Power Electronics
Chapter 6
PWM Techniques
Power Electronics
The most widely used control technique
in power electronics
DC/DC
AC/AC
Pulse Width Modulation (PWM)
(Chopping control)
DC/AC
AC/DC
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Power Electronics
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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Power Electronics
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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Power Electronics
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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Power Electronics
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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Power Electronics
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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Power Electronics
Triangular-wave natural sampling
Uni-polar PWM in single-phase VSI
V1
Ud
+
V3
VD1
R
L
uo
V2
V4
VD2
Control
signal
VD3
VD4
ur
Carrier
uc
Mudulation
Carrier
Uni-polar sampling is used to
realize uni-polar PWM.
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Power Electronics
Triangular-wave natural sampling
Bi-polar PWM in single-phase VSI
V1
Ud
+
V3
VD1
R
L
uo
V2
V4
VD2
Control
signal
VD3
VD4
ur
Carrier
uc
Mudulation
Carrier
Bi-polar sampling is used to
realize bi-polar PWM.
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Power Electronics
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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Power Electronics
Triangular-wave uniform sampling
Easier to realize
by computercontrol
Modulation factor
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Power Electronics
Selective harmonics elimination
PWM (SHEPWM)
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Power Electronics
Frequency relationship between triangularwave carrier and control signal
Asynchronous Modulation
Synchronous Modulation
13
Spectrum of 1-phase
bridge PWM inverter
output voltage
1.4
a=1.0
a=0.8
a=0.5
a=0
1.2
1.0
No lower order
harmonics
The lowest frequency
harmonics is wc and
adjacent harmonics.
wc has the highest
harmonic content.
Magnitude(%)
Power Electronics
Harmonics in the PWM inverter
output voltages
0.8
0.6
0.4
0.2
k 1
n
0
0 +- 2 +- 4 0 +- 1 +- 3 +- 5 0 +- 2 +- 4
1
2
3
(nωc +kωr )
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Spectrum of 3-phase
bridge PWM inverter
output voltage
No lower order
harmonics
No harmonics at ωc.
The lowest
frequency and
highest content
harmonics are
ωc±2ωr and 2ωc±ωr.
1.2
a=1.0
a=0.8
a=0.5
a=0
1.0
Magnitude(%)
Power Electronics
Harmonics in the PWM inverter
output voltages
0.8
0.6
0.4
0.2
k 1
n
0
0 +- 2 +- 4 0 +- 1 +- 3 +- 5 0 +- 2 +- 4
1
2
3
(nωc +kωr )
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Power Electronics
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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Power Electronics
Ways to improve utilization of DC input
voltage and reduce switching frequency
Use 3k order harmonics
bias in the modulating
signal
u
1
uc
t
O
-0.5
O
t
urU
urV
urW
uc
t
-1
uUN'
ur3
Ud
2
ωt
O
−
ur1
urW1
-1
uP
ur1
O
urV1
O
u
1
u
urU1
Ud
2
t
uVN'
ur uc
u
O
t
uWN'
O
ωt
O
t
uUV
Ud
O
t
-Ud
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Power Electronics
Connection of multiple PWM inverters
Purposes
– Expand output power rating
– Reduce harmonics
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Power Electronics
6.3 PWM techniques with
feedback control
Current hysteric control
Voltage hysteric control
Triangular-wave comparison (sampling) with
feedback control
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Power Electronics
Current hysteretic control
In Single-phase VSI
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Power Electronics
Current hysteretic control
In 3-phase VSI
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Power Electronics
Voltage hysteretic control
Ud
2
Ud
2
Filter
+ u*
u
u
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Power Electronics
Triangular-wave comparison (sampling)
with feedback control
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Power Electronics
6.4 PWM rectifiers
Operation Principles
a) Rectification mode
c) Reactive power
compensation mode
b) Inversion mode
d) Current leading by ϕ
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Power Electronics
PWM rectifiers
Three-phase circuit
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Power Electronics
PWM rectifiers
Indirect current control
Triangular-wave
u*d
+
ud
PI
id
uR +
+
R
- uA,B,C
sin(ωt+2kπ/3)
(k=0,1,2) uL
XL
cos(ωt+2kπ/3)
(k=0,1,2)
R
L
ua,ub,uc
ud +
Load
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Power Electronics
PWM rectifiers
Direct current control
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