppress current harmonics generated by nonlinear loads. Passive filters have many disadvantages, such as resonance, large size, fixed compensation character and possible overload. To overcome these disad-vantages, active power filters have been presented as a current-harmonic compensator for reducing the total harmonic distortion of the current and correcting the power factor of the input source .Fig. 3.1 shows the configuration of a three-phase active power filter.

A personal computer (PC) based digital control is used to implement the control scheme. The active power filter is connected in parallel with a nonlinear load. Its main power circuit is composed of a pulse-width- modulation (PWM) converter. The inductor L2is used to perform the voltage boost operation in combination with the DC-link capacitor C2 and functions as a low pass filter for the line current of an active power filter. The principle of operation of an active power filter is to generate compensating currents into the power system for canceling the current harmonics contained in the nonlinear load current. This will thus result in sinusoidal line currents and unity power factor in the input power system. At present, calculation of the magnitude of the

1 G.NAGESWARA RAO. Vijaya institute of technology for women ,electrical dept, vijayawada ,a.p, India. 2Dr .K.CHANDRA SEKHAR prof & hod electrical dept ,rvr & jc college of eng, guntur., a.p, India. 3Dr. P.SANGAMESWARA RAJU associate prof, s.v. university, tirupathi, a.p, India.

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compensating currents of an active power filter is based either on the instantaneous real and reactive powers of nonlinear loads or the integrative methods of Fourier analysis

Both these approaches neglect the delay time caused by low pass high pass filters when compensating current calculations. The method considered the instantaneous power delay caused by the current regulators and DC-link voltage feedback circuit and presented a load power estimation method to improve the dynamic response of input power regulatioSn. In this paper, besides considering the current regulator delay and the DC-link voltage feedback delay, the low pass filter delay is also discussed. In addition, the design of the cutoff frequency for the low pass filter, current regulators and DC-link voltage regulator are also given. The control strategies of the active power filter focus on the controller

design for both the line current regulators of the active power filter and the DC-link voltage regulator. A simplified analytical model of the active power filter system is proposed. Using the derived analytical model, analyses of DC-link voltage response and current tracking capability for the active power filter will be easier. Applying the proposed control strategy, the current harmonics of a nonlinear load can be compensated quickly and the fluctuations of DC-link voltage during transient and steady states are effectively suppressed. The exclusive features of this paper are summarised as follows:

2. Active power filter control 2.1. Introduction:

The active power filter was a recently developed piece of equipment for simultaneously suppressing the current harmonics and compensating the reactive power. Fig 1 shows the configuration of a three-phase active power filter. A personal computer (PC) based digital control is used to implement the control scheme. The active power filter is connected in parallel with a nonlinear load. Its main power circuit is composed of a pulse-width modulation (PWM) converter.

The inductor L2 is used to perform the voltage boost operation in combination with the DC-link capacitor

2

C and functions as a low pass filter for the line current of an active power filter. The principle of operation of an

active power filter is to generate compensating currents into the power system for canceling the current harmonics contained in the nonlinear load current. This will thus result in sinusoidal line currents and unity power factor in the input power system.

2. 2. principle of operation:

The proposed three-phase active power filter consists of a power converter, a DC-link capacitor and a filter inductor. To eliminate current harmonic Components generated by nonlinear loads, the active power filter produces equal but opposite harmonic currents to the point of connection with the nonlinear load. This results in a reduction of the original distortion and correction of the power factor. For the sake of simplicity, in the calculation of reference currents and description of the control scheme, the reference frame transformation method will be used.

2.3. compensating current calaulations

:

Consider Fig 1 where

e

a

,

e

b

,

e

cand

v

af ,

v

bf,

v

cf represent the phase voltages of a power system

and the input voltages of a power converter,

i

af,

i

bf ,

i

cf and

v

dc2denote the input currents of the active power filter and the DC-link voltage, respectively. Neglecting the reactors

L

s of the input power system, the differential

equations of the three-phase active Power filter in Fig.1 can be described as follows

.

2 2

2 2

2 2

2 2

... (1) ... (2) ... (3)

C ...

af a af af

bf b bf bf

cf c cf cf

dc a af b bf c cf

d

L i e R i v

dt d

L i e R i v

dt d

L i e R i v

dt d

v f i f i f i

dt

  

  

  

   ... (4)

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Vol. 2(9), 2010, 4072-4082

3 2 3

1 ,

0  and  . For model analysis and controller design, the three-phase voltages, currents and switching functions can be transformed to a d-q-o rotating frame. This yields,

e

e

2 2

sin sin sin

3 3

2 2 2

cos cos cos ...(5)

3 3 3

1 1 1

2 2 2

e e

d a

q e e b

o c

x x

x x

x x

 

  

 

  

    

   

 

   

   

   

    

   

 

   

   

 

 

Where

e is the transformation angle of the rotating frame and x denotes currents, voltages or switching functions. From equations (3.1)-(3.5), the state model in the rotating frame Can be written as.

