PWM Methods

8/19/2019 PWM Methods

1/100

Switch-Mode DC-AC Inverter

Four quadrants of operation


2/100

The most widely used control technique in power

electronics


3/100


4/100

Basic principles of PWM

Similar response to diferent shape o impulseinput


5/100

Application o the equal-area theorem


6/100


7/100

The question then becomes how to change the duty

cycle with a sinusoidal rule. The ollowing gure

illustrates one o the methods, which is named as

sinusoidal P! "SP!#.


8/100

A list of PWM techniques

• Triangular-wa$e sampling

– %atural sampling

– &niorm sampling

• 'alculation

– 'alculation based on equal-area criterion

– Selecti$e harmonics elimination

• (ysteresis band control

• Space )ector !odulation "S)!, or S)P!#

• *andom P!


9/100

Some major PWM techniques

• Natural sampling

• Uniform sampling

• Selectie harmonics elimination

• Some practical issues – Synchronous modulation and asynchronous

modulation

– !armonics in the PWM inerter output oltages

– Ways to improe "# input oltage utili$ation andreduce switching frequency

– #onnection of multiple PWM inerters


10/100

Pulse%Width Modulated &S'

• PWM Methods

– Single Pulse-width !odulation

– !ultiple+&niorm Pulse idth !odulation

– sine P! "SP!#

– !odied sine P!

– (armonic limination Technique "S(#

– !inimum ripple current P!

– (ysteresis "ang-bang#

– Space )ector P!


11/100

Control circuit waveforms for a square wave PM inverter

a!Comparator input volta"es#

$!Comparator output volta"e and pole volta"e

mf ( f c )f o and p % mf &' % pulses&half c(cle

M' ( Am)Ac) MI is amplitude modulation inde*) Ac pea* carrier amplitude

and Am is pea* amplitude of modulatin" wave

here) mf is frequency modulation inde*) f c carrier freq#) and f o output freq#


12/100

+olta"e waveforms for a ,ph square wave PM inverter

a!)$!)c! comparator input volta"es

d!)e!)f! pole volta"es "! pole volta"es h! line to neutral volta"e#


13/100

+olta"e waveforms for a ,ph square wave PM inverter when the carrier

wave is shifted $( one quarter-c(cle #

a!)$!)c! comparator input volta"es

d!)e!)f! pole volta"es "! pole volta"es


14/100

.armonic content of the

square wave PM

volta"e as a function ofthe modulation inde/#

a!.armonic amplitude

relative to ma/imum

fundamental amplitude#

$!.armonic amplitude

relative to actual

fundamental amplitude#


15/100

In synchroni$ed PWM the frequency of the triangle signal is an integral multiple of

that of the reference signal # 0herefore) the "enerated PM si"nal is identical inever( c(cle of the reference si"nal# 0his ensures a sta$le volta"e output where the

trian"le si"nal has low frequencies in order to reduce the switchin" loss of the

power transistors#

Asynchronous PM doesn1t ensure the relation $etween the frequencies of $oth

si"nals# 0he method is simple $ut causes different volta"e forms in different c(cles#

.owever) if the trian"le frequenc( is much hi"her than the reference frequenc() thisinfluence is ne"li"i$le#


16/100

Triangular%wae natural sampling

&ni-polar P! in single-phase )S

&ni-polar sampling is used to reali/e uni-olar P!.


17/100

In symmetric PWM) the positie +or negatie, pulse of ever( PM c(cleis located in the middle of the c(cle period) while in the asymmetric PWM-

the pulses are usuall( aligned to the start or end of the PM c(cle#

Practicall() asymmetric methods are relativel( easier to realise) $ut

symmetric methods evo*e fewer harmonics# 0herefore) s(mmetric PM

should $e used when possi$le#

Symmetric and Asymmetric PWM


18/100


19/100

S(mmetric and As(mmetric PM


20/100

Dead time

0he insertion of the dead time in ever( PM c(cle distorts the output volta"es#

In accurate motor control) this ne"ative effect will $e compensated $(

prolon"in" some of the pulses#


21/100


22/100


23/100


24/100

Triangular%wae uniform sampling

asier toreali/e by

computercontrol!odulationactor


25/100

i-polar sampling is usedto reali/e bi-polar P!.

i-polar P! in single-phase )S


26/100


27/100


28/100


29/100

'n .%phase &S'

Three-phasebridge in$erter

can only reali/e bi-polar P!thereore shouldbe controlledby bipolarsampling.


