PWM Inverters - nitc.ac.in Dr. Rijil Ramachand/02_PWM... · 8 Characteristics of Six-stepVSI It is...

PWM Inverters

Rijil RamchandAssociate Professor

NIT Calicut

Inverters

Classifications

Single phase & three phase

Voltage Source & Current source

Two-level & Multi-level

5/15/2015 2PEGCRES 2015

Voltage Source Inverter

Sinusoidal PWM

Space vector modulation

Topics

To control inverter output frequency (fundamental)

To control inverter output voltage (fundamental)

To minimize harmonic distortion

Why Use PWM Techniques?

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Open loop voltage control

Closed loop current-control

VSIAC

motorPWMiref

if/back

VSI AC

motorPWMvref

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Inverter Configuration

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4

Voltage Source Inverter (VSI)Six-Step VSI

Waveforms of gating signals, switching sequence, line to negative

voltages for six-step voltage source inverter.

Gating signals, switching sequence and line to negative voltages

where, 561 means that S5, S6 and S1 are switched on

Six inverter voltage vectors for six-step voltage source inverter.

Switching Sequence:

561 (V1) 612 (V2) 123 (V3) 234 (V4) 345 (V5) 456 (V6) 561 (V1)

5


5/15/2015 7PEGCRES 2015

Waveforms of line to neutral (phase) voltages and line to line voltages

for six-step voltage source inverter.

Line to line voltages (Vab, Vbc, Vca) and line to neutral voltages (Van, Vbn, Vcn)

Vab = VaN -VbN

Vbc = VbN -VcN

Vca = VcN -VaN

Line to line voltages

Van = 2/3VaN - 1/3VbN - 1/3VcN

Phase voltages

Vbn = -1/3VaN + 2/3VbN - 1/3VcN

Vcn = -1/3VaN - 1/3VbN + 2/3VcN

6


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Harmonic spectrum of a square wave

Voltage Source Inverter (VSI)

Six-Step VSI

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Amplitude of line to line voltages (Vab, Vbc, Vca)

Fundamental Frequency Component (Vab)1

Harmonic Frequency Components (Vab)h

: amplitudes of harmonics decrease inversely proportional to their harmonic order

dcdcdc V78.0V

6

2

V4

2

3

(rms))(V 1ab

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

V78.0

dcab

h

(rms))(V h

7


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8

Characteristics of Six-stepVSI

It is called“six-step inverter” because of the presence of six“steps”

in the line to neutral (phase) voltage waveform

Harmonics of order three and multiples of three are absent

from both the line to line and the line to neutral voltages and

consequently absent from the currents

Output amplitude in a three-phase inverter can be controlled

by only change of DC-link voltage (Vdc)


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Sinusoidal PWM

Modulating and Carrier Waves

• vcr – Carrier wave (triangle) • Amplitude modulation index

cr

m

aV

Vm

ˆ

ˆ

• Frequency modulation index

m

cr

ff

fm

0

v mAv BmvCmvcrv

crV̂ mV̂

t

• vm – Modulating wave (sine)

