Power Electronics
Chapter 4
AC to AC Converters
( AC Controllers and
Frequency Converters )
Power Electronics
Classification of AC to AC converters
Same frequency
variable magnitude
AC power
AC power
AC controllers
Variable
frequency
AC power
Frequency converters
(Cycloconverters)
AC to AC converters
2
Power Electronics
Classification of AC controllers
Phase control: AC voltage controller
(Delay angle control)
Integral cycle control: AC power controller
AC controller
PWM control: AC chopper
(Chopping control)
On/off switch: electronic AC switch
PWM: Pulse Width Modulation
3
Power Electronics
Classification of frequency converters
Frequency converter
(Cycloconverter)
Phase control: thyristor cycloconverter
(Delay angle control)
PWM control: matrix converter
(Chopping control)
Cycloconverter is sometimes referred to
– in a broader sense—any ordinary AC to AC converter
– in a narrower sense—thyristor cycloconverter
4
Power Electronics
Outline
4.1 AC voltage controllers
4.2 Other AC controllers
4.3 Thyristor cycloconverters
4.4 Matrix converters
5
Power Electronics
4.1 AC voltage controllers
4.1.1 Single-phase AC voltage controller
4.1.2 Three-phase AC voltage controller
Applications
Lighting control
Soft-start of asynchronous motors
Adjustable speed drive of asynchronous motors
Reactive power control
6
Power Electronics
4.1.1 Single-phase AC voltage controller
Resistive load
u1
VT1
io
O
ωt
uo
u1
VT2
uo
R
O
io
ωt
O
ωt
u VT
The phase shift range
(operation range of phase
delay angle):
O
ωt
0≤α≤π
7
Power Electronics
Resistive load, quantitative analysis
RMS value of output voltage
Uo =
(
π∫
1
π
α
)
2U1 sinω t d(ω t ) = U1
2
π −α
1
sin 2α +
π
2π
(4-1)
RMS value of output current
Io =
Uo
R
(4-2)
RMS value of thyristor current
2
U1
1 ⎛⎜ 2U1 sinω t ⎞⎟
(
)
IT =
d
ω
t
=
⎟
R
R
2π ∫α ⎜⎝
⎠
π
α sin 2α
1
(1 − +
) (4-3)
π
2
2π
Power factor of the circuit
P UoIo Uo
λ= =
=
=
S U1 I o U1
π −α
1
sin 2α +
π
2π
(4-4)
8
Power Electronics
Inductive (Inductor-resistor) load,
operation principle
u1
VT1
u1
VT2
uo
ωt
O
io
uG1
R
The phase shift range:
ϕ≤α≤π
0.6
O
uG2
ωt
O
uo
ωt
O
io
ωt
O
ωt
uVT
O
ωt
9
Differential equation
180
di
L o + Rio = 2U 1 sin ω t
dt
(4-5)
io ω t =α = 0
90°
ϕ= °
75 °
60 °
45 °
30 °
15 °
0
140
Solution
θ /(°)
Power Electronics
Inductive load, quantitative analysis
100
60
(4-6)
Considering io=0 when ωt=α+θ
We have
sin( α + θ − ϕ ) = sin( α − ϕ ) e
20
0
−θ
tg ϕ
20
60
100
α /(°)
140
180
(4-7)
The RMS value of output voltage, output current, and thyristor
current can then be calculated.
10
Power Electronics
Inductive load, when α < ϕ
The circuit can still work.
u1
The load current will be
continuous just like the
thyristors are short-circuit,
and the thyristors can no
longer control the
magnitude of output voltage.
The start-up transient will be
the same as the transient
when a RL load is
connected to an AC source
at ωt =α (α < ϕ).
ωt
O
iG1
π
Oα
ωt
iG2
O
io
iT1α+π
Oα θ
ϕ
iT2
ωt
ωt
Start-up transient
11
There is no DC component and
even order harmonics in the
current.
– The current waveform is halfwave symmetric.
The higher the number of
harmonic ordinate, the lower the
harmonic content.
100
80
In/I*/%
Power Electronics
Harmonic analysis
Fundamental
60
40
3
20
5
7
α = 90° is when harmonics is the
most severe.
