Chapter 4 AC to AC Converters Outline

4.1 AC voltage controllers

4.2 Other AC controllers

4.3 Thyristor cycloconverters

4.4 Matrix converters

4.1.1 Single-phase AC voltage controller

R u 1 u o

i o

VT 1

VT 2

u

O

u 1

u o

i o

VT

t

O t

O t

O t

The phase shift range (operation range of phase delay angle): 0 ≤α ≤ π

Resistive load, quantitative analysis

RMS value of output voltage

RMS value of output current

RMS value of thyristor current

Power factor of the circuit

2sin

2

1dsin2

11

2

1o UttUU (4-1)

(4-2) R

UIoo

(4-3) )2

2sin1(

2

1sin2

2

1 1

2

1

R

Utd

R

tUIT

(4-4)

2sin2

1

1

o

o1

oo

U

U

IU

IU

S

P

Inductive (Inductor- resistor) load , operation principle

R

L

u 1 u o

i o

VT 1

VT 2

O

u 1

u o

i o

u VT

O

O

t O

u G1

u G2

O

O

t

t

t

t

t

The phase shift range:

φ ≤α ≤ π

Inductive load, quantitative analysis Differential equation

The RMS value of output voltage, output current, and thyristor current can then be

calculated.

0

sin2d

d

o

1oo

ti

tURit

iL

0 20 10060 140 180

20

100

4-3图

60

/(°

)

180

140

/(° )

( 4 - 5 )

S o l u t i o n

tetZ

Ui

t

tg1o )sin()sin(

2

( 4 - 6 ) C o n s i d e r i n g i o = 0 w h e n ω t = α + θ

W e h a v e

tg)sin()sin(

e ( 4 - 7 )

4.1.2 Three-phase AC voltage controller

Classification of three- phase circuits

n

a

c

n '

a

b

c

Y connection

Line- controlled Δ connection

a

b

c

Branch-controlled Δ connection

b

Neutral-point controlled Δ connection

a

b

c

u a

u b

u c

i a U a0'

n

u a

u b

u c

i a

n

u a

u b

u c

i a

n

u a

u b

u c

i a

VT 1

VT 3 VT 4

VT 5 VT 6

VT 2

3- phase 3- wire Y connection AC voltage controller

For a time instant, there are 2 possible conduction states:

–Each phase has a thyristor conducting. Load voltages are the same as the source voltages.

–There are only 2 thyristors conducting, each from a phase. The load voltages of the two conducting phases are half of the corresponding line to line voltage, while the load voltage of the other phase is 0.

n n '

a

b

c

u a

u b

u c

i a U a0' VT 1

VT 3 VT 4

VT 5 VT 6

VT 2

4.2 Other AC controllers

4.2.1 Integral cycle control—AC power controller

Circuit topologies are the same as AC voltage controllers.

Only the control method is different.

Load voltage and current are both sinusoidal when thyristors are conducting.

R u 1 u o

i o

VT 1

VT 2

M

Line period

Control period

= M *Line period

= 2

4

M O

Conduction

angle

=

2 N M

3

M

2

M

u o

u 1 u o , i o

t

U 1 2

Spectrum of the current inAC power controller

There is NOharmonics in theordinary sense.There is harmonicsas to the controlfrequency. As to theline frequency, thesecomponents becomefractional harmonics.

0 12 14 Harmonic order as to control frequency

Harmonic order as to line frequency

2 4 6 10 8

0.6

0.5

0.4

0.3

0.2

0.1

0 5 1 2 3 4

IO/I0m

4.2.2 Electronic AC switch

Circuit 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.

