Chapter_11 DC  AC Converter

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Chapter 11
DC AC Converters (Invertors)

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10
ThreePhase, StepWave InverterCircuits
10.1 SKELETON INVERTER CIRCUIT
The form of voltagesource inverter (VSI) most commonly used consists of athreephase, naturally commutated, controlled rectifier providing adjustable direct
voltage Vdc as input to a threephase, forcecommutated inverter (Fig. 10.1). The
rectifier outputinverter input section is known as the dc link. In addition to a
shunt capacitor to aid direct voltage stiffness the link usually contains series
inductance to limit any transient current that may arise.
Figure 10.2a shows the skeleton inverter in which the semiconductor recti
fier devices are shown as generalized switches S. The notation of the switching
devices in Fig. 10.2 is exactly the same as for the controlled rectifier in Fig. 7.1
and the naturally commutated inverter ofFig. 9.1. In highpower applications theswitches are most likely to be SCRs, in which case they must be switched off
by forced quenching of the anode voltages. This adds greatly to the complexity
and cost of the inverter design and reduces the reliability of its operation.
If the inverter devices are GTOs (Fig. 10.2b), they can be extinguished
using negative gate current. Various forms of transistor switches such as BJTs
(Fig. 10.2c), and IGBTs (Fig. 10.2d) can be extinguished by control of their base
currents, as briefly discussed in Chapter 1. In Fig. 10.2 the commutating circuitry
is not shown. It is assumed in the following analysis that each switch can be
opened or closed freely.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
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FIG. 1 Basic form of voltagesource inverter (VSI) [20].
From the power circuit point of view all versions of the skeleton inverterofFig. 10.2 are identical. In each case the frequency of the generated voltages
depends on the frequency of gating of the switches and the waveforms of the
generated voltages depend on the inverter switching mode.The waveforms of the
associated circuit currents depend on the load impedances.
Manydifferent voltage waveforms canbe generated bythe use ofappropriate
switching patterns in the circuit of Fig. 10.2. An invariable requirement in three
phase systems is that the threephase output voltages be identical in form but phase
displaced by 120 electrical from each other. This does not necessarily create a bal
anced set of load voltages, in the sinusoidal sense of summing to zero at every in
stant of the cycle, but it reduces the possibility of gross voltage unbalance.
A voltage source inverter is best suited to loads that have a high impedance
to harmonic currents, such as a series tuned circuit or an induction motor. The
series inductance of such loads often results in operation at low power factors.
10.2 STEPWAVE INVERTER VOLTAGEWAVEFORMS
For the purpose of voltage waveform fabrication it is convenient to switch thedevices of Fig. 10.2 sequentially at intervals of 60 electrical or onesixth of a
period. The use of a dc supply having equal positive and negative voltage values
Vdc is common. The zero point of the dc supply is known as the supply zero
pole but is not grounded.
10.2.1 Two Simultaneously Conducting Switches
If two switches conduct at any instant, a suitable switching pattern is defined in
Fig. 10.3 for noload operation. The devices are switched in numerical order, and
each remains in conduction for 120 electrical. Phase voltages vAN, vBC, and vCN
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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FIG. 2 Skeleton switching circuit of voltage source inverter: (a) general switches, (b)
GTO switches, (c) BJT switches, and (d) IGBT switches [20].
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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FIG. 3 Load voltage waveforms with two simultaneously conducting switches. No load
and resistive load [20].
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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consist of rectangular pulses of heightVdc. If equal resistors R are now con
nected in star to the load terminals A, B, and C of Fig. 10.2, the conduction
pattern ofFig. 10.4 ensues for the first half period.
In interval 0 t /3,
22
0
2
2
= = =
=
= = = +
v I R VR
R V
v
v I RV
RR V
v
AN Ldc
dc
BN
CN Ldc
dc
AB == + = = v v v v V AN NB AN BN dc (10.1)
In the interval /3 t 2/3,
0== = +
= = +
= +
v
v I R V
v I R V
v V
AN
BN L dc
CN L dc
AB dc(10.2)
In the interval 2/3 t ,
0
2
= = +
= = =
=
v I R V
v I R V
v
v V
AN L dc
BN L dc
CN
AB dc(10.3)
For each interval it is seen that the load current during conduction is
IV
R
V
RL
dc dc=
= 2
2 (10.4)
The results of Eqs. (10.1)(10.4) are seen to be represented by the waveforms
ofFig. 10.3. For this particular mode of switching the load voltage and current
waveforms with starconnected resistive load are therefore identical with the
pattern of the opencircuit voltages. The potential of load neutral point Nis always
midway between Vdc and Vdc and therefore coincides with the potential of
the supply midpoint 0.
Phase voltage waveform vAN in Fig. 10.3 is given by an expression
v AN dc dct V V= = ( ),
,
240
120
60 360
0 300
(10.5)
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FIG. 4 Current conduction pattern for the case of two simultaneously conducting
switches: (a) 0 t 60, (b) 60 t 120, and (c) 120 t 180 [20].
This has the rms value
V t d t V V AN AN dc dc= = =1
2
2
30 816
2
0
2
v
( ) .
(10.6)
The fundamental Fourier coefficients of waveform vAN (t) are found to be
a t t d t V AN dc1 0
21 2 3
= = v
( ) cos
(10.7)
b t t d t AN1 0
210= = v
( ) sin
(10.8)
c a b a V dc1 12
12
1
2 3= + = =
(10.9)
11 1
1
1 90= = = tan tan ( )a
b
(10.10)
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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It is seen from Eqs. (10.9) and (10.10) that the fundamental (supply frequency)
component of the phase voltages has a peak value (23/) Vdc, or 1.1Vdc withits origin delayed by 90. This (23/)Vdc fundamental component waveformis sketched in Fig. 10.3.
The distortion factor of the phase voltage is given by
= = =V
V
c
V
AN
AN AN
1 1 2 3/
Distortion factor
(10.11)
Line voltage vAB (t) in Fig. 10.3 is defined by the relation
v AB dc dc dct V V V ( ),
,
,
,= +
120 240
60 180
60 300
0 240
1802
120
360
3002Vdc (10.12)
This is found to have fundamental frequency Fourier coefficients of value
a V
b V
c V
dc
dc
dc
1
1
1 11
3 3
3
63 60
=
= +
= = =
Therefore, tan
(10.13)
The fundamental component ofvAB (t) is therefore given by
v
AB dct V t16
60( ) sin( )= (10.14)
It is seen in Fig. 10.3 that vAB1 (t) leads vAN1 (t) by 30, as in a balanced three
phase system, and comparing Eqs. (10.9) and (10.13), the magnitude VAB1 is3 times the magnitude VAN1.
With a firing pattern of two simultaneously conducting switches the load