30/100

Ways to improe utili$ation of "# input oltage

and reduce switching frequency

2se trape3oidal waveform as modulatin" si"nal instead of sinusoidal


31/100

&se 01 order harmonics biasin the modulating signal

4eference si"nal of third-harmonic PM


32/100

Concept of si/t(-de"ree PM

Si*ty%degree PWM

The sixty-degree PWM is an extension of third-harmonic PWM. It

is also implemented in the same manner as SPWM. It is based

on the consideration that not only third harmonic b!t also allnon-e"en triplen harmonics are #ltered o!t by the delta

connected motor $indings. Adding all these harmonics $ith the

f!ndamental together a f!nction $ith %at segments is obtained

as sho$n in the #g!re. The period of the %at part co"ers &'(

signal phase

The modulation inde* of this method also reaches /0


33/100

P!rpose)– *xpand o!tp!t po$er rating– +ed!ce harmonics

'onnection o multiple P!in$erters


34/100

PWM techniques with feed1ac2 control

• Current h(steresis control

• +olta"e h(steresis control

• 0rian"ular-wave comparison 5samplin"!with feed$ac* control


35/100

Si*%Step three%phase &oltage Source 'nerter

3ig0 / Three%phase oltage source inerter0

'0 &oltage Source 'nerter +&S',A0 Si*%Step &S'


36/100

4ating signals- switching sequence and line to negatie oltages

3ig0 5 Waeforms of gating signals- switching sequence- line to negatie oltages

for si*%step oltage source inerter0

'0 &oltage Source 'nerter +&S',

A0 Si*%Step &S'


37/100

&oltage Source 'nerter +&S', Si*%Step &S' /677 operation

• Switching Sequence8

• 9:/ +&/, → :/5 +&5, → /5. +&., → 5.; +&;, → .;9 +&9, → ;9: +&:, → 9:/ +&/,

where- 9:/ means that S9- S: and S/ are switched on

3ig0 . Si* inerter oltage ectors for si*%step oltage source inerter0


38/100

,-ph 6rid"e

Inverter outputvolta"e waves

in square wave

5or Si/ Step!

mode


39/100


A0 Si*%Step &S'


40/100


A0 Si*%Step &S'

dcdcdc V78.0V

6

2

V4

2

3) ≈==

π π

(rms)(V 1ab

Amplitude of line to line oltages +&a1- &1c- &ca, 3undamental 3requency #omponent +&a1,/

!armonic 3requency #omponents +&a1,h

8 amplitudes of harmonics decrease inersely proportional to

their harmonic order

3,.....)2,1,(n16nhwhere,

V78.0

dcab

=±=

=h

(rms))(V h


41/100


>1jectie of PWM #ontrol of inerter output oltage

?eduction of harmonics

"isadantages of PWM

'ncrease of switching losses due to high PWM frequency

?eduction of aaila1le oltage

@M' pro1lems due to high%order harmonics


42/100

Pulse%Width Modulation +PWM,

3ig0 9 Sinusoidal Pulse%width modulation0


43/100


'nerter output oltage

When control tri- &A7 ( &dc )5

When control tri- &A7 ( %&dc )5

#ontrol of inerter output oltage

PWM frequency is the same as the frequency of tri

Amplitude is controlled 1y the pea2 alue of control

3undamental frequency is controlled 1y the frequency of

control Modulation 'nde* +m,

A01A0

10

Vof componentfrequecnyfundamenta!)(Vwhere,

,2"

)(

dc

A

tri

control

V

V of peak

v

vm ==


44/100

PWM M@T!>"S Sine PWM

Amplitude modulation ratio +ma,

A01A0

10

Vof componentfrequecnyfundamenta!)(Vwhere,

,2"

