Novel Control Strategy for VSI and CSI Active Filters and Comparing These Two Types of Filters

1393

CSI

VSI

! "# $

) 1 (

#() $ (

) 2 (

+ , -./

) 3 (

) 1 ( & ' ( )*+, - . / * 01 2+3 41 )* 5 * 6 7& ' 8 9

) ' 9 :&

) 2 ' < 9 (

–

9 :& ' ) * 5 7& '

) 3 8 ' (

–

7& ' )

= > ' *8 :& '

: 6 @ A 24

/ 2 / 1393 :D E @ A

23 / 10 / 1393

1 2

:

' G 5 HEI ' J' , (7K =' A 2 L M NA '

5 89' 80 6 )O 3 (86 P ' 3 =' ' 6 (Q A

R ' ' 5 ' . '

=/ 8 *P 9 =' KQ O TU&5 8 9 I ) 80 6 ( P . ' V 80 6 ( KV

(. N5 R ' W ' R *. 8 9 XA' 8 '

89' 80 6

VSI CSI

80 6 W R ' YZ ' & [ 9 =' 5 \ '

THD

Q *+, - = 5

(V N5 (86 P ' .

89' 80 6 ' & *. 8 9 XA' 8 '

VSI

5]1 * 8K5 89' 80 6 & *. 8 9 XA' 8 ' = Q ^K 5 D _.

CSI

( 09 . ' D _. 5]1 * 8K5 `N6 ( K

` a5

MATLAB/Simulink

8 . ' (86 P b ' c

( K *5 = & (9

D D ' 8 80 6 W ' & *. 8 9 *5 *0K3 *. 8 9

89' 80 6

CSI

89' 80 6 ( KV 8 70 1

VSI

( I R86 P \ 5

) ^K 5 = A 9 TA' ' P 0Q ' (

. '

: # 4 ( 6

.* _. . I 8 9 )*+, - )d 8. ^K 5 A ' )= Q ^K 5 A ' ) 89' 80

Novel Control Strategy for VSI and CSI Active Filters and

Comparing These Two Types of Filters

Gholam Reza Arab(1) – Somayeh Yarahmadi(2) – Jafar Soltani(3) (1) Associate Professor - Department of Electrtical Engineering, Shahrekord University

arab-gh@eng.sku.ac.ir

(2) MSc - Department of Electrtical Engineering, Shahrekord University somayeh.yarahmadi@gmail.com

(3) Professor - Department of Electrtical Engineering, Isfahan University of Technology j1234sm@ece.iut.ac.ir

Recently to eliminate the harmonics and improve the power factor of the power networks, much attention has been attracted to active filters. The advantages of these filters are lower volume and their better compensating characteristics than the passive filters. In conventional sliding mode controllers, the source current waveform is fluctuated in near to zero values. In this paper, using a new sliding technique, lower Total Harmonic Distortion (THD) in source current is obtained and the current waveform is improved. As well as, two novel control strategies for two types of active filters, VSI and CSI is proposed and then these two types of filters are compared to reduce THD value of source current.The proposed controlled strategies are simulated by MATLAB/Simulink. The Simulation results confirm that the proposed strategies reduce the THD of source current more than other strategies, and active filter based on CSI has a better performance than active filter based on VSI with a dead time area (for avoiding short circuit of the source) in high powers.

Index Terms: Active filter, current source inverter, voltage source inverter, non-linear load, sliding mode control.

: 5 "#

) 9 :& ' )e 1 L

5]-arab-gh@eng.sku.ac.ir

1 6 # h h V7 ' h1' *h+, - h ' >8h ' 5'

9 ) 8V A &i j ( ... * N.'

