8 Power Electronics Unit 6

1

6

(AC-AC Converter)

6.1 6.2 6.3

2

[1] Muhammuad H.Rashid , Power Electronics, Pearson Prentice Hall, 3th edition, 2004. [2] Muhammuad H.Rashid , Power Electronics Handbook, Butterworth-Heinemann, 3th edition,

2011. [3] .. . , ..

,2550 [4] W.G.HURLEY and W.H.WOLFLE,Transformers and Inductors for Power Electronics, John

Wiley Sons L.td. [5] . ,Power Electronic 1,

[6] Dr.P.S.BIMBHRA , Power Electronics , KHANNA PUBLISHERS , 1999

3

6

(AC-AC Converter)

6.1 6.1.1 (ac voltage controller) 1. (Single phase half wave ac voltage controller) (phase control)

OR OV

OI

1T

SI

SV

D

6.1.1

4

6.1.1 T D 6.1.2

0

t

gi

2 43

2 43

sv

mV

mV

t

t

oi

2 43

t

ov

2 430

m

o

V

R

m

o

V

R

mV

mV

6.1.2

5

2. (Single phase full wave ac voltage controller) (phase control) 6.1.2 6.1.2() (anti-parallel)

1T

2T

6.2

OR OV

OI

1T

2T

SI

SV

OR OV

OI

TS

I

SV

1D

2D

3D

4D

() ()

OR OV

OI

1T

SI

SV

1D

2D

2T

OR OV

OI

T

SI

SV

() ()

6.1.2

6.1.2() 6.1.2() 6.1.2()

6

6.1.2() 6.1.2() 3. - -(on-off control) 6.1.2 (zero-voltage crossings) 6.2.4 (mechanical time constant)(thermal time constant) 4. 6.1.3 6.1.4

1 2 3 4 5T T T T T

6T

A

B

C

1T

4T

3T

6T

5T

2T

OR

ORO

R

a

b

c

n

6.1.3

7

A

B

C

OR

OR

OR

1T

2T

3T

6T

5T

4T

a

bc

6.1.4 6.1.2 (cycloconverters) (Positive converter) (Negative converter) 6.1.5 6.1.6

Load

1T

2T

3T

4T

3T

1T

2T

4T

L

N

Positive Converter Negative Converter

6.1.5

8

Load

3T

2T

5T

6T

3T

1T

2T

4T


1T

4T

6T

5T

A

B

C A

B

C

6.1.6

9

6.2 6.2.1 6.2.1

1T

2T

1

T 2

T 6.2.2

1T

(trigger angle) 2

T

OR OV

OI

1T

2T

1I

2I

SI

SV

TV

6.2.1

0

t

1gi

2gi

2 43

2 43

2 43

sv

mV

mV

t

t

6.2.2

10

6.2.2 6.2.1 6.2.3

0 2 43

sv

mV

mV

t

t

oi

2 43

t

ov

2 430

m

o

V

R

m

o

V

R

mV

mV

6.2.3

1

T

1T

2

T

2T 2

2 s in

s sv V t 6.2.1

11

6.2.3

2 s in

0

s

o

V t

v

; 2

0 ;

t t

t t

6.2.2

1.

1

2212 s in

O sV V t d t

1

2s in 21

2S

V

6.2.3

6.2.3 S

V

1

2s in 21

2

S

O

O

VI

R

6.2.4

(S

I )(

OI )

1

22s in 2

12

O OO

S S S O

I RPp f

V I V I

6.2.5

6.2.3 6.2.4 6.2.5 2. (Fourier series)

,1

( ) co s s inO O av n n

n

v t V a n t b n t

6.2.6

6.2.6

1 , 3 , 5 ,

( ) co s s inO n n

n

v t a n t b n t

6.2.7

12

0

2( ) co s

n Oa v t n t d t

6.2.8

0

2( ) s in

n Ob v t n t d t

6.2.9

1

( )O

v t 6.2.8 6.2.9

,

2s in co s

n O ma V t n t d t

, co s ( 1) 1 co s ( 1) 11 1

O m

n

V n na

n n

6.2.10

,

2s in s in

n O mb V t n t d t

, s in ( 1) s in ( 1)1 1

O m

n

V n nb

n n

6.2.11

6.2.10 6.2.11 n (

, ,O n mV )

n n

2 2, ,O n m n n

V a b 6.2.12

1ta n nn

n

a

b

6.2.13

, ,, ,

O n m

O n m

O

VI

R 6.2.14

6.2.10 6.2.11 6.2.12 6.2.13

1

2 2 2

1 ,

s in 2 co s 2 1( )

2 2

m

m

VV

6.2.15

11

co s 2 1tan

s in 2 2 ( )

6.2.16

13

6.2.1 3 220 V 50 Hz

.

