Power Electronics

Semester : V
Branch : Electrical
Engineering

Prof. Omprakash Kumar, Electrical Engineering

Government Engineering College

K Kishanganj, Bihar
Syllabus

Unit 1: Power Switching Devices

Unit 2: Thyristors Rectifiers

Unit 3: DC-DC Converters

Unit 4: Power Circuit of BOOST Converter

Unit 5: Single Phase Voltage Source
Inverter
Unit 6: Three phase Voltage Source
Inverter
 Unit 5

Single – Phase Voltage Source

Inverter
 CONTENT
Power Circuit of Single – Phase Voltage Source
Inverter

Switch States and Instantaneous Output Voltage

Square wave Operation of the Inverter

Concept of Average Voltage Over a Switching Cycle

Bipolar Sinusoidal Modulation & Unipolar Sinusoidal

Operation

Modulation Index and Output Voltage

 DC-AC Converters / Inverters
• Inverter circuit convert DC power to AC power
at required output voltage and frequency.

• Classification of Inverters:
• I. Depending on the nature of input source
a. Voltage Source Inverter – DC Voltage Input
b. Current Source Inverter – DC Current Input

• II. Nature of Output voltage waveform

a. Square – wave Inverters – Square wave AC
voltage
b. Quasi – square wave Inverters
c. Pulse – width modulated (PWM) Inverters
 DC-AC Converters / Inverters
• Classification of Inverters:
• III. Depending on the type of commutation
a. Line – commutated Inverters
b. Force – commutated Inverters

• IV. Depending on the type of configuration of

switching devices
a. Half – Bridge Inverters
b. Full – Bridge Inverters
c. Series Inverters
d. Parallel Inverters
 DC-AC Converters / Inverters
Invert
er

• Frequency of AC Output Voltage is controlled by

varying the rate at which the device is turned ON
and OFF (switching frequency).

• Magnitude of AC Output voltage is controlled as:-

• Internal Control: RMS value of output voltage is
controlled by PWM technique.
• External Control: By using another kind of
converters like, rectifier (α), chopper.
1 – Φ Voltage Source Inverter (VSI)
 1 – Φ Half Bridge VSI : R Load
• and :- BJT, MOSFET, IGBT, GTO
or Thyristor
• AO : Pole
• : Output voltage or Pole Voltage

• The switches in inverter are

complementary i.e.
if is ON , should not be turned ON and
if is ON , should not be turned ON.

• Otherwise, DC source will be short circuited and will

damage the circuit.
 1 – Φ Half Bridge VSI : R Load
• When is ON for 0 to • When is turned OFF
and
is Turned ON for

Note: Diodes do not conduct in case of R

load.
1 – Φ Half Bridge VSI : R Load
 1 – Φ Half Bridge VSI : R Load
RMS value of output voltage,

Note: for square wave, RMS value =

Amplitude
RMS value of output current,
 1 – Φ Half Bridge VSI : R Load
The instantaneous output voltage, is rectangular in
shape. It can be expressed in Fourier series as:

Due to quarter wave symmetry, and are zero.

1 – Φ Half Bridge VSI : R Load
 1 – Φ Half Bridge VSI : R Load

RMS value of fundamental

component of output voltage,
(As sinusoidal)

RMS value of third component

of output voltage,
(As sinusoidal)
 1 – Φ Half Bridge VSI : R Load

RMS value of fundamental

component of output current,

RMS value of third component

of output current,
 1 – Φ Half Bridge VSI : R Load
Fundamental load power,

Where : fundamental displacement factor. It is cosine of

angle between fundamental voltage, and fundamental
current,

For R load,
()()=

()()=

Note: So, fundamental output power does the useful

work in most of the applications (electric motor drives,
etc.). The other harmonic power does not do the useful
work and are dissipated as heat leading to rise in
 1 – Φ Half Bridge VSI : R Load
Harmonic factor (): it is the measure of individual
harmonic contribution.

Total Harmonic Distortion (THD): is defined as the

ratio of RMS value of higher harmonic components to
the RMS value of fundamental component.
1 – Φ Half Bridge VSI : R Load
 1 – Φ Half Bridge VSI : R Load
-- the output voltage waveform has 48.43% of harmonic
content.

• THD is the measure of total harmonic content in the

waveform.
• Lower the value of THD, lower is the harmonic content
present and lower is amount of distortion in the
waveform and therefore, closer is the waveform to a
sine wave.
 1 – Φ Half Bridge VSI : R Load
Distortion Factor (DF): it indicates the amount of
harmonics that remain in the output waveform after the
harmonic in the output voltage have been subjected to

for n>1
second order attenuation (i.e. divided by ).