[ ' h6' hI h P

*+, - 5 j U *A' A R i . ' Q =

= k5 h *

G 5 ' * l j *5 ' 8V (

(h )R ' m 9

8V T83' O 3 NA ' [ ' 6' I ( 6 GA

hh ' ] 1 [ ] 4 [ Ghh 5 e 0+5 hh hhn/ (hh0 Q ' . = hh Q hh

8V `h A *h Kj - O h . A : ' ' O K1 O 3

2 / ) 8V I ' [ O ' I . A )=' A 2 L o] ' = , 5 P k . ( A 5 >V ' A p 1

G 5 '

d h8.

O 3 8V ] 5 [ ) ] 6 [ .

=' KQ ' *>08U5 W' ' = 9 A [ 9 \ 5 ( 9

nqA

8V *+, -& O 3 G 87.'

' *7 . '

=' KQ R ' ' 9

* , V 80 6 ) *>0

LC

R ' . ' (

*5 =' ' *I' j > 9 2 L K r1 80 6 m P

= )* ' 5 ) I k K3 ' *As 7 ' ' ' Q R ' ( E_A 8V ` ' ( *:8V ' 8V =' A

] 7 [ ) ] 8 [ 5' .

0 3 ) V 80 6 ( KV 8 70 1 01 ( 89' 80 6 G 5 HEI Q ) 8 9 = I ) 8& \ A K

(86 P ' 3 8& (Q A 5 =' A 2 L ' ] 9 [ ) ] 10 [ . ' 85 *5 A ' 8, 89' 80 6 8, R A .

89' 80 6 *5 VNA (8 ( A ' 8,

:

) d 8. ^K 5 A '

VSI

) = Q ^K 5 A ' (

CSI ( ] 11 [ ' . A

V3 v = , G )d 8. ^K 5 dc

09 P' . '

2Q 5 R * A 9 = 5 A ' R ' G *5 G . = , dc

9 TA' ' V = Q A

09 2 / r1 R ' (9 E: 09 ( *

*5 ] 12 [ .

d 8. ^K 5 A ' ( KV 8& O >0A ' ' = Q ^K 5 A ' b N5 8, ' ' = Q ^K 5 A ' 5' ' ' A

] 13 [ .

D ' 5'

D 5 Q

PWM ] 14 [ ] 16 [ ) (7K *KT1 ] 17 [ 6 p+ 5 ) ] 18 [ ] 21 [ * _. . I )

] 22 [ ] 26 [ . *5 >8 ' 89' 80 6 8 9 ' . I 8 9 .

k . ( ' . ' 89' 80 6 8 9 ' D R A 9 * _. 5 _85 8, 8& 2 A )= 5 _85 8, R8 ' =

' 89' 80 6 ]

6 [ *A T, * _. . I 8 9 R ' ]1 .

8V 85' _A ( KV = K < VI ) 5 N5 5 *P *5 ' ' '

] 4 [ ) ] 27 [ ) ] 28 [ . Os N5 ] 13 [ ] 29 [ G 5 [ 9 ' ' = Q ^K 5 A '

GA 8V G = Q (86 P 9 ( 6

& 8 9 D . '

p8&5 ' )^Q 5 : . A ' *y0y5 z 5 P

= 5 6

A ' 09

CSI *5

p8&5 (7 ' k . ( . Q P

9 *. 8 9 D R ' ' E ^Q 5 . V

] 13 [ D *5 & ' *. 8 9 Y. (9

' >8 ' ' A ' = 5 6

6 H]8,' *y0y5 z 5 = Q +, 180

*5 . A (Q . 9

89' 80 6 8 9 ' * _. . I 8 9 )p NaA R ' CSI

9{ O T, ]1 = i . ' & G 5

*5 [ 9 8& ' =' A 2 L ( 8 = Q . ^Q' 5 ] 22 [ ) ] 24 [ ] 26 [ 89' 80 6 VSI

. I 8 9 ' 5

G 5 [ 9 ' ' * _. GA *+, - = Q

6 9 (

(86 P ^Q 5 . ' ] 24 [ Q * 3' ^K 5 = Q kL >A k I ^K 5 =

^Q 5 . ' 9 l A D _. _85 =' 1 ( ' ^Q 5 ]

22 [ D '

^Q 5 ( &5 ] 24 [ ' 8 9 80 6 89' >8 ' *5 9 . R ' O >A (9 ( \ 5 K ) P 5 . I _85 D _. ' ( O W 5 +, :8 ' ' *5 l A ^K 5 = Q +, 8 9 D R ' 2 1 . 9

*.

