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Advanced Topics in PWM for Voltage Source Converters
Assoc. Prof. Laszlo Mathe
Aalborg University, Dept. of Energy Technology
www.et.aau.dk
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Outline
• Introduction
• Basic inverter topologies
• Basic Modulation techniques
• Zero vector placement modulation techniques
• Performance of different PWM methods
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Electrical energy conversion
• The residential and industrial electric grid supplies AC voltage with fixed amplitude and frequency
• Most of the low power devices like TV, PC etc. are using DC voltages typically 3-5-12V, - AC to DC conversion is needed
• Devices like washing machine, vacuum cleaner uses electrical motor drives, where the rotor speed is controlled through the amplitude and the frequency of the supplied voltage, - AC to AC conversion is needed
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Electrical energy conversion
• The AC to AC conversion can be done by using a transformer. However, only the amplitude of the voltage can be changed to a fixed value
• DC to AC conversion can be done with transistors operating in linear range, typical application is the audio amplifier, the conversion efficiency is very low
• In order to achieve high efficiency in energy conversion, modulation based on on-off switching converters should be used
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Modulation
• Modulation is a method to transmit a low frequency signal by varying a high frequency signal’s amplitude, frequency or phase
• It is the basic element for telecommunication and power electronics
• In power converters Pulse Width Modulation (PWM) technique is used, which is a method to create the on-off switching pattern for the power switches
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Power semiconductor switches
• The converters are built from semiconductors based power switches which are: – Uncontrolled (Diode) – conducts the current when the
voltage across the anode and cathode is positive
– Half Controlled (Thyristor) – conduct current when the gate signal is applied and the anode and cathode is positive (it turns off uncontrolled when anode-cathode voltage is negative)
– Full Controlled (Transistor) – When a pulse is applied on the gate signal the transistor conducts (it can be turned on-off any time)
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Power semiconductor switches
• Ideal switches do not exist (only in simulation), parasitic resistance, inductance and capacitance is always present
• The losses in a switch are caused by:
– On-resistance - when the switch is in conduction mode it acts like a resistor
– Switching loss – energy is need in order to turn on and off the device
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Outline
• Introduction
• Basic inverter topologies
• Basic Modulation techniques
• Zero vector placement modulation techniques
• Performance of different PWM methods
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Half Bridge (HB) Voltage Source Inverter (VSI)
– It has to be avoided to turn on both Sw1 and Sw2 at the same time (Vdc shoot through is created)
– The antiparallel diodes are needed to give free path for the current in case of inductive load
qa State Vl
0 Sw1 – off & Sw2 – on -Vdc/2
1 Sw1 – on & Sw2 – off Vdc/2
+
-dcV
2
dcV
2
dcV
aq
aq
lV
Loadn
li
1Sw
2Sw
Modulator
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Hardware limitation – Dead time
• Due to the parasitic inductance and capacitance the voltage/current is maintained for a short time after the gate signal goes to zero (highlighted region in the fig.)
Turn off transient of a MOSFET
• The other switch should be turned on always after this transient period is over, otherwise, shoot-through appears which destroys the semiconductor device
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Hardware limitation – Minimum Pulse Width
• The MPW filters duty is to block the pulses which duration is less than the double of the dead-time
• The short pulses creates only losses because the switch is not able to turn on-off properly
• MPW filter and dead-time causes nonlinearities which has to be considered in some application, compensation techniques have to be applied
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Full Bridge (H-bridge) VSI
• Positive and negative Vdc can be applied on the load
• Three voltage levels can be applied on the load (± Vdc and 0)
qa qb Vl
0 0 0
0 1 Vdc
1 0 -Vdc
1 1 0
+
-dcV
2
dcV
2
dcV
aq
aq
lV
Load
nai
1Sw
2Sw
bq
bq
3Sw
4Sw
li
Modulator
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1
2dcV
1
2dcV
Aq
Aq
dcV
nA
Bq
B
Cq
Cq
C
ANv BNv CNv
Bq
ABv
BCv
ACv
Modulator
Three phase bridge-type VSI
• Phase (VAN, VBN ,VBN) and line-to-line (VAB, VAC ,VBC) Voltages are created
• Relationship between them:
• Half-bridge arrangement can be extended to ‘n’ phases
3AB AN BN ANV V V V
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Applications
• Electrical motor drives:
• Single phase grid connected PV systems:
Grid
N
L
FilterFilterBoost without trafo FB inverterFilterPV Array
S5
S1 S3
S2 S4
D1 D3
D2 D4
D5
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Outline
• Introduction
• Basic inverter topologies
• Basic Modulation techniques
• Zero vector placement modulation techniques