: - Thus, only 3.8% of harmonics will remain in the

output waveform after the harmonics in the output
voltage have been subjected to second order
attenuation.
• The DF for nth harmonic individual component is
 1 – Φ Half Bridge VSI : R Load
Lowest order harmonic (LOH): the lowest order
harmonic is that component whose frequency is
closest to the fundamental and has an amplitude
greater than or equal to 3% of the fundamental
component.

Cond 1: frequency closest to fundamental.

fundamental frequency = ω
frequency of 3rd harmonic = 3ω --- closest to
fundamental
frequency of 5th harmonic = 5ω

Cond 2: amplitude>=3% of fundamental component

 1 – Φ Half Bridge VSI : R Load

As the frequency of 3rd harmonic component is closest to

fundamental and its amplitude is greater than 3% of
fundamental component, satisfies both the condition, 3rd
harmonic is the lowest order harmonic.
 1 – Φ Half Bridge VSI : R Load
Question: A single – phase half bridge inverter,
connected to 230 V DC source, feeds a resistive load of
10 ohm. Determine
1. Fundamental RMS output voltage
2. Total output power and fundamental frequency power
3. Average and peak current of each switch
4. Peak reverse blocking voltage of each switch
5. Input power factor
6. Distortion factor
7. THD
8. Harmonic factor and Lowest order harmonic
1 – Φ Half Bridge VSI : R Load
1 – Φ Half Bridge VSI : R Load
1 – Φ Half Bridge VSI : R Load
 1 – Φ Half Bridge VSI : RL Load

When is turned ON at time

 1 – Φ Half Bridge VSI : RL Load
When is turned OFF at time Output current falls to zero
For inductive load, the load at time, say . And will get
current cannot change reverse biased and do not
immediately. The current conduct.
will continue to flow through Now is turned ON at time
diode , load, lower half of
the DC source until the
current falls to zero.

Output current will flow in

opposite direction as shown
in fig.
Inductor will store energy.
 1 – Φ Half Bridge VSI : RL Load
Now is turned OFF at time
For inductive load, the load
current cannot change
immediately. The current
will continue to flow through
diode , load, upper half of
the DC source until the
current falls to zero.

Output current falls to zero

at time, say . And will get
reverse biased and do not
 1 – Φ Half Bridge VSI : RL Load
RMS value of output voltage,

Note: for square wave, RMS value =

Amplitude
 1 – Φ Half Bridge VSI : RL Load
The instantaneous output voltage, is rectangular in
shape. It can be expressed in Fourier series as:

Due to quarter wave symmetry, and are zero.

1 – Φ Half Bridge VSI : RL Load
 1 – Φ Half Bridge VSI : RL Load

RMS value of fundamental

component of output voltage,
(As sinusoidal)

RMS value of third component

of output voltage,
(As sinusoidal)
 1 – Φ Half Bridge VSI : RL Load
Fourier series expansion of instantaneous output
current can be given as:

Where,
 1 – Φ Half Bridge VSI : RL Load

RMS value of fundamental component of output

current,
(As sinusoidal)

RMS value of third component of output current,

(As sinusoidal)
 1 – Φ Full Bridge VSI : R Load
and are turned OFF and
and are turned ON for to

and are turned ON for 0 to

Diodes will not conduct in

case of R load.
Switches , and , are in
series across the source.
They should not be turned
1 – Φ Full Bridge VSI : R Load
1 – Φ Full Bridge VSI : RL Load
and are turned ON at time
 1 – Φ Full Bridge VSI : RL Load
When and are turned OFF at Now and are turned ON at
time time
For inductive load, the load
current cannot change
immediately. The current
will continue to flow through
diode and until the current
falls to zero.
 1 – Φ Full Bridge VSI : RL Load
Now and are turned OFF at
time
For inductive load, the load
current cannot change
immediately. The current
will continue to flow through
diode and until the current
falls to zero.
 Three Phase Inverters
• Three-phase inverters are normally used for high-
power applications. Ex: Wind generator connected to
the AC grid.

• A three-phase output can be obtained from a

configuration of six switches and six diodes.