voltages of Fig. 10.3 are not retained with inductive load. Instead, the load voltages become irregular with dwell periods that differ with load phaseangle. Be
cause of this, the pattern of two simultaneously conducting switches has only
limited application.
10.2.2 Three Simultaneously Conducting Switches
A different load voltage waveform is generated if a mode of switching is used
whereby three switches conduct at any instant. Once again the switching devices
conduct in numerical sequence but now each with a conduction angle of 180
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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electrical. At any instant of the cycle three switches with consecutive numbering
are in conduction simultaneously. The pattern of waveforms obtained on no load
is shown in Fig. 10.5. With equal starconnected resistors the current conduction
patterns ofFig. 10.6 are true for the first three 60 intervals of the cycle, if the
load neutral N is isolated.
For each interval,
IV
R R
V
R
dc dc=+
=2
2
4
3/ (10.15)
FIG. 5 Output voltage waveforms with three simultaneously conducting switches. No
load [20].
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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FIG. 6 Current conduction pattern for the case of three simultaneously conducting
switches. Starconnected R load: (a) 0 t 60, (b) 60 t 120, and (c) 120
t 180 [20].
In the interval 0 t /3,
2
2
3
4
3
2
= = =
= =
= =
v vI
R V
v IR V
v v v V
AN CN dc
BN dc
AB AN BN dc (10.16)
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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In the interval /3 t ,
1
2
2
3
4
32
= = =
= =
=
v v R V
v IR V
v V
AN BN dc
CN dc
AB dc(10.17)
In the interval 2/3 t ,
1
2
2
3
4
3
0
= = =
= =
=
v v R V
v IR V
v
AN BN dc
CN dc
AB(10.18)
The load voltage waveforms obtained with starconnected resistive load are plot
ted inFig. 10.7. The phase voltages are seen to be different from the corresponding
noload values (shown as dashed lines), but the line voltages remain unchanged.
Although the noload phase voltages do not sum to zero, the load currents, with
threewire star connection, must sum to zero at every instant of the cycle. In Fig.
10.7 the phase voltage vAN is given by
v AN dc dct V V( ),
,
,
,= +
2
3
2
3
4
3
60 180
0 120
240 360
180 300VV Vdc dc
120
60
300
240
4
3
(10.19)It can be seen by inspection in Fig. 10.7 that the fundamental frequency compo
nent ofvAN (t) is in time phase with it, so that
1
11 1
1
0
0
=
= =tanb (10.20)
Fundamental frequency Fourier coefficient b1 for the load peak phase voltage is
found to be
b c Vdc1 14
= = (10.21)
The corresponding fundamental (supply) frequency Fourier coefficients for line
voltage vAB (t) are given by
a
1
1
2 3
6
=
=
V
b V
dc
dc
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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FIG. 7 Output voltage waveforms with three simultaneously conducting switches. Star
connected R load, isolated neutral. Noload waveforms [20].
1
11
43 3
1
330
= =
= =
c Vdc the phase value
tan(10.22)
The positive value30 for 1 implies that its origin lies to the left of the zero
on the scale of Fig. 10.7. Line voltage component AB (t) is plotted in Fig. 10.7,
consistent with Eq. (10.22).
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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The fundamental components of the load voltages, plotted in Fig. 10.7
show that, as with a threephase sinusoidal system, the line voltage leads its
corresponding phase voltage by 30. The rms value of phase voltage vAN (t) is
found to be
V t d t V V AN AN dc dc= = =1 2 23 0 9432
0v ( ) . (10.23)
Combining Eqs. (10.21) and (10.23) gives the distortion factor of the phase
voltage,
= = =V
V
c
V
AN
AN AN
1
1
2 3
Distortion factor
(10.24)
This is seen to be identical to the value obtained in Eq. (10.11) for the phasevoltage waveform of Fig. 10.3 obtained with two simultaneously conducting
switches. Although the distortion factors are identical, waveform AN (t) of Fig.
10.7 has a slightly greater fundamental value (4/)Vdc than the corresponding
value (23/)Vdc for AN (t) of Fig. 10.3, given by Eq. (10.7). The switchingmode that utilizes three simultaneously conducting switches is therefore poten
tially more useful for motor speed control applications. The properties of relevant
step waves and square waves are summarized in Table 10.1.
It can be deduced from the waveforms of Fig. 10.7 that load neutral point
N is not at the same potential as the supply neutral point 0. While these pointsremain isolated, a difference voltage VNO exists that is square wave in form, with
amplitudeVdc/3 and of frequency three times the inverter switching frequency.
If the two neutral points are joined, a neutral current will flow that is square wave
in form, of amplitudeVdc/R, and of three times the inverter switching frequency.
10.3 MEASUREMENT OF HARMONICDISTORTION
The extent of waveform distortion for an alternating waveform can be definedin a number of different ways. The best known of the these, the distortion factor
defined by Eq. (10.24), was used in connection with the rectifier circuits of
Chapters 29.
An alternative measure of the amount of distortion is by means of a property
known as the total harmonic distortion (THD), which is defined as
THDV V
V
V
V
AN AN
AN
AN
AN
h=
=2 2
2
1
1 1 (10.25)
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Chapter 6
Digitally Controlled DC/ACInverters
As described in Chapter 3, all DC/AC pulsewidthmodulation (PWM) inverters aretreated as a firstorde hold (FOH) element in digital control systems. We will discuss
this model in various circuits in this Chapter.
6.1 INTRODUCTION
DC/AC inverters are a newly developed group of the power switching circuits applied
in industrial applications in comparison with other power switching circuits. Althoughchoppers were popular in DC/AC power supply long time ago, power DC/AC invert
ers were used in industrial application since later 1980s. Semiconductor manufacture
development brought power devices, such as gate turnoff thyristor,Triac, bipolar tran
sistor, insulated gate bipolar transistor and metaloxide semiconductor fiel effected
transistor (GTO, Triac, BT, IGBT, MOSFET, respectively) and so on, in higher switch
ing frequency (say from thousands Hz upon few MHz) into the DC/AC power supply
since 1980s. Due to the devices such as thyristor (silicon controlled rectifie , SCR)
with low switching frequency, the corresponding equipment is low power rate.Squarewaveform DC/AC inverters were used in early ages before 1980s. In those
equipment thyristors, GTOsandTriacscouldbeused in lowfrequency switching opera
tion. Highfrequency/highpower devices such as power BTs andIGBTs wereproduced
in the 1980s. The corresponding equipment implementing the PWM technique has
large range of the output voltage and frequency, and low total harmonic distortion
(THD). Nowadays, most DC/AC inverters are DC/AC PWM inverters in different
prototypes.

