3 Pulse Width Modulation of Power Electronic DC-AC Converter Pulse Width Modulation (PWM) . The Pulse Width Modulation (PWM) technique is applied in the inverter (DC/AC converter) to output an AC waveform with variable voltage and variable frequency for use in mostly variable speed motor drives. . The implementation of the complex PWM algorithms have been made much easier due to the advent of fast digital signal processors, microcontrollers, and Field Programmable Gate Arrays (FPGA). Pulse Width Modulated Inverters Two Level Inverters 1. Single Phase Half Bridge Inverters 2. Single Phase Full Bridge Inverters 3. Three-phase PWM voltage source inverter Multi Level Inverters 1. Diode Clamped or Neutral point clamped multi-level inverters 2. Capacitor clamped or flying capacitor multi-level inverters 3. Cascaded H-bridge multi-level inverters Special Type Inverters 1. Impedance Source or Z-Source Inverter 2. Quasi Impedance Source or qZSI Inverter High Performance Control of AC Drives with MATLAB/Simulink Models, First Edition. Haitham Abu-Rub, Atif Iqbal, and Jaroslaw Guzinski. Ó 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.
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3
Pulse Width Modulation of PowerElectronic DC-AC Converter
Pulse Width Modulation (PWM)
. The PulseWidthModulation (PWM) technique is applied in the inverter (DC/AC converter)
to output an AC waveform with variable voltage and variable frequency for use in mostly
variable speed motor drives.. The implementation of the complex PWMalgorithms have beenmademuch easier due to the
advent of fast digital signal processors, microcontrollers, and Field Programmable Gate
Arrays (FPGA).
Pulse Width Modulated Inverters
Two Level Inverters
1. Single Phase Half Bridge Inverters
2. Single Phase Full Bridge Inverters
3. Three-phase PWM voltage source inverter
Multi Level Inverters
1. Diode Clamped or Neutral point clamped multi-level inverters
2. Capacitor clamped or flying capacitor multi-level inverters
3. Cascaded H-bridge multi-level inverters
Special Type Inverters
1. Impedance Source or Z-Source Inverter
2. Quasi Impedance Source or qZSI Inverter
High Performance Control of AC Drives with MATLAB/Simulink Models, First Edition.Haitham Abu-Rub, Atif Iqbal, and Jaroslaw Guzinski.� 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.
1. Single Phase Half Bridge Inverters
The operation of the inverter can be well understood from Figure 3.2
(a) (b)
(c) (d)
Figure 3.2 Switching States in half-bridge inverter; a and c iao > 0 b and d. iao < 0.
vao
S1Da1
2dcV
vao
S’
2
V
Load AV
S1 Da22dcV
Figure 3.1 Power Circuit of a half wave bridge inverter.
2 High Performance Control of AC Drives
The output voltage is a square wave as shown in Figure 3.3
A graphical view shows that the output contains a considerable amount of low-order
harmonics such as 3rd, 5th, 7th, etc and the magnitude of the harmonics varies as the inverse of
its order.
If the modulating or control signal amplitude (Vm) > carrier signal (Vc)
The upper switch S1 is on vao ¼ Vdc
2
If the modulating or control signal amplitude (Vm) < carrier signal (Vc)
The upper switch S1’ is on vao ¼ � Vdc
2
Figure 3.4 A typical harmonic spectrum of output voltage in a half-bridge inverter.
Figure 3.3 Switching signal and the output voltage and current in a half-bridge inverter.
Pulse Width Modulation 3
The value of the average leg voltage VAO during a switching period TC can be determined
from Figure 3.6 (this shows one period of the triangular waveform).
. Matlab/Simulink Model of Half Bridge Inverter
Figure 3.6 One switching cycle in carrier-based sinusoidal PWM.
Figure 3.5 Bipolar PWM of single inverter leg.
Half-Bridge Inverter
voltage
Discrete,Ts = Ts s.
Vdc/2 = 0.5 p.u.
Vdc/2 = -0.5 p.u.
v+-
V1
Double click here to plotthe Valeg FFT
Scope2
g CE
S1'
g CE
S1
R-L Load
i+ -
I1
S1
S1'
Gate-signal Generation
Current
V inverter
I loadI load
Figure 3.7 Simulink model to implement carrier-based sinusoidal PWM.
4 High Performance Control of AC Drives
1
Out1-1double Convert1
Gain1Discrete
Edge Detector1
Data Type Conversion2 Data Type Conversion1In1
Figure 3.9b Dead band circuit.
