power electronics chapter 7
TRANSCRIPT
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DC TO AC CONVERTERMohd Shawal Bin JadinMohd Shawal Bin Jadin
Faculty of Electrical & Electronic EngineeringFaculty of Electrical & Electronic Engineering
[email protected]@ump.edu.my
BEE4223 BEE4223 Power Electronics & Power Electronics &
Drives SystemsDrives Systems
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OVERVIEW1. Introduction
2. Principle of operation
3. Performance parameter
4. The half-bridge inverter
5. Pulse Width Modulation (PWM)
6. PWM Generation
7. PWM Harmonics
8. Current Source Inverter
9. Introduction to three-phase inverter
10.Conclusions
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LEARNING OUTCOMESAt the end of the lecture, student should be able to:
1.State the operation and characteristics of Inverter.
2.Discuss the performance parameters and use different technique for analyzing and designing of DC to AC Converter.
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INTRODUCTION• Inverters are circuits that converts dc
input voltage to a symmetric ac output voltage by which both magnitude and frequency can be controlled.
• Applications :– adjustable speed ac motor drives,
uninterruptibleuninterruptible power supplies (UPS), and ac appliances run from an automobile battery.
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TYPES OF INVERTER• Voltage Source Inverter (VSI):
• Current Source Inverter (CSI)
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VOLTAGE SOURCE INVERTER (VSI) WITH VARIABLE DC LINK• DC link voltage is varied by a DC-to DC
converter or controlled rectifier.
• Generate “square wave” output voltage.
• Output voltage amplitude is varied as DC link is varied.
• Frequency of output voltage is
varied by changing the
frequency of the square
wave pulses.
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VOLTAGE SOURCE INVERTER (VSI) WITH VARIABLE DC LINK• Advantages:
– simple waveform generation
– Reliable
• Disadvantages:– Extra conversion stage
– Poor harmonics
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VSI WITH FIXED DC LINK• DC voltage is held
constant.
• Output voltage amplitude and frequency are varied simultaneously using PWM technique.
• Good harmonic control, but at the expense of complex waveform generation
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SQUARE WAVE INVERTER• Square wave inverter can be
simplifying justified with a switching scheme of full bridge converter.
• An square wave ac output voltage is synthesized from a dc input by closing and opening the switches in an appropriate sequence.
• The output voltage can be +Vdc, -Vdc, or zero, depending on which switches are closed.
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OPERATION OF SIMPLE SQUARE-WAVE INVERTER
• Parallel diode is used when the current in the switch is negative
• Diode will reverse-biased when current is positive in the switch
SQUARE-WAVE SQUARE-WAVE INVERTERSINVERTERS
EQUIVALENT EQUIVALENT CIRCUITCIRCUIT
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WHEN S1-S2 TURN ON & S3-S4 OFF FOR T1 < T < T2
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WHEN S1-S2 TURN OFF& S3-S4 ON FOR T2 < T < T3
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PERFORMANCE PARAMETERS
sdcdc
T
T
dc
Tt
dcdc
tdcdc
o
IVP
e
eVII
TtT
eV
IV
Tte
VI
V
tI
2
2
maxmin
2
min
min
1
1
R
2RR
20
R-
R)(
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EXAMPLE• A square-wave inverter has a dc source
of 125V, an output frequency of 60 Hz, and R-L series load with R = 20 Ohm and L = 20 mH. Determine
a) An expression for load current
b) Rms load current and
c) Average source current
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FOURIER SERIES ANALYSIS FOR SQUARE WAVE INVERTER
• Fourier series method is often the most practical way to analyze load current and to compute power absorbed by load.
,
22
2,
2
2,
1 1
4
4
2
dco
n odd
dc
nn
no
n n rms
nrms n rms
n n
VV
n
VV n
IZ R n L
P I R
II I
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FOURIER SERIES ANALYSIS FOR SQUARE WAVE INVERTER
2,
2
1,
2 21,
1,
2 4
4
n rmsn
vrms
rms rms
rms
dcdc
dc
V
THDV
V V
V
VV
nV
n
2,
2
1,
n rmsn
Irms
I
THDI
• The quality of ac output voltage or current can be expressed by total Harmonic Distortion (THD)
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EXAMPLE 1• Consider a square wave inverter
with Vdc=100V, R=10, L=25mH, and f=60Hz. Determinei. Fundamental output voltage
ii. THD for output voltage and current and power absorbed by load
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EXAMPLE 2i. Fundamental output voltage
1
4 4100 127.3
(1)dcVV Vn
4
4 100
127.3....
dcn
VV
n
n
in
ii.THDv and THDI
22
22 3
2
2
2
10 2 60 25 10
100 9.43 ....
