Hacettepe University

Electrical and Electronics Engineering Department

H.U. ELE 454 Lecture Notes

ELE 454
Power Electronics

Lecture Notes
Chapter VIII

Instructor: Dr. Işık Çadırcı

 OUTLINE

I. INTRODUCTION
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II. POWER SEMICONDUCTOR DEVICES

III. LOSS CALCULATIONS AND COOLING
IV. RECTIFIER CIRCUITS (AC-DC Converters)
V. CONVERTER OPERATION IN FOUR-QUADRANTS
VI. AC VOLTAGE CONTROLLERS
VII. CHOPPERS (DC-DC Converters)
VIII. INVERTERS (DC-AC Converters)
IX. PROTECTION OF POWER CONVERTERS
 VIII. INVERTERS

An inverter circuit links a dc supply to an ac load, i.e. it

converts a dc input voltage into an ac voltage at the output,
H.U. ELE 454 Lecture Notes

at a certain frequency, and magnitude.

Conversion of dc to ac is commonly achieved by using

power transistors (Mosfet, IGBT,...). Major application
areas are: switch-mode power supplies, speed control of ac
motors (adjustable speed ac drives), UPS
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The AC frequency is adjusted by:

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¾ Adjustment of the switching frequency of power semi-

conductors within the inverter. This is usually determined by the
frequency of a clock oscillator in the switching control section.
The magnitude of AC voltage is adjusted basically in two
ways:
¾ The voltage can be varied by varying the dc input voltage to
the inverter. In that case, adjustment is independent of inverter
switching.
¾ The alternative way is within the inverter by a technique
called pulse width modulation (PWM).
 VIII. INVERTERS

¾ Electrical power is usually available as AC at a fixed

frequency, such as 50 Hz or 60 Hz. For some applications, we
H.U. ELE 454 Lecture Notes

may need a frequency that is not the same as the available

supply frequency, or we may need an adjustable frequency. The
AC voltages we need may be three-phase or single-phase. All
these requirements can be met by the use of static inverters.

¾ Usually, the input AC is first converted to DC by a rectifier

circuit. This may be an uncontrolled rectifier using power
diodes, or a controlled one using thyristors (adjustable dc
voltage). The output of the rectifier serves as a DC input to
the inverter.
This scheme is called the ‘dc link inverter’
 VIII. INVERTERS

The dc link inverter

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Types of inverters:
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Inverters may be classified as:

¾ Voltage source inverter (most commonly used type, the AC
that it provides on the output side functions as a voltage
source)
¾ Current source inverter (it functions as a current source in
its output)
¾ Phase controlled inverter (do not generate independent
AC, only serves to feed power from a dc source into an
existing ac source)

There are two circuit topologies commonly used for

inverters: The half bridge, and the full-bridge inverter
 VIII. INVERTERS

The half bridge voltage-source inverter

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Load side

(Two switching elements: S1 and S2,

with antiparallel diodes: D1 and D2)
 VIII. INVERTERS
The half bridge voltage-source inverter
voltage-source
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¾ The input DC power supply to the half bridge has to be a

split power supply. The positive (P), the negative (Q), and the
midpotential (N) terminals must be available. Therefore, the
DC input is shown as two identical sources labeled V1 .

¾ In the case the midpoint terminal is not available (in the

case only a single power supply is available), two identical
capacitors (large electrolytic capacitors C1 &C2) are connected
in series across the DC source. Two large and equal resistors,
R, may be connected as shown in the previous Figure to ensure
correct voltage division. They also enable the capacitors to
discharge when the DC power supply is switched-off.
 VIII. INVERTERS

The half bridge voltage-source inverter

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¾ To operate the inverter to provide an AC output of frequency

f, the switches S1 and S2 are turned ON and OFF alternately,
each switching block is being kept ON for one half-period of
AC, while the other is kept OFF.

¾ It is important to ensure that both switches are never ON

simultaneously. If this happens, it is equivalent to a short-circuit
across the dc input, resulting in possible damage of switching
elements by excessive current.

In practice, a dead time is provided after turn-off of one switch,

and the turn-on of the other.
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Commutation sequence in the

half bridge inverter
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The output voltage and current waveforms for an R-L load
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Analysis of Half-Bridge Inverter with an R-L Load

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After several cycles:
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Example 1
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The single-phase full-bridge inverter

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The full-bridge inverter

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The full-bridge inverter
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In the operation without PWM,

switching blocks 1 and 4 are
turned-on for one half period of
AC. Next, they are turned off, and
switching blocks 2 and 3 are kept
on. For an inductive load, in the
transition from negative to
positive current (from t1 to t2), D1
and D4 are on. Similarly, from t3
to t4, D2 and D3 are on because
the direction of load current
cannot suddenly change.
 VIII. INVERTERS

The full-bridge inverter operation without PWM

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The full-bridge inverter operation without PWM

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be the same, with the sign reversed, and zero for t taken at beginning of this half cycle.
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Adjustment of AC frequency and voltage

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For most applications, there will be need to adjust the AC

frequency and voltage magnitude:

¾ Frequency is adjusted by variation of the clock oscillator

frequency of the switching control circuit.