2 2 2

2 2 2

2 2

df 2

... (6)

... (7)

3

C ( ) ... (8)

2 where

v ...

df d df e qf df qf q qf e df qf

dc d df q qf

d dc

d

L i e R i L i v

dt d

L i e R i L i v

dt d

v f i f i

dt

f v

   

   

 

qf 2

... (9)

v  f vq dc ... (10)

e

is the frequency of the power system and the subscripts ‘d and ‘q’ are used to denote the components of the d-

and q-axis in the rotating frame, respectively. Equations will be used to derive the block diagram of the active power

fitter and calculate the input voltage commands of power converter.

Let transformation angle

e be equal to the angle of phase voltage. Assume that the three-phase voltages are balanced. This yields the voltage components:

edVm ... ... ( 1 1 ) eq  0 .... ... ( 1 2 )Where

V

m is the peak value of the phase voltage of the input power system. Under the above balanced three-phase voltage condition, the instantaneous real power

p

Land reactive power

q

Lon the load side can be expressed as:

L L

3

P . . . ( 1 3 ) 0 . . . ( 1 4 )

2 Vmid L q

 

Equations. (13) and (14) are suitable for both balanced and unbalanced loads. When the phase voltages of power system are balanced,

p

Land

q

Ldepend only on

i

dLand

i

qL, respectively. For a fully harmonic-current

compensated active power filter system, the instantaneous real power

p

sand reactive power

q

sfrom the power system can be expressed as:

1

3 . . . ( 1 5 )

2 m

P sV i

q

s

0 ... (16)

Where the fundamental component of the load current

i

1can be obtained from the d-axis current

i

dLby means of a

low pass filter. The corresponding reference currents,

idf

* and iqf

* of the active power filter in the rotating filter are.

*

1 d l . . . ( 1 7 )

d f i i

i

 

*

... (18)

ql

qf i

i

 

(4)

noted that the reference currents can be obtained simply by subtracting the fundamental component from the measured load currents regardless of whether the load is balanced or not.

2.4 power converter control:

To reduce the DC-link capacitor fluctuation voltages and compensate the system loss, a proportional-integral controller

G

DC

(S

)

is used in the DC-link voltage control loop. As a result, the d-axis reference current of

the active power filter has to be modified to:

*

1 d l d c . . . ( 1 9 ) d f I I I

I   

* '

2 2

( ) . . . .. ( 2 0 )

d c d c d c d c

IG s

V

V

Where

I

dc is the current command of the DC-link voltage regulator, V dc *

2and

V

dc

'

2are the command and feedback of

the DC-link voltage, respectively. The variables in capitals represent the Laplace transforms of the corresponding variables in the time domain. The block diagram of d-and q-axis reference currents of an active power filter are

shown in Fig. 3.2, where the voltage detection represents the Dclink voltage detecting circuits.

The input voltage commands,

Vdf

* and Vaf

* of the power converter can be obtained by using equations. This yields

:

*

2 2

*

2 2

. . . ( 2 1 )

. . . ( 2 2 )

m d f e q f d f

d f

q f e d f q f

q f

V R I L I U

R I L I U

V V

 

   

   

Where

U

df and

U

qf are the voltage commands of current regulators of an active power filter.

Fig.2 Block diagram of d- and q-axis reference current of active power filter.

It is seen from equations. (21) and (22) that the cross coupling terms

e

L

2

I

df, and

e

L

2

I

qfexist in the d-q current

control loops. To decouple the d-q current loops and simplify the control scheme, the voltage de couplers can be

designed as follows:

*

*

( ) ( ) . . . ( 2 3 )

( ) ( ) . . . ( 2 4 )

d f d f d f d f

q f q f q f q f

U G s I

U G s I

I

I

 

 

Where Gdfand

qf

G are the proportional-integral controllers' gain of d- and q-axis current control loops of the active

power filter, respectively. The block diagram of the d-q current control loops can be derived from equations. as

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Vol. 2(9), 2010, 4072-4082

) (s Gd f

2 R 2 L e  2 L e  2 R 2 2 1 sL R  ) (s Gq f

d F 2 3 q F 2 3 2 1 s C 2 L e  2 L e  2 2 1 sL R  * d f i d f i q f i * q f i       

E d = V m E d =V m

E q = 0 E q =0

*

d f V Vd f

*

q f V Vq f

2

d c

V

A c tive p o w e r f ilte r M o d el

Fig.3 Control block diagram of d- and q- axis current controllers of active Power filter.