• Performance of different PWM methods
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Modulation techniques for half bridge
• Spectrum of rectangular signal contains low frequency harmonics
• Amplitude of the signal is fixed
• Modulation allows amplitude control
+
-dcV
2
dcV
2
dcV
aq
aq
lV
Loadn
li
1Sw
2Sw
Modulator
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Pulse generation techniques
• In order to generate the train of pulses several methods exist:
– Carrier Based PWM (ST, SVM, RPWM, DPWM)
– Hysteresis Based PWM
– Programmed PWM (MP-PWM, Optimum PWM, HE-PWM)
Remark: During one modulation period unity gain has to be ensured
PWM Vref Vout
Filter
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Sine Triangular PWM
• Oldest and simplest method to generate PWM pulses
• High frequency triangular or saw-tooth carrier signal is compared with the reference signal
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Triangular vs. Saw tooth Carrier
• Different spectral properties can be achieved
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Over-modulation
1
0
1
t
1
0
1
t
• In case the amplitude of the reference signal is larger than the amplitude of the carrier wave, low frequency harmonics are introduced
• A little increase in the amplitude of the fundamental component can be achieved
• In over-modulation the modulator is not linear
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Modulation index
• Normalized output voltage amplitude
00
2,
dc
VMi whereV is the RMS reference voltage
V
Output Mi
1
0
0.785
Refrernce Mi0.785 1,57
Linear
region
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Modulation for H-bridge
Unipolar PWM
+
-dcV
2
dcV
2
dcV
aq
aq
lV
Load
nai
1Sw
2Sw
bq
bq
3Sw
4Sw
li
Modulator
+
- Sw1
Sw2
Sw3
Sw4
+
-
+
-
Sw1
Sw2
Sw3
Sw4
-1
Bipolar PWM Hybrid PWM +
- Sw1
Sw2
+
-Sw3
Sw4
+
-
• More possibilities with different advantage / disadvantage
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1
2dcV
1
2dcV
Aq
Aq
dcV
nA
Bq
B
Cq
Cq
C
ANv BNv CNv
Bq
ABv
BCv
ACv
Modulation for Three phase inverter
• Three 1200 shifted reference signals are compared with triangular carrier
t
T
t
1
0
Reference Signals PWM Signals
t
t
t
aq
bq
cq
Reference voltage for Phase A
Reference voltage for Phase BReference voltage for Phase C
1
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Outline
• Introduction
• Basic inverter topologies
• Basic Modulation techniques
• Zero vector placement modulation techniques
• Performance of different PWM methods
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Magnetic force between a coil and PM • Passing a current through a coil alines the magnet; reversing the current the
magnet will rotate the magnet by 1800 (direction of the rotation is not defined)
• With second pair of coils the direction of the rotation can be defined
• Better space usage can be achieved by placing three pair coils, 1200 shifted in space
• The three or multi phase system can always be reduced to a d-q system
i
i
s
n
n
n
s
s
q
s
n
n
n
s
i
n
i
n
s
s
s
d
q
s
nd
q
a
b
c
nn
ss
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Rotating field generation
- During one fundamental period one revolution of the voltage vector is obtained through 6 fixed vectors
110v010v
011v
001v 101v
100vd
q
Vmax
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Six Step mode operation
• Highest amplitude for the fundamental (end of over-modulation range)
• The RMS of the phase-neutral voltage is:
• Low frequency components appears in the output voltage spectrum
Van
Vbn
Vcn
2Vdc /3
-2Vdc /3
Vdc /3
-Vdc /30
2Vdc /3
-2Vdc /3
Vdc /3
-Vdc /30
-2Vdc /3
Vdc /3
-Vdc /30
t
t
t
2Vdc /3
2 DCV
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t
t
t
t
aq
bq
cq
T
0zvt 1zvt 0zvtavt avt
XcXaXb
+Vdc
Xc
Xa
Xb
-Vdc
+Vdc
Xc
Xa Xb
+Vdc
-Vdc
XcXaXb
-Vdc
Xc
Xa Xb
+Vdc
-Vdc
Xc
Xa
Xb
-Vdc
+Vdc
XcXaXb
-Vdc
Space vector representation
- With the two level VSI 6 active and 2 zero sequence voltage vectors can be generated
- The ratio between the time while two active vectors are generated gives the position of the resultant voltage vector (Vs) in d-q plain
- The ratio between the time when active and zero vectors are applied sets the amplitude of the same vector
1
2dcV
1
2dcV
Aq
Aq
dcV
N
A
Bq
B
Cq
Cq
C
ANv BNv CNv
Loadcmvv
Bq
ABv
BCv
ACv
sV
110v010v
011v
001v 101v
100vd
q
211
0
dv
1 100d v
Xc
Xb
Xa
-Vdc
+Vdc
Xa
Xc Xb
+Vdc
-Vdc
Xc
Xa
Xb
-Vdc
+Vdc
Xa
Xc
Xb
-Vdc
+Vdc
Xb
Xa Xc
+Vdc
-Vdc
XcXa Xb
-Vdc
XcXa Xb
+Vdc
zero sequence voltage vectorsXc
Xa Xb
+Vdc
-Vdc
t
T
1
0
zoom
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Calculation of timing for the vectors
- where d is the duty cycle (number between 0-1) multiplied with Tmod gives the timing
- Vs varies between 0-1 and it does not depend on the ratio between tzv1 and tzv2
1 2s x yV d v d v
1
2
1 2
3 sin( )
3 sin( )3
1
s
dc
s
dc
zv
Vd
V
Vd
V
d d d
t
t
t
t
aq
bq
cq
0zvt 1zvt 0zvtavt avt
modT
sV
110v010v
011v
001v 101v
100vd
q
211
0
dv
1 100d v
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Third harmonic injection (TH-PWM)
:
AB AN BN AN T BN T
BC BN CN BN T CN T
AC AN CN AN T CN T
T
v v v v v v v
v v v v v v v
v v v v v v v
where v is the third harmonic
Again, relationship between the phase and line voltages:
Note: by adding the same voltage (VT) to the phase voltages it will not affect the line to line voltage!
