DC to AC Converter (Inverter)
• DEFINITION: Converts DC to AC power by switching the DC input voltage (or current)
in a pre-determined sequence so as to generate AC voltage (or current) output.
General block diagram
IDC Iac
+ +
VDC Vac
TYPICAL APPLICATIONS:
– Un-interruptible power supply (UPS), Industrial (induction motor) drives,
Traction, HVD
Simple square-wave inverter (1)
• To illustrate the concept of AC waveform generation
SQUARE-WAVE
INVERTER
T1 T3
D1 D3
+ VO -
VDC
IO
T4 T2
D2 D4
EQUIVALENT
CIRCUIT
S1 S3
S4 S2
AC Waveform Generation
S1,S2 ON; S3,S4 OFF for t1 < t < t2
vO
S1 S3 VDC
VDC
t
+ vO t1 t2
S4 S2
S3,S4 ON ; S1,S2 OFF for t2 < t < t3
vO
S1 S3
VDC t2 t3
+ vO t
S4 S2
-VDC
AC Waveforms
INVERTER OUTPUT VOLTAGE
Vdc
-Vdc
FUNDAMENTAL COMPONENT
V1
4VDC
3RD HARMONIC
V1
3
5RD HARMONIC
V1
5
Harmonics Filtering
DC SUPPLY INVERTER (LOW PASS) FILTER LOAD
L
+ +
C
vO 1 vO 2
BEFORE FILTERING AFTER FILTERING
vO 1 vO 2
• Output of the inverter is “chopped AC voltage with zero DC components”. It contains
harmonics.
• An LC section low-pass filter is normally fitted at the inverter output to reduce the high
frequency harmonics.
• In some applications such as UPS, “high purity” sine wave output is required. Good
filtering is a must.
• In some applications such as AC motor drive, filtering is not required.
Variable Voltage Variable Frequency Capability
Vdc2 Higher input voltage
Higher frequency
Vdc1 Lower input voltage
Lower frequency
T1 T2 t
• Output voltage frequency can be varied by “period” of the square-wave pulse.
• Output voltage amplitude can be varied by varying the “magnitude” of the DC input
voltage.
• Very useful: e.g. variable speed induction motor drive
Output voltage harmonics/ distortion
• Harmonics cause distortion on the output voltage.
• Lower order harmonics (3rd, 5th etc) are very difficult to filter, due to the filter size and
high filter order. They can cause serious voltage distortion.
• Why need to consider harmonics?
– Sinusoidal waveform quality.
– “Power Quality” issue.
– Harmonics may cause degradation of equipment. Equipment need to be “de-
rated”.
– Total Harmonic Distortion (THD) is a measure to determine the “quality” of a
given waveform.
Quasi-square wave (QSW)
Vdc
2
-Vdc
Half-bridge inverter (1)
S1 ON
Vdc S2 OFF
+
S1 2
VC1
-
V +
Vdc o
G 0
t
RL
+
VC2 S2
- Vdc
2 S1 OFF
S2 ON
Also known as the “inverter leg”.
• Basic building blocks for full bridge, three phase and higher order inverters.
• G is the “centre point”.
• Both capacitors have the same value. Thus the DC link is equally “spilt” into two.
• The top and bottom switch has to be “complementary”, i.e. If the top switch is closed
(on), the bottom must be off, and vice-versa.
Single-phase, full-bridge (1)
• Full bridge (single phase) is built from two half-bridge leg.
• The switching in the second leg is “delayed by 180 degrees” from the first leg.
VRG
Vdc
2
LEG R LEG R' 2 t
+
Vdc Vdc
S1 S3
2 VR 'G 2
+ - Vdc
Vo - 2
Vdc R R'
G 2 t
-
+ Vdc
2
Vdc S4 S2 Vo
2
Vdc
-
2 t
Vo V RG VR 'G
G is " virtual groumd"
Vdc
Three-phase inverter
• Each leg (Red, Yellow, and Blue) is delayed by 120 degrees.
• A three-phase inverter with star connected load is shown below
+Vdc
+
Vdc/2 S1 S3 S5
G R Y B
iR iY iB
+
S4 S6 S2
Vdc/2
ia ib
ZR ZY ZB
N
Voltage Source Inverter (VSI)
A. Six-Step VSI (1)
Six-Step three-phase Voltage Source Inverter
Fig. 1 Three-phase voltage source inverter.
Voltage Source Inverter (VSI)
A. Six-Step VSI (2)
Gating signals, switching sequence and line to negative voltages
Fig. 2 Waveforms of gating signals, switching sequence, line to negative voltages for six-step
voltage source inverter.
I. Voltage Source Inverter (VSI)
A. Six-Step VSI (3)
Switching Sequence:
561 (V1) 612 (V2) 123 (V3) 234 (V4)
345 (V5) 456 (V6) 561 (V1)
Where, 561 means that S5, S6 and S1 are switched on
Fig. 3 Six inverter voltage vectors for six-step voltage source inverter.
