Pulse-Width Modulation (PWM) Techniques

Mohammed Salah Yousef

• To control inverter output frequency (fundamental)

• To control inverter output voltage (fundamental)• To minimize harmonic distortion

Why Use PWM Techniques?

Objective of PWM

Disadvantages of PWM

Increase of switching losses due to high PWM frequency

Reduction of available voltage

EMI problems due to high-order harmonics

Control of inverter output voltage

Reduction of harmonics

Basic principles of PWM

-Application of the equal-area theoremThis is sinusoidal

PWM (SPWM)-The equal-area

theorem can be appliedto realize any shape of

waveforms

Pulse-Width Modulation (PWM)

Fig. Pulse-width modulation.

Inverter output voltage

When vcontrol > vtri, VA0 = Vdc/2

When vcontrol < vtri, VA0 = -Vdc/2

A01A0

10

Vofcomponentfrequecnylfundamenta:)(Vwhere,

,2/

)(

dc

A

tri

control

V

Vofpeak

v

vm

Modulation Index (m)

Control of inverter output voltage

Amplitude is controlled by the peak value of vcontrol

Fundamental frequency is controlled by the frequency of vcontrol

PWM frequency is the same as the frequency of vtri

II. PWM METHODSA. Sine PWM (1)

Fig. Three-phase Sine PWM inverter.

Three-phase inverterTwo Level Voltage Source Inverter

• Inverter Configuration

Assumption:

dc capacitor very large dc voltage ripple free

dC

1S

2S

3S 5S

4S 6S

A

B

C

P

N

LOAD

Ai

OBi

CidV

• Modulating and Carrier Waves

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

cr

ma V

Vm

ˆ

ˆ

• Frequency modulation index

m

crf f

fm

0

v mAv Bmv Cmvcrv

crV̂ mV̂t

• vm – Modulating wave (sine)

• 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

• Line-to-Line Voltage vAB

ABv

BNv

ANv

0

0

0

v mAv Bmv Cmvcrv

crV̂ mV̂

dV

dV

dV

2t

t

t

t

1ABv

1S

2S

3S 5S

4S 6S

B

C

P

N

dV

A

VA

0V

B0

VC

0V

AB

VB

CV

CA

t

Fig. Waveforms of three-phase sine PWM inverter.

Three-phase sine PWM waveforms

where, VAB = VA0 – VB0

VBC = VB0 – VC0

VCA = VC0 – VA0

When vcontrol > vtri, VA0 = Vdc/2

When vcontrol < vtri, VA0 = -Vdc/2

Frequency of vtri = fs

Frequency of vcontrol = f1

Frequency of vtri and vcontrol

where, fs = PWM frequency

f1 = Fundamental frequency

Inverter output voltage

Amplitude modulation ratio (ma)

A01A0

10

Vofcomponentfrequecnylfundamenta:)(Vwhere,

,2/

)(

dc

A

tri

controla V

Vofvaluepeak

vofamplitude

vofamplitudepeakm

Frequency modulation ratio (mf)

frequencylfundamentafandfrequencyPWMfwhere,, 1s1

f

fm sf

mf should be an odd integer

if mf is not an integer, there may exist sunhamonics 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