The situation for the inductive
load is similar to that for the
resistive load except that the
corresponding harmonic content
is lower and is even lower as ϕ is
increasing.
0
60
120
α/( °)
180
Current harmonics
for the resistive load
12
Power Electronics
4.1.2 Three-phase AC voltage controller
Classification of three-phase circuits
Y connection
Branch-controlled ∆ connection
Line-controlled ∆ connection
Neutral-point-controlled ∆ connection
13
Power Electronics
3-phase 3-wire Y connection
AC voltage controller
ia
U a0'
VT 1
a
ua
VT 3
VT 4
b
n
u
b
VT 5
n'
VT 6
c
u
c
VT 2
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.
14
Power Electronics
3-phase 3-wire Y connection
AC voltage controller
Resistive load, 0° ≤ α < 60°
VT
VT
VT
VT 4
1
VT 1
VT 3
6
VT
5
u ab
2
ua
VT 6
VT
2
5
u ac
2
u ao'
0
π
3
α
t
1
t
2
2π
4π
5 π
3
t
3
3
2 π
3
15
Power Electronics
3-phase 3-wire Y connection
AC voltage controller
Resistive load, 60° ≤ α < 90°
VT
VT
5
VT
u
u
2
u
VT
6
ab
VT
1
u
a
α
π
3
t
1
2π
3
t
2
VT
2
4
5
VT
6
ac
2
4π
3
ao'
0
VT
3
π
t
5π
3
2π
3
16
Power Electronics
3-phase 3-wire Y connection
AC voltage controller
Resistive load, 90° ≤ α < 150°
VT
5
VT
VT VT
u 4
ab
u
5
6
VT
1
VT VT
1
VT VT
u 6u
a
2
VT
VT
3
2
VT
3
4
VT
VT
VT
5
4
VT
5
6
ac
2
5π
2
ao'
3
0
π
2π
3
3
α
π
4π
2π
3
17
Power Electronics
3-phase 3-wire branch-controlled
∆ connection AC voltage controller
The operation principle is the same as 3 independent singlephase AC voltage controllers.
Application—Thyristor-controlled reactor (TCR)
– To control the effective current flowing through the reactor by
controlling delay angle, therefore control the reactive power
absorbed by the reactor.
ua
n
ia
a
b
ub
c
uc
a)
b)
c)
18
Power Electronics
4.2 Other AC controllers
4.2.1 Integral cycle control—AC power controller
4.2.2 Electronic AC switch
4.2.3 Chopping control—AC chopper
19
Power Electronics
4.2.1 Integral cycle control
—AC power controller
uo
VT1
2 U1
io
O
u1
VT2
uo
Conduction 2πN
= M
angle
R
π
M
2π
M
uo,io
3π
M
u1
4π
M
ωt
Line period
Control period =M *Line period =2π
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.
20
There is NO
harmonics in the
ordinary sense.
There is harmonics
as to the control
frequency. As to the
line frequency, these
components become
fractional harmonics.
0.6
In/I0m
Power Electronics
Spectrum of the current in
AC power controller
0.5
0.4
0.3
0.2
0.1
0
0
2 4 6 8 10 12 14
Harmonic order as to
control frequency
1
2
3
4
5
Harmonic order as to
line frequency
21
Power Electronics
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
22
Power Electronics
TSC waveforms when the capacitor is
switched in/out
us
uVT
1
iC
us
uC
uC
C
uVT1
t
t
VT1
VT2
iC
t
VT1
VT2
t
t1
t2
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.
23
Power Electronics
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).
24
Power Electronics
4.2.3 Chopping control—AC chopper
Principle of chopping control
The mean output voltage over
one switching cycle is
proportional to the duty cycle in
that period. This is also called
Pulse Width Modulation
(PWM).
Advantages
Much better output waveforms,
much lower harmonics
For resistive load, the
displacement factor is always
1.