127.3.......( )
100 9.43
n
nn
n
Z R fnL
n
n ii
VI iii
Z n n
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EXAMPLE 2
n fn (Hz) Vn (V) Zn () In (A) Pn (W)
1 60 127.3 13.7 9.27 429.3
3 180 42.3 30 1.42 10
5 300 25.5 48.2 0.53 1.4
7 420 18.2 66.7 0.27 0.37
9 540 14.1 85.4 0.17 0.14
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EXAMPLE 1 (CONT)
2
2 4 100100
2 1
4 100
2 1
10000 8106
90.030.484
48.4%
vTHD
2,
2
1,
2 2 2 21.42 0.53 0.27 0.17
2 2 2 29.27
2
0.167
16.7%
n rmsn
Irms
I
THDI
2
2,
2
429.3 10 1.40 0.37 0.14
441
nn n rms
n
IP I R R
P P
W
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AMPLITUDE & HARMONIC CONTROL• The amplitudeamplitude of the fundamental frequency for a square-wave output from the full-bridge inverter is is determined by the dc input determined by the dc input voltagevoltage.
• A controlled output can be controlled output can be produced by modifying the produced by modifying the switching schemeswitching scheme.
• This output voltage can be controlled by adjusting the adjusting the interval interval on each side of the pulse where the output is zero.
• Harmonic also can be eliminated by choosing a value of which which make the sine terms go to zero.make the sine terms go to zero.
n
o90
1 1 1
4cosdcVV I Z
1
22
4
nn
no
VV n
IZ R n L
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EXAMPLE 2
• Design an inverter that will supply the series R-L load of R=10, L=25mH with a fundamental frequency of 60Hz and current amplitude of 9.27A and THD less than 10%. A variable source is available.
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EXAMPLE 2 (CONT)• The dominant harmonic current is for n = 3 (third harmonic), so the switching scheme must eliminate the third harmonic.
1 1 1
221
22(9.27) 10 1 2 60 0.025
127
o
V I Z
I R n L
V
rdeliminate the 3 harmonic,
9030
3
oo
1
4cos
127
4cos30
116
dc
o
VV
V
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EXAMPLE 1 (CONT)
22
22 3
2
2
2
10 2 60 25 10
100 9.43 ....
127.......( )
100 9.43
n
nn
n
Z R fnL
n
n ii
VI iii
Z n n
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EXAMPLE 1 (CONT)n fn (Hz) Vn (V) Zn () In (A)
1 60 127.3 13.7 9.27
3 180 0 30 0
5 300 25.5 48.2 0.53
7 420 18.2 66.7 0.27
9 540 0 85.4 02 2
0.53 0.27
2 29.27
2
0.067
6.7% 10%
ITHD
than
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TRY THIS………
–Ω
( )a α( )b
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PULSE-WIDTH MODULATED OUTPUT
• In square wave inverters, maximum output voltage maximum output voltage is achievableis achievable.
•However there in NO control in harmonics and NO control in harmonics and output voltage magnitudeoutput voltage magnitude.
i.e the harmonics are always at three, five, seven harmonics are always at three, five, seven etc times the fundamental frequencyetc times the fundamental frequency.
•Hence the cut-off frequency of the low pass filter is cut-off frequency of the low pass filter is somewhat fixedsomewhat fixed. The filter size is dictated by the VA ratings of the inverter.
• To reduce filter size, the PWM switching To reduce filter size, the PWM switching scheme can be utilizedscheme can be utilized.
• In this technique, the harmonics are “pushed” to the harmonics are “pushed” to higher frequencieshigher frequencies. Thus the cut-off frequency of cut-off frequency of the filter is increased.the filter is increased. Hence the filter components (i.e. L and C) sizes are reduced.
•The trade off for this flexibility is complexity in the complexity in the switching waveformsswitching waveforms.
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PULSE WIDTH MODULATION (PWM)
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PULSE WIDTH MODULATION (PWM)• 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.
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PULSE WIDTH MODULATION (PWM)• Production of PWM waveform using reference
sinewave:
• Comparator determines instants at which waveforms cross in order to produce switching waveform
• PWM output waveform tracks amplitude and frequency of reference sinewave
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PULSE WIDTH MODULATION (PWM)• As switching frequency is increased,
switching loss becomes issue
• Implementation by ICs which essentially contain tables of pre-calculated values of switching angles covering range of output frequencies
• As computational speeds of ICs increase, it is now possible to calculate required firing angles in real time in order to optimise strategy for harmonic elimination, and control, further improving inverter performance
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PULSE WIDTH MODULATION (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
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BIPOLAR SWITCHING
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UNIPOLAR SWITCHING
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PULSE WIDTH MODULATION IN UNIPOLAR INVERTERS
The square wave output can be produced using a comparator to compare the triangle wave with the sine wave.
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HALF-BRIDGE INVERTER
• 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.
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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.
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INTRODUCTION TO THREE-PHASE INVERTER
• Each leg (Red, Yellow, Blue) is delayed by 120 degrees.
• A three-phase inverter with star connected load is shown below
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THREE PHASE INVERTER WAVEFORMS
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SUMMARY• Have examined operation of inverters as
means of producing variable-frequency, variable voltage AC source from DC supply
• PWM provides amplitude control of the fundamental output frequency although the harmonics have large amplitudes, they occur at high frequency and are filtered easily.
• Considered voltage-sourced and current-sourced inverters which operate from DC supplies which approximate constant voltage source
• Introduced pulse-width-modulated inverter