* . I ' > ' K1 b : ^K 5 = Q (9 ' R ' *5 ^Q 5 . ' z Q 1' ' N5 ]

26 [ H' j' l A

*5 l A ( I R ' *A >85 * 09 :.' )^K 5 d 8. > 9

(9 *5 > ' K1 b : ^K 5 = Q K r1 .

A R ' 8 9 \ 5 ( Q * _. . I 8 9 D ' p Na

89' 80 6 VSI

*5 >8 ' :.' l A ( = (9

^K 5 = Q 86 )^K 5 d 8. > *.' I O >85 * 09 *5 K ' > ' K1 b : . &U

* 8K5 89' 80 6 )(. N5 R ' b ' VSI

CSI \ ' '

G 5 [ 9 =' 5 D )*+, -

* _. 8 9

*5 (V N5 ) & . 9

2 6 #

7 8

) k7 1 *5 = & ' * 5 8V ( k5 h 8hV Rh ' . h

*5 ' 5 89' 80 6 *+, - )^K 5 .

) k7 1 ' 5 89' 80 6 :( *+, -

Fig. (1): Shunt active filter with nonlinear load

GA 89' 80 6 ' 85 A ' 8, ) k7 6

2 ' = & (

= . ' ) k7 (9 j 2

*5 (l.'. 89' 80 6 )

8, VSI V3 v = , G ' ' dc

(0 ( '

l0 G *5 k *+, - ( ) k7 .

2 89' 80 6 (e.

8, CSI *5 = & ' .

CSI V3 l0 G ' '

(0 ( ' *5 k ( EP R | 80 6 G

80 6 R ' .

G 5 K1 ^ 5 (9 s Y 9 6 80 6 G EP R | 09 ' * *

Q ( *5 ^K 5 = .

1393 (l.') (e) ) k7 2 (l.' :( 8, 89' 80 6

VSI

8, 89' 80 6 (e )

CSI

Fig. (2): a) Active power filter with VSI structure, b) Active power filter with CSI structure

3 6 +9:;< =< )

h ' R ' 89' 80 6 P 9 ( ' H b h6 (h `h, = h Q (h9

* p +5 e 0+5 `, = Q R ' . `, d 8. 6

(+ ' ) 1 *5 l A (

.

S *

S

v

i

=

α

(9

α

(9 ' _85 = 5 *K L (

*8 ' , =' A

*5 \ A (+ ' O ( = Q +, .

) 2 *5 = ( . S S * S

S

i

i

v

i

e

=

−

=

−

α

80 6 ^Q 5 = Q O R ' ) k7 ( (Q A

1 (+ ' p +5 )(

) 3 *5 l A ( .

L S *

F

v

i

i

=

α

−

(. 5 = ' ' 3 > ' P' )

2 ' * _. }+ ( (

. I 8 9 . ' , P 5 . I +, ' ' 8V ) / +, P 5 . I +, *.' :8 ' [U R8 ' 01 ( * _. - 85' _A *5 (K0

. I +, [ 9 ' k . R ( m 9

(. 5 5 ' D _. _85 P 5 )

4 *5 l A ( . 9

∫

λ +

= e e

S ( 4 ) *. 8 9 85' (9

λ

*5 5 D _. 2 L .

> ' ' * _. }+ (+ ' = ' ' 3

) 4 *5 ( ( ' . /

D _. ~ )* _. . I 70 1 ' = j'

0 S . S lim 0 S→ <

*5 (9 . /

(+ ' O ( ' A )

5 . = (

0

S

+

<

4 6 ? VSI ^Q 5 ] 22 [

89' 80 6 8 9 \ 5 (

VSI

h. I h8 9 D '

. ' 9 >8 ' * _. O R ' ( ^Q 5 R ' * 09 :.'

