POWER FACTOR IMPROVEMENT OF AN AC-DC

CONVERTER USING SINUSOIDAL

PULSE WIDTH MODULATION

A REPORT SUBMITTED FOR PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

BACHELOR OF TECHNOLOGY
IN
ELECTRICAL ENGINEERING
SUBMITTED BY

Name Univ. Roll No.

AKASH KUMAR MANDAL 11101621001
ANINDYA PAUL 11101621002
ADITYA DAS 11101621024
SUVAJIT MONDAL 11101622031
ANUSHREE DAS 11101622027
RAHIMA KHATUN 11101622032

UNDER THE GUIDANCE OF

DR. SANKAR DAS
(ASST. PROFESSOR)
DEPARTMENT OF ELECTRICAL ENGINEERING

GOVT. COLLEGE OF ENGINEERING AND TEXTILE TECHNOLOGY, BERHAMPORE

AFFILIATED TO

MAULANA ABUL KALAM AZAD UNIVERSITY OF TECHNOLOGY

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 CERTIFICATE OF APPROVAL

This is to certify that the thesis entitled, “Power factor Improvement of an AC-DC
Converter via sinusoidal pulse width modulation” submitted by ANINDYA PAUL,
AKASH KR .MANDAL,ADITYA DAS,SUVAJIT MONDAL, RAHIMA
KHATUN,ANUSHREE DAS in partial fulfillment of the requirements for the award of
Bachelor of Technology Degree in Electrical Engineering at the Govt. college of
engineering and textile technology, Berhampore (MAKAUT University) is an authentic
work carried out by them under my supervision and guidance.
To the best of my knowledge, the matter embodied in the thesis has not been submitted
to any other University / Institute for the award of any Degree or Diploma.

………………………. ……………………..
Dr. Sankar Das Dr. Bikash Das
(Supervisor & Prof.) (Prof. & H.O.D)
Dept. of Electrical Engineering Dept. of Electrical Engineering
 ACKNOWLEDGMENT

It is our great privilege to express profound and sincere gratitude to our Project Supervisor, Dr.
SANKAR DAS for providing us a very cooperative and precious guidance at every stage of the
present project work being carried out under his supervision. His valuable advice and
instructions in carrying out the present study has been a very rewarding and pleasurable experience
that has greatly benefited us throughout the course of work.

We would like to convey our sincere gratitude towards Dr. BIKASH DAS, Head of the
Department of Electrical Engineering, GOVT. COLLEGE OF ENGINEERING AND TEXTILE
TECHNOLOGY, BERHAMPORE for providing us the requisite support for time completion of our
work. We would also like pay our heartiest thanks and gratitude to all the teachers of the Department
of Electrical Engineering, GOVT. COLLEGE OF ENGINEERING AND TEXTILE
TECHNOLOGY, BERHAMPORE for various suggestions being provided in attaining success in
our work.

Finally, we would like to express our deep sense of gratitude to our parents for their constant
motivation and support throughout our work.

………………………
(Anindya Paul)

………………………
(Akash Kumar Mandal)

……………………
(Aditya Das)

………………………
(Suvajit Mondal)

………………………
(Rahima Khatun)

………………………
(Anushree Das)

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 ABSTRACT

AC to DC converters are widely used in industrial applications to supply DC power to

drive systems. However, a major drawback of these converters is the significant
harmonic distortion they introduce, which leads to a poor overall power factor and
reduced system efficiency.

This study focuses on improving the power factor of such converters by implementing
Sinusoidal Pulse Width Modulation (SPWM) on the load current waveform. A
simulation-based model is developed using MATLAB to analyze the impact of SPWM
on harmonic reduction and power factor enhancement.

The model is designed to determine the optimal value of lag angle, (a) for various
combination of load inductance L and resistance R .To yields the maximum power
factor. Various waveform generation techniques are employed in the simulation to
evaluate performance under different load conditions.

The proposed model demonstrates practical applicability for large industrial drive
systems, offering an effective method for reducing harmonic content and improving
power factor, thus enhancing overall energy efficiency.
 CONTENT
TOPIC PAGE NO.

Certificate…………………………………………………………………………………………………….. 1
Acknowledgment………………………………………………………….....................………………………. 2
Abstract…………………………………………………………………………...………………………….. 4
Contents………………………………………………………………………………………………………. 5
List of Figures………………………………………………………………………………………………. 6

Literature survey …………………………………………………………………………………………….. 8-9

( Limitations of previous work , our contribution )…………………………………………………………..

