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Lecture Note

10

DC-AC PWM Inverters

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Lecture Note 10: DC-AC PWM Inverters

Instructure: Dr. Oday A Ahmed

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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.



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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



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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.



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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.



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To illustrate the concept of AC waveform generation, see the following figure:

where the inverter states shown below:



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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



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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



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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.



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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”.



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Total Harmonic Distortion (THD) is a measure to determine the “quality” of a

given waveform.

V∞,

5t



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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.



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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



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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



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Thus the following output voltage can be obtained:



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Example :



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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



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In this mode the inverter switches states are:



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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:



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Example:

Compare between 1800 and 1200 conduction modes for three-phase DC-AC converter



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Example:



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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.



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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



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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.

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