AC voltagecontrollers

1Semnan Un. N. Esakandarian

2Semnan Un. N. Esakandarian

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39Semnan Un. N. Esakandarian

4.1.1 Single-phase AC voltage controller

Ru 1 u o

ioV T 1

V T 2

u 1

u o

O tRu 1 u o

u

O

i o

V T

t

O t

O t

T h e p h a s e s h i f t r a n g e( o p e r a t i o n r a n g e o f p h a s e

d e l a y a n g l e ) :

0

4 0S e m n a n U n . N . E s a k a n d a r i a n

Resistive load, quantitative analysis

RMS value of output voltage

RMS value of output current

( ) ( )

+== 2s i n2

1ds i n21 12

1o UttUU ( 4 - 1 )

p

R M S v a l u e o f t h y r i s t o r c u r r e n t

P o w e r f a c t o r o f t h e c i r c u i t

( 4 - 2 )RUI oo =

( 4 - 3 )( ) )2

2s i n1(2

1s i n22

1 12

1

+=

= R

UtdR

tUI T

( 4 - 4 )

+==== 2s i n

21

1

o

o1

oo

UU

IUIU

SP

4 1S e m n a n U n . N . E s a k a n d a r i a n

Inductive (Inductor- resistor) load , operation principle

R

io

VT1

VT2

u1

O

tOuG1

uG2 t

Lu1 uo

O

uo

io

uVT

O

O

O

t

t

t

t

The phase shift range:

42Semnan Un. N. Esakandarian

Inductive load, quantitative analysisDifferential equation

0

s i n2d

d

o

1oo

=

=+

=

ti

tUR it

iL

1 0 0

/

(

)

1 8 0

1 4 0

=90

75

6045

30150

( 4 - 5 )

S o l u t i o n U t2

T h e R M S v a l u e o f o u t p u t v o l t a g e , o u t p u t c u r r e n t , a n d t h y r i s t o r c u r r e n t c a n t h e n b ec a l c u l a t e d .

0 2 0 1 0 06 0 1 4 0 1 8 0

2 0

6 0

/ ( )

+

= tet

ZUi t g1o )s i n ()s i n (

2

( 4 - 6 )C o n s i d e r i n g i o = 0 w h e n t = + W e h a v e

tg)sin()sin(

=+ e (4-7)

43Semnan Un. N. Esakandarian

4.1.2 Three-phase AC voltage controllerClassification of three- phase circuits

n n'

a

b

c

a

b

u a

u b

i a U a 0 '

n

u a

u b

i a

V T 1

V T 3 V T4

V T 5 V T6

a

c

Y c o n n e c t i o n L i n e - c o n t r o l l e d c o n n e c t i o n

a

b

c

B r a n c h - c o n t r o l l e d c o n n e c t i o n

b

N e u t r a l - p o i n t c o n t r o l l e d c o n n e c t i o n

cu c

n

u a

u b

u c

i a

n

u a

u b

u c

i a

u cV T 2

4 4S e m n a n U n . N . E s a k a n d a r i a n

3- phase 3- wire Y connection AC voltage controller

n n'

a

b

c

u a

u b

i a U a 0 'V T 1

V T 3 V T 4

V T 5 V T6

F o r a t i m e i n s t a n t , t h e r e a r e 2 p o s s i b l e c o n d u c t i o n s t a t e s : E a c h p h a s e h a s a t h y r i s t o r c o n d u c t i n g . L o a d v o l t a g e s a r e t h e s a m e a s t h e s o u r c e

v o l t a g e s . T h e r e a r e o n l y 2 t h y r i s t o r s c o n d u c t i n g , e a c h f r o m a p h a s e . T h e l o a d v o l t a g e s o f

t h e t w o c o n d u c t i n g p h a s e s a r e h a l f o f t h e c o r r e s p o n d i n g l i n e t o l i n e v o l t a g e ,w h i l e t h e l o a d v o l t a g e o f t h e o t h e r p h a s e i s 0 .

c

u c V T 2

4 5S e m n a n U n . N . E s a k a n d a r i a n

4.2 Other AC controllers4.2.1 Integral cycle controlAC power controller

ioVT1

VT2

C o n d u c t i o na n g l e =

2 NMu o

C i r c u i t t o p o l o g i e s a r e t h e s a m e a s A C v o l t a g e c o n t r o l l e r s .O n l y t h e c o n t r o l m e t h o d i s d i f f e r e n t .

