Điện tử công suất (inverter chapter 4 )

DC to AC Converter Inverter• DEFINITION: Converts DC to AC power by switching the DC input voltage or current in a pre-determined sequence so as to generate AC voltage or current output

DC to AC Converter (Inverter)

• DEFINITION: Converts DC to AC power by

switching the DC input voltage (or current) in a pre-determined sequence so as to generate AC

voltage (or current) output.

• General block diagram

Simple square-wave inverter (1)

• To illustrate the concept of AC waveform

generation

S2 S4

Harmonics Filtering

• Output of the inverter is “chopped AC voltage with zero DC component” It contain harmonics.

• An LC section low-pass filter is normally fitted at

the inverter output to reduce the high frequency

harmonics

• In some applications such as UPS, “high purity” sine

wave output is required Good filtering is a must

• In some applications such as AC motor drive,

Variable Voltage Variable

• Output voltage frequency can be varied by “period”

of the square-wave pulse

• Output voltage amplitude can be varied by varying the “magnitude” of the DC input voltage

• Very useful: e.g variable speed induction motor drive

Output voltage harmonics/

distortion

• Harmonics cause distortion on the output voltage

• Lower order harmonics (3rd, 5th etc) are very

difficult to filter, due to the filter size and high filter order They can cause serious voltage distortion

• Why need to consider harmonics?

– Sinusoidal waveform quality must match TNB supply

– “Power Quality” issue

– Harmonics may cause degradation of

equipment Equipment need to be “de-rated”

• Total Harmonic Distortion (THD) is a measure to determine the “quality” of a given waveform

Total Harmonics Distortion (THD)

is

:THDCurrent

known,is

vaveformfor the

voltagerms

the

If

voltage,harmonic

th theisIf

:THD

Voltage

, 1 2

2 ,

, 1 2

2 ,

1 2

, 1

2 ,

2

2 ,

3

2 ,

2

, 1 2

2 ,

n

n

n n

V

V

V THDv

V

V V

V

V

V THDv

n V

n b

n a

a v

f

d n v

f b

d n v

f a

d v f a

θ θ

θ

θ π

θ

θ π

θ π

πππ

=

+ +

sin

cos 2

1 ) (

Fourier Inverse

term) sin"

("

sin

) ( 1

term) cos"

("

cos

) ( 1

term) DC"

("

)

( 1

Series Fourier

1

2 0

2 0 2 0

πππ

πππ

πππ

θ θ

θ

θ π

θ θ

θ

θ π

θ

θ π

20

20

20

sin sin

0 cos

cos

0 1

d n

d n

V

b

d n

d n

V

a

d V d

V a

Harmonics of square wave (2)

π

π π

π π

π π

n n

V

n

n n

V

n n

n n

V

n

n n

odd, is

n

When

exist) not

do harmonics even

i.e.

(

0

1 cos

even, is

When

) cos

1 ( 2

) cos

1 ( ) cos

1

(

) cos

2 (cos )

cos 0

(cos

cos cos

Solving,

2 0

−

=

− +

Spectra of square wave

Normalised Fundamental

3rd (0.33)

5th (0.2) 7th (0.14)

9th (0.11)

11th (0.09) 1st

n

• Spectra (harmonics) characteristics:

– Harmonic decreases with a factor of (1/n)

– Even harmonics are absent

– Nearest harmonics is the 3rd If fundamental is 50Hz, then nearest harmonic is 150Hz

– Due to the small separation between the

fundamental an harmonics, output low-pass filter design can be very difficult

α π

α π

α π

α π

α π

α π

α π

α π

θ π

θ

θ

απα

n n

V

n n

n n

V b

n n

n n

n n

n n

n

n

n n

V

n n

V d

n V

b

a

dc

dc n

dc

dc dc

n

n

cos 1

cos

2

cos cos

cos 2

cos cos

sin sin

cos cos

cos cos

: Expanding

cos cos

2

cos

2 sin

1 2

symmetry) wave

half to

-(due

0 that

Harmonics control

( ) ( )

n

n

b

b Note

V

b

n n

V b

b

o

dc

dc n

n

o

3

1 1

90

: if eliminated be

will harmonic

general,

In waveform.

the from eliminated

is harmonic

third

or the ,

0 then

, 30 if

example

For

: n Eliminatio Harmonics

, adjusting

by controlled be

also can

Harmonics

by varying controlled

is , , l fundamenta

The

:

cos 4

: is l fundamenta the

of amplitude ,

particular

In

cos

4 odd,

is

n

If

, 0 even,

α π

harmonicszero

none

-first thre the

using

by THDi

the

a)and L 10mHin series. Calculate:

