Chapter 4 DC to AC Conversion (INVERTER) • General concept • Singlephase inverter • Harmonics • Modulation • Threephase inverter
Jan 14, 2016
Chapter 4DC to AC Conversion
(INVERTER)
• General concept
• Singlephase inverter
• Harmonics
• Modulation
• Threephase inverter
DC to AC Converter (Inverter)
• DEFINITION: Converts DC to AC power by switching the DC input voltage (or current) in a predetermined sequence so as to generate AC voltage (or current) output.
• General block diagram
IDCIac
+
VDC Vac
+
• TYPICAL APPLICATIONS:
– Uninterruptible power supply (UPS), Industrial (induction motor) drives, Traction, HVDC
Simple squarewave inverter (1)
• To illustrate the concept of AC waveform generation
VDC
T1
T4
T3
T2
+ VO 
D1
D2
D3
D4
SQUAREWAVEINVERTER
IO
S1 S3
S2S4
EQUIVALENTCIRCUIT
AC Waveform Generation
VDC
S1
S4
S3
+ vO
VDC
S1
S4
S3
S2
+ vO
VDC
vO
t1 t2
t
S1,S2 ON; S3,S4 OFF for t1 < t < t2
t2 t3
vO
VDC
t
S3,S4 ON ; S1,S2 OFF for t2 < t < t3
S2
AC Waveforms
FUNDAMENTAL COMPONENT
3RD HARMONIC
5RD HARMONIC
DCV4
Vdc
Vdc
V1
3
1V
5
1V
INVERTER OUTPUT VOLTAGE
Harmonics Filtering
• Output of the inverter is “chopped AC voltage with zero DC component”. It contain harmonics.
• An LC section lowpass 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.
vO 1
+
L
CvO 2
(LOW PASS) FILTER
+
vO 1vO 2
BEFORE FILTERING AFTER FILTERING
INVERTER LOADDC SUPPLY
Variable Voltage Variable Frequency Capability
T1 T2 t
Vdc1
Vdc2 Higher input voltageHigher frequency
Lower input voltageLower frequency
• Output voltage frequency can be varied by “period” of the squarewave 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 “derated”.
• Total Harmonic Distortion (THD) is a measure to determine the “quality” of a given waveform.
Fourier Series
• Study of harmonics requires understanding of wave shapes. Fourier Series is a tool to analyse wave shapes.
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Harmonics of squarewave (1)
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Quasisquare wave (QSW)
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Halfbridge inverter (1)
Vo
RL
+
VC1
VC2
+

+
S1
S2
Vdc
2
Vdc
2
Vdc
S1 ONS2 OFF
S1 OFFS2 ON
t0G
• Also known as the “inverter leg”.
• Basic building block 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 viceversa.
Singlephase, fullbridge (1)
• Full bridge (single phase) is built from two halfbridge leg.
• The switching in the second leg is “delayed by 180 degrees” from the first leg.
S1
S4
S3
S2
+

G
+
2dcV
2dcV

2dcV
2dcV
dcV
2dcV
2dcV
dcV
2
2
2
t
t
t
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oV
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dcV
+

