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Power ElectronicsPower Electronics
Chapter 6
PWM Techniques
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The most widely used control techniqueThe most widely used control technique
in power electronicsin power electronics
Pulse Width Modulation (PWM)(Chopping control)
DC/DC AC/AC
DC/AC AC/DC
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OutlineOutline6.1 Basic principles6.1 Basic principles
6.2 Some major PWM techniques in DC/AC inverters6.2 Some major PWM techniques in DC/AC inverters
6.3 PWM techniques with feedback control6.3 PWM techniques with feedback control
6.4 PWM rectifiers6.4 PWM rectifiers
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6.1 Basic principles of PWM6.1 Basic principles of PWMSimilar response to different shape of impulse inputSimilar response to different shape of impulse input
The equalThe equal--area theorem:area theorem:
Responses tend to be identical when input signalsResponses tend to be identical when input signals
have same area and time durations of input impulseshave same area and time durations of input impulses
become very small.become very small.
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Basic principles of PWMBasic principles of PWMApplication of the equalApplication of the equal--area theoremarea theorem
This is sinusoidalThis is sinusoidal
PWM (SPWM)PWM (SPWM)
The equalThe equal--areaarea
theorem can be appliedtheorem can be appliedto realize any shape ofto realize any shape of
waveformswaveforms
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A list of PWM techniquesA list of PWM techniquesTriangularTriangular--wave samplingwave sampling
Natural samplingNatural sampling
Uniform samplingUniform sampling
CalculationCalculation
Calculation based on equalCalculation based on equal--area criterionarea criterion
Selective harmonics eliminationSelective harmonics elimination
Hysteric controlHysteric control
Space Vector Modulation (SVM, or SVPWM)Space Vector Modulation (SVM, or SVPWM)
Random PWMRandom PWM
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6.2 Some major PWM techniques6.2 Some major PWM techniques
Natural samplingNatural sampling
Uniform samplingUniform samplingSelective harmonics eliminationSelective harmonics elimination
Some practical issuesSome practical issues
Synchronous modulation and asynchronous modulationSynchronous modulation and asynchronous modulation
Harmonics in the PWM inverter output voltagesHarmonics in the PWM inverter output voltages
Ways to improve DC input voltage utilization and reduceWays to improve DC input voltage utilization and reduce
switching frequencyswitching frequency Connection of multiple PWM invertersConnection of multiple PWM inverters
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TriangularTriangular--wave natural samplingwave natural samplingUniUni--polar PWM in singlepolar PWM in single--phase VSIphase VSI
UniUni--polar sampling is used topolar sampling is used torealizerealize uniuni--polar PWM.polar PWM.
Controlsignal
CarrierMudulation
Carrier
Ud
+
V1
V2
V3
V4
VD1
VD2
VD3
VD4
uo
R L
ur
uc
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TriangularTriangular--wave natural samplingwave natural samplingBiBi--polar PWM in singlepolar PWM in single--phase VSIphase VSI
Control
signal
CarrierMudulation
Carrier
Ud
+
V1
V2
V3
V4
VD1
VD2
VD3
VD4
uo
R L
ur
uc
BiBi--polar sampling is used topolar sampling is used to
realize birealize bi--polar PWM.polar PWM.
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TriangularTriangular--wave natural samplingwave natural samplingIn 3In 3--phase VSIphase VSI
ThreeThree
--phase bridge inverterphase bridge inverter
can only realize bican only realize bi--bolarbolarPWMPWM
therefore should be controlledtherefore should be controlled
by bipolar sampling.by bipolar sampling.
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TriangularTriangular--wave uniform samplingwave uniform sampling
Easier to realizeEasier to realize
by computerby computer--controlcontrol
Modulation factorModulation factor
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Selective harmonics eliminationSelective harmonics elimination
PWM (SHEPWM)PWM (SHEPWM)
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Frequency relationship between triangularFrequency relationship between triangular--
wave carrier and control signalwave carrier and control signal
Asynchronous ModulationAsynchronous Modulation
Synchronous ModulationSynchronous Modulation
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Harmonics in the PWM inverterHarmonics in the PWM inverter
output voltagesoutput voltages
No lower orderNo lower order
harmonicsharmonics
The lowest frequencyThe lowest frequencyharmonics isharmonics is wwcc andand
adjacent harmonics.adjacent harmonics.
wwcc has the highesthas the highest
harmonic content.harmonic content.