¾ The technique used for implementing voltage control within

the inverter is known as pulse width modulation (PWM).
The sinusoidal waveform is usually the most desirable for
many applications, either using bulky output filters, or using
a suitably designed switching strategy within the inverter,
such as sinusoidal pulse width modulation (SPWM).
 VIII. INVERTERS
Control of ac output voltage by PWM
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The output
voltage and
current
waveforms:
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Conduction sequence:
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From t1 to tx : D1 and D4

From tx to t2: S1 and S4

From t2 to t3: S1 and D3

From t3 to ty: D2 and D3

From ty to t4: S2 and S3

From t4 to t5: S2 and D4

tx ty
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The single-phase
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full-bridge
inverter:
Square-wave and
quasi square-wave
outputs
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Shaping the output voltage by SPWM

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™ The concept underlying SPWM is to build up the total

waveform of the AC output voltage by means of multiple
pulses, with pulse widths distributed sinusoidally. In SPWM,
it is desirable to use a large number of pulses to form the AC
output voltage waveform.

™ A high pulse repetition frequency serves to shift the

harmonic components in the output towards the high
frequency direction in the frequency spectrum of output
voltage. It becomes then easier to filter them out by means
of small size LC filters.
 VIII. INVERTERS
Sinusoidal PWM (Sine –triangle comparison)
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Two voltage waveforms are used: A sine wave of the same

frequency as the inverter (called reference voltage), and a high
frequency triangular voltage (called carrier). The triangular
carrier waveform has a fixed amplitude. The amplitude of the
reference sine wave is usually made adjustable. We define the
modulation index as:
M = Amplitude of reference wave
amplitude of carrier wave

The adjustment of the modulation index gives us a convenient

way of adjusting the AC output voltage of the inverter. The
inverter output frequency is the same as the reference sine
wave frequency.
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Formation of firing instants for PWM wave

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at maximum output voltage

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Formation of firing instants for PWM wave at

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half of maximum output voltage

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Formation of firing instants for PWM wave

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at half voltage and half frequency

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The three-phase full-bridge inverter

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The 3-phase inverter derives its importance from the fact that
most AC industrial equipment are designed to work from
three-phase AC.
 VIII. INVERTERS
Three-phase square-wave inverter operation
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The three-phase power transistor inverter with

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a delta-connected load
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There are six controlled

switches S1 -S6, each with
S1-S6,
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its own anti-parallel diode

anti-parallel

There are three legs of the

inverter: A, B, and C.

It is in fact a superposition
of three single -phase, half
single-phase,
bridge configurations. For
example, on leg A, S1 is ON,
S4 is OFF for one half period
of AC, for the next half
period, S1 is OFF, S4 is ON.
 VIII. INVERTERS

When a top-side switch of an inverter leg is ON, output terminal

of that leg gets connected to positive terminal of DC input.
H.U. ELE 454 Lecture Notes

Similarly, when the lower switch of an inverter leg is ON, the

output terminal of that leg is connected to negative terminal of
DC input.

A line-to-line voltage is the voltage difference between two

output terminals. For example, VAB is the voltage of terminal A
wrt to terminal B. Since the potentials of terminals A and B wrt
to DC source midpoint (as in the case of a 1-ph. half bridge
inverter) are VAN and VBN , VAB = VAN –VBN.

All other line-to-line voltages can be determined in a similar

manner.
 VIII. INVERTERS
The switches belonging to phases A, B, and C operate in the
same manner, with a phase delay of 120° w.r.t. each other.
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Line currents
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SPWM waveforms
for 3-phase
bridge inverter:
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Programmed harmonic elimination of 5th and 7th harmonics

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This technique combines the square wave switching and PWM

to control the fundamental output voltage, as well as to eliminate
the designated harmonics from the output.
 VIII. INVERTERS

¾ The normalized voltage of an inverter leg is plotted where 6

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notches are introduced in the otherwise square wave output to

control the magnitude of the fundamental voltage , and to a
elminate for example the 5th and 7th harmonics.

¾ On half cycle basis, each notch provides one degree of

freedom, i.e. having 3 notches per half cycle provides control
of fundamental, and elimination of two harmonics.

¾ The required angles of notches α1, α2, and α3 are plotted as

a function of fundamental component in the output voltage
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