Power Electronics Power Electronics
Chapter 6 AC to AC Converters
( AC Controllers and
Frequency Converters )
Classification of AC to AC converters Classification of AC to AC converters
Same frequency Same frequency variable magnitude variable magnitude
AC power
AC power AC powerAC power
Variable Variable frequency frequency AC power AC power
AC controllers Frequency converters (Cycloconverters)
AC to AC converters
P ow e r E le ct ro ni cs
P ow e r E le ct ro ni cs
Classification of AC controllers Classification of AC controllers
AC controller AC controller
Phase control:
Phase control: AC voltage controllerAC voltage controller (Delay angle control)
(Delay angle control) Integral cycle control:
Integral cycle control: AC power controllerAC power controller
PWM control:
PWM control: AC chopperAC chopper (Chopping control)
(Chopping control) On/off switch:
On/off switch: electronic AC switchelectronic AC switch PWM: Pulse Width Modulation
PWM: Pulse Width Modulation
Classification of frequency converters Classification of frequency converters
Frequency converter Frequency converter
(Cycloconverter) (Cycloconverter)
Phase control:
Phase control: thyristor cycloconverterthyristor cycloconverter (Delay angle control)
(Delay angle control) PWM control:
PWM control: matrix convertermatrix converter (Chopping control)
(Chopping control)
P ow e r E le ct ro ni cs
Cycloconverter is sometimes referred to Cycloconverter is sometimes referred to
– in a broader sensein a broader sense—any ordinary AC to AC converter—any ordinary AC to AC converter – in a narrower sense—thyristor cycloconverterin a narrower sense—thyristor cycloconverter
P ow e r E le ct ro ni cs
Outline Outline
6.1 AC voltage controllers 6.1 AC voltage controllers
6.2 Other AC controllers 6.2 Other AC controllers
6.3 Thyristor cycloconverters 6.3 Thyristor cycloconverters
6.4 Matrix converters 6.4 Matrix converters
P ow e r E le ct ro ni cs
6.1 AC voltage controllers 6.1 AC voltage controllers
6.1.1 Single-phase AC voltage controller 6.1.1 Single-phase AC voltage controller 6.1.2 Three-phase AC voltage controller 6.1.2 Three-phase AC voltage controller
Applications Applications
Lighting control Lighting control
Soft-start of asynchronous motors Soft-start of asynchronous motors
Adjustable speed drive of asynchronous motors Adjustable speed drive of asynchronous motors
Reactive power control Reactive power control
6.1.1 Single-phase AC voltage controller 6.1.1 Single-phase AC voltage controller
The phase shift range The phase shift range
(operation range of phase (operation range of phase delay angle):
delay angle):
Resistive load Resistive load
P ow e r E le ct ro ni cs
u1 uo R
io
VT1
VT2
O u1
uo
io
uVT
t
O t
O t
O t
P ow e r E le ct ro ni cs
RMS value of output voltageRMS value of output voltage RMS value of output current RMS value of output currentRMS value of thyristor current RMS value of thyristor current
Power factor of the circuit Power factor of the circuit
Resistive load, quantitative analysis Resistive load, quantitative analysis
1
2 1 sin 2 d 1 21 sin2o U t t U
U
R Io Uo
)2 2 1 sin
2( sin 1
2 2
1 1 2 1
U R t d t UR IT
sin2 2
1
1 o o
1 o o
U U I
U I U S
P
(6-1) (6-1)
(6-2) (6-2)
(6-3) (6-3)
(6-4) (6-4)
P ow e r E le ct ro ni cs
Inductive (Inductor-resistor) load, Inductive (Inductor-resistor) load, operation principle
operation principle
The phase shift The phase shift
range:
range:
u
1u
oR
i
oVT
1VT
2P ow e r E le ct ro ni cs
Differential equationDifferential equation SolutionSolution
Considering
Considering iioo=0 when =0 when tt==++
We have We have
Inductive load, quantitative analysis Inductive load, quantitative analysis
The RMS value of output voltage, output current, and thyristor The RMS value of output voltage, output current, and thyristor current can then be calculated.
current can then be calculated.