1. INTRODUCTION……………………………………………………………………... 7

1.1 Theory (Definition of Power factor)………………………………………………………………….. 10

1.2 Importance of Power Factor in Electrical System………………………………………………… 11
1.3 Impact of Low Power Factor on Efficiency and Grid Performance……………………………… 12-15
1.4 Active and Reactive Power concepts…………………………………………………………….. 16
1.5 AC DC converter and its working………………………………………………………………… 17-20

2. SINUSOIDAL PULSE WIDTH MODULATION …………………………………….. 21-23

2.1 Role of SPWM in power factor improvement of AC DC converter 24-26

27-29
2.2 How this SPWM technique targets the optimum power factor

3. SIMULATION ANALYSIS …………………………………………………………….. 30

3.1 Developed circuit in MATLAB simulation ……………………………………………….. 30-35

3.2 Calculation of the power factor and Simulation results……………………………………. 38-40
3.3 Study of harmonics in current waveform of AC DC converter ……………………………. 41-43
3.4 Advantages and Disadvantages of using this method………………………………………. 44

45
5. CONCLUSION……...…………………………………………….……………………...

6. REFERENCES…………………………………………………………………………….. 46

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 LIST OF FIGURES
PAGE NO.
Fig. 1 POWER FACTOR DIAGRAM 10

16
Fig. 2 POWER TRIANGLE DIAGRAM

Fig. 3 SCHEMATIC DIAGRAM OF AC DC CONVERTER WITH 17

A R L LOAD

Fig. 4 FULL WAVE BRIDGE CONVERTER (MOSFET WITH 18

BODY DIODE) OUTPUT

Fig. 5 SPWM GENERATION WAVEFORM 22

Fig. 6 SIMULATION MODEL 30

Fig. 7 SUBSYSTEM OF SPWM GENERATOR 31

Fig. 8 MOSFET BLOCK PARAMETER 32

Fig. 9 POWER FACTOR MEASURING BLOCK INTERNAL 33

DIAGRAM
Fig. 10 CONVERTER BLOCK 34

Fig. 11 SINUSOIDAL O/P OF FULL WAVE RECTIFIER 35

Fig. 12 SPWM CHOPPED VOLTAGE WAVE FORM FOR 30% 36

DUTY CYCLE

Fig. 13 SPWM CHOPPED VOLTAGE WAVE FORM FOR 50% 36

DUTY CYCLE

Fig. 14 VARIATION OF POWER FACTOR WITH LAG 39

ANGLE FOR DIFFERENT LOADS IN SAME PLOT

Fig. 15 FFT ANALYSIS RESULT 1 42

Fig. 16 FFT ANALYSIS RESULT 2 42

Fig. 17 FFT ANALYSIS RESULT 3 43

 1. INTRODUCTION

In modern electrical systems, power factor improvement is essential for

enhancing efficiency and reducing losses project focuses on improving the
power factor of an AC-DC converter using Sinusoidal Pulse Width Modulation
(SPWM).

Traditional rectifiers and converters often introduce power quality issues, such as
harmonic distortion and poor power factor, leading to inefficiencies in power
transmission and utilization. The proposed system utilizes SPWM-based switching
techniques to achieve a near-unity power factor by shaping the input current
waveform to follow the input voltage.

This technique helps in reducing harmonic distortions, improving voltage

regulation, and enhancing the overall efficiency of the converter. The project
involves MATLAB/Simulink-based simulations to analyze the performance of the
converter under different operating conditions.

The results will demonstrate the effectiveness of SPWM in achieving better power
quality and efficiency compared to conventional rectifiers. This study is
particularly relevant for industrial applications, renewable energy systems, and
power electronics, where maintaining a high power factor is crucial for system
reliability and cost-effectiveness.

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 LITERATURE SURVEY

► Previous Work on Power Factor Improvement Using SPWM -

Tore M Mohan et al. , In the year of 1995 "Power Electronics: Converters, Applications, and
Design"[Ref. 1]
introduced SPWM-based rectifiers and their impact on power factor
improvement. He Demonstrated that sinusoidal modulation of the duty cycle reduces harmonic
distortion compared to conventional switching techniques. Singh et al. , in the year of 2003
"Power Quality Enhancement in AC-DC Converters" [Ref. 2] Explored active and passive power
factor correction techniques. Found that SPWM significantly improves power factor, but
residual harmonics still exist. Proposed additional filtering methods for further harmonic
suppression. Gupta et al. , in the year of 2010 "Harmonic Analysis of SPWM-Based
Rectifiers"[Ref. 3] Conducted a detailed study on the harmonic spectrum of SPWM-controlled
converters. Showed that higher-order harmonics persist, affecting overall system efficiency.
Zhang et al. , in the year of 2017, "Optimization of SPWM Switching for Power Factor
Correction"[Ref. 4] developed an optimized SPWM algorithm for better power factor correction.
Demonstrated that harmonic reduction is possible with adaptive SPWM switching.

