Advanced Topics in PWM for Voltage Source …...1 Advanced Topics in PWM for Voltage Source...
Transcript of Advanced Topics in PWM for Voltage Source …...1 Advanced Topics in PWM for Voltage Source...
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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
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
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
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
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
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
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
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!
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%
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
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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
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