0
sin d 2
d
o
1 o
o
i t
t U
t Ri L i
(6-5) (6-5)
0 20 60 100 140 180
20 100
图4-3 60
/(°)
180
140
/ (° )
(6-6) (6-6)
) sin( ) tg
sin(
e (6-7)(6-7)
2 1
[sin( ) sin( ) ]
t
o U tg
i t e
Z t
P ow e r E le ct ro ni cs
Inductive load, when
Inductive load, when < <
The circuit can still work.
The circuit can still work.
The load current will be co The load current will be co ntinuous just like the thyrist ntinuous just like the thyrist ors are short-circuit, and th ors are short-circuit, and th e thyristors can no longer c e thyristors can no longer c ontrol the magnitude of out ontrol the magnitude of out
put voltage.
put voltage.
The start-up transient will b The start-up transient will b e the same as the transient e the same as the transient
when a RL load is connect when a RL load is connect
ed to an AC source at
ed to an AC source at t t ==
< <
t
t
t
t
图4-5
O O O O u 1
iG1
iG2
io iT1
iT2
Start-up transient Start-up transient
Harmonic analysis Harmonic analysis
There is no DC component There is no DC component
and even order harmonics in and even order harmonics in
the current.
the current.
– The current waveform is half-The current waveform is half- wave symmetric.
wave symmetric.
The higher the number of The higher the number of
harmonic ordinate, the lower harmonic ordinate, the lower
the harmonic content.
the harmonic content.
is when harmonics is is when harmonics is the most severe.
the most severe.
The situation for the inductive The situation for the inductive
load is similar to that for the load is similar to that for the
resistive load except that the resistive load except that the
corresponding harmonic corresponding harmonic
content is lower and is even content is lower and is even
lower as
lower as is increasing. is increasing.
P ow e r E le ct ro ni cs
Current harmonics Current harmonics for the resistive load for the resistive load
0 60 120 180
Fundamental
3 5 7
/ ( °) In/I* /%
20 40 60 80 100
P ow e r E le ct ro ni cs
6.1.2 Three-phase AC voltage controller 6.1.2 Three-phase AC voltage controller
Classification of three-phase circuits Classification of three-phase circuits
Y connection
Y connection Line-controlled Line-controlled ∆ connection∆ connection
Branch-controlled
Branch-controlled ∆ connection∆ connection Neutral-point-controlled ∆ connectionNeutral-point-controlled ∆ connection
P ow e r E le ct ro ni cs
3-phase 3-wire Y connection 3-phase 3-wire Y connection AC voltage controller
AC voltage controller
For a time instant, there are 2 possible conduction states:
For a time instant, there are 2 possible conduction states:
– Each phase has a thyristor conducting. Load voltages are the saEach phase has a thyristor conducting. Load voltages are the sa me as the source voltages.
me as the source voltages.
– There are only 2 thyristors conducting, each from a phase. The lThere are only 2 thyristors conducting, each from a phase. The l oad voltages of the two conducting phases are half of the corresp oad voltages of the two conducting phases are half of the corresp onding line to line voltage, while the load voltage of the other pha onding line to line voltage, while the load voltage of the other pha se is 0.
se is 0.