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Sinusoidal PWM

mf should be an odd integer

if mf is not an integer, there may exist sub-hamonics at

output voltage

if mf is not odd, DC component may exist and even

harmonics are present at output voltage

mf should be a multiple of 3 for three-phase PWM inverter

An odd multiple of 3 and even harmonics are suppressed

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Sinusoidal PWM

Gate Signal Generation

1gv

4gv

dV

0

ANv

2

mAv crv

0

crmA vv 01 gv )0( 4 gv 1S on )off( 4S dAN Vv

Phase A crmA vv 04 gv )0( 1 gv

4S on )off( 1S 0ANv

Vg1 and Vg4 are complementary 5/15/2015 14PEGCRES 2015

Sinusoidal PWM

Line-to-Line Voltage vAB

ABv

BNv

ANv

0

0

0

v mAv BmvCmvcrv

crV̂ mV̂

dV

dV

dV

2t

t

t

t

1ABv

1S

2S

3S 5S

4S 6S

B

C

P

N

dV

A

5/15/2015 15PEGCRES 2015

Sinusoidal PWM

Waveforms and FFT

ma = 0.8, mf = 15,

fm = 60Hz, fcr = 900Hz

Switching frequency

fsw = fcr = 900Hz

0.1

0.2

0

0

0

THD = 92.07%

THD = 92.07%

THD = 7.73%

THD = 92.07%

dV

3/2 dV

ABv

AOv

Ai

2fm

12 fm

23 fm 14 fm

n

3

32

2

0

1 5 10 15 20 25 30 35 40 45 50 55 60

dVVAB 49.01

dn VVAB /

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Sinusoidal PWM

Over-Modulation

Fundamental voltage ↑

Low-order harmonics ↑

0

0.1

0.2

0dV

2 3

0

1

2

-1

-2

mAvmCvmBv

crv

ABv

n

0

Ai

2 3

dVVAB 744.01

dn VVAB /

n1 5 10 15 20 25 30 35 40 45 50 55 605/15/2015 17PEGCRES 2015

Sinusoidal PWM

(a)

c c m1 AO DC

c m2 c c AO DC

c c m c c m DCAO c

c c c

DC m

c

T V v (t)S ON period = 2 V is V 2

2 2Vc

V v (t)S ON period = T T V is V 2

2Vc

T T v (t) T T v (t) V1V average for a period T + +

T 2 2V 2 2V 2

V v (t)..........(5)

2 V

5/15/2015 18PEGCRES 2015

Space Vector Modulation

Switching States (Three-Phase)

Eight switching states

1S

2S

3S 5S

4S 6S

B

C

P

N

dV

A

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Space Vector Diagram

a1Vr

0Vr

3Vr

2Vr

4Vr

5Vr

6Vr

bj

POO

PPOOPO

OPP

OOP POP

refVr

q

OOOPPP

SECTOR ISECTOR III

SECTOR IV SECTOR VI

SECTOR V

SECTORII

Active vectors: to

(stationary, not rotating)

Zero vector:

1Vr

6Vr

0Vr

Six sectors: I to VI

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Space Vectors

Three-phase voltages

0)()()( tvtvtvCOBOAO

Two-phase voltages

)(

)(

)(

3

4sin

3

2sin0sin

3

4cos

3

2cos0cos

3

2

)(

)(

tv

tv

tv

tv

tv

CO

BO

AO

b

a

Space vector representation

)()()( tvjtvtVba

r

(2) (3)

3/43/20 )()()(3

2)( j

CO

j

BO

j

AOetvetvetvtV

r

where xjxe jx sincos

(3)

(1)

(2)

(4)

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Space Vectors (Example)

Switching state [POO] S1, S6 and S2 ON

dCOdBOdAOVtvVtvVtv

3

1)(,

3

1)(,

3

2)(

(5) (4)

0

13

2 j

deVV

r

3)1(

3

2

kj

dkeVV

r

.6...,,2,1k

a1Vr

0Vr

3Vr

2Vr

4Vr

5Vr

6Vr

bj

POO

PPOOPO

OPP

OOP POP

refVr

q

OOOPPP

SECTOR ISECTOR III

SECTOR IV SECTOR VI

SECTOR V

SECTORII

5/15/2015 22PEGCRES 2015


Active and Zero Vectors

Space Vector Switching State

(Three Phases) On-state Switch

Vector

Definition

[PPP] 531 ,, SSS Zero

Vector 0Vr

[OOO] 264 ,, SSS

00 Vr

1Vr

[POO] 261 ,, SSS 0

13

2 jd eVV

r

2Vr

[PPO] 231 ,, SSS 32

3

2

j

d eVVr

3Vr

[OPO] 234 ,, SSS 3

2

33

2

j

d eVVr

4Vr

[OPP] 534 ,, SSS 3

3

43

2

j

d eVVr

5Vr

[OOP] 564 ,, SSS 3

4

53

2

j

d eVVr

Active

Vector

6Vr

[POP] 561 ,, SSS 3

5

63

2

j

d eVVr

Active Vector: 6

Zero Vector: 1

Redundant switching

states: [PPP] and [OOO]