► Previous Work on Harmonic Reduction in SPWM-Based Converters -

Akagi et al. , in the year of 2005 "Active and Passive Filtering for Harmonic
Mitigation"[Ref.5] . He Compared passive LC filters and active harmonic filtering techniques.
Concluded that while LC filters effectively reduce low-order harmonics, they are less effective
for higher-order harmonics. Rashid et al. In the year of 2012 ,"Harmonic Elimination in PWM
Converters Using Advanced Filtering"[ Ref. 6] ,who Studied the impact of different filter
designs (L, LC, LCL) on harmonic suppression.Found that LCL filters offer better attenuation
of high-frequency harmonics. Kumar et al. In the year of 2019 "Hybrid Harmonic Reduction in
SPWM-Based Rectifiers"[Ref.7] . He Proposed a hybrid filtering approach combining passive
and active filters.Achieved a significant reduction in Total Harmonic Distortion (THD) below
IEEE-519 standards.
► Limitations of Previous Work

Most studies focus on either power factor improvement or harmonic reduction, but not both
together in SPWM-based converters. Effect of SPWM on DC output voltage stability is not
extensively studied. Optimization of SPWM parameters for both power factor improvement
and harmonic reduction remains unexplored. No existing research proposes a graph-based
optimization algorithm to determine the best operating conditions for SPWM.

► Our Contribution

1.We are conducting a detailed harmonic analysis in SPWM-based AC-DC converters

using MATLAB/Simulation.

2.A direct relationship between lag angle ‘α′ as a function of resistance (R) and
inductance (L) has been formulated using curve fitting technique.

3 Exploring different filter configurations (RC, active filters) to find the most effective
solution for harmonic suppression.

4.And Developed an optimized condition or algorithm based on graph analysis to

power factor improvement, harmonic reduction.

This research will contribute to the field by providing a comprehensive approach to

improving power quality in SPWM-based AC-DC converters.

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 1.1 THEORY

► Definition of Power Factor :

Power factor is the ratio of the real power () that performs useful work to the apparent power
() flowing in the circuit. It is a dimensionless number, ranging between 0 and 1, and is often
expressed as a percentage.

Figure 1: POWER FACTOR DIAGRAM

Power Factor (PF)= {Real Power (kW)}/{Apparent Power (kVA)}

 Distortion power factor -Distortion power factor is the inverse of the square root of 1 plus the square of
the Total Harmonic Distortion (THD). It is given by:

Distortion power factor - 1/√(1+THD² )

 True power factor -It is ratio the power factor to the square root of 1 plus the square of the
Total Harmonic Distortion (THD). It is given by:

True power factor – cosⱷ / √(1+THD² )

Alternatively, power factor can also be expressed as the cosine of the phase angle (Φ) between
the voltage and current waveforms:
PF = cos(Φ)

 Types of Power Factor :

1.Lagging Power Factor: Caused by inductive loads (e.g., motors, transformers), where
current lags behind the voltage.
2.Leading Power Factor: Caused by capacitive loads (e.g., capacitor banks), where current
leads the voltage.
3.Unity Power Factor: Achieved when the current and voltage are in phase .

1.2 Importance Power Factor in Electrical Systems :

1.Efficient Use of Power:
a. A high power factor (close to 1) ensures that most of the supplied power is used
for productive work.
b. Low power factor indicates wasted energy, as more apparent power is required to
deliver the same real power.

2.Reduced Energy Costs:

a. Many utilities charge penalties for low power factor. Improving power factor can
reduce electricity bills.
3.Decreased Line Losses:
a. High power factor minimizes losses in transmission and distribution lines by
reducing the current flow.
4.Optimal Equipment Utilization:
a. Equipment like transformers and generators can handle more load efficiently with a high
power factor, reducing the risk of overloading
5.Improved Voltage Regulation:

a. A higher power factor improves voltage stability across the system, preventing
voltage drops and ensuring reliable operation.
6.Environmental Benefits:
a. A higher power factor reduces the energy waste, contributing to a reduction in carbon
footprint.
7.Compliance with Standards:
a. Many regulatory frameworks mandate maintaining a certain power factor for
industrial and commercial facilities.

Maintaining a high power factor is critical for enhancing the efficiency, reliability, and
sustainability of electrical systems. It minimizes energy wastage, reduces costs, and ensures
the optimal operation of electrical infrastructure.