(hh9 hh ' hh 09

1

S

2

S

hh ) ^hhK 5 = hh Q hh+, < hh '

09 3

S

4

S

*h5 * h 09 ^K 5 d 8. 5]1 < ' . h

^Q 5

]

26

[

d 8. l A

Vp >8h ' d 8. ^K 5 > *.' I

^Q 5 * 09 :.' '

]

22

[

) :.' *5 l A Q * 09 . 9

r1 *0K3 * 09 :.' (V N5 * 09 :.' R ' ' >8 ' G 5 8& [ 9 *.' hI = h Q hK = h Q

*5 > :.' R ' . * 09

G l A

Vp

h 09 )^hK 5 d h8. >h H' j'

S3

S4 h ' (h9 * h5

P S| V

v | ≤

5 2 A A (

S2

S1 *h5 * 09 h:.' Rh ' . h 9

) Q * 09 1

* 09 :.' R ' P' . ' 5/ (

Vp '

^Q 5 ( &5 * 09 :.' >

] 22 [ . ' , Table (1): Switching pattern of [26]

) Q 1 ^Q 5 * 09 :.' :(

] 26 [ VF iF S4 S3 S2 S1 vS 0 0 off on off on P S V

v ≤−

-VC iC off on on off 0 0 on off on off P S V v ≥ VC -iC on off off on VC -iC on off off on P S| V

v | ≤ -VC iC off on on off :.' & * 09 ) Q (. N5 R '

2 . ' 5/ (

09 S1

S2 ' . I ( KV ^K 5 = Q +, < ' )

09 =/ ^Q 5 * / S3

S4 = Q 5]1 < '

*5 * 09 ^K 5 )

Vc>|vS| *83 (9 j ( .( • 6

0<iS 09 ) S4 ' R = R

S2 ( 5' iF [ ' 6'

*5 = R S1

) iF *5 [ 9 (9 *5 : m

0>iS 09

S3 = R ' R S2

( 5' iF *5 [ ' 6'

= R S1 ) iF *5 [ 9 (9) *. 8 9 85 R ' ' >8 ' .

09 S3

S4 Q 5]1 * 09 ^K 5 =

( 5]1 d 8. (=/ r1 *5 (\a. (9 K1 ' > = Q ^K 5 ( . I

* 09 l A ( =/ K ' G * . K > *.' I O >85

Table (2): Proposed switching pattern ) Q 2 & * 09 :.' :(

F i 4 S 3 S 2 S 1 S S i 0 off on off on 0 S i ≥ i − off on on off 0 on off on off 0 S i _< i on off off on

) = , d 8. P' Vc

) l0 = Q ( iF

80 6 . I _85 ' (

89' 80 6 . I 46 Os 5 ) : \ 89' VSI p +5 ) ` ' 6 ) ( 7 *5 = ( .

F S

F _{v v}

dt di

L = − (6)

C

c _i

dt dV

C = ( 7 )

: ' l A ( P R ' * 09 ^ A (. N5 R ' gi=1

*

09 i ' R b' gi=0

09 * ) i

' D 5 , b'

) i = ) 09 .( 09 S1

S2 ) )( S3

S4 < 7 5 ' (

*5 k 1 ) Q ( (Q A . 9 2

p +5 (9 80 6 . I Os 5 (

) 6 ) ( 7 : ' ) 8V ( C 3 2 4 1 S

F _{v (gg g g )V}

dt di

L = − − (8 )

C 3 2 4 1

C _{(g g g g )i}

dt dV

C = − (9 )

(+ ' ' >8 ' )

6 ) ' D _. p8&5 ( 10

*5 ( ( . / x ~ x ~

S= +λ (10 )

(+ ' R86 P \ )

4 ) ` ' 'E: Q ( 8 ) ( 9 (+ ' ( ) 10 : ' )( ) v i i ( ) v i ( ) g g g g ( L V L v S S L F S L 3 2 4 1 C S α − + λ + α − + − −

= _{(11 )}

(. 5 = ' ' 3 > ' ) 11 : ' )( ) v i i ( V L ) v i ( V L V v g g g g S L F C S L C C S 3 2 4 1 α − + λ + α − − = − ) 12 ( *5 ' g2=1-g1 ) g3=1-g4

2 ) i sgn( 1 g S 4 + =

= ' ' 3 .