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Digitally controlled DC/AC inverters 163
DC/AC inverters areused for inverting DCpowersource intoAC power applications.
They are generally used in following applications:
1. Variable voltage/frequency AC supplies in adjustable speed drives (ASDs), suchas induction motor drives, synchronous machine drives and so on.
2. Constant regulated voltage AC power supplies, such as uninterruptible power
supplies (UPSs).
3. Static var compensations.
4. Active filters
5. Flexible AC transmission systems (FACTSs).
6. Voltage compensations.
Adjustable speed induction motor drive systems are widely applied in industrial
applications.These systemsrequestedtheDC/AC powersupply with variable frequency
usually from 0 to 400 Hz in fractional horsepower (HP) to hundreds of HP. A large
number of the DC/AC inverters were in the world market. The typical block circuit is
shown in Figure 6.1.
From this block diagram we can see that the power DC/AC inverter produces
variable frequency and voltage to implement the ASD.
The power devices used for ASD can be thyristors, Triacs and GTOs in the 1970s
and early 1980s. Power IGBT was popular in the 1990s, and greatly changed the
manufacturing of DC/AC inverters. The DC/AC power supply equipment is totally
changed. The corresponding control circuit is gradually changed from analog control
to digital control system since late 1980s. The mathematical modeling for all AC/DC
rectifier is well discussed widely in worldwide. Finally, an FOH is generally accepted
to be used for simulation of all DC/AC inverters.
The generally used DC/AC inverters are introduced below:
1. Singlephase halfbridge voltage source inverter (VSI)2. Singlephase fullbridge VSI
3. Threephase fullbridge VSI
4. Threephase fullbridge current source inverter (CSI)
5. Multistage PWM inverters
Vi
C
Rectifier Inverter
DC link
ASD
IM
Figure 6.1 A standard ASD scheme.