2. Single Phase Full Bridge Inverters
Figure 3.9 Power circuit topology of a single-phase full-bridge inverter.
0.04 0.05 0.06 0.07 0.08 0.09 0.1–1
0
1
Vol
tage
[p.
u.]
Spec
trum
[p.
u.]
Time [s]
0 1000 2000 3000 4000 5000 60000
0.2
0.4
0.6
0.8 Fundamental = 0.472721
Frequency [Hz]
fc
fc-2f
mfc+2f
mfc+4f
mfc-4f
m
Figure 3.8 Output voltage and its spectrum for half bridge inverter.
Figure 3.9a Dead Band between upper and lower gating signals.
Pulse Width Modulation 5
(a) (b)
(c) (d)
Figure 3.10 Switching States in full-bridge inverter; a and c iao > 0 b and d. iao < 0.
Da1,
Db2
ON
S1,S2'
ONDa2,
Db1
ON
S2,S’1
ON
2
TT 2
3TT2
dcV
dcV−
abi,
S1, S2'
abv
S2, S1'
dcV.50
dcV.50dcV.50−
dcV.50−
aov
bov
Da1,
Db2
ON
S1,S2'
ONDa2,
Db1
ON
S2,S’1
ON
Figure 3.11 Switching signal and the output voltage and current in a half-bridge inverter.
6 High Performance Control of AC Drives
0
Vm
Vdc
0
0.5Vdc
–0.5Vdc
0
0.5Vdc
–0.5Vdc
0
VA
BV
BO
VA
O
Vdc
–Vdc
Figure 3.12 Unipolar PWM scheme for single-phase full-bridge inverter.
Pulse Width Modulation 7
. Matlab/Simulink Model of Single-phase Full-Bridge Inverter
DC/AC Full-Bridge Inverter
Discrete,Ts = 1e-005 s.
Vdc = 1 p.u.
VAB
v+-V2
Double click here to plotthe Valeg FFT
g CE
S2'
g CE
S2
g CE
S1'
g CE
S1
R-L Load
I_Load
i+ -I2
S1
S1'
S2
S2'
Gate Signal
V inverter
I load
Figure 3.13 Simulink model to implement unipolar PWM scheme in a full bridge 1-phase inverter.
0.04 0.05 0.06 0.07 0.08 0.09 0.1–2
0
2
Time [s]
0 1,000 2,000 fc 4,000 5,000 2fc 7,0000
0.2
0.4Fundamental = 0.94638
Frequency [Hz]
Spec
trum
[p.
u.]
Vol
tage
VA
B [
p.u.
]
2fc+3f
m2fc-3f
m
2fc-f
m 2fc+f
m
Figure 3.14 Voltage (VAB) and its spectrum for unipolar PWM scheme in a single-phase inverter.
8 High Performance Control of AC Drives
Three-phase PWM voltage source inverter
Figure 3.15 Power circuit topology of a three-phase voltage source inverter.
Figure 3.16 Waveforms for square wave/six-step mode of operation of a three-phase inverter.
Pulse Width Modulation 9
The maximum output phase-to-neutral voltage in the six-step mode is 0.6367 Vdc or (2/p)Vdc and that of the line to line voltage is 1.1Vdc.
vanðtÞ ¼ 2
pVDC sin vtþ 1
5sin 5vtþ 1
7sin 7vtþ 1
11sin 11vtþ 1
13sin 13vtþ . . . . . .
� �
vabðtÞ ¼ 2ffiffiffi3
p
pVDC sin vt� p
6
� �þ 1
5sin 5 vt� p
6
� �þ 1
7sin 7 vt� p
6
� �þ . . . . . .