Spectrum of 1Spectrum of 1--phasephase
bridge PWM inverterbridge PWM inverter
output voltageoutput voltage
1
0
0 2+-1 2 3
4+- 0 2+- 4+-0 1+- 3+- 5+-
Magnitu
de(%)
(nc+k
r)
0.2
0.4
0.6
0.8
1.0
1.2
1.4
k
n
a=1.0a=0.8a=0.5
a=0
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Harmonics in the PWM inverterHarmonics in the PWM inverter
output voltagesoutput voltages
No lower orderNo lower order
harmonicsharmonics
No harmonics atNo harmonics at cc..The lowestThe lowest
frequency andfrequency and
highest contenthighest content
harmonics areharmonics arecc22rr and 2and 2ccrr..
Spectrum of 3Spectrum of 3--phasephase
bridge PWM inverterbridge PWM inverter
output voltageoutput voltage
1
0
0 2+-1 2 3
4+- 0 2+- 4+-0 1+- 3+- 5+-
agntue
0.2
0.4
0.6
0.8
1.0
1.2
k
n
a=1.0a=0.8a=0.5
a=0
(nc+k
r)
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Ways to improve uti lization of DC inputWays to improve uti lization of DC input
voltage and reduce switching frequencyvoltage and reduce switching frequencyUse trapezoidal waveform as modulating signalUse trapezoidal waveform as modulating signal
instead of sinusoidalinstead of sinusoidal
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Ways to improve utilization of DC inputWays to improve uti lization of DC input
voltage and reduce switching frequencyvoltage and reduce switching frequency
Use 3k order harmonicsUse 3k order harmonics
bias in the modulatingbias in the modulating
signalsignal
uc
ur1
u
Ot
ur
ur1
u
O t
ur3
uc
urU1
urV1
urW1
u
uUN'
Ud
-Ud
Ot
O
urU
urV
urW uc
O t
O
O
O
O
t
t
t
t
t
uVN'
uWN'
uUV
u
1
-1
1
-1
-0.5
uP
2Ud
2
Ud
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Connection of multiple PWM invertersConnection of multiple PWM inverters
PurposesPurposes
Expand output power ratingExpand output power rating
Reduce harmonicsReduce harmonics
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6.3 PWM techniques with6.3 PWM techniques with
feedback controlfeedback controlCurrent hysteric controlCurrent hysteric control
Voltage hysteric controlVoltage hysteric control
TriangularTriangular--wave comparison (sampling) withwave comparison (sampling) withfeedback controlfeedback control
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Current hysteretic controlCurrent hysteretic controlIn SingleIn Single--phase VSIphase VSI
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Current hysteretic controlCurrent hysteretic control
In 3In 3--phase VSIphase VSI
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Voltage hysteretic controlVoltage hysteretic control
Filter
+
-
u
u*
u
2
Ud
2
Ud
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TriangularTriangular--wave comparison (sampling)wave comparison (sampling)
with feedback controlwith feedback control
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6.4 PWM rectifiers6.4 PWM rectifiersOperation PrinciplesOperation Principles
a) Rectification modea) Rectification mode b) Inversion modeb) Inversion mode
c) Reactive powerc) Reactive power
compensation modecompensation mode
d) Current leading byd) Current leading by
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PWM rectifiersPWM rectif iers
ThreeThree--phase circuitphase circuit
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PWM rectifiersPWM rectif iersIndirect current controlIndirect current control
PI+-
Load
Triangular-wave
sin(t+2k/3)(k=0,1,2)
cos(t+2k/3)
(k=0,1,2)
u*d
ud
+
-
+
-
-
+
id
uR
uL
XL
Ru
A,B,C
ud
R L
ua,u
b,u
c
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PWM rectifiersPWM rectif iersDirect current control