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Lecture Note
10
DC-AC PWM Inverters
Prepared by Dr. Oday A Ahmed Website: https://odayahmeduot.wordpress.com Email: [email protected]
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Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
1
DC-AC PWM Inverters
Inverters are AC converters used to convert the DC input into a sinusoidal AC
output with variable frequency and amplitude.
Applications of Inverter:
➢ adjustable-speed ac drives
➢ Induction heating,
➢ stand by air-craft power supplies,
➢ UPS (uninterruptible power supplies) for computers,
➢ HVDC transmission lines
Inverters can be broadly classified into two types; voltage source inverters
and current source inverters.
█ A voltage-source inverter (VSI), is one in which the DC source has small
or negligible impedance. In other words, a voltage source inverter has stiff
DC voltage source at its input terminals.
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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█ A current-source inverter (CSI) is fed with adjustable current from a DC
source of high impedance, i.e. from a stiff DC current source. In a CSI fed
with stiff current source, output current waves are not affected by the load.
voltage-source inverter (VSI),
Current-source inverter (CSI),
Inverter Switch Control
The inverter output voltage can be shaped based on the switch ON/OFF control
that use with the inverter. Thus, two types of switch control can be used which
are
• Square Wave Scheme
• PWM variable width Scheme
• Square Wave Scheme
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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• PWM variable width Scheme
Single-Phase Inverter
• Single-phase inverters classified generally into two types, Half-Bridge
and H-Bridge inverters as shown in the figures below:
Half-Bridge inverter H-Bridge inverter
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.
• Suitable for low power inverter. Big capacitor size and not economic, for high
power rating.
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Single-phase, Full-bridge
• 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.
• Same time closing would cause a short circuit from Vdc to ground (shoot-
through)
• To avoid shoot-through when using real switches (i.e. there are turn-on
and turn-off delays) a dead-time or blanking time is implemented
• Either S1,2 or S3,4 at the same time
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.
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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To illustrate the concept of AC waveform generation, see the following figure:
where the inverter states shown below:
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Square-wave Inverter with RL load
With an inductive load “i” is delayed behind the voltage “vℓ” although the voltage
wave is still a square.
At steady circuit conditions, the current wave-shape becomes repetitive. The
current will grow up exponentially during the positive half cycle from (-In) up to
(Ip) through:
instantaneous output current can be found
grows exponentially
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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The output voltage for square wave inverter with R or RL load is as shown below:
Load instantaneous voltage can be expressed as
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Variable Voltage Variable Frequency Capability
• 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
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.
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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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
Harmonics in square Wave Inverters
The output voltage of an inverter is rectilinear in nature, and therefore contains
harmonics. Harmonics reduce the efficiency and may have adverse effects on
the load. Harmonic reduction can be achieved by filtering and/or using harmonic
elimination techniques
For example, the Harmonic Effect on Induction machines can generate three
different sequences which are effect of stable operation of motor:
• 1, 7,13 are produce +ve sequence (a b c)
• 5,11,17 produce –ve sequence (acb)
• Triple harmonics: 3, 9, 15 produce zero sequence
• 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?
• –– “Power Quality” issue.
• – Harmonics may cause degradation of equipment. Equipment need
to be “de-rated”.
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Total Harmonic Distortion (THD) is a measure to determine the “quality” of a
given waveform.
V∞,
5t
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Harmonics Filtering
• Output of the inverter is “chopped AC voltage with zero DC component”. 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.
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Fourier Series
• Study of harmonics requires understanding of wave shapes. Fourier Series is a
tool to analyze wave shapes.
Harmonics of Square-wave
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Spectra of Square Wave
• Spectra (harmonics) characteristics:
– Harmonic decreases with a factor of (1/n).
– Even harmonics are absent
– Nearest harmonics is the 3rd. If fundamental is 50 Hz, then nearest harmonic
is 150 Hz.
– Due to the small separation between the fundamental an harmonics, output
low-pass filter design can be very difficult.
