1. INVERTERS
(DC-AC Converters)

2. INVERTERS for SEE 4433 Square wave inverters (1-phase)
Amplitude and harmonic control (quasi square wave)
Total Harmonic Distortion
INVERTERS for SEE 4433
Pulse Width Modulation (PWM) (1-phase)
Bipolar and unipolar
Harmonics
3-phase inverters
Square wave (six-step)
PWM

3. INVERTERS
In SEE 4433, regardless of the control method, the circuit topology of single-phase inverter are of two types: Full-bridge and half-bridge
A. Full-bridge inverter
Vdc Q1 Q2 Q3 Q4
vo − D1 D3 D2 D4 io
Upper and lower switches cannot be ON simultaneously
Depending on the switches positions, there can be 3 possible output voltage:
(Vdc), (-Vdc) and 0

4. INVERTERS
In SEE 4433, regardless of the control method, the circuit topology of single-phase inverter are of two types: Full-bridge and half-bridge
B. half-bridge inverter
The capacitors equally devide the voltage Vdc
Depending on the switches positions, the output voltage can be either (Vdc/2) or (−Vdc/2) Q1 D1 C1 +
Vdc/2 −
Vdc
vo − C2 +
Vdc/2 − D2 Q2

5. INVERTERS Square-wave inverter (with full-bridge)
It can be shown that:
Can also be implemented using half-bridge inverters

6. INVERTERS Square-wave inverter (with full-bridge)
Current path for inductive load:
Vdc Q1 Q2 Q3 Q4
vo − D1 D3 D2 D4 io
SEE EXAMPLE 8-2

7. INVERTERS TOTAL HARMONIC DISTORTION
THD is used to measure the quality of the AC voltage or current
The closer the waveform to sinusoidal, the smaller is the THD
Can be applied to voltage or current
SEE EXAMPLE 8-3

8. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control
Duration of ZERO output voltage is introduced and it can be shown that:
Amplitude of the fundamental component can be controlled (by controlling α)
Certain harmonic contents can be eliminated (also by controlling α !)
Amplitude and harmonics cannot be controlled independently
Cannot be implemented using the half-bridge inverter.

9. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control
Fourier series of the output voltage is given by:
where

10. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control
Amplitude control
Amplitude of fundamental component:
 By changing α the amplitude of the fundamental will change
Harmonic control
The nth harmanic can be eliminated if its amplitude made zero
For example, the amplitude of the third harmonic (n=3) is zero when α = 30o

11. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control
Simultaneous control of amplitude and harmonic
In order to be able to control amplitude and harmonic simultaneously, variable Vdc has to be added
Controlled via DC link
Fixed DC voltage
Variable DC
Load
Inverter
DC-DC
converter

12. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control
Switching signals (full-bridge inverter)       
2 
2 S1 S1 S2 S2 S3 S3 S4 S4

13. INVERTERS Pulse Width Modulation
Is a method used to control the output voltage (amplitude and frequency) of an inverter by modulating the width of the pulses of the output waveform
Main advantages of PWM control:
Filter requirement is reduced
Amplitude and frequency can be control independently
Significant reduction in THD of load current (inductive load)
Disadvantages of PWM control:
More complex control circuit
Higher switching losses
In SEE4433, two switching scheme for single-phase inverter will be discussed:
Bipolar switching scheme
Unipolar switching scheme

14. INVERTERS Pulse Width Modulation Bipolar switching scheme
(vsine > vtri) : Q1 and Q2 ON; vo=Vdc
(vsine < vtri) : Q3 and Q4 ON; vo=-Vdc

15. INVERTERS Pulse Width Modulation Bipolar switching scheme
fsine
Frequency modulation index
ftri
Vm,tri
Vm,sine
Amplitude modulation index
The amplitude of the fundamental component of vo is proportional to ma:
V1=maVdc

16. INVERTERS
Harmonics in PWM single-phase inverter

17. INVERTERS
Harmonics in PWM single-phase inverter : Bipolar switching scheme
If mf is chosen as odd integer with the triangular wave synchronize with the modulating signal, then the PWM output is an odd quarter-wave symmetry.
an = 0 and bn exist only for odd 
Graphically, this can be represented using frequency spectrum diagram :
OR using a normalized Fourier coefficients table:

18. INVERTERS Pulse Width Modulation Unipolar switching scheme
(vsine > vtri) : Q1 ON, Q4 OFF; va= Vdc
(vsine < vtri) : Q1 OFF, Q4 ON; va= 0
(-vsine > vtri) : Q3 ON, Q2 OFF; vb= Vdc
(-vsine < vtri) : Q3 OFF, Q2 ON; vb= 0
Vab = va - vb

19. INVERTERS
Harmonics in PWM single-phase inverter : Unipolar switching scheme
The frequency of the output voltage is doubled.
If mf is chosen as even integer then the first cluster of harmonics appear around 2mf (the harmonic at 2mf itself is zero)
Graphically, this can be represented using frequency spectrum diagram :
Or using a normalized Fourier coefficients table:

20. INVERTERS Harmonics in PWM single-phase inverter :
Comparison between square wave and PWM
SQUARE-WAVE
Contains harmonics at relatively low frequency: 3rd, 5th, 7th, 9th, etc.
In order to improve the THDV , a low pass filter can be employed  filter will be bulky since cutoff frequency is low  difficult to remove harmonics since at the same time must ensure fundamental component is not attenuated.
PWM
Harmonics appear around mf which is further away from fundamental.
To improve THDV, filter with higher cutoff can be used  smaller in size  easier to filter out harmonics.
Square wave
PWM
mf = 21 n

21. INVERTERS Three-phase inverters Six-step inverter
Vdc S4 S5 S6 C B n S3 S1 o S1 S2 S3 S4 S5 S6
vAo
Vdc
THDV of line-line and line-n are both 31%
THDI of line current depends on load, however it will be smaller than the single phase
vBo
vCo
vAB
vAn

22. INVERTERS Three-phase inverters PWM inverter
mf is chosen to be multiple of 3 so that the harmonic at multiple of 3, including mf (and its multiple) are suppressed (or canceled out) in the line-line voltage