* *

s i n c o s e e 1

2 2 2

* *

s i n ( ) c o s ( ) 1 . . . . ( 2 5 )

3 3 3

* 2 2 0

s i n ( ) c o s ( ) 1

3 3

v a f v d f

e e

v b f v q f

v c f e e

                                            

The output for three-phase input voltage commands

v

*af ,

v

bf* and

v

*cfcan be obtained through the input/output (o/p)interfaces of a personal computer. These commands are then compared with a 10khz triangular-wave carrier to

produce the switching pattern for the IGBT devices. 3.model establishment and stability analysis:

The analytical model for the active power filter can be established as shown in Fig.4. It consists of a calculation circuit for the reference currents, a DC-link voltage regulator and a simplified model for the relation between reference and real currents of the active power filter. Based on the analytical model, the following design of the proportional-integral controller parameters,

K

Pdcand

K

Idcof the DC-link voltage regulator and analysis of the DC-link voltage response are given. From Fig.4.5, the closed-loop transfer functions can be derived as:

d c s T  1 1 s K K I d c

p d c 2 d c V * 2 d c V ' 2 d c V

_ Id c

a s T  1 1 1  f s T  1 1 f s T  1 1 d F 2 3 q F 2 3 2 1 s C * d f I * q f I d f I q f I   2 d c V d L I q L I    _ 1 I L o w p a s s f i l t e r

R e f e r e n c e c u r r e n t c a l c u l a t o r

C u r r e n t r e g u l a t o r & a c t i v e p o w e r F i l t e r m o d e l

Fig.4 Analytic model for active power filter

.

2 2

2 2

( ) 2 (1 )

... (2 6 )

( ) (1 ) ( )

( ) 3(1 )

... (2 7 )

( ) (1 ) ( )

d f d c a

d L a

d c d c d a

d L a

I s s T C T s

I s s T s

V s s T F T s

I s s T s

         

( ) 1 ...( 2 8 ) 1 q f f I s s T   

2( ) 3 (1 ) ...( 2 9 )

( ) ( )

d c q d c

q L

s I F s

V s

I s s

 

Where

F

dand

Fq

are the Laplace transforms of

f

dand

f

q respectively, while the symbol

(

s

)

is the

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4 3

( ) 2 2 2 2( )

2

2 2 3 3 ...( 3 0 )

s C T f Td cs C Tf Td c s

C s Fd P d cs Fd K I d c

    

 

The DC-link voltage variation is imposed basically by

i

df because the switching function in the d-axis

component is much greater than that of the q-axis, i.e.

f

d



f

qin addition, since the voltage drop across the inductors

L

2 of an active power filter is small as compared to the phase voltage magnitude

V

m the inductor voltage

of

L

2can be neglected. This yields

e

d

V

df and

2 dc m d V V

F  . ………(31)

the closed-loop transfer functions and the characteristic polynomial can be written, respectively, as

)

(

)

1

(

)

1

(

2

)

(

)

(

3 2 2

s

sT

s

T

V

C

sT

s

I

s

I

a a dc dc dL df

(32)

)

(

)

1

(

)

1

(

3

)

(

)

(

2 2

s

sT

s

T

V

sT

s

I

s

V

a a m dc dl dc

(33)

4 3

( ) 2 2 2 2 2 2( )

2

2 2 2 3 32 2

s C V T T s C V T T s

d c f d c d c f d c

C Vd c s CmKp d cs C VmKId c

   

  

…. (34)

Assume that the steady-state value of the DC-link voltage is equal to the DC-link voltage command,

V

dc2

V

'dc2. By using Routh-Hurwitz criterion, it is easy to find that the DC-link voltage regulator

parameters, an

K

Idcmust satisfy the following relations for stable operation.