. . 6 0 .

60 . .

.

,

1s in (1 co s )

2 2

m m

T AV

V VI t d t

R R

, ,

21 2 220(1 co s 0 ) 3 3 A

2 2 3

m m

T AV m

V VI

R R

1

12 2

21 1 1s in 1 (s in 2 )

2 22 2

m m

T

V VI t d t

R R

,

1 1 2 2205 1 .8 6 A

2 2 2 2 3

m

T m

VI

R

. 1 10 m sec

2 2 50o fft

f

14

. 6 0

1 1

22 2s in 2 s in 2 ( 3)

1 1 0 .8 9 72 3 2

O O

S O

I Rp f

V I

. 6 0 6.2.10 6.2.11

3

co s 2 40 1 co s 1 20 10 .3 7 5

4 2

m mV V

a

s in 2 40 s in 1 20 0 .6 4 9524 2

m m

n

V Vb

2 2

2 2

3 , 3 30 .3 7 5 0 .6 4 9 5 2 0 .7 5

m m m

m

V V VV a b

1

2 2 2

1,

s in 120 co s 120 1( ) 2 .6 3634

2 2 2

m m

m

V VV

6 0

3 ,1,

0 .7 50 .2 845

2 .6 3634

m

m

V

V

.

, s in0

O mTIi

t

. 6.2.3 331 V -311 V 9 0 6.2.3 1. 6.2.4

1T

2T

( ) 1

T

15

6.2.5

OR

OV

OI

1T

2T

1I

2I

SI

SV

TV

OL

6.2.4 RL

mV

0 2 43

sv

mV

t

t

oi

2 43

t

ov

2 430

mV

mV

6.2.5 RL

2.

1T

2 s in ( ) s in ( )O

O

Rt

LS

O

Vi t e

Z

t 6.2.17

16

1tan OO

L

R

22O OZ R L

1

T 6.2.17

2 s in ( ) s in ( ) 0O

O

R

LSV

eZ

s in ( ) s in ( )

O

O

R

L

e

6.2.18 6.2.18 6.2.19 6.2.17 sin ( ) 0 180 6.2.5

1

1

22 21 1 12 s in s in 2 s in 2

2 2

S

O S

VV V t d t

6.2.20

6.2.5

1

221

( )O OI i t d t

2

22

s in ( ) s in ( )

O

O

Rt

LS

O

VI t e d t

Z

tdetZ

VI

tL

R

so

o

o

2

)(

2

22

)sin()(sin2 6.2.21

6.2.18 6.2.19 6.2.6

17

6.2.6

mV

0 2 43

sv

mV

t

t

oi

2 43

t

ov

2 430

mV

mV

6.2.7

18

3. RL 6.2.5 6.2.7 6.2.2 6.2.8

mV

0 2 43

sv

mV

t

t 2 43

t 2 43

oi

t 2 430

1gi

2gi

6.2.8

1T 2

2T

1

T 2

2T

19

6.2.9

1T

2

T

mV

0 2 43

sv

mV

t

t 2 43

t 2 43

oi

t 2 430

1gi

2gi

6.2.9

6.2.9 0

1T t

2T

20

6.2.2 3 12.7 mH 220 V 50 Hz

. . . .

. 0 120

.

3

1 1

m in

2 5 0 1 2 .7 1 0tan tan 5 3 .3

3

O

O

L

R

180 53 .3 180 . 53 .3

2 2 2 3 2

22 0 2 2 04 4 A

5( ) 3 ( 2 5 0 1 2 .7 1 0 )

S

O

O

VI

R L

. 53 .3 2 244 3 5808 W

O O OP I R

5808 0 .6

220 44

Pp f

S

.