L o a d v o l t a g e a n d c u r r e n t a r e b o t h s i n u s o i d a l w h e n t h y r i s t o r s a r e c o n d u c t i n g .

Ru 1 u o

V T2

M

L i n e p e r i o d

C o n t r o l p e r i o d = M * L i n e p e r i o d = 2

4 M

O 3 M

2 M

u 1u o , i o

t

U12

4 6S e m n a n U n . N . E s a k a n d a r i a n

Spectrum of the current inACpower controller

There is NOharmonics in theordinary sense.

0 . 6

0 . 5

0 . 4

0 3I O / I 0 myT h e r e i s h a r m o n i c s

a s t o t h e c o n t r o lf r e q u e n c y . A s t o t h e

l i n e f r e q u e n c y , t h e s ec o m p o n e n t s b e c o m e

f r a c t i o n a l h a r m o n i c s .

0 1 2 1 4H a r m o n i c o r d e r a s t o

c o n t r o l f r e q u e n c y

H a r m o n i c o r d e r a s t ol i n e f r e q u e n c y

2 4 6 1 08

0 . 3

0 . 2

0 . 1

0 51 2 3 4

4 7S e m n a n U n . N .

E s a k a n d a r i a n

4.2.2 Electronic AC switchCircuit topologies are the same as AC voltage controllers. But the back- to- back

thyristors are just used like a switch to turn the equipment on or off.ApplicationThyristor-switched capacitor (TSC)

I

U

4 8S e m n a n U n . N . E s a k a n d a r i a n

TSC waveforms when the capacitor is switched in/out

i CuC

CV T 1 t

tu s

u C

uV T 1

T h e v o l t a g e a c r o s s t h e t h y r i s t o r m u s t b e n e a r l y z e r o w h e n s w i t c h i n g i n t h ec a p a c i t o r , a n d t h e c u r r e n t o f t h e t h y r i s t o r m u s t b e z e r o w h e n s w i t c h i n g

o u t t h e c a p a c i t o r .

u sC

V T2

t

t

i CV T 1

V T 2t 1 t 2

uV T 1

4 9S e m n a n U n . N . E s a k a n d a r i a n

TSC with the electronic switch realized by a thyristor and an anti-parallel diode

t

t

t

u

iC

uVTuC

CVT

us

uVT

uC

The capacitor voltage will be always charged up to the peak of sourcevoltage.

The response to switching- out command could be a little slower(maximum delay is one line-cycle).

t

tus VD

iC

uVT

VT

VD

t 1 t2 t3 t4

50Semnan Un. N. Esakandarian

4.2.3 Chopping controlAC chopper AC chopperModes of operation

i 1

V 1V D 1

R

L

u 1 u oV 2 V D 2 V 3

V 4

V D 4

V D 3

u > 0 , i o > 0 : V 1 c h a r g i n g , V 3 f r e e w h e e l i n g

u > 0 , i o < 0 : V 4 c h a r g i n g , V 2 f r e e w h e e l i n g

u < 0 , i o > 0 : V 3 c h a r g i n g , V 1 f r e e w h e e l i n g

u < 0 , i o < 0 : V 2 c h a r g i n g , V 4 f r e e w h e e l i n g

5 1S e m n a n U n . N . E s a k a n d a r i a n

Typical waveforms

2 0 0 t / msO u t p u t v o l t a g e

I n p u t c u r r e n t w i t hS i n g l e - p h a s e o u t p u t

I n p u t c u r r e n t w i t h3 - p h a s e o u t p u t

2 0 0 t / ms

2 0 0 t / ms

5 2S e m n a n U n . N . E s a k a n d a r i a n