n n '
a
b
c u
u aa
uu
b b
uu
cc
iiaa Ua0'
VT5 VT3
VT6 VT4
VT2 VT1
P ow e r E le ct ro ni cs
3-phase 3-wire Y connection 3-phase 3-wire Y connection AC voltage controller
AC voltage controller
Resistive load, 0
Resistive load, 0 < 60< 60
4
3 2
3
5 3
3
0 2
u ao'
u a u ab
2 u ac
2
t1 t
2 t
3
VT 1
VT3 VT 6
VT4 VT 6
VT 2 VT 5
VT 5
VT1
P ow e r E le ct ro ni cs
3-phase 3-wire Y connection 3-phase 3-wire Y connection AC voltage controller
AC voltage controller
Resistive load, 60
Resistive load, 60 < 90< 90
4 3 2
3
5 3
3
0 2
u ao'
u a
u ab
2 u
ac
2
t1 t
2 t
3
VT 5 VT
1 VT
3
VT 4 VT
VT 6
VT 2 6
VT 5
P ow e r E le ct ro ni cs
3-phase 3-wire Y connection 3-phase 3-wire Y connection AC voltage controller
AC voltage controller
Resistive load, 90
Resistive load, 90 < 150< 150
4 3 2
3
5 3
3
0 2
uao'
ua
u ab
2
uac
2
VT 5 VT
1 VT
3
VT 4 VT VT 6
VT 2 6
VT 5
VT 5 VT
1 VT
3 VT
5
VT 4
VT 2
VT 4VT
6
P ow e r E le ct ro ni cs
6.2 Other AC controllers 6.2 Other AC controllers
6.2.1 Integral cycle control
6.2.1 Integral cycle control—AC power controller—AC power controller
6.2.2 Electronic AC switch 6.2.2 Electronic AC switch
6.2.3 Chopping control
6.2.3 Chopping control—AC chopper—AC chopper
P ow e r E le ct ro ni cs
6.2.1 Integral cycle control 6.2.1 Integral cycle control —AC power controller —AC power controller
Circuit topologies are the same as AC voltage contr Circuit topologies are the same as AC voltage contr
ollers. Only the control method is different.
ollers. Only the control method is different.
Load voltage and current are both sinusoidal when t Load voltage and current are both sinusoidal when t
M
Line period Line period
Control period=M *Line period=2
4M O
Conduction Conduction angle
angle =2N
M
3M 2M
uo
u1 uo,io
t U1
2
u
1u
oR i
oVT1
VT2
P ow e r E le ct ro ni cs
Spectrum of the current in Spectrum of the current in
AC power controller AC power controller
There is NO There is NO
harmonics in the harmonics in the ordinary sense.
ordinary sense.
There is harmonics There is harmonics
as to the control as to the control
frequency. As to the frequency. As to the line frequency, these line frequency, these components become components become fractional harmonics.
fractional harmonics.
Harmonic order as to control frequency
Harmonic order as to line frequency
0 1 2 3 4 5
0 2 4 6 8 1012 14 0.6
0.5 0.4 0.3 0.2 0.1 I n/I 0m
P ow e r E le ct ro ni cs
6.2.2 Electronic AC switch 6.2.2 Electronic AC switch
Circuit topologies are the same as AC voltag Circuit topologies are the same as AC voltag
e controllers. But the back-to-back thyristors e controllers. But the back-to-back thyristors
are just used like a switch to turn the equipm are just used like a switch to turn the equipm
ent on or off.
ent on or off.
P ow e r E le ct ro ni cs
6.2.3 Chopping control
6.2.3 Chopping control —AC chopper —AC chopper
Principle of chopping control Principle of chopping control
The mean output voltage over The mean output voltage over one switching cycle is
one switching cycle is
proportional to the duty cycle in proportional to the duty cycle in that period. This is also called that period. This is also called Pulse Width Modulation
Pulse Width Modulation (PWM)
(PWM)..
Advantages Advantages
Much better output waveforms, Much better output waveforms, much lower harmonics
much lower harmonics For resistive load, the For resistive load, the
displacement factor is always displacement factor is always 1.1.