)(dc

A

tri

control a

V V of value peak

vof amplitudevof amplitude peak m ==∴

3requency modulation ratio)inde* +mf ,

frequencyfundamentaf andfrequency#$%f where,, 1&1

=== f

f m s f

mf should 1e an odd integer

if mf is not an integer- there may e*ist su1hamonics at output oltage if mf is not odd- "# component may e*ist and een harmonics are

present at output oltage

mf should 1e a multiple of . for three%phase PWM inerter

An odd multiple of . and een harmonics are

suppressed

PWM M@T!>"S


45/100

PWM M@T!>"SSine PWM

Three%phase inerter

3ig0 : Three%phase Sine PWM inerter0


46/100


47/100


48/100

P! !T(23S i P!


49/100

P! !T(23S sine P!

V A

0

V

B 0

V C 0

V A

B

V B C

V C A

t

3ig0 C Waeforms of three%phase sine PWM inerter0

tri controlDA controlDB controlD#

Three%phase sine PWM waeforms

3requency of tri and control

3requency of tri ( f s

3requency of control ( f /

where- f s ( PWM frequency f / ( 3undamental frequency

'nerter output oltage

When control tri- &A7 ( &dc )5

When control tri- &A7 ( %&dc )5

where) &AB ( &A7 E &B7

&B# ( &B7 E

A ( E &A7


50/100

V

A

0

V B 0

V C 0

V A

B

V B C

V C A

t


51/100


52/100

PWM M@T!>"S Modified sine PWM

Improves short comin"s of sine PM techniques) while

retainin" its merits#

For 7 connected load +an % +d&' and +an8% '+d&9 % #:,:+d

Correspondin" fundamental rms line to line volta"es are

+a$8 % ;#:8+d for SPM technique and ;#ection sine PM technique


53/100

?ffect of 6lan*in"

0ime

• 4esults in nonlinearit(


54/100

?ffect of 6lan*in" 0ime

• +olta"e >ump when the current reverses direction


55/100

?ffect of 6lan*in" 0ime

• ?ffect on the output volta"e

Pro"rammed .armonic ?limination 5S.?!


56/100

" 5 !

An"les $ased on the desired output

9th and Cth harmonic elimination


57/100


58/100

• 0he "eneral fourier seriesof the wave is "iven as

• here)

• For quarter c(cles(mmetr(

∑∞

=+=

1

)&'nco&()(n

nn t nbt nat v ω ω

t d t nt vb

t d t nt va

n

n

ω ω

π

ω ω π

π

π

∫

∫

=

=

2

0

2

0

&'n)(1

co&)(1

∫ = π

ω ω

π

2

0 &'n)(

40 t d t nt vband a nn

Assumin" that the wave has unit amplitude i#e# +t, ( F /)

1n can $e e/panded as

4


59/100

t d t nt d t nt d t nbn ω ω ω ω ω ω π

α

α

α

α

α

∫ ∫ ∫ −+−++= 32

2

1

1 &'n)1(&'n)1(&'n)1(4

0

&'n)1(&'n)1(....2"

1

1

t d t nt d t nk

k

k

k ω ω ω ω

π

α

α

α ∫ ∫ ++−++ −−

)co&(co&1

&'n 212

1

θ θ ω ω θ

θ nnn

t d t n −=∫ 2sin" the relation

8st and the last terms

are

∫ −=+1

0 1)co&1(

1&'n)1(

α

α ω ω nn

t d t n

k n

nt d t n

k

α ω ω π

α co&1&'n)1(2"∫ =+

Inte"ratin" the other components of the a$ove ?qn and su$stitutin"

∑=

−+=

+−+−+=

k

k k

k

k n

nn

nnnn

b

1

21

co&)1(21(4

)co&.......co&co&(214

α

π

α α α

π

A$ove eqn has * varia$les and needs * simultaneous eqns to solve their

values

?/ample@ Sa( we need to eliminate th B


60/100

?/ample@ Sa() we need to eliminate th B


61/100

Programmed

!armonic

@limination

Method

An"les $ased on

the desired output


62/100


63/100

+s 8 ' ,

, ; 8#E ''#;,

E ; 8:#8< '8#:

