1

AC-to-DC PWM Converters

Week 4

What is it?

• Output signal alternates between on and off within specified period

• Controls power received by a device

• The voltage seen by the load is directly proportional to the source voltage

2

PWMPULSE WIDTH MODULATION

3

Switching pattern of a hypothetical four-state

PWM converter

STATE: 0 2 3 2 0

0 5 0 9 0 1 10 1 50 2 00

t s( )

t s( )

x 1

x 2

4

Stator of a three-phase electric ac machine

A

A'

B

B '

C

i A

i A

i B

i B

C'i C

i C

d

q

5

Generation of a space vector of the stator MMFs in a three-phase electric ac machine: (a) phasor diagram of stator currents, (b) vectors of MMFs

s

(b)(a)

A

A '

B

B '

C

C '

C

A

B

^I A

^I B

^IC

Re

Im

jq

d

6

MMFMagnetomotive force is a quantity appearing in the equation for the magnetic flux in a magnetic circuit, sometimes known as Hopkinson's law:

where Φ is the magnetic flux and R is the reluctance of the circuit. Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is analogous to resistance in an electrical circuit, but rather than dissipating electric energy it stores magnetic energy

7

Magnetic flux in a magnetic circuit

1. ℱ = NI where N is the number of turns in the coil and I is the electric current through the circuit

2. ℱ = ΦR where Φ is the magnetic flux and R is the reluctance

3. ℱ = HL where H is the magnetizing force (the strength of the magnetizing field) andL is the mean length of a solenoid or the circumference of a toroid

8

Space vector of stator MMFs and its components

d

jq

j qs

ds

s

s

s

9

Introduction and definitions Types of PWM Methods of generation Characteristics of PWM Applications and examples

Definitions

• Duty Cycle: on-time / period• Vlow is often zero

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LOWHIAVG VDDVV )1(

Types of Pulse Width

• Pulse center fixed, edges modulated

• Leading edge fixed, tailing edge modulated

• Tailing edge fixed, leading edge modulated

• Pulse Width constant, period modulated

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Types of Pulse Width

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Analog PWM signals can be made by combining a saw- tooth waveform and a sinusoid

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PWM output is formed by the intersection of the saw-tooth wave and sinusoid

Analog Generation of PWM

Digital Methods of Generating PWM

• Digital: Counter used to handle transition

• Delta : used to find the PWM at a certain limit

• Delta Sigma: used to find the PWM but has advantage of reducing optimization noise

14

Applications to DC Motors

17

• The voltage supplied to a DC motor is proportional to the duty cycle

• Both brushed and brushless motors can be used with PWM

• Both analog and digital control techniques and components are available

Three Phase AC motors with PWM

• 3 different AC currents at different phases• Phase: 120 degrees apart

• Creates constant power transfer• Rotating magnetic field• Pulses substitute for AC current

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Space Vector Modulation

• Used for three-phase AC motors• Convert DC current to AC current• Gates turned on/off at different

intervals• 3 PWM created

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Motor Control Diagrams

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• Average value proportional to duty cycle, D

• Low power used in transistors used to switch the signal

• Fast switching possible due to MOSFETS and power transistors at speeds in excess of 100 kHz

• Digital signal is resistant to noise

• Less heat dissipated versus using resistors for intermediate voltage values

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Advantages of PWM

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• Cost• Complexity of circuit• Radio Frequency Interference• Voltage spikes • Electromagnetic noise

Disadvantages of PWM

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• Introduction and definitions• Types of PWM • Methods of generation• Characteristics of PWM• Applications and examples

• In the past, motors were controlled at intermediate speed by using resistors to lower delivered power

• Electric stove heater• Lamp dimmers• Voltage regulation – convert 12 volts to

5 volts by having a 41.7% duty cycle• Sound production: PWM controlled

signals give sound effects similar to a chorus

• Power transfer: PWM used to reduce the total power given to a load without relying on resistive losses

