Điện tử công suất (inverter chapter 4 )

Chapter 4
DC to AC Conversion
(INVERTER)
•
•
•
•
•

General concept
Single-phase inverter
Harmonics
Modulation
Three-phase inverter

Power Electronics and
Drives (Version 3-2003):
Dr. Zainal Salam UTM-JB

1


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

Vac

VDC

−

−

• TYPICAL APPLICATIONS:
– Un-interruptible power supply (UPS), Industrial
(induction motor) drives, Traction, HVDC
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Drives (Version 3-2003):
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2


Simple square-wave inverter (1)
• To illustrate the concept of AC waveform
generation

S1

S3

S4

S2

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3


AC Waveform Generation
S1,S2 ON; S3,S4 OFF
vO

S1
VDC

for t1 < t < t2

VDC

S3

+ vO −

t1

S4

t

t2

S2

S3,S4 ON ; S1,S2 OFF

for t2 < t < t3
vO

S1
VDC

S3
t2

+ vO −
S4

t3

t

S2
-VDC

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4

AC Waveforms
INVERTER OUTPUT VOLTAGE
Vdc
π

2π

-Vdc
FUNDAMENTAL COMPONENT
V1

4VDC

π

V1
3

V1
5

3RD HARMONIC

5RD HARMONIC

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5


Harmonics Filtering
DC SUPPLY

INVERTER

(LOW PASS) FILTER

LOAD

L
+
vO 1

C

+
vO 2

−

BEFORE FILTERING
vO 1

−
AFTER FILTERING
vO 2

• Output of the inverter is “chopped AC voltage with
zero DC component”. It contain 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.
Power Electronics and
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6


Variable Voltage Variable
Frequency Capability
Vdc2

Higher input voltage
Higher frequency

Vdc1

Lower input voltage
Lower frequency
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
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7


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 must match TNB
supply.
– “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.

Power Electronics and
Drives (Version 3-2003):

Dr. Zainal Salam UTM-JB

8


Total Harmonics Distortion (THD)
Voltage THD : If Vn is the nth harmonic voltage,
∞

(Vn, RMS )2

THDv = n= 2
V1, RMS
=

V2, RMS 2 + V3, RMS 2 + .... + V2, RMS 2
V1, RMS

If the rms voltage for the vaveform is known,
∞

(VRMS )2 − (V1, RMS )2

THDv = n= 2

V1, RMS

Current THD :
∞

(I n, RMS )2

THDi = n =2
I1, RMS
V
In = n
Zn

Z n is the impedance at harmonic frequency.
Power Electronics and
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9


Fourier Series
• Study of harmonics requires understanding of wave
shapes. Fourier Series is a tool to analyse wave
shapes.

Fourier Series
ao =
an =
bn =

1 2π

π
1

π
1

π

0
2π
0
2π

f (v )dθ (" DC" term)
f (v) cos(nθ )dθ

(" cos" term)

f (v) sin (nθ )dθ

("sin" term)

0

Inverse Fourier
∞
1
f (v) = ao + (an cos nθ + bn sin nθ )
2
n =1
where θ = ωt
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Harmonics of square-wave (1)
Vdc

π

2π

θ ω

-Vdc

ao =
an =
bn =

1 π

π

0

2π

Vdc dθ + − Vdc dθ = 0

π

Vdc π

π

0

Vdc π

π

0

2π

cos(nθ )dθ − cos(nθ )dθ = 0
π
2π

sin (nθ )dθ − sin (nθ )dθ
π

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11

Harmonics of square wave (2)
Solving,
V
π
2π
bn = dc − cos(nθ ) 0 + cos(nθ ) π
nπ
Vdc
[(cos 0 − cos nπ ) + (cos 2nπ − cos nπ )]
=
nπ
Vdc
[(1 − cos nπ ) + (1 − cos nπ )]
=
nπ
2V
= dc [(1 − cos nπ )]
nπ

[

]

When n is even, cos nπ = 1
bn = 0
(i.e. even harmonics do not exist)
When n is odd, cos nπ = −1
4Vdc
bn =
nπ

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12


Spectra of square wave
Normalised
Fundamental
1st

3rd (0.33)
5th (0.2)
7th (0.14)
9th (0.11)
11th (0.09)
1

3

5

n

7

9

11

• Spectra (harmonics) characteristics:
– Harmonic decreases with a factor of (1/n).
– Even harmonics are absent
– Nearest harmonics is the 3rd. If fundamental is
50Hz, then nearest harmonic is 150Hz.
– Due to the small separation between the
fundamental an harmonics, output low-pass
filter design can be very difficult.
Power Electronics and
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13


Quasi-square wave (QSW)
Vdc

α

α

α

π

2π

-Vdc

Note that an = 0. (due to half - wave symmetry)

[

2V
1 π −α
π −α
bn = 2
Vdc sin (nθ )dθ = dc − cos nθ α
π α
nπ

]

2Vdc
[cos(nα ) − cos n(π − α )]
=
nπ
Expanding :

cos n(π − α ) = cos(nπ − nα )