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164 Digital power electronics and applications
6. Multilevel PWM inverters
7. Softswitching inverters.
As mentioned in Chapter 3, we list some parameters as follows:
The modulation index ma (also known as the amplitudemodulation ratio in
Chapter 3):
ma =VC
V(6.1)
where VC is the amplitude of the control or the preliminary reference signal, and
V is the amplitude of the triangle signal. Generally, linearmodulation operation
is considered, so that ma is usually smaller than unity (e.g. ma = 0.8). The normalized carrier frequency index mf (also known as the frequency
modulation ratio in Chapter 3):
mf =f
fC(6.2)
where f is the frequency of the triangle signal, and fC is the frequency of the
control signal or the preliminary reference signal. Generally, in order to obtain
low THD, the mf has usually taken large number (e.g. mf= 9).
In order to wellunderstand each inverter, we have shown some typical circuits below.
6.1.1 SinglePhase HalfBridge VSI
A singlephase halfbridge VSI is shown in Figure 6.2. The carrierbased PWM tech
nique is applied in this singlephase halfbridge VSI. Two large capacitors are required
to provide a neutral point N, therefore, each capacitor keep the half of the input DCvoltage. Two switches S+ and S are switched by the PWM signal.
Figure 6.3 shows the ideal waveforms associated with the halfbridge VSI. We can
fin out the output of the phase delayed between the output current and voltage.
Vi
S
S D
Vi/2
Vi/2
N
iiD
aIO
VO_
C
C
Figure 6.2 Singlephase halfbridge VSI.