*

2 2 ( )

2

.. ... ... ... ... ... .. ... ... .( 3 5 ) d c

3 ( )

*

2 2 ( ) 3 d c ( )

2

0 d c * d c... ... ..( 3 6 )

2

2 2 ( )

2

C Tf Td c

V d c K P

Vm TfTd c

C Tf Td c VmKP Tf Td c

V d c

KI KP

C Tf Td c

V d c

      

Satisfaction of equations (35)and (36) will be assured during the determination of

K

Pdcand

K

Idc for the active

power filter.Parameters of non linear load: L1= 3.mH R1 =0.03Ω R0= 8.67 Ω C0 =3300 Μf

4.design of low pass filter for reference current caluclation:

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Vol. 2(9), 2010, 4072-4082

s i n s i n ( ) . . . ( 3 7 )

1 1 2

2 2

s i n s i n [ ( ) ] . . . ( 3 8 )

1 1 2

3 3

2 2

s i n s i n [ ( ) ] . . . . ( 3 9 )

1 1 2

3 3

ia L i e in n e n

n

ib L i e in n e n

n

ic L i e in n e n

n

   

 

   

 

   

 

   

 

     

 

     

For an unbalanced load assume that nonlinear load of phase b is open i.e.

i

bl

0

and

i

cL

 

i

aL

...(40)

.

' ' ' ' '

s i n s i n ( ) . . . ( 4 1 )

1 1 2 1

'

i 0 . . . ( 4 2 )

' ' ' ' '

s i n s i n [ ] . . . ( 4 3 )

1 1 2

ia L i e i n e n

n

b L

ic L ia L i e in n e n

n

   

   

 

   

 

      

Where

i

nand

i

n' represent the peak values of the th

n

current harmonic for balanced and un balanced loads,

n and

'

n

denote the power factor angle of the th

n

harmonic component for balanced and unbalanced loads respectively. 5.design of current regulators:

As mentioned earlier, the choice of cutoff frequency

f in the simplified analytical model will influence the line current tracking capability of the active power filter. To obtain a fast response and low overshoot for the current of an active power filter, a higher value of

f must be chosen. Unfortunately, the maximum value is limited by the maximum IGBT device switching frequency. In the proposed system, the IGBT's operating frequency is 1OkHz. Therefore, the cutoff frequency

f is designed to be

5

p

(or) 12500 rad/sec. The delay time constant

f

T

is equal to0.08 ms.this yields, from equation (4.4) the proportional-integral controller parameters of current regulators,

K

Pdf

K

Pqf =62.5 and

K

Idf

K

Iqf =375.

6. design of dc-link voltage regulator

:

For the sake of simplicity in the design of a DC-link voltage regulator, the cutoff frequency

dc of a low -pass filter in the voltage detection block of Fig. (4.4) is equal to

athis gives

dc

a

100 rad/s...(44)

Thus, the delay time constant

T

dcis equal to 10 ms and equation (40) can be written as.

' 2( ) 3 2... (45)

( ) ( )

dc m a

dL

s V T s

I s s

V

(8)

2 3

. . . ( 4 6 )

2 2

2 C 2 Vd c 2 ( ) ( s 2 )

( )

( )

d c

d L

VmTas

Tf Td c n n

V

s

I

s

   

 

3 V m . . . ( 4 7 )

2 C 2 2 ( )

2 2 . . . ( 4 8 )

6 (m 2 )

K P d c n

V d c T f T d c

C V d c

V V d c T f T d c

 

To obtain low overshoot for the DC-link voltage, the damping coefficient = 0.707 is chosen..The corresponding proportional gain of a DC-link voltage controller can then be obtained from equation.(4.10)

*

2 2

d c . . . ( 4 9 )

3 ( )

d c P

m f d c

C K

V T T

V

2

C

DC-link voltage command

V

dc

*

2 peak value of phase voltage

V

m and delay times

T

f and

T

dc It is worth

noting that

K

pdc is independent of delay time constant

T

a Substituting equation (4.30) into equation (4.29), one obtains

)

(

2

1

dc f n

T

T

……

(50)

Finally, substitution of the system parameters into equations. (49) and (50) yields

K

pdc= 0.381 and

n

=70.15 rad/sec The value of

K

pdc=0.381 is reasonable because the limiting value for

K

pdccorresponding to equation ( 49) for stable operation .