21

53 .3

,

0 .6361 0 .636 311s in ( ) 1 9 .7 A

2 2 2 5

m m

T AV

V VI t d t

Z Z

1

2 20 .7 0 71 0 .7 0 7 3 1 1

s in ( ) 3 1 A2 2 2 5

m m

T

V VI t d t

Z Z

. 0 120 6.2.6 0

0180

120

12053 .1

6.2.4 - 1. 6.2.2 6.2.3 ( ) - 6.2.10 (zero-voltage crossings) - 6.2.11

1T

2T n

m n m n m (mechanical time constant) (thermal time constant)

22

OR OV

OI

1T

2T

1I

2I

SI

SV

TV

6.2.10 -

0

sv

t

t

t

1gi

2gi

ov

t0

n m

mV

mV

mV

mV

()

6.2.11

2. n m

23

1

2 2

2 2

0

s in ( )2 ( )

O m

nV V t d t

n m

1

2 22

0

(1 co s 2 ) ( )4 ( )

mn V

t d tn m

2

m

S

V nV k

n m

6.2.22

S

V k ( )n n m

OO

O

VI

R

2 2

O S

O

O O

V k VP

R R 6.2.23

( S )

2

S

i S S S O

O

k VS V I V I

R 6.2.24

(O

P )

2

2

Oi O S

i i O S

RP P k Vp f k

S S R k V

6.2.25

n

,

0

s in ( )2

m

T a v m

IkI I t d t k

6.2.26

1

22

0

s in ( )2 2

m

T m

IkI I t d t k

6.2.27

24

6.2.3 - 220 V 50 Hz 20 8 4

. . .

.

8 220 179 .6 3 V8 4

O S S

nV k V V

n m

.

8 0 .8 1 68 4

p f k

. (,T a v

I )(TI )

,

8 2 2 2 03 .3 A

(8 4 ) 2 0

m m

T a v

O

I VI k k

R

8 2 2 20 6 .3 5 A2 8 4 2 20

m

T

II k

6.2.5 6.2.1 6.2.4

,m ax( )

swV

,m ax m axswV V

,m ax( )

avI

,m ax2 2

0 .6 3 6

2

S

T

O L

VI

R X

25

6.3 6.3.1 6.3.1 6 6.3.2 2 s in ( )

AB ABv V t 6.3.1

2 s in ( 2 )3

BC BCv V t

6.3.2

2 s in ( 4 )3

C A C Av V t

6.3.3

2 s in ( )6

AN ANv V t

6.3.4

2 s in ( 5 )6

BN BNv V t

6.3.5

2 s in ( 3 )2

CN CNv V t

6.3.6

A

B

C

1T

4T

3T

6T

5T

2T

OR

ORO

R

a

b

c

n

aI

bI

cI

a nV

b nV

cnV

6.3.1

26

OR A

t 6 6 6.3.1 A (

1T )

B (6

T )