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Applications of PWM

• Commonly used in toys• Lowpass filter smooths out transients

from harmonic effects• Frequency values of harmonics doesn’t

change, but the amplitude does, which adjusts the analog output signal

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PWM used with D/A conversion

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• Clock signal is found “inside” PWM signal

• More resistant to noise effects than binary data alone

• Effective at data transmission over long distance transmission lines

PWM used to transmit data in telecommunications

1. Must be at least 10 times higher than the control system frequency

2. Higher than 20kHz – audible frequency of sounds to avoid annoying sound disturbances, caused by magnetostriction

3. If too low the motor is pulsed, not continuous, because the motor’s inductance can not maintain the current

4. Inverse of frequency should be much less than the motor/load time constant

5. Higher error from ripple voltages

Frequency of the PWM Signal

Upper LimitsLower Limits

1. If too high the inductance of the motor causes the current drawn to be unstable

2. MOSFET transistor generates heat during switching

3. Limited by resolution of controller

4. Eddy currents generated in electromagnetic coils which lead to adverse heating

5. Heat losses in electromagnetic materials is proportional to frequency squared

10/29/2009 28

29

Single-phase PWM rectifier with an LC input filter

L

C

f

f

i i,1

i i

i i,h

voPW M RECTIFIER

Potentiometer is used to adjust the duty cycle

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Example: PWM with 555 Timer

1.Maxon EC-16 brushless motor, Time constant = 8.75 ms2. Want to avoid audible frequencies

f ≥ 20 kHz3. PID control loop running at 150 Hz

f ≥ 10 ∙ 150 Hz

Requirements

Hz1175.81

fmsf

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Example: Specifying circuit elements

11

44.1

CRf

Set f to 25 kHz to add in a factor of safety

Choosing C1 to be 100 nF, R1

is 576 Ω ~ 500 Ω

Recalculating with these values f = 28.8 kHz

This circuit has a PWM frequency according to:

≥ 117 Hz≥ 20 kHz≥ 1.5 kHz

f

Check constraints

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Example: Specifying circuit elements

18 kHz frequencyContinuous 28 amps$55.95

Where can I buy a PWM controller?

Texas InstrumentsDigikeyMouser ElectronicsCritical Velocity Motor Control

Texas Instruments TAS5508B8-Channel Digital Audio PWM Processor64 pin chip, max 192 kHz frequency$7.25

120 amps, used for hybrid vehicles$469.00

SMALL

BIGGER HUGE

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SAMPLE PWM CIRCUITS

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Current-type PWM rectifier

iA

iB

iC

ia

ib

ic

LOA

D

Io

VovCN

v BN

vAN

SA SB SC

SA' SB' SC'

36

Reference current vector in the vector space of input currents of a current-type

PWM rectifier

d

jq

i*

I

I

3

2

I1

I 6

I5

I 4

I

IIIII

IV

V VI

2_3 Io

Ioj 3

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Example waveforms of switching variables in one

switching cycle of a current-type PWM rectifier

0.0 0.2 0.4 0.6 0.8 1.0

t / Tsw

a

b

c

a'

b'

c'

1

0

0

1

0

0

STATE: 2 3 9 3 2 9

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Control scheme of a current-type PWM rectifier

VOLTAGE VECTOR CALCULATOR

m

a...c '

SVPWMMODULATOR

RECTIFIER

vA

vB

LOA

D

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Waveforms of output voltage and current in a current-type PWM

rectifier: (a) m = 0.75, (b) m = 0.35 (fsw/fo = 24, RLE load)

io

vo

0 t

(a)

io

vo

0 t

(b)

40

Waveforms of the input current and its fundamental in a current-type PWM rectifier: (a) m = 0.75,

(b) m = 0.35 (fsw/fo = 24, RLE load)

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Waveforms of (a) output voltage and current, (b) input current and its fundamental, in a current-type

PWM rectifier: in the inverter

vo

io

0 t

(a)

ia

ia,1

(b)