I. Voltage Source Inverter (VSI)
A. Six-Step VSI (4)
Line to line voltages (Vab, Vbc, Vca)
and line to neutral voltages (Van, Vbn, Vcn)
Line to line voltages
Vab = VaN - VbN
Vbc = VbN - VcN
= VcN - VaVca N
Phase voltages
Van = 2/3VaN - 1/3VbN - 1/3VcN
Vbn = -1/3VaN + 2/3VbN - 1/3VcN
Vcn = -1/3VaN - 1/3VbN + 2/3VcN
Fig. 4 Waveforms of line to neutral (phase) voltages and line to line voltages for six-step
voltage source inverter.
I. Voltage Source Inverter (VSI)
B. Pulse-Width Modulated VSI (1)
Objective of PWM
Control of inverter output voltage
Reduction of harmonics
Disadvantages of PWM
Increase of switching losses due to high PWM frequency
Reduction of available voltage
EMI problems due to high-order harmonics
I. Voltage Source Inverter (VSI)
B. Pulse-Width Modulated VSI (2)
Pulse-Width Modulation (PWM)
I. Voltage Source Inverter (VSI)
B. Pulse-Width Modulated VSI (3)
Inverter output voltage
When vcontrol > vtri, VA0 = Vdc/2
When vcontrol < vtri, VA0 = -Vdc/2
Control of inverter output voltage
PWM frequency is the same as the frequency of vtri
Amplitude is controlled by the peak value of vcontrol
Fundamental frequency is controlled by the frequency of vcontrol
PWM METHODS
A. Sine PWM (1)
Three-phase inverter
Fig. 6 Three-phase Sine PWM inverter
Pulse Width Modulation (PWM)
Modulating Waveform Carrier waveform
1
M1
1
Vdc
2
0 t0 t1 t 2 t5
t3 t 4
Vdc
2
Triangulation method (Natural sampling)
– Amplitudes of the triangular wave (carrier) and sine wave (modulating) are
compared to obtain PWM waveform. Simple analogue comparator can be used.
– Basically an analogue method. Its digital version, known as REGULAR sampling
is widely used in industry.
PWM types
• Natural (sinusoidal) sampling (as shown on previous slide)
– Problems with analogue circuitry, e.g. Drift, sensitivity etc.
• Regular sampling
– simplified version of natural sampling that results in simple digital
implementation
• Optimised PWM
– PWM waveforms are constructed based on certain performance criteria, e.g.
THD.
• Harmonic elimination/minimisation PWM
– PWM waveforms are constructed to eliminate some undesirable harmonics from
the output waveform spectra.
– Highly mathematical in nature
• Space-vector modulation (SVM)
– A simple technique based on volt-second that is normally used with three-phase
inverter motor-drive
Regular sampling
h( x) if ( k ( x) c ( x) 1 if ( k ( x) c ( x) 1 0) )
1
t1 t2 Gelombang memodulat, vm(t) Gelombang pembawa, vc(t)
2
t
vs (t )
t'1 t'2
v pwm t
Rajah 2-4: Pesampelan regular pemodulatan lebar denyut
Asymmetric and symmetric regular sampling
T
1 M1 sin mt
sample
point
t
T 3T 5T
4 4 4 4
1
Vdc
2 asymmetric
sampling
t
t0 t1 t2 t3
symmetric
sampling
V
dc
2
Generating of PWM waveform regular sampling
Bipolar Switching
Modulating Waveform Carrier waveform
1
M1
1
Vdc
2
0 t0 t1 t 2 t3 t4 t5
Vdc
2
Unipolar switching
1
A Gelombang pembawa B
(a)
S1
(b)
S3
(c)
V pwm
(d)
Rajah 2-7: Pensuisan bipolar yang menggunakan dua
gelombang sinus yang berbeza fasa 180 0
Bipolar PWM switching: Pulse-width characterization
modulating carrier
4 waveform waveform
2
kth
pulse
2
1k
2k
k
Three-phase harmonics
• For three-phase inverters, there is significant advantage if MR is chosen to be:
– Odd: All even harmonic will be eliminated from the pole-switching waveform.
– triplens (multiple of three (e.g. 3,9,15,21, 27..):
All triplens harmonics will be eliminated from the line-to-line output voltage.
• By observing the waveform, it can be seen that with odd MR, the line-to-line voltage
shape looks more “sinusoidal”.
• As can be noted from the spectra, the phase voltage amplitude is 0.8 (normalised). This is
because the modulation index is 0.8. The line voltage amplitude is square root three of
phase voltage due to the three-phase relationship
Effect of odd and “triplens”
2
Vdc
2 V RG
Vdc
2
Vdc
2 VYG
Vdc
2
Vdc
V RY
Vdc
p 8, M 0.6
Vdc
2 V RG
Vdc
2
Vdc
2 VYG
Vdc
2
Vdc
VRY
Vdc
p 9, M 0.6
ILLUSTRATION OF BENEFITS OF USING A FREQUENCY RATIO
THAT IS A MULTIPLE OF THREE IN A THREE PHASE INVERTER
