Power Electroni
cs
Chapter 6
PWM Techniques
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The most widely used control technique
in power electronics
AC/AC
DC/DC
Pulse Width Modulation (PWM)
(Chopping control)
AC/DC
DC/AC
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Outline
6.1 Basic principles
6.2 Some major PWM techniques in DC/AC inverters
6.3 PWM techniques with feedback control
6.4 PWM rectifiers
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6.1 Basic principles of PWM
Similar response to different shape of impulse input
The equal-area theorem:
Responses tend to be identical when input signals
have same area and time durations of input impulses
become very small.
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Basic principles of PWM
Application of the equal-area theorem
This is sinusoidal
PWM (SPWM)
The equal-area
theorem can be applied
to realize any shape of
waveforms
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A list of PWM techniques
Triangular-wave sampling
– Natural sampling
– Uniform sampling
Calculation
– Calculation based on equal-area criterion
– Selective harmonics elimination
Hysteric control
Space Vector Modulation (SVM, or SVPWM)
Random PWM
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6.2 Some major PWM techniques
Natural sampling
Uniform sampling
Selective harmonics elimination
Some practical issues
– Synchronous modulation and asynchronous modulation
– Harmonics in the PWM inverter output voltages
– Ways to improve DC input voltage utilization and reduce
switching frequency
– Connection of multiple PWM inverters
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Triangular-wave natural sampling
Uni-polar PWM in single-phase VSI
Uni-polar sampling is used to
realize uni-polar PWM.
$ P O U S P M
T J H O B M
$ B S S J F S
Mudulation
Carrier
U
d
+
V
1
V
2
V
3
V
4
VD
1
VD
2
VD
3
VD
4
u
o
R
L
u
r
u
c
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Triangular-wave natural sampling
Bi-polar PWM in single-phase VSI
$ P O U S P M
T J H O B M
$ B S S J F S
Mudulation
Carrier
U
d
+
V
1
V
2
V
3
V
4
VD
1
VD
2
VD
3
VD
4
u
o
R
L
u
r
u
c
Bi-polar sampling is used to
realize bi-polar PWM.
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Triangular-wave natural sampling
In 3-phase VSI
Three-phase bridge inverter
can only realize bi-bolar PWM
therefore should be controlled
by bipolar sampling.
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Triangular-wave uniform sampling
Easier to realize
by computer-
control
Modulation factor
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Selective harmonics elimination
PWM (SHEPWM)
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Frequency relationship between triangular-
wave carrier and control signal
Asynchronous Modulation
Synchronous Modulation
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Harmonics in the PWM inverter
output voltages
Spectrum of 1-phase
bridge PWM inverter
output voltage
No lower order
harmonics
The lowest frequency
harmonics is w
c
and
adjacent harmonics.
w
c
Has the highest
harmonic content.
1
0
0 2
1
23
4
0 2
+
4
0 1
3
5
+
Ma
gnit
ude
(%)
(nω
c
+kω
r
)
0.2
0.4
0.6
0.8
1.0
1.2
1.4
k
n
a=1.0
a=0.8
a=0.5
a=0
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Harmonics in the PWM inverter
output voltages
No lower order
harmonics
No harmonics at ω
c
.
The lowest
frequency and
highest content
harmonics are
ω
c
±2ω
r
and 2ω
c
±ω
r
.
Spectrum of 3-phase
bridge PWM inverter
output voltage
1
0
0 2
1
23
4
0 2
4
0 1
3
5
M
agn
i
tu
d
e
(%)
0.2
0.4
0.6
0.8
1.0
1.2
k
n
a=1.0
a=0.8
a=0.5
a=0
(nω
c
+kω
r
)
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Ways to improve utilization of DC input
voltage and reduce switching frequency
Use trapezoidal waveform as modulating signal
instead of sinusoidal
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Ways to improve utilization of DC input
voltage and reduce switching frequency
Use 3k order harmonics
bias in the modulating
signal
u
c
u
rU1
u
rV1
u
rW1
u
u
UN'
U
d
U
d
O
t
O
u
rU
u
rV
u
rW
u
c
O
t
O
O
O
O
t
t
t
t
t
u
VN'
u
WN'
u
UV
u
1
1
1
1
0.5
u
P
2
U
d
?
2
U
d
u
c
u
r1
u
O
ωt
u
r
u
r1
u
O
ωt
u
r3
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Connection of multiple PWM inverters
Purposes
– Expand output power rating
– Reduce harmonics
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6.3 PWM techniques with
feedback control
Current hysteric control
Voltage hysteric control
Triangular-wave comparison (sampling) with
feedback control
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Current hysteric control
In Single-phase VSI
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Current hysteric control
In 3-phase VSI
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Voltage hysteric control
Filter
+
u
u
*
u
2
U
d
2
U
d
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Triangular-wave comparison (sampling)
with feedback control
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6.4 PWM rectifiers
Operation Principles
a) Rectification mode
b) Inversion mode
c) Reactive power
compensation mode
d) Current leading by ?
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PWM rectifiers
Three-phase circuit
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PWM rectifiers
Indirect current control
PI
+
- P B E
Triangular-wave
sin(ωt+2kπ 3)
(k=0,1,2)
cos(ωt+2kπ 3)
(k=0,1,2)
u
*
d
u
d
+
+
+
i
d
u
R
u
L
X
L
R
u
A,B,C
u
d
RL
u
a
,u
b
,u
c
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PWM rectifiers
Direct current control
PI
- P B E
sin(ωt+2kπ 3)
(k=0,1,2)
u
*
d
u
d
+
+
i
d
i
a,b,c
u
d
RL
u
a
,u
b
,u
c
i
*
a,b,c