; 8:#E8 ';#=:

: ; 8:#== ';#,

< ; 8


64/100

S.? t(pical waveform at = output


65/100


66/100

Minimum ?ipple #urrent PWM

∑∞

=

∧

∧∧∧

=

+++=

+++=

11,7,*

2

211

27

2*

211

27

2*

)(2

1

...222

...

n

n

ripple

Ln

V

I I I

I I I I

ω

here) I) I< G#% rms harmonic currents

H is the effective lea*a"e inductance of the machine per phase

n % order of harmonics and % fundamental frequenc(

current&harmon'cof +aue pea ......,, 7* =∧∧ I I

0he harmonic loss in a m&c isdictated $( the rms ripple

current) therefore) rms ripple

current should $e minimi3ed

instead of individualharmonics# 0he rms ripple

current in a m&c is "iven $( @


67/100


68/100

!ysteresis +Bang%1ang, PWM

Three%phase inerter for hysteresis #urrent #ontrol

Three%phase inerter for hysteresis current control0

!ysteresis +Bang%1ang, PWM


69/100

y + g g,

!ysteresis #urrent #ontroller

!ysteresis current controller at Phase HaI0

Tolerance%Band #urrent #ontrol


70/100

4esults in a varia$le frequenc( operation


71/100

Current

control

6loc*Dia"ram

B0 !ysteresis +Bang%1ang, PWM


72/100

#haracteristics of hysteresis #urrent #ontrol

Adantages @*cellent dynamic response


73/100

Space &ector Modulation

• PM can $e "enerated $( analo"ue or di"ital control

techniques#

The adantages of digital control oer analogue are8

• Sta$ilit( 5no drift) offsets or a"in" effects!

• Precision 5noise immunit(!

• Fle/i$ilit( 5can $e customi3ed $( chan"in" software!

?ven if done di"itall() si"nificant computin" time is required)

as the PM si"nals have to $e calculated in real time# 6(usin" Space +ector Modulation this calculation process is

simplified# As it is simplified) less computin" time is required)

and therefore $etter performance can $e o$tained#

Space &ector PWM


74/100

>utput oltages of three%phase inerter

where- upper transistors8 S/- S.- S9 lower transistors8 S;- S:- S5

switching aria1le ector8 a- 1- c

Three%phase power inerter0


75/100

, Phase +olta"e Source Inverter 5+SI!


76/100

Sinusoidal Pulse WidthModulation +SPWM,

Space &ector Modulation+S&M,

Comparin" hi"h frequenc(trian"ular carrier si"nal with ,sinusoidal reference si"nals5treated as separate identit(!

0a*in" all , modulatin" si"nalsinto account simultaneousl( withina 'D reference frame 5in d-q a/isor comple/ form!

Availa$le DC suppl( volta"e notfull( utili3ed

Increased utili3ation of DC suppl(volta"e) 8 more than SPM

More 0otal .armonic Distortion Hess 0otal .armonic Distortion

Does not facilitate advancedvector control implementation

?na$les advanced vector controlimplementation

Comparison $etween SPM and S+M


77/100

,-ph 6rid"e

Inverter output

volta"e waves

in square wave

5or Si/ Step!

mode



78/100


A0 Si*%Step &S'


79/100


S8

throu"h S:

are the si/ power transistors that shape the output volta"e

hen an upper switch is turned on 5i#e#) a) $ or c is J8K!) the

correspondin" lower switch is turned off 5i#e#) aL) $L or cL is J;K!