Waveforms when the load Waveforms when the load
is pure resistor is pure resistor
P ow e r E le ct ro ni cs
AC chopper AC chopper
Modes of operation Modes of operation
>0, >0, iioo>0: V>0: V11 charging, V charging, V33 freewheeling freewheeling >0, >0, iioo<0: V<0: V44 charging, V charging, V22 freewheeling freewheeling <0, <0, ii >0: V>0: V charging, V charging, V freewheeling freewheeling u
uo
uo
P ow e r E le ct ro ni cs
6.3 Thyristor cycloconverters 6.3 Thyristor cycloconverters
(Thyristor AC to AC frequency converter) (Thyristor AC to AC frequency converter)
Another name—direct frequency converter (as com Another name—direct frequency converter (as com pared to AC-DC-AC frequency converter which is di pared to AC-DC-AC frequency converter which is di
scussed in Chapter 8) scussed in Chapter 8)
Can be classified into single-phase and three-phase Can be classified into single-phase and three-phase
according to the number of phases at output according to the number of phases at output
6.3.1 Single-phase thyristor-cycloconverter 6.3.1 Single-phase thyristor-cycloconverter 6.3.2 Three-phase thyristor-cycloconverter 6.3.2 Three-phase thyristor-cycloconverter
P ow e r E le ct ro ni cs
6.3.1 Single-phase thyristor-cycloconverter 6.3.1 Single-phase thyristor-cycloconverter
Circuit configuration and operation principle Circuit configuration and operation principle
Z
P N
uo
O
uo P= 2 P=0 P= 2
t
Output v oltage
Average output voltage
P ow e r E le ct ro ni cs
Single-phase thyristor-cycloconverter Single-phase thyristor-cycloconverter
Modes of operation Modes of operation
t t t t t
O O O O O uo,io uo
io
t1 t2 t3 t4 t5 uo
uP
uN
uo iP
iN
Rectifi Rectifi cation cation InverInver
sion sion
Blocking Blocking PP
N N
Inver Inver sionsion
Blocking Blocking
Rectifi Rectifi cation cation
u P u o u N
io
iN iP
P ow e r E le ct ro ni cs
Single-phase thyristor-cycloconverter Single-phase thyristor-cycloconverter
Typical waveforms Typical waveforms
1 O
O
2
3 4
5
6 u o
io
t
t
P ow e r E le ct ro ni cs
Calculation methodCalculation method– For the rectifier circuitFor the rectifier circuit
– For the cycloconverter outputFor the cycloconverter output
– Equating (6-15) and (6-16)Equating (6-15) and (6-16)
– ThereforeTherefore
Cosine wave-crossing met Cosine wave-crossing met hodhod
Modulation methods for firing delay angle Modulation methods for firing delay angle
Principle of cosine wave-crossing method
图4-21
u2 u 3 u 4 u 5 u6 u 1
us2 u s3 u s4 u s5 u s6 u s1
u o
P3 P4
t
t
d0 cos
o U
u
t U
uo om sino
t U t
U
o o
d0
om sin sin
cos
) sin (
cos 1 ot
(6-(6- 15)15)
(6-(6- 16)16)
(6-(6- 17)17) (6-(6- 18)18)
P ow e r E le ct ro ni cs
Calculated results for firing delay angle Calculated results for firing delay angle
Output voltage ratio Output voltage ratio
(Modulation factor) (Modulation factor)
) 1 0
(
d0
om
r
U
U = 0 = 0.1
/(°)
Output voltage phase angle
0 t 120
150 180
30 60 90
0
0.1 0.2 0.3 0.8 0.9 1.0
0.8 0.2 0.3 0.91.0
2
2
32
P ow e r E le ct ro ni cs
Input and output characteristics Input and output characteristics
Maximum output Maximum output
frequency: 1/3 or 1/2 of the frequency: 1/3 or 1/2 of the
input frequency if using 6- input frequency if using 6-
pulse rectifiers pulse rectifiers
Input power factor Input power factor
Harmonics in the output Harmonics in the output
voltage and input current voltage and input current
are very complicated, and are very complicated, and
both related to input both related to input
frequency and output frequency and output
frequency.
frequency.