10RR

isloadThe

100V

isgelink voltaDC

Thesignals.full-bridgesinglephaseinverter is fed by square wave

A

=

α

S1 OFF S2 ON

t 0

G

• Also known as the “inverter leg”

• Basic building block for full bridge, three phase

and higher order inverters

• G is the “centre point”

• Both capacitors have the same value Thus the DC link is equally “spilt” into two

• The top and bottom switch has to be

“complementary”, i.e If the top switch is closed (on), the bottom must be off, and vice-versa

Shoot through fault and

“Dead-time”

• In practical, a dead time as shown below is required

to avoid “shoot-through” faults, i.e short circuit

across the DC rail

• Dead time creates “low frequency envelope” Low frequency harmonics emerged

• This is the main source of distortion for high-quality sine wave inverter

t d t d

"Dead time' = t

S1signal (gate)

S2signal (gate)

"Shoot through fault"

I short is very large

I short

π 2

π 2

V '

o

V

G R

G

R + V o - R'dc

V

+

Three phase inverter waveforms

1 3 2,4

2 3,5 4

3 5 4,6

4 1,5 6

5 1 2,6

6 1,3 2

Negative device(s) on

2VDC/3

VDC/3

-VDC/3 -2VDC/3

VDC

-VDC

VDC/2 -VDC/2

Quasi-square wave operation voltage waveforms

120 0

VDC/2

VDC/2 -VDC/2

Pulse Width Modulation (PWM)

Modulating Waveform Carrier waveform

• Triangulation method (Natural sampling)

– Amplitudes of the triangular wave (carrier) and sine wave (modulating) are compared to obtain PWM waveform Simple analogue comparator can be used

– Basically an analogue method Its digital

version, known as REGULAR sampling is

widely used in industry

– simplified version of natural sampling that

results in simple digital implementation

• Optimised PWM

– PWM waveform are constructed based on

certain performance criteria, e.g THD

• Harmonic elimination/minimisation PWM

– PWM waveforms are constructed to eliminate some undesirable harmonics from the output waveform spectra

– Highly mathematical in nature

• Space-vector modulation (SVM)

– A simple technique based on volt-second that is normally used with three-phase inverter motor-drive

Modulation Index, Ratio

waveform modulating

the of

Frequency

veform carrier wa

the of

Frequency M

) (

M Ratio)

(Frequency Ratio

Modulation

veform carrier wa

the of

Amplitude

waveform modulating

the of

Amplitude

M

: M Depth)

n (Modulatio Index

( )

(1,2,3 ) integer

an is

and

signal modulating

the of

frequency

the is where

M

: at located normally

are harmonics

The

spectra.

in the harmonics

of

(location) incident

the determines ratio

dulation

M

ly.

respective voltage,

(DC) input

and voltage

output the

of l fundamenta are

,

where

M

1, M

0

If

component l

fundamenta voltage

output the

s deterrmine Index

f

o

V V

V V

m m

in in

Asymmetric and symmetric

regular sampling

T

sample point

symmetric sampling

t

Generating of PWM waveform regular sampling

Bipolar PWM switching:

carrier waveform

modulating waveform

pulse kth

The k th Pulse

pulse PWM

kth The

Determination of switching angles

for kth PWM pulse (1)

2 2

1 1

second, -

volt the

Equating

p s

p s

A A

Similarly,

) sin(

sin 2

cos )

2 cos(

sin

sinusoid,

by the supplied

second -

volt

The

2 2

2

half, second

for the Similarly

2 2

2

: as given is

pulse PWM

the

of

cycle half

first the

during second

Volt

-The

2

2 1

2

2 2

2

1

1 1

1

o k

m o s

o k

o m

k o

k m

m s

o k

dc

k o

dc k

dc p

o k

dc

k o

dc k

dc p

V A

V

V d

V A

V

V

V A

δ α

δ

δ α

δ

α δ

α θ

θ

δ δ

δ δ

δ

δ δ

δ δ

δ

αδα

waveformPWM

the

of

cyclehalf

first for the

width pulse

the

Thus,

modulationas

known is

2

Ratio,Modulation

the,definition

By

sin(

2

)sin(

2

pulse,PWM

ofcyclehalf

first the

thederive

To

)sin(

2

)sin(

2

, sin

anglesmall

1 1

2

1

o k

I o

k

dc

m I

o k

o dc

m o

k

o k

m o o

m o s

o k

m o s

o o

o

M

) (V

V

M

V V

V V

V A

δα

δδ

δα

δδ

δ

δα

δδ

δ

δα

δ

δα

δ

δδ

δ

−+

PWM switching angles (4)

o k

k k

o k

I o

k

k k

M

M

α δ

δ

δ δ

δ

δ δ

δ

α

δ α

Hence

, Modulation Symmetric

For

different.

