Tải bản đầy đủ

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

2


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

S1

S3

S4


S2

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

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

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

4


AC Waveforms
INVERTER OUTPUT VOLTAGE
Vdc
π



-Vdc
FUNDAMENTAL COMPONENT
V1

4VDC

π

V1
3

V1
5

3RD HARMONIC

5RD HARMONIC

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

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

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

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

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

0


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

10


Harmonics of square-wave (1)
Vdc

π



θ ω

-Vdc

ao =
an =
bn =

1 π

π

0



Vdc dθ + − Vdc dθ = 0
π

Vdc π

π

0

Vdc π

π

0



cos(nθ )dθ − cos(nθ )dθ = 0
π


sin (nθ )dθ − sin (nθ )dθ
π

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

11


Harmonics of square wave (2)
Solving,
V
π

bn = dc − cos(nθ ) 0 + cos(nθ ) π

Vdc
[(cos 0 − cos nπ ) + (cos 2nπ − cos nπ )]
=

Vdc
[(1 − cos nπ ) + (1 − cos nπ )]
=

2V
= dc [(1 − cos 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 =

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

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

13


Quasi-square wave (QSW)
Vdc

α

α

α

π



-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


]

2Vdc
[cos(nα ) − cos n(π − α )]
=

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 ]


2Vdc
=
cos(nα )[1 − cos nπ ]

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

14


Harmonics control
If n is even,

bn = 0,

4Vdc
If n is odd, bn =
cos(nα )

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

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):
Dr. Zainal Salam UTM-JB

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):
Dr. Zainal Salam UTM-JB

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

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

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



ωt

π



ωt

π



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

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

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

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

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

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

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):
Dr. Zainal Salam UTM-JB

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

24


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

25


Tài liệu bạn tìm kiếm đã sẵn sàng tải về

Tải bản đầy đủ ngay

×