� �
Table 3.2 Phase-to-neutral voltages for six-step mode of operation
Switching
mode
Switches ON Phase voltage
van
Phase voltage
vbn
Phase voltage
vcn
1 S1, S’2, S3 1/3Vdc � 2/3Vdc 1/3Vdc
2 S1, S’2, S’3 2/3Vdc � 1/3Vdc � 1/3Vdc
3 S1, S2, S’3, 1/3Vdc 1/3Vdc � 2/3Vdc
4 S’1, S2, S’3 � 1/3Vdc 2/3Vdc � 1/3Vdc
5 S’1, S2, S3 � 2/3Vdc 1/3Vdc 1/3Vdc
6 S’1, S’2, S3 � 1/3Vdc � 1/3Vdc 2/3Vdc
Table 3.3 Line voltages for six-step mode of operation
Switching mode Switches ON Line voltage vab Line voltage vbc Line voltage Vca
1 S1, S02, S3 Vdc �Vdc 0
2 S1, S02, S
03 Vdc 0 �Vdc
3 S1, S2, S03, 0 Vdc �Vdc
4 S01, S2, S03 �Vdc Vdc 0
5 S01, S2, S3 �Vdc 0 Vdc
6 S01, S02, S3 0 �Vdc Vdc
Table 3.1 Leg/Pole voltages of a three-phase VSI during six-step mode of operation
Switching
Mode
Switches ON Leg voltage
VA
Leg voltage
VB
Leg voltage
VC
1 S1, S’2, S3 0.5Vdc � 0.5Vdc 0.5Vdc
2 S1, S’2, S’3 0.5Vdc � 0.5Vdc � 0.5Vdc
3 S1, S2, S’3, 0.5Vdc 0.5Vdc � 0.5Vdc
4 S’1, S2, S’3 � 0.5Vdc 0.5Vdc � 0.5Vdc
5 S’1, S2, S3 � 0.5Vdc 0.5Vdc 0.5Vdc
6 S’1, S’2, S3 � 0.5Vdc � 0.5Vdc 0.5Vdc
10 High Performance Control of AC Drives
. Matlab/Simulink Model of Three-phase PWM voltage source inverter
0.04 0.05 0.06 0.07 0.08 0.09 0.1–1
0
1
Van
[p.
u.]
Spec
trum
[p.
u.]
Time [s]
0 100 200 300 400 500 600 700 800 900 10000
0.5
1Fundamental = 0.63642
Frequency [Hz]
5th 7th 11th 13th 17th 19th
Figure 3.18 Harmonic spectrum for six-step phase voltage.
DC/AC Three-phase Inverter
Discrete,Ts = 1e-005 s.
Vdc = 1 p.u.1
Vdc = 1 p.u.
Van
VAB
VA0
v+-
V4
v+-
V3
v+-
V1
Double click here to plotthe Valeg FFT
g CE
S3
g CE
S2'1
g CE
S2'
g CE
S2
g CE
S1'g C
E
S1
R-L Load1
S1
S1'
S2
S2'
S3
S3'Gate Signal
R-LLoad2
R-LLoad3
Figure 3.17 Simulink for Six-step operation of inverter.
Pulse Width Modulation 11
Pulse Width Modulation Schemes
. Classification of PulseWidthModulation Schemes for Three Phase Voltage source inverters
a. Continuous PWM
1. Carrier Based PWM Scheme
2. Third Harmonic Injection Carrier-based PWM
3. Carrier-based PWM with Offset Addition
4. Space Vector PWM
5. Artificial Neural Network Based PWM
b. Discontinuous PWM
1. Carrier based Sinusoidal PWM
VAm VBm VCm Vdc/2 V AO
Vdc/2
Van
2/3Vdc
1/3Vd
V AB
Vdc
1/3Vdc
Figure 3.18 Carrier-based sinusoidal PWM of a three-phase inverter.
12 High Performance Control of AC Drives
2
S1'
1
S1VA
>= boolean
NOT
4
S2'
3
S2VB
>= boolean
NOT
6
S3'
5
S3VC
>= boolean
NOT
Carrier Wave
Figure 3.19 Gate signal generation in Matlab for three-phase inverter.
0.04 0.05 0.06 0.07 0.08 0.09 0.1-1
0
1
Van
[p.
u.]
Time [s]
0 1,000 2,000 4000 50000
0.2
0.4Fundamental = 0.47479
Spec
trum
[p.
u.]
Frequency [Hz]fc
fc+2f
mfc-2f
m
2fc
3fc
4fc
2fc+f
m2f
c-f
m 3fc+2f
m3f
c-2f
m3f
c-2f
m 3fc+2f
m
Figure 3.20 Phase-to-neutral voltage and spectrum for carrier-based PWM.
Pulse Width Modulation 13
2. Third Harmonic Injection Carrier-based PWM
vAm ¼ Vm1sin vtð ÞþVm3sin 3vtð ÞvBm ¼ Vmsin vt� 2
p
3
� �þVm3sin 3vtð Þ
vCm ¼ Vmsin vtþ 2p
3
� �þVm3sin 3vtð Þ
Figure 3.21 Varying frequency modulation ratios for different output frequency.