7. simulation results

waveform for source current without apfc

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Vol. 2(9), 2010, 4072-4082

fet analysis for load currents without apfc:

thd calculation for source current

waveform for source current with apfc

(10)

thd calculation for source current

total harmonic distortion (thd):

The Total Harmonic Distortion (THD) in the source current of the proposed three phase system of non linear balanced and unbalanced load with and with out active power filter controller. Similarly from section 5.1 the Harmonic order and Total Harmonic Distortion (THD) in the source current of three phase system connected to unbalanced nonlinear load (Diode bridge rectifier)with ActivePower Filter Controller. Then the corresponding Harmonic order as follows

thd without apfc with apfc

initial 22.93 22.93

final 22.93 1.54

7. Results

Results for following foure cases of three-phase power system connected to non-linear load. For the design of active power filter controller, the proposed tree phase system parameter uses as follows

Peak value of the phase voltage (

V

m) = 98 V., Frequency of the power system (

e) = 377 rad/sec., DC-link voltage

(

v

dc2) = 240 V., Resistance and inductance of the line (R1,L1)=3.1 mH ,0.03 Ω

Resistance and capacitor of the nonlinear load(R0,C0)=8.67Ω,3300μF DC-link capacitor (

C

2) = 4700 μF

Resistance and inductance of the active power filter (

R

2

,

L

2)=0.03 Ω,5 m., DC-link voltage (

v

dc2) = 240

8. Conclusion

The active power filter controller has become the most important technique for reduction of current harmonics in electric power distribution system. In this project a model for three-phase active power filter for balanced non-linear load is made and simulated using Matlab/Simulink software for the reduction harmonics in source current. The simulation result indicates that the total harmonic distortion (THD) of the current reduced from 0.1725 with out active power filter to 0.0726 with active power filter for balanced nonlinear load and 0.3577 with out active power filter to 0.1912 with active power filter for unbalanced nonlinear load and the power factor improved .

9.Future work:The hardware implementation of active power filter can be done with DSP controller 10. References

[1] IEE proc –electr., power app(2001): A novel and analytical model for design and implementation of active power filter’ l.,vol.148,no.4,july

[2] Nassar Mendalek and Kamal Al-Haddad(2000) IEEE: Modeling and Nonlinear Control of Shunt Active Power Filter in the Synchronous Reference Frame..

[3] FUJITA, H., and AKAGI, H(1991): ‘A practical approach to harmonic compensation in power system-series connection of passive and series active filters’, IEEE Trans. Ind. Appl., 27, (6), pp. 1020-1025.

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Vol. 2(9), 2010, 4072-4082 [5] H. Akagi, Y. Kanazawa and A. Nabae,( 1984): “Inatanataneous reactive power compensators comprising devices without energy storage

components” IEEE Trans. Ind. Appl. Vol. IA-20, No-3, pp625-630

[6] Kishore Chatterjee, B.G. Fernandes and G.K Dubey; (1999) : “An instantaneous Reactive Volt-Ampere Compensator and Harmonic Suppressor System”; IEEE transaction on power electronics vol 14 no 2 march .

[7] B. N. Singh, Ambrish Chandra and Kamal Al-Haddad,(1998): “Performance comparison of two current control techniques applied to an active filter” ICHQP’ IEEE.

[8] ( 2003 ) Filter for Selective Harmonic Compensation” ; IEEE

[9] Marks, J.H.; Green, T.C.; (2001): “Ratings analysis of active power filters”;Power Electronics Specialists Conference, 2001. PESC. 2001 IEEE 32nd Annual , Volume: 3 , Page(s): 1420 -1425 vol. 3

Bibliographies

G.N.Rao was born in Guntur, India, in 1975.

He received the AMIE (electrical ) degree from the Institute of Engineers (India ) and the M.Tech degree from Nagarguna University, Nambur,AP,India., and currently pursuing his Ph.d from J.N.T.University Kakinada .Working as Sr. Asst .Prof & H.O.D ,electrical and electronics engineering in VIJAYA INSTITUTE OF TECHNOLOGY FOR WOMEN ,Vijayawada. His areas of interest are in power systems, electrical machines, electromagnetic fields. Mr.Rao is a Life Member of the Indian Society for Technical Education ( ISTE ) and Associate Member of the Institution of Engineers ( India )[ IE(I)].

Dr. K.Chandra Sekhar received his

B.Tech degree in Electrical & Electronics Engineering from V.R.Siddartha Engineering College, Vijayawada, India in 1991 and M.Tech with Electrical Machines & Industrial Drives from Regional Engineering College, Warangal, India in 1994, He Received the Ph.D , degree from J.N.T.U College of Engineering, Hyderabad-500072,India. From 1994 to 1995, he was the Design & Testing Engineer in Maitreya Electricals(P) Ltd, Vijayawada. From 1995 to 2000,he worked with Koneru Lakshmaiah College of Engineering as a Lecturer ,since 2000,he has been with R.V.R & J.C.College of Engineering as Prof & H.O.D ,electrical and electronics engineering. Mail

Dr. P.Sangameswararaju did his Ph.D

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References

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