• There are two possible pattern of gating the switching

devices:-
• 180-degree conduction :- Each switch conduct for
180 degree.
•
Three Phase Load
Three Phase 180-degree Mode VSI
 Three Phase 180-degree Mode VSI
1. Each switch conducts for 180 degree of angle.

2. Switch pairs in each arm ( & , & , & ) turned ON with

a time interval of 180 degree i.e. conducts for 180
degree and conducts for next 180 degree of the
cycle.

3. Switches in upper group (, , ) conducts at an interval

of 120 degree i.e. if is gated at , then must be gated
at and at This also applies for switches in lower
group (, , ).
 Three Phase 180-degree Mode VSI
Step I: Switches , & are conducting for 0 to 60 degree
 Three Phase 180-degree Mode VSI
Step II: Switches , & are conducting for 60 to 120
degree
 Three Phase 180-degree Mode VSI
Step III: Switches , & are conducting for 120 to 180
degree
 Three Phase 180-degree Mode VSI
Step IV: Switches , & are conducting for 180 to 240
degree
Three Phase 180-degree Mode VSI
Line voltages , &
= -; = -; = -
 Three Phase 180-degree Mode VSI
• Phase voltages have six steps per cycle.
• Line voltages have two pulses per cycle.
• Phase as well as line voltages are out of phase by
120 degree.
• The function of diodes is to allow the flow of
current through them when the load is reactive in
nature.
 Three Phase 180-degree Mode VSI
• RMS value of phase voltages:
 Three Phase 180-degree Mode VSI
• RMS value of line voltages:
 3-Φ180-degree Mode VSI: Fourier
Analysis
• The instantaneous output phase voltage can be
expressed in Fourier series as:-
3-Φ180-degree Mode VSI: Fourier
Analysis
3-Φ180-degree Mode VSI: Fourier
Analysis
3-Φ180-degree Mode VSI: Fourier
Analysis
Pulse Width Modulated Inverter
Pulse Width Modulated Inverter

𝑉 𝑆
𝑉 𝑂𝑅𝑀𝑆 =
2
∞
2𝑉 𝑆
𝑉 𝑂= ∑ sin ⁡(𝑛𝜔 𝑡)
𝑛=1, 3,5, …. 𝑛 𝜋

𝑉 𝑂𝑅𝑀𝑆 =𝑉 𝑆
∞
4𝑉 𝑆
𝑉 𝑂= ∑ sin ⁡(𝑛 𝜔𝑡)
𝑛=1, 3,5, …. 𝑛 𝜋
 Pulse Width Modulated Inverter
∞
𝑉 𝑂𝑅𝑀𝑆 =𝑉 𝑆 4𝑉 𝑆
𝑉 𝑂= ∑ sin ⁡(𝑛 𝜔𝑡)
𝑛=1, 3,5, …. 𝑛 𝜋

• Magnitude of Output voltage can not be controlled

as
• is fixed.
• Pulse width is fixed.
• We could control only frequency of output voltage.

• To control magnitude as well as frequency of

output voltage, PWM inverter can be used.
 Pulse Width Modulated Inverter
• Previously, and were ON from
0 to and and were ON from
to .
• Now if and are made to turn
ON for 2d i.e. from () to ()
and and are made to turn
ON for 2d i.e. from () to ().
• Pulse width=width of pulse per half cycle=2d
• RMS value of output voltage=
• Thus, magnitude of the output voltage can be
controlled as now it will depend on pulse width 2d.
• This is called single pulse modulation(SPM).
 Pulse Width Modulated Inverter
• Pulse width/half cycle=2d/N;
where, N = No of pulse.
PW= 2d/2=d

• This is called multiple pulse modulation(MPM).

 Pulse Width Modulated Inverter

• As the width increases, the average value also

increases in the form of sine wave.
• This is called unipolar sinusoidal pulse
modulation(SPM).
 Pulse Width Modulated Inverter

• As the width increases, the average value also

increases in the form of sine wave.
• This is called bipolar sinusoidal pulse
modulation(SPM).
 Single & Multiple PWM
• How to generate these symmetrical pulses?

square wave of frequency ω (called reference

• These pulses can be generated by comparing a

waveform) with a triangular waveform of frequency

(called carrier waveform) using a comparator.
 Single & Multiple PWM
• If then and will be
turned ON.

• if then and will

be turned ON.

No. of pulse generated per half cycle?

=
 Single & Multiple PWM
Total pulse width in half cycle=2d
Width of each pulse = 2d/N
Width of each pulse in terms of
modulation index?

From the right-angle triangles-

Where,