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120oConduction

For this type of conduction, each switch

conducts for 120o.

At any instant only two switches

conduct and the resulting outputvoltage waveforms are quasi-square

wave.

The gating signals for the switches and

the circuit voltage waveforms are

shown on the next slide (Figure 5.7).

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( g )

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120oconduction contdHere also, there is a shift of 60obetween a

gating signal and the next gating signal, andthe switches are turned on and then after

120oturned off in the sequence Q1to Q6.

In this method of control, a 60odead time

exists between two series switches in a leg.

This provides a safety margin against

simultaneous conduction of the two

switches connected across the dc voltage

source.

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The circuit operates in six modes percycle and each mode lasts for 60o.

From Figure 5.7, the sequence of

conducting switches for the six modes

is 61, 12, 23, 34, 45 and 56.The line-to-neutral output voltage

waveforms can be derived by

analyzing the circuit with a resistive

star load and considering each mode of

operation.

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We may also use the star-connectedresistors to obtain only the phase van

waveform and obtain vbn and vcnwaveforms by shifting it to the right by

120 and 240

o

respectively.If the circuit is analyzed, it is observed

that van= Vs/2when Q1is conducting,

van= -Vs/2when Q4is conducting andvan= 0 when none of the two is

conducting.

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120oconduction contdThe line voltages are obtained using these

equations: vab= van- vbn, vbc= vbn- vcn,

and vca= vcn- van.

The line-to-neutral voltages have the sameshape as the line-to-line voltages for the

180oconduction.

The Fourier series of these line-to-neutralvoltages can be derived from equation

(5.14) to equation (5.16) by replacing Vsby

Vs/2(See next slide):

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,..5,3,1 6sin

6cos

2

n

San tn

n

n

Vtv

,..5,3,1 2

sin

6

cos2

n

Sbn tn

n

n

Vtv

,..5,3,1 6

7

sin6cos

2

n

S

cn tn

n

n

V

tv

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Inverter Output Voltage andFrequency Control

It is often required that

- the output voltage of an inverter is

varied in order to regulate the voltageof the inverter in power supplies or

- the output voltage and/or frequencybe varied as in adjustable or variable

speed drives.

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Inverter output voltage andfrequency control contdThe voltage source inverters can be

classified into three general groups:

- Pulse-width-modulated inverters

- Square-wave inverters

- Single-phase inverters with

voltage cancellation

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Pulse-width-modulated invertersThe input dc voltage is constant and the

inverter switches are pulse-width

modulated to control the magnitude and the

frequency of the ac output voltage.

There are a number of pulse-width-

modulation techniques.

Among them is the sinusoidal pulse-widthmodulation, known by its abbreviation

SPWM, which is commonly used in

industrial applications.

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Square-wave invertersFor the square-wave inverters, the rms

output voltage is controlled by varying

the dc source voltage and the

frequency controlled with the inverter.A variable dc voltage can be achieved

with a dc chopper or controlled

rectifier.

A suitable link LC filter is usually

necessary.

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Single-phase inverters with voltagecancellationThe input dc voltage is constant and

the inverter controls both the

magnitude and frequency with a

technique that cannot be considered

as PWM.It works only on single-phase full-

bridgeinverters.

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In this section, we discuss

- the voltage cancellationtechnique and

- the SPWM as applied toboth single-phase and three-

phase inverters

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In the pulse-width-modulated

switching scheme, the gating signals

are generated

-by comparing a control signal at the

desired frequency- with a triangular waveform.

The frequency of the triangularwaveform establishes the inverter

switching frequency.

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Letcf frequency of the control signal also known as modulating

signal cv

cv

amplitude of control signalf frequency of the triangular signal v also known as carrier

signal

v amplitude of the triangular signal

Then amplitude modulation ratio ( am ) and frequency modulation

ratio ( fm ) are defined as follows:

v

vm ca

c

ff

fm

The peak of the triangular signal is generally kept constant.

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Output control by voltage cancellationThis is the same as the single-pulse-

width modulation.

There is only one pulse per half-cycle

and the width of the pulse is varied tocontrol the inverter output voltage.

Referring to figure on the next slide

(Figure 5.8), the switches in the two

inverter legs are controlled separately.

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We note that for each leg- when a positive switch is on then the

negative switch is off,

- and when the positive switch is off

the negative switch is on.- Again at any given instant one switch

must be on.

- All switches have a duty cycle of 0.5,

similar to a square wave control.

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This method is known as output control byvoltage cancellation because its

implementation is easily achieved by usingtwo phase-shifted square-wave switching

signals as shown on the next slide

The width of the pulse is controlled bycontrolling the overlap angle .

During the overlap interval the output

voltage is zero because

- either both top switches are on

- or both bottom switches are on.

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Output control by voltage cancellationcontd

The Fourier series of the output voltage

shown on the previous slide (Figure 5.9c)

has only odd sine terms.

The coefficients are given by11

1

cos2)(sin

2

ntnv

tdtnv

b iin

111 cos4

coscos2

nn

vnn

n

v ii

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Output control by voltage cancellationcontd

The output voltage vo(t)is then given

by

The rms output voltage

,..5,3,1

1 sincos4

n

iO tnn

n

vtv

1

21

iL vV

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Output control by voltage cancellationcontd

And the rms of the fundamental component

is

As alpha oneincreases (beyond 30o), the

magnitude of the harmonics, particularlythe third becomes significant as compared

with the fundamental magnitude.

11 cos

22

iv

V

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Sinusoidal pulse width modulation

Single-phase half-bridge VSIThe figure on the next slide (Figure

5.10) shows the single-phase half-bridge used for the discussion in

this section.

At any instant one of the switches

should be on but not both.

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Single-phase half-bridge VSI contdReferring to the figure, the PWM technique

is used to define the on and off states of the

switches by comparing a control signal vc

and a triangular waveform v.

In practice, when vc > vthe positive

switch S+is on and the negative switch S-

is off.Similarly, when vc < v the positive

switch S+is off and the negative switch S-

is on.

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Single-phase half-bridge VSI contd

We have

Since the two switches are never off

simultaneously, the output voltage

toggles between these two values.

2iao

vv when the positive switch

S is on and

2iao vv when the negative switch S is on

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Single-phase half-bridge VSI contdFor sinusoidal pulse-width modulation the

gating signals are generated by comparing asinusoidal reference signal with a triangular

carrier wave as shown on the next slide

(Figures5.9a, b and c).

The resulting output voltage is shown in

Figure 5.9d.

SPWM is used with the aim of producing

sinusoidal output waveform with magnitude

and frequency controllable.

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