Waveforms when the load
is pure resistor
25
Power Electronics
AC chopper
Modes of operation
u o >0, io>0:
u o >0, io<0:
u o <0, io>0:
u o <0, io<0:
V1 charging, V3 freewheeling
V4 charging, V2 freewheeling
V3 charging, V1 freewheeling
V2 charging, V4 freewheeling
26
Power Electronics
4.3 Thyristor cycloconverters
(Thyristor AC to AC frequency converter)
Another name—direct frequency converter (as
compared to AC-DC-AC frequency converter which
is discussed in Chapter 8)
Can be classified into single-phase and threephase according to the number of phases at output
4.3.1 Single-phase thyristor-cycloconverter
4.3.2 Three-phase thyristor-cycloconverter
27
Power Electronics
4.3.1 Single-phase thyristor-cycloconverter
Circuit configuration and operation principle
N
P
uo
uo
O
αP= π
2
Output
voltage
Z
α P=0
Average
output voltage
αP= π
2
ωt
28
Power Electronics
Single-phase thyristor-cycloconverter
uo,io
Modes of operation
uo
O t1
uP
io
iP
uP
uo
iN
io
t2
t3
t4
t
uo
t
O
uN
t5
uN
O
uo
t
iP
O
iN
t
O
t
P
Rectifi Inver
cation sion
N Blocking
Blocking
Rectifi Inver
cation sion
29
Power Electronics
Single-phase thyristor-cycloconverter
Typical waveforms
uo
O
ωt
io
O
ωt
3
1
2
4
6
5
30
Power Electronics
Modulation methods for firing delay angle
Calculation method
– For the rectifier circuit
u o = U d0 cos α
(4-15)
u2
– For the cycloconverter
output
uo = U om sinω o t
(4-16)
– Equating (4-15) and (4-16)
U
cos α = om sin ω o t = γ sin ω o t
U d0
(4-17)
– Therefore
u3
u4
u5
u6
u1
ωt
αP3
us2
us3
αP4
us4
us5
us6
us1
uo
ωt
α = cos −1 (γ sin ω o t ) (4-18)
Cosine wave-crossing
method
Principle of cosine
wave-crossing method
31
Output voltage ratio
(Modulation factor)
U om
γ =
(0 ≤ r ≤ 1)
U d0
180
α/(°)
Power Electronics
Calculated results for firing delay angle
1.0
0.9
0.8
0.3
0.2
0.1
150
120
90
γ=0
γ = 0.1
0.2
0.3
0.8
0.9
1.0
60
30
0
π
2
π
3π
2
2π
ω0t
Output voltage phase angle
32
Maximum output
frequency: 1/3 or 1/2 of the
input frequency if using 6pulse rectifiers
Input power factor
Harmonics in the output
voltage and input current
are very complicated, and
both related to input
frequency and output
frequency.
Input displacement factor
=1
.0
0.8
γ
Power Electronics
Input and output characteristics
0.6
0. 8
0 .6
0 .4
0. 2
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1.0 0.8 0.6 0.4 0.2 0
Load power factor Load power factor
(lagging)
(leading)
33
Power Electronics
4.3.2 Three-phase thyristor-cycloconverter
The configuration with common input line
34
Power Electronics
Three-phase thyristor-cycloconverter
The configuration with star-connected output
35
Power Electronics
Three-phase thyristor-cycloconverter
Typical waveforms
Output voltage
Input current with
Single-phase output
Input current with
3-phase output
0
200 t/ms
0
200 t/ms
0
200 t/ms
36
Power Electronics
Input and output characteristics
The maximum output frequency and the harmonics
in the output voltage are the same as in singlephase circuit.
Input power factor is a little higher than singlephase circuit.
Harmonics in the input current is a little lower than
the 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 phase voltages
37
Power Electronics
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
38
Power Electronics
4.4 Matrix converter
Circuit configuration
Input
Output
39
Power Electronics
Matrix converter
Usable input voltage
U1m
Um
a)
a) Single-phase input
voltage
3
2
1
2 Um
b)
b) Use 3 phase voltages
to construct output
voltage
U1m
c)
c) Use 3 line-line voltages
to construct output
voltage
40
Power Electronics
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
operation
Output frequency is not limited by input frequency
No need for bulk capacitor (as compared to indirect
frequency converter)
Very complicated—too many power semiconductor
devices
Output voltage magnitude is a little lower as
compared to indirect frequency converter.
41