PWM Techniques

P Po ow we er  r  E Elle ec cttrro on niic cs s

Chapter 6 PWM Techniques

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The most mos t wide wid ely use u sed d contro co ntrol te chnique que con control troll techni techn ique in power power electro ele ctronic nics s electro

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DC/DC

 AC/AC

Puls ul s e Widt id t h Modul Mod ula ation ti on (PWM) (Choppin hop ping g control) contr ol)

DC/AC

 AC/DC 2

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Outline 6.1 Basic principles 6.2 Some major PWM techniques in DC/AC inverters 6.3 PWM techniques with feedback control

    r 6.4 PWM rectifiers     e     w     o       P

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6.1 Basic principles of PWM

     s  Similar response to different shape of impulse input      c          i n      o       r        t      c         le         E

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The equal-area theorem: Responses tend to be identical when input signals have same area and time durations of input impulses become very small. 4

Basic principles of PWM

     s       c   Application of the equal-area theorem        i n      o  This is sinusoidal      r       t  PWM (SPWM)      c         le  The equal-area        E theorem can be applied     r to realize any shape of      e     w waveforms

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 A list of PWM techniques Triangular -wave sampling  – Natural sampling  – Uniform sampling

Calculation  – Calculation based on equal -area criterion

 – Selective harmonics elimination     r     e Hysteric control     w     o Space Vector Modulation (SVM, or SVPWM)       P

Random PWM

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6.2 Some major PWM techniques

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Natural sampling Uniform sampling Selective harmonics elimination Some practical issues  – Synchronous modulation and asynchronous modulation  – Harmonics in the PWM inverter output voltages  – Ways to improve DC input voltage utilization and reduce switching frequency  – Connection of multiple PWM inverters

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Triangular -wave natural sampling Uni-polar PWM in single-phase VSI V1

U d 

V3

VD1

VD3 L

 R

+

uo

V2

V4

VD2 Control u r  signal

VD4

    r     e     w     o       P Uni-polar sampling is used to Carrier

uc

Mudulation Carrier 

realize uni-polar PWM.

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Triangular -wave natural sampling

     s  Bi-polar PWM in single-phase VSI      c          i n      o  V V      r        t VD VD      c  L  R + U         le  u V V VD VD        E 1

3

1

3

d 

o

2

4

2

4

    r     e     w     o       P Bi-polar sampling is used to Control u r  signal

Mudulation

Carrier

uc

Carrier 

realize bi-polar PWM.

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Triangular -wave natural sampling In 3-phase VSI

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can only realize bi-bolar PWM therefore should be controlled by bipolar sampling. 10

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Triangular -wave uniform sampling Easier to realize by computer control

    r Modulation factor      e     w     o       P

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Selective harmonics elimination PWM (SHEPWM)

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Frequency relationship between triangular wave carrier and control signal  Asynchronous Modulation Synchronous Modulation

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Harmonics in the PWM inverter  output voltages

     s       c  Spectrum of 1-phase        i n bridge PWM inverter       o  output voltage      r        t      c  No lower order         le  harmonics        E The lowest frequency     r harmonics is w and c     e     w adjacent harmonics.     o wc has the highest       P harmonic content.

1.4

a=1.0 a=0.8 a=0.5 a=0

1.2 1.0      ) 0.8     %      (    e      d 0.6    u     t      i    n    g 0.4    a     M 0.2

k  n

1 0

0 +- 2 +- 4 0 +- 1 +- 3 +- 5 0 +- 2 +- 4 1 2 3 (nω c +k ωr   )

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Harmonics in the PWM inverter  output voltages

     s       c  Spectrum of 3-phase        i n bridge PWM inverter       o  output voltage      r        t      c  No lower order         le  harmonics        E No harmonics at ω c.     r The lowest     e     w frequency and     o highest content       P harmonics are ω c±2ω r  and 2ω c±ω r .

1.2

a=1.0 a=0.8 a=0.5

1.0

a=0

   e 0.8    u     t    n 0.6    g    a

0.4 0.2 k  n

1 0

0 +- 2 +- 4 0 +- 1 +- 3 +- 5 0 +- 2 +- 4 1 2 3 (nω c +k ωr   )

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Ways to improve utilization of DC input voltage and reduce switching frequency Use trapezoidal waveform as modulating signal instead of sinusoidal

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Ways to improve utilization of DC input voltage and reduce switching frequency

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Use 3k order harmonics bias in the modulating signal

u 1

urV1

urW1

uc

O

t 

1 uP

-

O

t 

-0.5 u 1

u

urU1

ur1

O

urU

urV

urW

uc

t 

1 uUN'

-

ur3

U d  2

O

O

ω t 

U d 

− ur1

t 

2

uVN'

ur  uc

u

O

t 

uWN'

O

ω t 

O

t 

uUV U d 

O

t 

-U 

d 

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Connection of multiple PWM inverters

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6.3 PWM techniques with feedback control

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Current hysteric control

Voltage hysteric control

Triangular -wave comparison (sampling) with feedback control

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Current hysteretic control

     s       c  In Single-phase VSI        i n      o       r        t      c         le         E

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Current hysteretic control In 3-phase VSI

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Voltage hysteretic control

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U d 

2

+u

*

Filter  U d 

2

u

u

22

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Triangular -wave comparison (sampling) with feedback control

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6.4 PWM rectifiers

     s       c  Operation Principles        i n      o       r        t      c         le         E

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a) Rectification mode

c) Reactive power  compensation mode

b) Inversion mode

d) Current leading by ϕ 

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     s       c         i n      o       r        t      c         le         E

PWM rectifiers Three-phase circuit

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PWM rectifiers

     s       c  Indirect current control        i n      o       r        t      c         le  u* + id d        E  R PI

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u d

Triangular-wave uR 

-+

- uA,B,C

  2k π/3) sin(ω t+ (k =0,1,2) uL  X L

  2k π/3) cos(ω t+ (k =0,1,2)

 R

+

L ua,u b,uc

ud

+

Load

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     s       c         i n      o       r        t      c         le         E

PWM rectifiers Direct current control

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