Threephase inverter
• Each leg (Red, Yellow, Blue) is delayed by 120 degrees.
• A threephase inverter with star connected load is shown below
ZYZRZB
G R Y B
iR iYiB
ia ib
+Vdc
N
S1
S4 S6
S3 S5
S2
+
+
Vdc/2
Vdc/2
I. Voltage Source Inverter (VSI)A. SixStep VSI (1)
3
SixStep threephase Voltage Source Inverter
Fig. 1 Threephase voltage source inverter.
4
I. Voltage Source Inverter (VSI)A. SixStep VSI (2)
Fig. 2 Waveforms of gating signals, switching sequence, line to negative voltagesfor sixstep voltage source inverter.
Gating signals, switching sequence and line to negative voltages
I. Voltage Source Inverter (VSI)A. SixStep VSI (3)
where, 561 means that S5, S6 and S1 are switched on
Fig. 3 Six inverter voltage vectors for sixstep voltage source inverter.
Switching Sequence:
561 (V1) 612 (V2) 123 (V3) 234 (V4)
345 (V5) 456 (V6) 561 (V1)
5
I. Voltage Source Inverter (VSI)A. SixStep VSI (4)
Fig. 4 Waveforms of line to neutral (phase) voltages and line to line voltagesfor sixstep voltage source inverter.
Line to line voltages (Vab, Vbc, Vca) and line to neutral voltages (Van, Vbn, Vcn)
Vab = VaN  VbN
Vbc = VbN  VcN
Vca = VcN  VaN
Line to line voltages
Van = 2/3VaN  1/3VbN  1/3VcN
Phase voltages
Vbn = 1/3VaN + 2/3VbN  1/3VcN
Vcn = 1/3VaN  1/3VbN + 2/3VcN
6
Three phase inverter waveforms
I. Voltage Source Inverter (VSI)A. SixStep VSI (5)
Amplitude of line to line voltages (Vab, Vbc, Vca) Fundamental Frequency Component (Vab)1
Harmonic Frequency Components (Vab)h
: amplitudes of harmonics decrease inversely proportional to their harmonic order
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6
2
V4
2
3
(rms))(V 1ab
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7
8
I. Voltage Source Inverter (VSI)A. SixStep VSI (6)
Characteristics of Sixstep VSI
It is called “sixstep inverter” because of the presence of six “steps”
in the line to neutral (phase) voltage waveform
Harmonics of order three and multiples of three are absent from
both the line to line and the line to neutral voltages
and consequently absent from the currents
Output amplitude in a threephase inverter can be controlled
by only change of DClink voltage (Vdc)
9
I. Voltage Source Inverter (VSI)B. PulseWidth Modulated VSI (1)
Objective of PWM
Disadvantages of PWM Increase of switching losses due to high PWM frequency
Reduction of available voltage
EMI problems due to highorder harmonics
Control of inverter output voltage
Reduction of harmonics
I. Voltage Source Inverter (VSI)B. PulseWidth Modulated VSI (2)
PulseWidth Modulation (PWM)
Fig. 5 Pulsewidth modulation.
10
I. Voltage Source Inverter (VSI)B. PulseWidth Modulated VSI (3)
Inverter output voltage
When vcontrol > vtri, VA0 = Vdc/2
When vcontrol < vtri, VA0 = Vdc/2
A01A0
10
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,2/
)(
dc
A
tri
control
V
Vofpeak
v
vm
Modulation Index (m)
Control of inverter output voltage
Amplitude is controlled by the peak value of vcontrol
Fundamental frequency is controlled by the frequency of vcontrol
PWM frequency is the same as the frequency of vtri
11
II. PWM METHODSA. Sine PWM (1)
Fig. 6 Threephase Sine PWM inverter.
Threephase inverter
12
II. PWM METHODSA. Sine PWM (2)
VA
0V
B0
VC
0V
AB
VB
CV
CA
t
Fig. 7 Waveforms of threephase sine PWM inverter.
Threephase sine PWM waveformsvtri vcontrol_A vcontrol_B vcontrol_C
where, VAB = VA0 – VB0
VBC = VB0 – VC0
VCA = VC0 – VA0
When vcontrol > vtri, VA0 = Vdc/2
When vcontrol < vtri, VA0 = Vdc/2
Frequency of vtri = fs
Frequency of vcontrol = f1
Frequency of vtri and vcontrol
where, fs = PWM frequency
f1 = Fundamental frequency
Inverter output voltage
13
II. PWM METHODSA. Sine PWM (3)
Amplitude modulation ratio (ma)
A01A0
10
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)(
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A
tri
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Vofvaluepeak
vofamplitude
vofamplitudepeakm
Frequency modulation ratio (mf)
frequencylfundamentafandfrequencyPWMfwhere,, 1s1
f
fm s
f
mf should be an odd integer
if mf is not an integer, there may exist sunhamonics at output voltage
if mf is not odd, DC component may exist and even harmonics are present at output voltage
mf should be a multiple of 3 for threephase PWM inverter
An odd multiple of 3 and even harmonics are suppressed
14
Pulse Width Modulation (PWM)
Modulating Waveform Carrier waveform
1M1
1
0
2dcV
2dcV
00t 1t 2t 3t 4t 5t
• 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 waveform 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
• Spacevector modulation (SVM)– A simple technique based on voltsecond that
is normally used with threephase inverter motordrive
Modulation Index, Ratio
waveformmodulating theofFrequency veformcarrier wa theofFrequency
M
)(MRatio) (Frequency Ratio Modulation
veformcarrier wa theof Amplitude waveformmodulating theof Amplitude
M
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R
I
I
p
p
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1M1
1
0
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2dcV
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m
m
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in
Modulation Index, Ratio
Regular samplingh x( ) if k x( ) c x( ) 1 if k x( ) c x( ) 1 0( )( )
1
Regular sampling PWM
Sinusoidal modulatingwaveform, vm(t)
Carrier, vc(t)t1 t2
t'1 t'2
t
t
2
)(tvs
pwmv
Regular sampling waveform,
Asymmetric and symmetric regular sampling
T
samplepoint
tM msin11
1
4
T
4
3T
4
5T4
2dcV
2dcV
0t 1t 2t 3tt
asymmetric sampling
symmetricsampling
t
Generating of PWM waveform regular sampling
Bipolar Switching
Modulating Waveform Carrier waveform
1M1
1
0
2dcV
2dcV
00t 1t 2t 3t 4t 5t
Unipolar switching1
Unipolar switching scheme
A BCarrier waveform
(a)
(b)
(c)
(d)
1S
3S
pwmV
Bipolar PWM switching: Pulsewidth characterization
k1k2
k
4
2
carrierwaveform
modulatingwaveform
pulse
kth
2
Threephase harmonics
• For threephase inverters, there is significant advantage if MR is chosen to be:
– Odd: All even harmonic will be eliminated from the poleswitching waveform.
– triplens (multiple of three (e.g. 3,9,15,21, 27..):
All triplens harmonics will be eliminated from the linetoline output voltage.
• By observing the waveform, it can be seen that with odd MR, the linetoline 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 threephase relationship
Effect of odd and “triplens”
2dcV
2dcV
2dcV
2dcV
2dcV
2dcV
2dcV
2dcV
dcV
dcV
dcV
dcV
2
RGV
RGV
RYV
RYV
YGV
YGV
6.0,8 Mp
6.0,9 Mp
ILLUSTRATION OF BENEFITS OF USING A FREQUENCY RATIOTHAT IS A MULTIPLE OF THREE IN A THREE PHASE INVERTER
Three phase inverter with RL load
• It is desirable to have MR as large as possible.
• This will push the harmonic at higher frequencies on the spectrum. Thus filtering requirement is reduced.
• Although the voltage THD improvement is not significant, but the current THD will improve greatly because the load normally has some current filtering effect.
• However, higher MR has side effects:– Higher switching frequency: More losses.
– Pulse width may be too small to be constructed. “Pulse dropping” may be required.