INVERTERS
(DC-AC Converters)
•
•
•
INVERTERS for SEE 4433
Square wave inverters (1-phase)
Amplitude and harmonic control (quasi
square wave)
Total Harmonic Distortion
Pulse Width Modulation (PWM) (1-phase)
• Bipolar and unipolar
• Harmonics
3-phase inverters
• Square wave (six-step)
• PWM
INVERTERS
In SEE 4433, regardless of the control method, the circuit topology of singlephase inverter are of two types: Full-bridge and half-bridge
A.
Full-bridge inverter
Q1
D1
+
Vdc
vo
Q3
D3
Q2
D2
−
io
Q4
D4
• Upper and lower switches cannot
be ON simultaneously
• Depending on the switches
positions, there can be 3 possible
output voltage:
(Vdc), (-Vdc) and 0
INVERTERS
In SEE 4433, regardless of the control method, the circuit topology of singlephase inverter are of two types: Full-bridge and half-bridge
B.
half-bridge inverter
C1
Vdc
C2
+
Vdc/2
−
+
Vdc/2
−
Q1
+
vo
D1
−
Q2
D2
• The capacitors equally devide the
voltage Vdc
• Depending on the switches
positions, the output voltage can
be either (Vdc/2) or (−Vdc/2)
INVERTERS
Square-wave inverter (with full-bridge)
S1, S2
S3, S4
S1, S2
• It can be shown that:
• Can also be implemented using
half-bridge inverters
INVERTERS
Square-wave inverter (with full-bridge)
Current path for inductive load:
Q1
D1
+
Vdc
vo
Q3
D3
Q2
D2
−
io
Q4
D4
SEE EXAMPLE 8-2
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
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.
INVERTERS
Quasi-square wave inverter – Amplitude and harmonic control
Fourier series of the output voltage is given by:
vo (t) =
å V sin ( nw t )
n
n,odd
where
Vn =
4Vdc
cos ( na )
np
o
INVERTERS
Quasi-square wave inverter – Amplitude and harmonic control
Amplitude control
Amplitude of fundamental component:
V1 =
4Vdc
cos (a )
p
 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
V3 =
4Vdc
cos ( 3(30 o )) = 0
3p
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
Vn =
4Vdc
cos ( na )
np
Controlled via DC link
Fixed DC voltage
DC-DC Variable
DC
converter
Inverter
Load
INVERTERS
Quasi-square wave inverter – Amplitude and harmonic control
Switching signals (full-bridge inverter)
0

2
S1
S1
S2
S2
S3
S3
S4
S4
 
 
 
0

2
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
INVERTERS
Pulse Width Modulation
Bipolar switching scheme
(vsine > vtri) : Q1 and Q2 ON; vo=Vdc
(vsine < vtri) : Q3 and Q4 ON; vo=-Vdc
INVERTERS
Pulse Width Modulation
Bipolar switching scheme
fsine
Frequency modulation index
ftri
Vm,sine
mf =
Vm,tri
ftri
fsin
Amplitude modulation index
ma =
Vm,sin
Vm,tri
The amplitude of the
fundamental component of
vo is proportional to ma:
V1=maVdc
INVERTERS
Harmonics in PWM single-phase inverter
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  vo (t )  Vn sin( no t )
n 1
Graphically, this can be represented using
frequency spectrum diagram :
OR using a normalized Fourier coefficients table:
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
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:
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.
PWM
mf = 21
Square wave
1
3
5
7
9
11
13
n
1
25
3
5
7
9
11
13
15
17
19
21
23
INVERTERS
Three-phase inverters
Six-step inverter
S1
S3
S1
S2
S3
A
Vdc
S4
S5
n
B
S5
C
S6
S4
Vdc
vAo
S2
o
• 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
S6
2
Vdc
3
1
Vdc
3
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