0 t

42

Harmonic spectra of input current in a current-type PWM

rectifier: (a) fsw/fo = 24, (b) fsw/fo = 48

(b)

(a)

HARMONIC NUMBER

0 20 40 60 80 100

AM

PLIT

UD

E (

pu

)

0.001

0.01

0.1

1

10

HARMONIC NUMBER

0 20 40 60 80 100

AM

PLIT

UD

E (

pu

)

0.001

0.01

0.1

1

10

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Voltage-type PWM rectifier

Vo

Io

iB

iC

iA

vCN

BN

ANv

v B

C

A

N

C'

A'

B '

SA SB SC

SA ' SB ' SC '

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Phase A branch of a voltage-type PWM rectifier

D A

D A'

iA

Vo

0

va

N ' A '

SA

SA'

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Input-voltage space vectors of a voltage-type PWM rectifier: (a) line-to-line voltages, (b)

line-to-neutral voltages

jq

d2_3 Vo

V3

V2 V4

V 5

V 6

V 1

'

'

'

'

'

'

_V 3j Vo

(a)

jq

d

__V 32

j Vo

Vo

V4

V 6V2

V3

V1

(b)

V 5

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Reference voltage vector in the vector space of line-to-neutral input voltages of a voltage-type PWM rectifier

V6V2

V3

V1

jq

d

VI

I

IV

II

V

III v *

V5

__V 32

j Vo

Vo

V4

47

Principle of voltage-oriented control of a voltage-type PWM

rectifier

d

jQ

jq

D

ji

ji D i D

vd

q

Q

i

v

v

id

t

jvq

48

Control system of a voltage-type PWM rectifier using a rotating

reference frame and Space Vector PWM (SVPWM)

iA

iBvB

SVPWMMODULATOR

a, b , c

dqDQ

dqABC

dqDQ

id iq

Av

vd

vq

iQ

iQ*

v *Dv *

Q

vd*vq

*

-+

Vo

Vo*

iDiD

* -

+ -

+

RECT IFIER

LO

AD

49

Direct power control system of a voltage-type PWM rectifier

iA

iBvB

Av

P OW ERC A LC ULA TOR

dq

AB C

S EC TOR ID E NTIF IE R

vqvd

Av vB

STA TES ELE C TOR

Vo

q p

x

y

a, b, c

*q

Vo

zV'o

p*p

-+

q

-

p q+

+-Vo

*

LOA

D

REC TIFIE R

50

Waveforms of input voltage and current in a voltage-type PWM rectifier at unity power factor

t2

vAN BN CNvv

i iiA B C

51

Waveforms of output voltage and current in a voltage-type

PWM rectifier

t

o

ov

i

52

Electromechanical representation of a DC

machine

nT

E a

L a

R a

ia

va

L O A D

D C M AC H INE

53

Plane of operation, operating area, and operating quadrants of

a rotating electric machine

CLOCKW ISE

II I

IVIIIT

nMOTORING

GENERATINGCLOCKW ISECOUNTERCLOCKW ISE

MOTORING

COUNTERCLOCKW ISEGENERATING n

T

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DC motor supplied from a rectifier with a mechanical

switch: first-quadrant operation

CBA

f < 90o

n

L a

R a

E a

i a

T

v a

Vo,dc

i o

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DC motor supplied from a rectifier with a mechanical switch: second-

quadrant operation

CBA

f > 90o

n

L a

R a

E a

ia

T

avVo,dc

i o

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High-voltage dc transmission system

SY

ST

EM

1

R C T1

TR 1

SY

ST

EM

2

R C T2

TR 2D C L IN E

L 1 L 2

L 3 L 4

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Switching pattern

0 50 100 150 200

a

b

c

a'

b'

c'

1

0

0

0

0

t s

0

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Schematic of a Vienna Rectifier

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Top and bottom views of an air-cooled 10kW-Vienna Rectifier (400kHz PWM).