N5 g2 ) g3 g4 (. 5 ) 12 *5 ( =' A g1eq ( ' . / ) v i i ( V L ) v i ( V L V v 2 ) i sgn( 1 g S L F C S L C C S S eq 1 α − + λ + α − + + − = ) 13 (

(+ ' ( (Q A )

13 ' )D _. ` ' ' 3 \ 5 ( (

1

g

0

≤

≤

g1 (14 )

(9 *5 : R ' S>0

) g1=1 (9 *5 :

S<0 ) g2=1

09 S3

S4 = Q 5]1 < '

iS *5 * 09 .

) k7 ( (Q A 2

K5 89' 80 6 P' (l.' . VSI 09 S1 S2 S3 S4 = , ) R = 5 C

TA'

*5 A 9 ' V = Q R ' . P K1 R • 09

*5 =/ R8, 2Q 5 (9 ) 9 *5

' R ' ' e 8Q' ' .

R 09 G = D 5 , R * A 9 V = 5 ' R86 P \ . (8 ' Q = : 09 =

Y. ' *7i 9 V ,qA 09 i = R = 5 6

)

G . = , = A 9 TA' 8I' dc

*5 R ' ) .

R ' ( 09 = 5 6 : ,qA

( I ) *5 (8>P 5 .

\ ' ' 9{ = 5 :VI ' A )

]1 D ' = V7 G ]9 D & D G . d 8. :VI DC

) . ' ^K 5 d 8. = Q :VI (

*5 ' 5]1 ‚ 0 9 (V N5 ƒ5' „/ *P ( =' A

) > ' N5 . 9 5 6 ? CSI A< 6 B +< C $

CSI ^Q 5 ] 13 [

*5 & ' *. 8 9 D (hV N5 h =/ (h9

h6 H]8h,' (9 *y0y5 : = Q +, 180

(hQ

: ) ' h 09 = h5 6 h

*h5 h . A h ha . h

h . A

: 09 = 5 6 k7 (. N5 =/ = Q ^K 5 A '

) 3 ' = & ( 9 8 9 ' 5 R ' . '

PI

(> … R 5qA

Q 5 : ^ 8 9 +, : (V N5 . ' 1 ' = Q

6 H]8,' *y0y5 z 5 = Q 180

8 9 P 9 ( (Q

9 *5 . A A ' 09 = 5 6 : )Y 8V .

^K 5 A ' * 8K5 89' 80 6 } a 70 1 R 4A \ 5 ( ' )k b A = Q Y 89

LF ( ( P ' N5 (9 P *I' j '

' N5 = Q 9 5 ' N5 ' 8P = Q ` 85 (\a. 80 6 ` A . A 89' =' A O R ' - . =/ '

* =' KQ ' 89' =' A } a j ( 89' . 9

) k7 3 89' 80 6 b 5 8 9 :( (

CSI

Fig. (3): The conventional control of active filter based on CSI

6 D E ? +< C $

CSI

) k7 ( (Q A 2

= 3 1 \ 5 ( (e.

KCL

09 ) h

S1

S2 ) )(

S3

S4 *5 * 09 k 75 O ( ( h 09 h:.' . h

& * ) Q

3 . ' 5/ (

Table (3): Proposed switching pattern for the CSI active filter control with sliding mode control

1393

(+ ' 5 D _. _85 )

4 ) & D . ' l A (

P 5 +, )* _. }+ ' *.' :8 ' 5 6 ' >8 ' k . ( 8 9 R † . ' kK3 D ' 8 9 9

@ 1 * _.