@ight possi1le com1inations of on and off patterns for the three upper

transistors +S/- S.- S9,


80/100


The eight inerter oltage ectors +&7 to &C,

Space &ector PWM


81/100


0he ei"ht com$inations) phase volta"es and output line to line volta"es

Space &ector PWM


82/100

Basic switching ectors and sectors0

Basic switching ectors and Sectors

: actie ectors +&/-&

5- &

.- &

;- &

9- &

:,

A*es of a he*agonal

"# lin2 oltage is supplied to

the load

@ach sector +/ to :,8 :7 degrees

5 $ero ectors +&7- &C,

At origin

No oltage is supplied to the

load

Space &ector PWM


83/100

#omparison of Sine PWM and Space &ector PWM +5,

Space &ector PWM generates less harmonic distortion

in the output oltage or currents in comparison with sine PWM

Space &ector PWM proides more efficient use of supply

oltage in comparison with sine PWM

Sine PWM 8


84/100

#omparison of Sine PWM and Space &ector PWM


85/100


86/100

raphs of , modulatin" volta"es where reference volta"e is shifted

from one sector to another

Space &ector PWM


87/100

−

−−=

∴

cn

bn

an

q

d

V

V

V

2

3

2

30

2

1

2

11

3

2

V

V

&oltage Space &ector and its

components in +d- q,0

cn bnan

cn bnq

cn bnan

cn bnand

V2

3V

2

3V

co&30Vco&30V0V

V2

1V2

1V

co&60Vco&60VVV

−+=

⋅−⋅+=

−−=

⋅−⋅−= Step /0 "etermine &d- &q- &ref - and angle + ,

#oordinate transformation8 a1c to dq

frequency)fundamentaf (where,

f 2t/)V

V(tan

VVV

&

&&

d

q1

2

q

2

dref

=

===

+=

− t π

Space &ector PWM


88/100

?eference ector as a com1ination of adjacent ectors at sector /0

Step 50 "etermine time duration T/- T5- T7

Space &ector PWM

Step 5 "etermine time duration T T T


89/100

Switching time duration at Sector /

)600(where,)3"(&'n

)3"(co&V

3

2

0

1V

3

2

)(&'n

)(co&V

)VV(V

VdtVdtVV

dc2dc1ref

2211ref

0

1

2

0

0

1ref

21

21 1

°≤≤

⋅⋅⋅+

⋅⋅⋅=

⋅⋅⇒

⋅+⋅=⋅∴

++= ∫ ∫ ∫ ∫ +

+

π

π

α

α

Step 50 "etermine time duration T/- T5- T7

==+−=∴

⋅⋅=∴

−⋅⋅=∴

dc

ref

&210

2

1

V3

2

Vaand

f

1where,),(

)3"(&'n

)(&'n

)3"(&'n

)3"(&'n

T T T T

aT T

aT T

z

z

z

π

α

π

α π


90/100


91/100

Al"orithms of S+M


92/100

Al"orithms of output si"nals $ased on sector 8


93/100

Nutput si"nal $ased on S(mmetrical Sequence al"orithm in sector 8

Space &ector PWM

1 d t i l


94/100

Space &ector PWM switching patterns at each sector0

+a, Sector /0 +1, Sector 50

Step .0 "etermine the switching time of each transistor +S/ to S:, +/,

1ased on symmetrical sequence

Space &ector PWM


95/100


+c, Sector .0 +d, Sector ;0

Step .0 "etermine the switching time of each transistor +S/ to S:, +5,

Space &ector PWM


96/100

Space &ector PWM


+e, Sector 90 +f, Sector :0

Step .0 "etermine the switching time of each transistor +S/ to S:, +.,


97/100


98/100

• '2!PA*S2% 24 SP!-S)!-S(-( P! T'(%5&S


99/100

• SHE

• , A++I*+ /AS* - ,!mber f ,otches 0etermine S$itching1re2!ency

• 0I11I34T T APP45 AT 4W 1+*63*,5• 3TP3T MA5 ,T /* 7A+M,IA445 PTIM3M

• MST 3S*134 W7*, SP*I1I +0*+ 1 7A+M,IS A+*7A+M134

• *AS5 4I,*A+I8ATI, I, W74* M034ATI, +A,9*

• 0 4I,: ;4TA9* +IPP4* I,T+03*S A00ITI,A4 3TP3T

+IPP4*• MI+MP3T*+


100/100

O8 Q# Mohan) # P# 4o$$in) and 0# 2ndeland) Power Electronics: Converters, Applications, and Design) 'nd ed# Qew 7or*@ ile() 8#

O' 6# R# 6ose) Power Electronics and Variable requency Drives:!echnology

and Applications# I??? Press) 8

PWM Methods

Documents

Transcript of PWM Methods