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.