( ' *P ' 5 85' ( 8 9 *:8V ' ) 8& ( & D (9 ' R ' : 9{ k 3 (87 . ' '

*5 8 O ( ' Q' k 3 *P *. I

D (9

] 13 [ k7&5 v . / O (

' A

*5 8 .

6 6 G9 H 8

hh 89' hh 80 6 *hh09 o hhj

VSI CSI

2hh A A (hh hh&

k7 ) 4 ) ( 5 . ' 5/ (

) k7 4 & 89' 80 6 *09 o j :(

VSI

Fig. (4): Block diagram of the proposed VSI active filter

) k7 5 89' 80 6 *09 o j :( &

CSI

Fig. (5): Block diagram of the proposed CSI active filter ) Q O TU&5 4

. ' 5/ (

Table (4): The load parameters ) Q 4 O TU&5 :( M' Q' N5

LS 0.8mH

RS 10Ω

RO 60Ω

CO 500µF

( K ( 09

‡ | >8 ' 5

89' 80 6

VSI CSI

W '

IGBT

e U8 ' (\a. =' A . '

*6 T5 '

y9' I (

4000VA

( ' H]8,' =/ = Q d 8.

5°

)

φ

(

*5 (> … 89' 80 6 (9 ' 9{ ( b s . =' A k9 R 5qA

^K 5 = Q z 5 k7 A ' ' 89' k7 6

d 8. z 5

. ^K 5

k7 ) 6

. ' A = Q (

) k7 7 ( K c 8 ( 89' 80 6

VSI

D ( ' >8 '

^Q 5 *. 8 9 ]

22 [ ^Q 5 ] 26 [ ' (. N5 R ' & 8 9

) Q 9E5 3

. ' 5/ (

) k7 6 = Q :(

Fig. (6): Load current

(l.')

(z)

) k7 7 80 6 ' >8 ' (R | ) 89' 80 6 = Q (s ) ^K 5 = Q :(

89'

VSI

^Q 5 8 9 (l.' )

]

22

[

^Q 5 8 9 (e )

]

26

[

(z )

& 8 9

Fig. (7):Source current (up) and filter current (down) by using VSI active filter based on, a) proposed control of [22], b)

proposed control of [26], c) proposed control

THD

) k7 ( ' ^K 5 = Q 7

) )(l.' . 7 ) (e. 7 2 A A ( (z.

' 5 / 5 )% 9 / 3 % 5 / 3 ' K1 b : = Q K 01 . ' %

KV & D ( * 09 > D ( * 09 (

] 26 [ )

9E5 ^Q 5 D ' >8 ' * 09 (9 *A (9 ' R ' ( I > ' K1 b : P O vS>0

vS<0

' ' * 09 . I A .

' >8 ' (9 ' *A R '

' * 09 . I i & D ( * 09 . ' ( I

( I y5 j ( )20+5 R ' } L A ' P' > G '

vS>0 D ( * 09 )

] 26 [ ) S4 5]1 ' R

09 ' *7 )D _. S1

S2 *5 R . I Y m

>8 ' & D ( * 09 ' P' 5' . ' Q * 09 ) 09 ^K 5 = Q 5]1 S4

S3 ' R

09 ' *7 )D _. 5]1 S1

S2 *5 R i Y m

. ' ' , Q * 09 . I

) k7 8 ( K c 8 ( 89' 80 6 '

CSI D

. ' 5/ & * _. . I 8 9 b 5 *. 8 9

l.') (

(e)

) k7 8 80 6 ' >8 ' (R | ) 80 6 = Q (s ) ^K 5 = Q (l.' :(

89'

CSI

& * _. . I 8 9 (e )b 5 8 9 (l.' )

Fig. (8): Source current (up) and filter current (down) by CSI active filter based on a) conventional control, b) proposed

sliding mode control

THD

) k7 = Q 6

k7 ^K 5 = Q ( )

8 (l.'.