1S

2S

3S 5S

4S 6S

B

C

P

N

dV

A

5/15/2015 23PEGCRES 2015


(8)

Reference Vector Vref

Definition

a1Vr

0Vr

3Vr

2Vr

4Vr

5Vr

6Vr

bj

POO

PPOOPO

OPP

OOP POP

refVr

q

OOOPPP

SECTOR ISECTOR III

SECTOR IV SECTOR VI

SECTOR V

SECTORII

Angular displacement

t

dtt0

)( q (9)

qjrefref eVV

r

Rotating in space at ω

f 2

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Relationship Between Vref and VAB

Vref is approximated by two active

and zero vectors

Vref rotates one revolution,

VAB completes one cycle

Length of Vref corresponds to

magnitude of VAB

1Vr

2Vr

refVr

q

1VT

T

s

ar

2VT

T

s

br

SECTOR I

Q

5/15/2015 25PEGCRES 2015


Dwell Time Calculation

Volt-Second Balancing

0

0021

TTTT

TVTVTVTV

bas

basref

rrrr

(10)

Ta, Tb and T0 – dwell times for and ,21

VVrr

0Vr

Ts – sampling period

Space vectors

00V

r, and

(11) (10)

bdsref

bdadsref

TVTV

TVTVTV

3

1)(sin

3

1

3

2)(cos

q

q

:Im

:Re

(11)

(12)

1Vr

2Vr

refVr

q

1VT

T

s

ar

2VT

T

s

br

SECTOR I

Q

d

j

refrefVVeVV

3

2,

1

rrq 3

23

2 j

deVV

r

5/15/2015 26PEGCRES 2015


Dwell Times

Solve (12)

bas

d

refs

b

d

refs

a

TTTT

V

VTT

V

VTT

0

sin3

)3

(sin3

q

q

3/0 q (13)

5/15/2015 27PEGCRES 2015


Vref Location versus Dwell Times

refVr

Location 0q 6

0

q 6

q

36

q

3

q

Dwell Times 0

0

b

a

T

T ba TT ba TT ba TT

0

0

b

a

T

T

1Vr

2Vr

refVr

q

1VT

T

s

ar

2VT

T

s

br

SECTOR I

Q

5/15/2015 28PEGCRES 2015


Modulation Index

cbs

asb

asa

TTTT

mTT

mTT

0

sin

)3

(sin

q

q

(15)

d

ref

aV

Vm

3 (16)

5/15/2015 29PEGCRES 2015


Modulation Range

Vref,max

32

3

3

2max,

d

dref

VVV (17)

a1Vr

0Vr

3Vr

2Vr

4Vr

5Vr

6Vr

bj

POO

PPOOPO

OPP

OOP POP

refVr

q

OOOPPP

SECTOR ISECTOR III

SECTOR IV SECTOR VI

SECTOR V

SECTORII

(17) (16)

ma,max = 1

Modulation range: 0 ma 1 (18)5/15/2015 30PEGCRES 2015


Simulated Waveforms

ABv

AOv

0

0

0

Ai

dV

3/2 dV

2 3

2 3

VIVI

Sector

III

IIIIV

V

III

IIIIV

V

f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms5/15/2015 31PEGCRES 2015


Waveforms and FFT

0

0.1

0.2

n

0

0

ABv

AOv

Ai

THD =80.2%

THD =80.2%

THD =8.37%

THD =80.2%

dV

3/2 dV

2

dVVAB 566.01

1 5 10 15 20 25 30 35 40 45 50 55 60

dn VVAB /

02 3

5/15/2015 32PEGCRES 2015

SVPWM – Modified SinePWM

5/15/2015 PEGCRES 2015 33


5/15/2015 PEGCRES 2015 34


5/15/2015 PEGCRES 2015 35

PWM Inverters - nitc.ac.in Dr. Rijil Ramachand/02_PWM... · 8 Characteristics of Six-stepVSI It is...

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