Chapter_11 DC - AC Converter

8/7/2019 Chapter_11 DC - AC Converter

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Chapter 11

DC AC Converters (Invertors)


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10

Three-Phase, Step-Wave InverterCircuits

10.1 SKELETON INVERTER CIRCUIT

The form of voltage-source inverter (VSI) most commonly used consists of athree-phase, naturally commutated, controlled rectifier providing adjustable direct

voltage Vdc as input to a three-phase, force-commutated 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 high-power 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 voltage-source 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 three-phase 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 STEP-WAVE 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 one-sixth 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 no-load operation. The devices are switched in numerical order, and

each remains in conduction for 120 electrical. Phase voltages vAN, vBC, and vCN



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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].



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FIG. 3 Load voltage waveforms with two simultaneously conducting switches. No load

and resistive load [20].



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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 star-connected resistive load are therefore identical with the

pattern of the open-circuit 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)



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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 volt-ages become irregular with dwell periods that differ with load phase-angle. 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



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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 star-connected 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].



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FIG. 6 Current conduction pattern for the case of three simultaneously conducting

switches. Star-connected 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)



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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 star-connected resistive load are plot-

ted inFig. 10.7. The phase voltages are seen to be different from the corresponding

no-load values (shown as dashed lines), but the line voltages remain unchanged.

Although the no-load phase voltages do not sum to zero, the load currents, with

three-wire 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



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FIG. 7 Output voltage waveforms with three simultaneously conducting switches. Star-

connected R load, isolated neutral. No-load 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).



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The fundamental components of the load voltages, plotted in Fig. 10.7

show that, as with a three-phase 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 pulse-width-modulation (PWM) inverters aretreated as a first-orde -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 turn-off thyristor,Triac, bipolar tran-

sistor, insulated gate bipolar transistor and metal-oxide 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.Square-waveform DC/AC inverters were used in early ages before 1980s. In those

equipment thyristors, GTOsandTriacscouldbeused in low-frequency switching opera-

tion. High-frequency/high-power 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. Single-phase half-bridge voltage source inverter (VSI)2. Single-phase full-bridge VSI

3. Three-phase full-bridge VSI

4. Three-phase full-bridge 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. Soft-switching inverters.

As mentioned in Chapter 3, we list some parameters as follows:

The modulation index ma (also known as the amplitude-modulation 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, linear-modulation 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 Single-Phase Half-Bridge VSI

A single-phase half-bridge VSI is shown in Figure 6.2. The carrier-based PWM tech-

nique is applied in this single-phase half-bridge 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 half-bridge 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 Single-phase half-bridge VSI.


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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 single-phase half-bridge 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 Single-Phase Full-Bridge VSI

A single-phase full-bridge VSI is shown in Figure 6.4.

The carrier-based PWM technique is applied in this single-phase full-bridge 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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Vi

S1

S1 D1

Vi/2

Vi/2

N

iiD1

S2 D2

D2

a

b

iO

VO

S2

Figure 6.4 Single-phase full-bridge 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 full-bridge 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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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 Three-phase full-bridge VSI.

associated with the full-bridge VSI. We can fin out the output of the phase delayed

between the output current and voltage.

6.1.3 Three-Phase Full-Bridge VSI

A three-phase full-bridge VSI is shown in Figure 6.6.The carrier-based PWM technique is applied in this single-phase full-bridge 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 full-bridge

VSI. We can fin out the output of the phase delayed between the output current and

voltage.

6.1.4 Three-Phase Full-Bridge CSI

A three-phase full-bridge CSI is shown in Figure 6.8.

The carrier-based PWM technique is applied in this single-phase full-bridge 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 full-bridge 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 single-phase output VSI, which is shown in Figure 6.10. If the


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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 three-phase full-bridgeVSI (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 Three-phase full-bridge CSI.


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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 three-phase full-bridge 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 Three-phase input plus single-phase output VSI.


22/24


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.

three-phase 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 three-stage PWM inverter is shown in Figure 6.11. Each phase consist of three

cells with difference phase-angle shift by 20 each other.

The carrier-based PWM technique is applied in this three-phase multistage PWM

inverter. Figure 6.12 shows the ideal waveforms associated with the full-bridge VSI.

We can fin out the output of the phase delayed between the output current and voltage.

6.1.6 Multilevel PWM Inverter

A three-level PWM inverter is shown in Figure 6.13. The carrier-based 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.


23/24


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.


24/24


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 Three-phase three-level PWM VSI.

= 1/f

=L/

iO-k

= iO-(k

1)

(1 et/

iO-(k

=

+

Chapter_11 DC - AC Converter

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