Figure 3.22 Block diagram of carrier-based PWM with third-harmonic injection.
14 High Performance Control of AC Drives
Vm1Vm3
VcVm1+Vm3
Gain Margin
Figure 3.23 Modulating signals and carrier-wave for third harmonic injection PWM.
6
S3'
5
S3
4
S2'
3
S2
2
S1'
1
S1
VC
VB
VA
>=
>=
>=
boolean
boolean
boolean
Carrier Wave
NOT
NOT
NOT
3rd harmonic
Figure 3.24 Gate signal generation for third harmonic injection PWM.
Pulse Width Modulation 15
3. Carrier-based PWM with Offset Addition
vAm ¼ Vm1 sin vtð Þþ offset
vBm ¼ Vm sin vt� 2p
3
� �þ offset
vCm ¼ Vm sin vtþ 2p
3
� �þ offset
Where offset is given as;
Offset ¼ � Vmax þVmin
2; Vmax ¼ Max vAm; vBm; vCmf g; Vmin ¼ Min vAm; vBm; vCmf g
0.04 0.05 0.06 0.07 0.08 0.09 0.1–1
0
1
Va
[p.u
.]Sp
ectr
um V
a [p
.u.]
Time [s]
0 500 1000 1500 2000 2500 3000 3500 4000 45000
0.1
0.2
Fundamental = 0.57965
Frequency [Hz]
Figure 3.25 Spectrum of phase ‘a’ voltage for third-harmonic injection.
Gain Margin Vm1
+ Offset
Vm1
Offset
Figure 3.26 Modulating signals and carrier-wave for offset addition PWM.
16 High Performance Control of AC Drives
0.04 0.05 0.06 0.07 0.08 0.09 0.1–1
0
1
Time [s]
0 500 1000 1500 2000 2500 3000 3500 4000 45000
0.1
0.2Fundamental = 0.57758
Spec
turm
Va
[p.u
.]V
a [p
.u.]
Frequency [Hz]
Figure 3.28 Output voltage and voltage spectrum for offset addition PWM.
6S3'
5S3
4S2'
3S2
2S1'
1S1
VC
VB
VA
>=
>=
>=
min
MinMax1
max
MinMax –0.5
Gain
boolean
boolean
boolean
Carrier Wave
NOT
NOT
NOT
Figure 3.27 Matlab/Simulink for offset addition PWM (File name: PWM_3_phase_CB_offset.mdl).
Pulse Width Modulation 17
4. Space Vector PWM
Space vector is defined as;
fs¼ 2
3fa þ ej2
p3 fb þ ej4
p3 fc
� �
Where fa, fb and fc are the three-phase quantities that can as voltages, currents or
fluxes.
The total possible outputs are 23¼ 8 (000, 001, 010, 011, 100, 101, 110, 111). Here 0 indicates
the upper switch is ‘off’ and 1 represents the upper switch is ‘on’.
The space vectors can be shown graphically in Figure 3.29.
The maximum obtainable fundamental output voltage is calculated from the right angled
triangle (Figure 3.30) as;
Vmax ¼ 2
3
Vdc cos
p
6
� �¼ 1ffiffiffi
3p Vdc
Figure 3.29 Voltage space vector locations corresponding to different switching states.
18 High Performance Control of AC Drives
Discontinuous Space Vector PWM
Discontinuous space vector PWM results when one of the two zero vectors is not used in the
implementation of the space vector PWM. One of the leg of the inverter do not switch in
the whole switching period and remains tied to either the positive or negative dc bus. The nine
different discontinuous space vector PWM techniques are;
. t7¼ 0 for all sectors, known as DPWMMAX
. t8¼ 0 for all sectors, known as DPWMMIN
. Discontinuous modulation DPWM 0
. Discontinuous modulation DPWM1
. Discontinuous modulation DPWM 2
. Discontinuous modulation DPWM 3
. Discontinuous modulation DPWM 4
. Discontinuous modulation DPWM 5
. Discontinuous modulation DPWM 6
V max Vdc32
α = π/6
Figure 3.30 Determining the maximum possible output using space vector PWM.
SECTOR I
0
4/ot 2/at 2/bt 2/ot 2/bt 2/at 4/ot
ASdcV5.
dcV5.0
BS
dc.
B
SCS
7V 1V 2V 8V 2V 1V 7V2 1 7
Ts
−
Figure 3.31 Switching pattern for space vector PWM for sector I.