Quasi-Square Wave (QSW) Inverters
To reduce the harmonics order of the square wave inverter or to get a variable
rms voltage of the inverter output, QSW can be used. The QSW states are shown
below:
S1 S2 S3 S4
1 0 1 0
1 1 0 0
0 1 0 1
0 0 1 1
Lecture Note 10: DC-AC PWM Inverters
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Thus the following output voltage can be obtained:
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Example :
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Three-Phase Inverters
• Each leg (Red, Yellow, Blue) is delayed by 120 degrees.
• A three-phase inverter with star connected load is shown on the right
1800 Conduction Mode
In this mode, each switch conduct for 180 degree, in each 600 state three switches
conductus together either two positive switches and one negative or two negative
switches and one positive. For example, if T1, T5, and T6 conduct then the
equivalent circuit of the inverter can be derived as shown below:
T1 T5
T6
R R R
Vs
R Y B
N
T1 T5
T6
R
R
R Vs
R
B
Y
N
Vs/3
2Vs/
3
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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In this mode the inverter switches states are:
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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S1 1 1 1 0 0 0
S2 0 1 1 1 0 0
S3 0 0 1 1 1 0
S4 0 0 0 1 1 1
S5 1 0 0 0 1 1
S6 1 1 0 0 0 1
With R load. The diode across the transistors have no functions. If the load is
inductive, the current in each arm of the inverter would be delayed to the voltage
as shown in the figure below:
When T4 is off, the only path for the negative current iR is via D1. Hence the load
terminal R is connected to the DC source via D1 until the load current reverses
its polarity at t=t1. During period 0≤t≤ t1, T1 will not conduct. Similarly, T4 will
only start to conduct at t=t2. The transistors must be continually gated, since the
conduction time of transistors and diodes depends on the load power factor.
1200 Conduction Mode
In this mode, each switch conduct for 120 degree, in each 600 state two switches
conductus together one connected to the positive terminal and other one
connected to the negative. The equivalent circuit of inverter for each state can be
obtained as shown below:
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Example:
Compare between 1800 and 1200 conduction modes for three-phase DC-AC converter
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Example:
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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Multi Level Inverter
To reduce the effect of inverter harmonics and to increase the RMS Ac output
votlage multi-level inverter can be used.
These multilevel-output voltages are more sinelike in quality and thus
reduce harmonic content. The multilevel inverter is suitable for applications
including adjustable-speed motor drives and interfacing renewable energy
sources such as photovoltaics to the electric power grid.
Multilevel Converters with Independent DC Sources
One multilevel inverter method uses independent dc sources, each with an H
bridge.
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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EXAMPLE
For the two-source multilevel inverter with Vdc 100 V: (a) Determine the Fourier
coefficients through n =9, for α1=200 and α2= 400, (b) Determine α1 and α2 such
that the third harmonic (n 3) is eliminated .
Solution
a) to evaluate the Fourier coefficients,
resulting in V1 = 217, V3 = 0, V5 = -28.4, V7 = -10.8, and V9 = 0. Note that the
third and ninth harmonics are eliminated. The even harmonics are not present.
b) To achieve elimination of the third harmonic requires the solution to the
equations
Lecture Note 10: DC-AC PWM Inverters
Instructure: Dr. Oday A Ahmed
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The preceding concept can be extended to a multilevel converter having several
dc sources. For k separate sources connected in cascade, there are 2k1 possible
voltage levels. As more dc sources and H bridges are added, the total output
voltage has more steps, producing a staircase waveform that more closely
approaches a sinusoid. For a five-source system as shown in figure below, there
are11 possible output voltage levels.
Equalizing Average Source Power with Pattern Swapping
In the two-source inverter the source
and H bridge producing the voltage v1
supplies more average power (and
energy) than the source and H bridge
producing v2 due to longer pulse widths
in both the positive and negative half
cycles. If the dc sources are batteries,
one battery will discharge faster than
the other. A technique known as pattern
swapping or duty swapping equalizes
the average power supplied by each dc source.