Application—Thyristor-switched capacitor (TSC)

I

U

TSC waveforms when the capacitor is switched in/out

The voltage across the thyristor must be nearly zero when switching in the capacitor, and the current of the thyristor must be zero when switching out the capacitor.

u s

i C

u C

C VT 1

VT 2

t

t

t

t u s

i C

u C

VT 1

VT 2

t 1 t 2

u VT 1

u VT 1

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

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

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

t

t

t

t

u s

i C

u VT

u C

C

VT

VD

u s

i C

u VT

u C

VT

VD

t 1 t 2 t 3 t 4

4.2.3 Chopping control—AC chopper

AC chopper

Modes of operation

R

L

4-7图

u 1

i1

u o

V 1

V 2

VD 1

VD 2V 3

V 4

VD 4

VD 3

u>0, io >0: V 1 charging, V 3 freew heeling

u>0, io <0: V 4 charging, V 2 freew heeling

u<0, io >0: V 3 charging, V 1 freew heeling

u<0, io <0: V 2 charging, V 4 freew heeling

4.3 Thyristor cycloconverters 4.3.1 Single- phase thyristor-cycloconverter Circuit configuration and operation principle

P N

Z

t

uo ap= 2

π Output

voltage

ap=0

Average

output voltage

ap= 2

π

Single- phase thyristor-cycloconverter Modes of operation

t

t

t

t

t

O

O

O

O

O

u o , i o u o

i o

t 1 t 2 t 3 t 4 t 5 u o u P

u N

u o

i P

i N

u P u N u o

i o i N i P

bl ocki ng P

N

Rectifi

cation

Inver

sion

bl ocki ng Rectifi

cation

Inver

sion

Typical waveforms

1

O

O

2

3 4

5

6

u o

i o

t

t

Modulation methods for firing delay angle

Calculation method

– For the rectifier circuit

ω t

ω t

cosd0o Uu

tUu oomo sin

ttU

Uoo

d0

om sinsincos

)sin(cos o1 t

( 4 - 1 5 )

– F o r t h e c y c l o c o n v e r t e r

o u t p u t

( 4 - 1 6 )

– E q u a t i n g ( 4 - 1 5 ) a n d ( 4 - 1 6 )

– t h e r e f o r e

( 4 - 1 7 )

( 4 - 1 8 )

P r i n c i p l e o f c o s i n e

w a v e - c r o s s i n g m e t h o d

u 2 u 3 u 4 u 5 u 6 u 1

a p 3 a p 4

u o

u s 2 u s 3 u s 4 u s 5 u s 6 u s 1

O u t p u t v o l t a g e r a t i o

( M o d u l a t i o n f a c t o r )

)10(0

d

om

U

U

2

2 t 3

2

0

3 0

6 0

9 0

1 2 0

1 5 0

Ou t p u t v o l t a g e p h a s e a n g l e

/ ( º ) γ

γ

4.3.2 Three- phase thyristor-cyclo converter

The configuration with common input line

4-24图

The configuration with star-connected output

Typical waveforms

200 t / ms

Output voltage

Input current with Single-phase output

Input current with 3-phase output

200 t / ms

200 t / ms

Input and output characteristicsThe maximum output frequency and the harmonics in the output voltage a

re the same as in single-phase circuit. Input power factor is a little higher than single-phase circuit. Harmonics in the input current is a little lower thanthe single- phase circuit due to the cancellation of some harmonics among the 3 phases.

To improve the input power factor: –Use DC bias or 3k order component bias on each of the 3 output phas

e voltages Features and applications Features: –Direct frequency conversion—high efficiency –Bidirectional energy flow, easy to realize 4- quadrant operation –Very complicated—too many power semiconductor devices –Low output frequency –Low input power factor and bad input current waveform Applications: –High power low speed AC motor drive

4.4 Matrix converter Circuit configuration

i nput

output

a) b)

a b c

u

v

w

S 1 1

S 1 2

S 1 3

S 2

1 S 2

2 S 2

3

S 3

1

S 3

2

S 3

3

S ij

Usable input voltage

a) b) c) a) Single-phase input

voltage

b) Use 3 phase voltages to construct output

voltage

c) Use 3 line-line voltages to construct output

voltage

Um

U1m

Um 1

2

√ 3

2 U1m

Features

Direct frequency conversion—high efficiency can realize good input and output waveforms, low harmonics, and nearly unity displacement factor

Bidirectional energy flow, easy to realize 4- quadrant operationOutput frequency is not limited by input frequencyNo need for bulk capacitor (as compared to indirect frequency converter)Very complicated—too many power semiconductor devicesOutput voltage magnitude is a little lower as compared to indirect

frequency converter.