) 8 ' 2 A A ( (e. 120

)% 6.5 % 2.13 . ' %

) k7 ^K 5 = Q G [ 9 01 8

) k7 ( KV (l.'. 8

(e.

*5 * 80 6 = Q [ 9 ' Q W 5 ^K 5 = Q ' )

=

. ' = Q 89' 80 6

GA 6 80 6 a5 5 j ( 6

8 9) R | =' A

'

100kVA

*5 ' 3 >8 ' 5 ( V / * 5 @ P

R ) ' A 9 10us

A 10ms 1 5 .( GA 80 6

6

=' A K 5 = i (9 ' R ' R |

*5 9 9 ' A

Y 9 6 . K = 70 1 A 9 ( * s

Q >8 ' 5 † | O TU&5 )

5 ( . ' 5/

80 6 ) 80 6 = , d 8. ' N5 d 8. _A ' 9{ =

VSI

80 6 ) 80 6 = Q ' N5 ( CSI

*5 _A ( 9

~ A

VC>|vS|

If>Is ^Q 5 = Q d 8. ' N5 KV = ( (9

. ' _A ' 80 6

( K c 8 89' 80 6 '

VSI

( I 5

1µS 2µS

89' 80 6 R † CSI

) 07h 2h A A (h 9

) )(lh.'. 9 (e.

) 9 . ' ' = & (z.

THD

^K 5 = Q hA (l.') V3 '

2 A A ( (z) 31

/ 8 )% 45 / 9 % 13 / 2 % *5 . ' (h9

THD

80 6 ' >8 ' b : ^K 5 = Q CSI

80 6 ' 8 9

VSI

h

( I R86 P \ 8 9 * 09 Y 9 6 (7 ' k . ( . ' 5

J 8KV * _. . I ( I R ' ' _85 s

5 hNi

. ' ^K 5 = Q z 5 k7 nqA Gi 9

Table (5): Switch parameters ) Q 5 ‡ | O TU&5 :(

IGBT ‡ | W

0.001 Resistance Ron (ohms)

0 Inductance Lon (H)

1 Forward voltage vf(v)

1e-6 Current 10% fall time

2e-6 Current tail time Tt(S)

0 Intial current Ic (A)

1e5 Snubber resistance Rs (ohms)

1393

(l.')

(e)

(z)

) k7 9 89' 80 6 (l.' ) ' >8 ' ^K 5 = Q :(

VSI

Y. ,qA

= R

1µS

89' 80 6 (e )

VSI

R Y. ,qA =

2µS

)

89' 80 6 (z

CSI

& * _. 8 9 G 7A

Fig. (9): Source current by using, a) VSI active filter by 1µ s dead zone, b) VSI active filter by 2µs dead zone, c) proposed

CSI active filter 7

6 J K

89' 80 6 ' >8 ' )p NaA R '

VSI

* _. . I 8 9

5]1 < ' R ' (9 ' & D _. ^K 5 = Q

< ' * _. . I 8 9 ( KV 8 70 1 D 5]1 ' >8 ' Q ' R † . ' D _. ^K 5 d 8.

89' 80 6 8 9 ' * _. . I 8 9 D

CSI

o +5

5 D 9 (V N5 * 8K5 b 8 9 ' ( v . /

9

PI

89' 80 6 ( KV 80 6 R ' . ' (V N5

CSI

*5 k 1 8 b 5 8 9 ( K c 8 . 9

*5 = & (9

THD

80 6 ' >8 ' b : ^K 5 = Q

CSI

80 6 ' 8 9

VSI

R86 P \ ( I

. ' 5

References

[1] V. Pires, J. Silva, "A current source active power filter controlled by a sliding mode approach", Proceeding of the IEEE/EPEPEMC, Vol. 1, pp, 1654-1659, Portoroz, Aug. 2006.

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