0.8 0.6 0.4 0.2 0
=1.0 Input displacement factor Input displacement factor
Load power factor Load power factor
(lagging) (lagging) Load power factor
Load power factor (leading
(leading))
0 0.8 1.0 0.6 0.4 0.2 0
0.8 0.6 0.4 0.2
0.60.8 0.4 0.2
P ow e r E le ct ro ni cs
6.3.2 Three-phase thyristor-cycloconverter 6.3.2 Three-phase thyristor-cycloconverter
The configuration with common input line The configuration with common input line
P ow e r E le ct ro ni cs
Three-phase thyristor-cycloconverter Three-phase thyristor-cycloconverter
The configuration with star-connected output The configuration with star-connected output
P ow e r E le ct ro ni cs
Three-phase thyristor-cycloconverter Three-phase thyristor-cycloconverter
Typical waveforms Typical waveforms
200 t/ms
Output voltage Output voltage
Input current with Input current with 3-phase output 3-phase output
200 t/ms
200 t/ms
Input current with Input current with Single-phase output Single-phase output
0
0
0
P ow e r E le ct ro ni cs
Input and output characteristics Input and output characteristics
The maximum output frequency and the harmonics The maximum output frequency and the harmonics
in the output voltage are the same as in single- in the output voltage are the same as in single-
phase circuit.
phase circuit.
Input power factor is a little higher than single- Input power factor is a little higher than single-
phase circuit.
phase circuit.
Harmonics in the input current is a little lower than Harmonics in the input current is a little lower than
the single-phase circuit due to the cancellation of the single-phase circuit due to the cancellation of
some harmonics among the 3 phases.
some harmonics among the 3 phases.
To improve the input power factor:
To improve the input power factor:
– Use DC bias or 3k order component bias on each of the 3 Use DC bias or 3k order component bias on each of the 3 output phase voltages
output phase voltages
P ow e r E le ct ro ni cs
Features and applications Features and applications
Features Features
– Direct frequency conversion—high efficiencyDirect frequency conversion—high efficiency
– Bidirectional energy flow, easy to realize 4-quadrant Bidirectional energy flow, easy to realize 4-quadrant operation
operation
– Very complicated—too many power semiconductor devicesVery complicated—too many power semiconductor devices – Low output frequencyLow output frequency
– Low input power factor and bad input current waveformLow input power factor and bad input current waveform
Applications Applications
– High power low speed AC motor driveHigh power low speed AC motor drive
P ow e r E le ct ro ni cs
6.4 Matrix converter 6.4 Matrix converter
Circuit configuration Circuit configuration
a) b)
Input Input
Output Output
a b c
u v w S11 S12 S13
S21 S22 S23 S31 S32 S33
Sij
P ow e r E le ct ro ni cs
Matrix converter Matrix converter
Usable input voltage Usable input voltage
a ) b ) c )
U m
U 1 m
U 1 m
2 3
U m
12
a) Single-phase input a) voltage
b) Use 3 phase voltages b) to construct output voltag
e
c) Use 3 line-line voltages c) to construct output voltag
e
P ow e r E le ct ro ni cs
Features Features
Direct frequency conversion—high efficiency Direct frequency conversion—high efficiency
Can realize good input and output waveforms, low Can realize good input and output waveforms, low
harmonics, and nearly unity displacement factor harmonics, and nearly unity displacement factor
Bidirectional energy flow, easy to realize 4-quadrant Bidirectional energy flow, easy to realize 4-quadrant
operation operation
Output frequency is not limited by input frequency Output frequency is not limited by input frequency
No need for bulk capacitor (as compared to indirect No need for bulk capacitor (as compared to indirect
frequency converter) frequency converter)
Very complicated—too many power semiconductor Very complicated—too many power semiconductor
devices devices
Output voltage magnitude is a little lower as Output voltage magnitude is a little lower as
compared to indirect frequency converter.
compared to indirect frequency converter.