2

a b

a

O

vi

R 6.3.7

6 5 6

A Bv

ai

5 6 A (1

T ) B (6

T ) 5 6 0 5 6 6.3.2

1T 2T 3

3

1T

2T

1

T 3

T 5 6 1T t 4 3

2T t 5 3

A B

v

1T 6 4 3 4 3

2

T 2 3 5 3 5 3

27

2 43

av

bv

cv

a bv

b cv

c av

t

v

0

2gi

t 2 43

1gi

t 2 43

3gi

t 2 434g

i

t 2 435g

i

t 2 436g

i

t 2 43456

56

561

61

612

12

123

23

234

34

345

45

456

6

6.3.2 0 6

28

3

T 7 6 2 3 2 2

4T 3 2 7 3 7 3

5

T 11 3 4 3 8 3 8 3

6T 4 5 3 3 3

0 3 0 3 6.3.3

OR

O

R 3 2 3 2 6.3.4 6.3.5

OR

2 5 6 2 5 6

OR

0 3

1

12 2

22

0

1 1 s in 2( ) 6

2 6 4 8O an S

V v d t V

6.3.8

3 2

1

21 3 s in 2 3 co s 26

1 2 1 6 1 6O S

V V

6.3.9 2 5 6

1

21 5 s in 2 3 co s 26

2 4 4 1 6 1 6O S

V V

6.3.10

29

456

56

561

61

612

12

123

23

234

34

345

45

456

av

bv

cv

a bv

b cv

c ava

v

2 43 t0

av

bv

cv

a bv

b cv

c avb

v

2 43 t0

av

bv

cv

a bv

b cv

c avc

v

2 43 t0

6.3.3

0 3

30

45

56

61

12

23

34

45

2 43

av

bv

cv

a bv

b cv

c av

t

v

0

2gi

t 2 433g

i

t 2 434g

i

t 2 435g

i

t 2 436g

i

t 2 43

6

1gi

t 2 43

6.3.4 6 2

31

av

bv

cv

a bv

b cv

c ava

v

2 43 t0

av

bv

cv

a bv

b cv

c avb

v

2 43 t0

av

bv

cv

a bv

b cv

c avc

v

2 43 t0

45

56

61

12

23

34

45

6.3.5

3 2

32

6.3.1 6.3.1 380 V R-L 5 5 . . . ( min )

455

5tantan

11

min

R

X L

45 A31

553

380

3 22

Z

VI

LLL

A94.21

2

31

2

L

Th

II

. 15045

33

6.3.2 6.3.6 1 3

A

B

C

OR

OR

OR

1T

2T

3T

6T

5T

4T

a

bc

aI

bI

cI

a bI

b cI

caI

6.3.6

2 s in ( )

AB ABv V t 6.3.11

2 s in ( 2 )3

BC BCv V t

6.3.12

2 s in ( 4 )3

C A C Av V t

6.3.13

6.3.6

1T

A Bv t

0 6.3.7 2 3 ( )

34

6.3.8 6.3.9

v

2gi

t 2 433g

i

t 2 434g

i

t 2 435g

i

t 2 436g

i

t 2 43

1gi

t 2 43

5 6 1 2 3 4 5

2 43

a bv

b cv

c av

t0

6.3.7

35

a bv

b cv

c ava b

v

2 43 t0

a bv

b cv

c avb c

v

a bv

b cv

c avca

v

2 43 t0

2 43 t0

5 6 1 2 3 4 5

6.3.8 2 3

36

bi

ci

2 43 t0

2 43 t0

5 6 1 2 3 4 5

ai

2 43 t0

6.3.9 2 3

1 1

2 2 2

21 1 s in 2

( )2 2

O a b SV v d t V

6.3.14

37

6.3.2 6.3.6

OR 10

380 V 50 Hz 2 3 . . . .

V380 LLV 10oR rad

3

2

. 2 3

V1692

322(sin

3

21380

2

2sin1

2

1

2

1

,

sLLo VV

.

A9.1610

169,.

o

LLo

phoR

VI

. ( P ) ( S ) W3.8568109.1633 22, ophoo RIP VA192663809.1633 , phpho VIS (lagging)445.0

19266

3.8568

i

i

S

Ppf

.

A95.112

9.16

2

,

pho

Th

II

38

6.4 (cycloconverters) (DC link) .. 1930 50 Hz 50/3 Hz 400 hp 1960 15 MW (Positive converter) (Negative converter) 6.4.1 6.4.1 t

39

0 1

T 2

T 1

T 2

T t 2

3T

4T

3T

4T

6.1.2 0 2

OT

2O

T O

T

Load

1T

2T

3T

4T

3T

1T

2T

4T

L

N


6.4.1

0

sv

t

mV

mV

ov

t0

mV

mV

2

OT

OT

6.4.2

40

Load

3T

2T

5T

6T

3T

1T

2T

4T


1T

4T

6T

5T

A

B

C A

B

C

6.1.6

41

6 1. . . 2. RL . . . . 3. . R . R . RL . RL 4. 220 V 50Hz RL 2 6.36 mH . 0 180 . 18045 . 90 180 . 0 45 5. RL . . . .

42

6. RL . ( ) . ( ) . . 7.

1

2 3 0

t

Oi

. R .......

2

2 3 0

t

Oi

. RL .......

3

2 3 0

t

Oi

. RL .......

4

2 3 0

t

Oi

. L ....... 8. 4 230 V 50 Hz . . 60 120 45 . 45

43

. 90 325.27 V . 281.69 V 325.27 V . 27.284 V 63.435 9. RL . . . 10. 230 V 50 Hz RL 2.3 7.32 mH . . . . 90 . 90 . 45 180 . 7.07 A . 115 kW 0.707 . 31 A . 130 0.425 11. 230 V 50 Hz RL 20 50 mH 90 . . . . . 5.333 A 3.771 A . 2.019 A . 569 W 0.485

Documents

8 Power Electronics Unit 6