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Digitally controlled DC/AC inverters 165
VC
90180 270 360
V
vt
(a)
vt
90 180 270 3600
on
(b)
S
vt
90 180 270 3600
on
(c)
S
vt
1800 90 270 360
VO1
VO Vi/2
(d)
vt
iO
900 270 360
iO1
180
(e)
Figure 6.3 Ideal waveforms associated with the singlephase halfbridge VSI (ma = 0.8,
mf= 9). (a) Carrier and modulating signals, (b) switch S+ state, (c) switch S state, (d) AC
output voltage and (e) AC output current.
6.1.2 SinglePhase FullBridge VSI
A singlephase fullbridge VSI is shown in Figure 6.4.
The carrierbased PWM technique is applied in this singlephase fullbridge VSI.
Two large capacitors may be used to provide a neutral point N, therefore, each capacitor
keep the half of the input DC voltage. Four switches S1+ and S1plus S2+ and S2
are applied and switched by the PWM signal. Figure 6.5 shows the ideal waveforms

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166 Digital power electronics and applications
Vi
S1
S1 D1
Vi/2
Vi/2
N
iiD1
S2 D2
D2
a
b
iO
VO
S2
Figure 6.4 Singlephase fullbridge VSI.
VC
90 180 270 360
V
(a)
vt
90 180(b) 270 3600
onS1
vt
(c) 90 180 270 3600
onS2
vt
(d)
1800 90 270
VO1
VOVi
360
vt
(e)
iO
900
270 360180
vt
Figure 6.5 Ideal waveforms associated with the fullbridge VSI (ma = 0.8, mf= 8). (a) Carrier
and modulating signals, (b) switch S1+ and S1 state, (c) switch S2+ and S2 state, (d) AC
output voltage and (e) AC output current.

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Digitally controlled DC/AC inverters 167
Vi
S1
S4 D4
Vi/2
Vi/2
N
iiD1 S3
S6 D6
D3 S5
S2 D2
D5
a
b
c
ioa
Vab
Figure 6.6 Threephase fullbridge VSI.
associated with the fullbridge VSI. We can fin out the output of the phase delayed
between the output current and voltage.
6.1.3 ThreePhase FullBridge VSI
A threephase fullbridge VSI is shown in Figure 6.6.The carrierbased PWM technique is applied in this singlephase fullbridge VSI.
Two large capacitors may be used to provide a neutral point N, therefore, each capacitor
keep the half of the input DC voltage. Six switches S1S6 are applied and switched by
the PWM signal. Figure 6.7 shows the ideal waveforms associated with the fullbridge
VSI. We can fin out the output of the phase delayed between the output current and
voltage.
6.1.4 ThreePhase FullBridge CSI
A threephase fullbridge CSI is shown in Figure 6.8.
The carrierbased PWM technique is applied in this singlephase fullbridge CSI.
The main objective of these static power converters is to produce AC output current
waveforms from a DC current power supply. Six switches S1S6 are applied and
switched by the PWM signal. Figure 6.9 shows the ideal waveforms associated with
the fullbridge CSI.We can fin out the output of the phase ahead between the outputvoltage and current.
6.1.5 Multistage PWM Inverter
Multistage PWM inverter consists of many cells. Each cell can be a single or three
phase input plus singlephase output VSI, which is shown in Figure 6.10. If the