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Third harmonic injection waveform
- The peak of the phase voltages is reduced by around 15% - From modulation point of view 3rd harmonic injection
changes only the time ratio between the applied 2 zero vectors during a modulation period
- Same principles can work with 9th and 15th harmonics
t
rd3 Harmonic added to the reference signals
3rd harmonic
15%
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Implementation TH-PWM
qa
qb
• The 3rd harmonic has to be in phase with one of the three reference signals
• Usually the amplitude of the 3rd is 1/4th or 1/6th of the reference signal
qc
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Space Vector Modulation (SVM)
• Minimal current ripple can be achieved during one modulation period by applying for the two zero vectors the same duration
t
modT
1
1
Reference Signals SVM
0
cmvu
0 1 mod
1
2zv zv zvt t d T
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1200 Discontinuous PWM
t
T1
0
DPWM MAX
1
t
PWM Signals
t
t
t
aq
bq
cq
T
0zvt 0zvtavt
cmvu
t
1
0
1
0 mod 1
1 mod 0
0
0
zv zv zv
zv zv zv
t d T and t or
t d T and t
DPWM MIN
• Number of switching are reduced by 25%
• Only one zero voltage vector is generated for 1200
• Increased stress for the switch which conducts 1200
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300 Discontinuous PWM
DPWM0 DPWM1
DPWM2 DPWM3
• The increased stress, due to 1200 conduction of a switch, can be reduced by changing between DPWM-MAX and DPWM-MIN in each 300
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0.902MI
1V
refV
Output MI
1
0
0.902
0.785
0.900.78 1.57
Ove
r-M
od
ula
tio
n
reg
ion
Linear
region
Reference MI
2V
23
DCV
Modulation index – Three Phase Inverter
• Normalized output voltage amplitude
• Note: The modulation index can be also defined to be 1 at the end of the linear range
1
1 ,6
*
1 ,6
2
m
m step dc
m step
V V
VMI
V
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Other representation of the SVM • Time representation of 7th harmonic injected and SVM in Cartesian
coordinates
NOTE: In SVM representation the zero vector distribution is not visible
T
0tz0
tav1
tav2
tz1
tz0
tav1
tav2
tz1
Carrier wave Carrier wave
0.5*T
γ (deg)0 50 100 150 200 250 300 350
Position of reference voltage vectror γ (deg)
γ (deg)0 50 100 150 200 250 300 350
Position of reference voltage vectror γ (deg)
Polar coordinate representation
SVM representation
L. Mathe, et al., "Shaping the spectra of the line-to-line voltage using signal injection in the common mode voltage," IEEE conference proceedings, 2009.
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Zero vector-less modulation: AZSPWM
• In order to reduce the CMV instead the zero sequence vectors two opposite active vectors can be applied
sV
110v010v
011v
001v 101v
100vd
q
211
0
dv
1 100d v
3 010d v
4 101d v
3 4
1
2zvd d d
Disadvantage: • Very high current ripple • Implementation difficulties
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Outline
• Introduction
• Basic inverter topologies
• Basic Modulation techniques
• Zero vector placement modulation techniques
• Performance of different PWM methods
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Output Voltage Linearity
A. M. Hava, et al., "Simple analytical and graphical methods for carrier-based PWM-VSI drives," Power Electronics, IEEE Transactions on, vol. 14, pp. 49-61, 1999.
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Harmonic Distortion Function
A. M. Hava, et al., "Simple analytical and graphical methods for carrier-based PWM-VSI drives," Power Electronics, IEEE Transactions on, vol. 14, pp. 49-61, 1999.
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Switching Loss Function for DPWM
A. M. Hava, et al., "Simple analytical and graphical methods for carrier-based PWM-VSI drives," Power Electronics, IEEE Transactions on, vol. 14, pp. 49-61, 1999.
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Summary
• Half Bridge topology widely used in power electronics can be extend to poly-phase
• ST-PWM - has limited linear range • TH-PWM – extended linear range • SVM – has minimal current ripple • DPWM – Reduced switching losses • AZSPWM – Reduced CMV • Over-modulation – Fundamental amplitude increased, low
frequency harmonics are introduced Many more modulation strategies exit they offer no or very small benefit compared to the 5 basic method