= cos nπ cos nα + sin nπ sin nα = cos nπ cos nα
bn =

2Vdc
[cos(nα ) − cos nπ cos nα ]
nπ

2Vdc
=
cos(nα )[1 − cos nπ ]
nπ
Power Electronics and
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14


Harmonics control
If n is even,

bn = 0,

4Vdc
If n is odd, bn =
cos(nα )
nπ
In particular, amplitude of the fundamental is :
b1 =

4Vdc

π

cos(α )

Note :

The fundamental , b1 , is controlled by varying

Harmonics can also be controlled by adjusting α ,
Harmonics Elimination :

For example if α = 30 o , then b3 = 0, or the third
harmonic is eliminated from the waveform. In
general, harmonic n will be eliminated if :
90o
α=
n
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15


Example
A full - bridge single phase inverter is fed by square wave
signals. The DC link voltage is 100V. The load is R = 10R
and L = 10mH in series. Calculate :
a) the THDv using the " exact" formula.
b) the THDv by using the first three non - zero harmonics
c) the THDi by using the first three non - zero harmonics
Repeat (b) and (c) for quasi - square wave case with α = 30

degrees

Power Electronics and

Drives (Version 3-2003):
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16


Half-bridge inverter (1)
S1 ON
Vdc S2 OFF

+
VC1
Vdc

G
+
VC2
-

2

S1
− V +
o

0

t

RL

S2
−

Vdc
2

S1 OFF
S2 ON

•

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 vice-versa.
Power Electronics and
Drives (Version 3-2003):
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17


Shoot through fault and
“Dead-time”
•

In practical, a dead time as shown below is required
to avoid “shoot-through” faults, i.e. short circuit
across the DC rail.

•

Dead time creates “low frequency envelope”. Low
frequency harmonics emerged.

•

This is the main source of distortion for high-quality
sine wave inverter.

+ S1

Ishort

G

Vdc
RL
−

S1
signal
(gate)

S2
signal
(gate)

S2

"Shoot through fault" .
Ishort is very large

td

td

"Dead time' = td

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18

Single-phase, full-bridge (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.

LEG R

VRG
Vdc
2

LEG R'

π

2π

ωt

π

2π

ωt

π

2π

ωt

+
+

Vdc
2

S1

-

Vdc

G

-

R

S3
+ Vo -

R'

+
Vdc
2

VR 'G
Vdc
2

−

S4

S2

−

Vdc
2

Vdc
2
Vo

Vdc

Vo = V RG − VR 'G
G is " virtual groumd"

− Vdc

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Drives (Version 3-2003):
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19


Three-phase inverter
•

Each leg (Red, Yellow, Blue) is delayed by 120
degrees.

•

A three-phase inverter with star connected load is
shown below

+Vdc
+
Vdc/2
G

S1

S3

−
+

Vdc/2

S5

R

Y

iR

iY

S4

B
iB

S6

S2

−

ZR

ia

ib

ZY

ZB

N

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20


Three phase inverter waveforms
Inverter Phase
Voltage
VDC/2
(or pole switching
waveform)
VRG
-V /2
DC

1200
VDC/2

VYG

-VDC/2

2400

VDC/2
VBG
-VDC/2
lIne-to -ine
Voltage
VRY

Six-step
Waveform
VRN

VDC

-VDC
2VDC/3
VDC/3
-VDC/3
-2VDC/3

Interval
Positive device(s) on
Negative device(s) on

1
3
2,4

2
3,5

4

3
5
4,6

4
1,5
6

5
1
2,6

6
1,3
2

Quasi-square wave operation voltage waveforms

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21


Pulse Width Modulation (PWM)
Modulating Waveform

+1
M1

Carrier waveform

0

−1
Vdc
2
0

−

•

t 0 t1 t2

t3 t4 t5

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.
Power Electronics and
Drives (Version 3-2003):
Dr. Zainal Salam UTM-JB

22


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

• Space-vector modulation (SVM)
– A simple technique based on volt-second that is

normally used with three-phase inverter motordrive
Power Electronics and
Drives (Version 3-2003):
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23


Modulation Index, Ratio
Modulating Waveform

+1
M1

Carrier waveform

0

−1

Vdc
2
0

−

t0 t1 t 2

t 3 t 4 t5

Vdc
2

Modulation Index (Modulation Depth) = M I :
Amplitude of the modulating waveform
MI =
Amplitude of the carrier waveform
Modulation Ratio (Frequency Ratio) = M R (= p )
MR = p =

Frequency of the carrier waveform
Frequency of the modulating waveform
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Modulation Index, Ratio
Modulation Index deterrmines the output
voltage fundamental component
If 0 < M I < 1,
V1 = M I Vin
where V1 , Vin are fundamental of the output
voltage and input (DC) voltage, respectively.
−−−−−−−−−−−−−−−−−−−−−−−−−−−−
Modulation ratio determines the incident (location)
of harmonics in the spectra.
The harmonics are normally located at :

f = kM R ( f m )
where f m is the frequency of the modulating signal
and k is an integer (1,2,3...)
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25