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168 Digital power electronics and applications
90(b) 180 270 3600
onS1
vt
Vca Vcb
90 180 270 360
V
Vcc
(a)
vt
(c)
S3
0 90 270 360180
on
vt
(d)
1800 90 270 360
Vab1Vab Vi
vt
(e)
ioa
900 270 360180
vt
Figure 6.7 Ideal waveforms associatedwith the threephase fullbridgeVSI (ma = 0.8, mf= 9).
(a) Carrier and modulating signals, (b) switchS1+ state, (c) switch S3 state, (d)AC outputvoltage
and (e) AC output current.
Vi
S4
D4
iI
D1
S3
S6
D6
D3
S5
S2
D2
D5
ab
c
ioa
Vab
S1
C C C
Figure 6.8 Threephase fullbridge CSI.

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Digitally controlled DC/AC inverters 169
ica
i
icb icc
(a)
90 180 270 3600
onS1
(b)
0 90 270 360180
onS3
(c)
1800 90 270 360
ioa1ioa ii
(d)
vab
900 270 360180
vab1
(e)
t
t
t
t
t
90 180 270 360
Figure 6.9 Ideal waveformsassociatedwith the threephase fullbridge CSI (ma= 0.8, m
f= 9).
(a)Carrier and modulating signals, (b) switchS1+ state, (c) switch S3 state, (d)AC output current
and (e) AC output voltage.
D4 D6 D2
D5 S1
S1D1
D1S2
S2 D2
D2
a
b
iO
VO
N
ii
Vi/2
Vi/2
C
C
L
D1 D3
isa
Figure 6.10 Threephase input plus singlephase output VSI.

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170 Digital power electronics and applications
C13
C12
C11
C23
C22
C21
C33
C32
C31
IM
VO11
VO21
VO31
isa
Multicellarrangement
MultipulsetransformerAC
mains
isaVsa
3
n
Figure 6.11 Multistage converter based on a multicell arrangement.
threephase AC supply is a secondary winding of a main transformer, it is floatin
and isolated from other cells and common ground point. Therefore, all cells can be
linked in series or parallel manner.
A threestage PWM inverter is shown in Figure 6.11. Each phase consist of three
cells with difference phaseangle shift by 20 each other.
The carrierbased PWM technique is applied in this threephase multistage PWM
inverter. Figure 6.12 shows the ideal waveforms associated with the fullbridge VSI.
We can fin out the output of the phase delayed between the output current and voltage.
6.1.6 Multilevel PWM Inverter
A threelevel PWM inverter is shown in Figure 6.13. The carrierbased PWM technique
is applied in this multilevel PWM inverter. Figure 6.14 shows the ideal waveforms
associated with the multilevel PWM inverter. We can fin out the output of the phase
delayed between the output current and voltage.

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Digitally controlled DC/AC inverters 171
Vca Vca
90 180 270 360
(a)
V1
v
t
V2 V3
0
(b)
vt
90 180 270
360
ViVO211
VO21
0
(c)
vt
VO111VO11
90 180 270 3600
(d)
vt
Vi
Vi
VO311
VO31
90 180 270 360
0
(e)
vt
90 360180 270
3ViVaN
0
Figure 6.12 Ideal waveforms associated with the multicell PWM inverter (three stages,
ma = 0.8, mf= 6). (a) Carrier and modulating signals, (b) cell c11 AC output voltage, (c) cell c21AC output voltage, (d) cell c31 AC output voltage and (e) phase a load voltage.

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172 Digital power electronics and applications
S5a D5a
S1b
S4aD
4a
D1b
S3b
S6a
D6a
D3b
S5b
S2a D2a
D5b
a
b
c
ioa
S2b D2bS6b
D6b
S3a D3aS1a D1a
S4b D4b
Dc
DcDb
Db
Da
Da
Vi/2
Vi/2
C
C
VabN
ii
Figure 6.13 Threephase threelevel PWM VSI.
= 1/f
=L/
iOk
= iO(k
1)
(1 et/
iO(k
=
+