are and

i.e , Modulation

Asymmetric for

valid is

equation above

The

: angle edge

trailing the

And

) sin(

1

: waveform PWM

of cycle half

second

the of

width pulse

method, similar

Using

: is pulse kth

the

of angle switching

edge leading

the

Thus

k 2k

1k

2k 1k

=

−

t15 t16

t17 t18 2 π π

1

α

carrier waveform

modulating waveform

Harmonics of bipolar PWM

−+

k k

k k

k k

k k

o k

d n V

d n V

d n V

d n v

f b

dc dc dc

T nk

δ α

δ α

δ α

δ α

δ α

δ α

θ

θ π

θ

θ π

θ

θ π

θ

θ π

2

2 0

2

2 1 1

sin2

2

sin2

2

sin2

2

sin)(

12

:ascomputed

be

can

pulsePWM

(kth)

eachof

waveform

PWM the

n computatio the

shows slide

Next

: i.e.

period, one

over

pulses

for the of

sum isthe

waveform

PWM

for the coefficent

Fourier ly.The

productive

simplified be

cannot equation

This

2 cos cos

2

) 2 (

cos )

( cos 2

Yeilding,

) 2 (

cos )

( cos

) (

cos )

( cos

) (

cos )

2 (

cos

: to reduced be

can

Which

1

1 1

2

1 2

+

−

− +

k k

k k

dc nk

o k

k k

k k

k k

k k

o k

dc nk

b b

p b

n n

n

n n

V

b

n n

n n

n

n n

V b

δ α

α δ

α π

δ α

δ α

δ α

δ α

δ α

δ α

π

PWM Spectra

0 1

=

I

M

8 0

=

I

M

6 0

=

I

M

4 0

=

I

M

2 0

PWM spectra observations

• The harmonics appear in “clusters” at multiple of

the carrier frequencies

• Main harmonics located at :

• The amplitude of the harmonic changes with M I

Its incidence (location on spectra) is not

• When p>10, or so, the harmonics can be

normalised For lower values of p, the side-bands

clusters overlap-normalised results no longer apply

Tabulated Bipolar PWM Harmonics

Three-phase harmonics

• For three-phase inverters, there is significant

advantage if M R is chosen to be:

– Odd: All even harmonic will be eliminated

from the pole-switching waveform

– triplens (multiple of three (e.g 3,9,15,21, 27 ):All triplens harmonics will be eliminated from the line-to-line output voltage

• By observing the waveform, it can be seen that with odd M R, the line-to-line voltage shape looks more

“sinusoidal”

• As can be noted from the spectra, the phase voltage amplitude is 0.8 (normalised) This is because the modulation index is 0.8 The line voltage amplitude

is square root three of phase voltage due to the

three-phase relationship

Effect of odd and “triplens”

8 =

= M

p

6 0 ,

Spectra: effect of “triplens”

to (Line 8 0

Fundamental

41 43 39

23 19

61 59 57

65 67

69 7779

8183 8587

89 91

19 23 37 41 43 47 5961 6567 79 83 85 89

COMPARISON OF INVERTER PHASE VOLTAGE (A) & INVERTER LINE VOLTAGE

(B) HARMONIC (P=21, M=0.8)

A B

Harmonic Order

Comments on PWM scheme

• It is desirable to have M R as large as possible

• This will push the harmonic at higher frequencies

on the spectrum Thus filtering requirement is

reduced

• Although the voltage THD improvement is not

significant, but the current THD will improve

greatly because the load normally has some current filtering effect

• However, higher M R has side effects:

– Higher switching frequency: More losses.

– Pulse width may be too small to be constructed

“Pulse dropping” may be required.

is 1050Hz and the modulating frequency is 50Hz The modulation

index is 0.8 Calculate the harmonic amplitudes of the line-to-voltage (i.e red to blue phase) and complete the table.