1. Chapter 7 PWM Techniques
Power Electronics
Chapter PWM Techniques

2. The most widely used control technique in power electronics
AC/AC
DC/DC
Pulse Width Modulation (PWM) (Chopping control)
AC/DC
DC/AC

3. Outline 7.1 Basic principles
7.2 Some major PWM techniques in DC/AC inverters
7.3 PWM techniques with feedback control
7.4 PWM rectifiers

4. 7.1 Basic principles of PWM
Similar response to different shape of impulse input
The equal-area theorem: Responses tend to be identical when input signals have same area and time durations of input impulses become very small.

5. Basic principles of PWM
Application of the equal-area theorem
This is sinusoidal
PWM (SPWM)
The equal-area theorem can be applied
to realize any shape of
waveforms

6. A list of PWM techniques
Triangular-wave sampling
Natural sampling
Uniform sampling
Calculation
Calculation based on equal-area criterion
Selective harmonics elimination
Hysteretic control
Space Vector Modulation (SVM, or SVPWM)
Random PWM

7. 7.2 Some major PWM techniques
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

8. Triangular-wave natural sampling
Uni-polar PWM in single-phase VSI
Uni-polar sampling is used to realize uni-polar PWM.

9. Triangular-wave natural sampling
Bi-polar PWM in single-phase VSI
Bi-polar sampling is used to realize bi-polar PWM.

10. Triangular-wave natural sampling
In 3-phase VSI
Three-phase bridge inverter can only realize bi-bolar PWM therefore should be controlled by bipolar sampling.

11. Triangular-wave uniform sampling
Easier to realize by computer-control
Modulation factor

12. Selective harmonics elimination PWM (SHEPWM)

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

14. Harmonics in the PWM inverter output voltages
Spectrum of 1-phase bridge PWM inverter output voltage
No lower order harmonics
The lowest frequency harmonics is wc and adjacent harmonics. wc has the highest harmonic content.

15. Harmonics in the PWM inverter output voltages
Spectrum of 3-phase bridge PWM inverter output voltage
No lower order harmonics
No harmonics at wc. The lowest frequency and highest content harmonics are wc2wr and 2wcwr.

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

17. Ways to improve utilization of DC input voltage and reduce switching frequency
Use 3k order harmonics bias in the modulating signal

18. Connection of multiple PWM inverters
Purposes
Expand output power rating
Reduce harmonics

19. Space Vector PWM (SVPWM or SVM)
Vector Space of 3-phase Line-to-Line Variables
Phase variables (a, b and c) produce
line-to-line variables (ab, bc and ca) in plane-
Line-to-line variables (ab, bc and ca) do not have
-component in -coordinate system a c b ab bc ca  
[1 1 1]T 

20. Line-to-Line Voltage Space Vector
where
Space vector  bc v   ab  v
If Vm is the amplitude of balanced, symmetrical, three-phase line-to-line
voltages, then ca

21. Switching States for 3-phase Voltage Source Inverteria ib ic va vc vb sa sb sc p n
Vdc
idc
idc
vab
Vdc sa sc sb 1 ic ib
ib+ic ia
ia+ic
ia+ib
ia+ib+ic
Switching state
pnn
ppn
npn
npp
nnp
pnp
ppp
nnn
vca
vbc
-Vdc

22. Switching State Vector [pnn] bc v  
ab,  v ca

23. Switching State Vector [ppn] bc v  
ab,  ca

24. Switching State Vector [ppp] bc
ab,  ca

25. Switching State Vectors
Sector I IV
III II V VI
at center point
ab,  bc ca  30
150 90
-90
-150
-30 
 (°)

26. Reference Voltage Vector, Vref
ab,  bc ca   v v
where
In general, 
Assume 
at center point
ref V r

27. Definition of High Frequency Synthesis
For example v
V1()
V2()
Vref () t T1 T2 T0 TS
Total area of
= Area of

28. Synthesis of Vref using Switching State Vectors
ab,  bc ca   v v 
ref V r ia ib ic va vc vb sa sb sc p n
Vdc
idc a b c 1 I IV
III II VI 

29. Duty Ratio of Switching State Vectors in SVPWM
From HF synthesis definition,
Assume is constant in TS ,
where
ref V r  

30. 7.3 PWM techniques with feedback control
Current hysteretic control
Voltage hysteretic control
Triangular-wave comparison (sampling) with feedback control

31. Current hysteretic control
In Single-phase VSI

32. Current hysteretic control
In 3-phase VSI

33. Voltage hysteretic control

34. Triangular-wave comparison (sampling) with feedback control

35. 7.4 PWM rectifiers Operation Principles a) Rectification mode
b) Inversion mode
c) Reactive power compensation mode
d) Current leading by

36. PWM rectifiers
Three-phase circuit

37. PWM rectifiers
Indirect current control

38. PWM rectifiers
Direct current control