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1.3 Impact of Low Power Factor on Efficiency and Grid Performance :

Low power factor (PF) in electrical systems leads to inefficient energy utilization and various
challenges for the power grid. Below are the major impacts:

1. Increased Apparent Power Demand

 Explanation: Low power factor means a higher apparent power () is needed to deliver the
same amount of real power ().
 Impact:
A. Overloads transformers, generators, and transmission lines.
B. Increases the size and cost of equipment.

2. Higher Transmission Losses

 Explanation: Power losses in transmission lines are proportional to the square of the current
(). Low PF increases current flow.
 Impact:
A. Higher resistive losses in conductors.
B. Reduced system efficiency due to excessive heat
generation.

3. Reduced System Capacity

 Explanation: With a low PF, more of the system's capacity is consumed by reactive
power instead of real power.
 Impact:
A. Limits the ability to serve additional loads.
B. Necessitates expensive system upgrades to meet demand.

4. Increased Utility Costs

 Explanation: Utilities must compensate for inefficiencies caused by low PF, leading to higher
operational costs.
 Impact:
A. Penalties for consumers with low PF.
B. Additional costs to utilities for reactive power compensation (e.g.,
installing capacitor banks.

5. Environmental Impact
  Explanation: Low PF requires generators produce more apparent power, increasing fuel
consumption.
 Impact:
A. Higher greenhouse gas emissions.
B. Inefficient use of energy resources.

 Mitigation of Low Power Factor :

 Use of capacitor banks or synchronous condensers to compensate for reactive power.

 Adoption of advanced techniques such as active power factor correction in
electronic equipment.
 Monitoring and maintaining balanced loads in the system.
 Low power factor negatively affects both efficiency and grid performance by increasing losses,
reducing capacity, and incurring additional costs. Improving PF is essential to enhance energy
efficiency, reduce operational costs, and ensure grid stability and reliability.

 Causes Of Low Power Factor In AC-DC Converters :

AC-DC converters are widely used in electrical systems, but they can contribute to a low
power factor due to various factors. The primary causes are as follows:

1. Non-Linear Loads
 Explanation: AC-DC converters often feed non-linear loads, such as rectifiers,
variable speed drives, and electronic devices, which draw current in a non-sinusoidal
manner.
 Impact:
A. Non-linear loads distort the current waveform, leading to a phase shift
between voltage and current.
B. Results in a low power factor, with significant reactive power consumption.

2. Harmonics
 Explanation: AC-DC converters generate harmonics due to their switching operation.
Harmonics are higher-frequency components of the current that do not contribute to
useful power.
 Impact:
A. Increased total harmonic distortion (THD) reduces the power factor.

B. Harmonics cause additional losses in transformers, conductors, and other

13 | P a g e
 equipment.

3. Reactive Power Demand

 Explanation: Reactive components (e.g., inductors or capacitors) within AC-DC
converters store and release energy during operation, contributing to reactive power.
 Impact:
A. A higher proportion of reactive power relative to real power results in a lower
power factor.

4. Phase Angle Mismatch

 Explanation: In certain AC-DC converter designs, there is a phase shift between the
input current and voltage due to the converter topology or control method.
 Impact:
A. This mismatch leads to a lagging or leading power factor, depending on the
design.

5. Uncontrolled Rectification
 Explanation: In simple diode rectifiers, the current is drawn only during peaks of the
AC waveform, creating sharp pulses.
 Impact:
A. This pulse-like current waveform increases THD and reduces the power
factor.

6. Poor Load Matching

 Explanation: If the AC-DC converter is poorly matched to the load or operates outside
its optimal range, it may cause uneven power draw.
 Impact:
A. Leads to inefficient energy usage and a reduced power factor.

7. Low Input Inductance

Explanation: AC-DC converters with insufficient input inductance cannot
smooth the current waveform properly.
 Impact:
A. Results in highly distorted input current and a low power factor.

8. Switching Losses in Converters

 Explanation: AC-DC converters rely on high-speed switching devices (e.g.,
MOSFETs, IGBTs), which can cause losses and waveform distortion if not designed
properly.
  Impact:
A. Increases power factor degradation due to inefficient operation.

Mitigation of Low Power Factor in AC-DC Converters :

1. Power Factor Correction (PFC) Circuits:

Active PFC circuits ensure current waveform follows the voltage waveform closely,
reducing distortion.

2. Use of Filters:
Install harmonic filters to reduce THD.

3. Improved Converter Design:

Use advanced topologies like PWM (Pulse Width Modulation) or SPWM (Sinusoidal
PWM) to minimize waveform distortion.

4. Capacitor Banks:
Compensate for reactive power demand using capacitors or synchronous condensers.
Low power factor in AC-DC converters is mainly caused by non-linear loads, harmonics, and
reactive power. Addressing these issues through proper design and mitigation techniques can
improve efficiency, reduce energy losses, and enhance the overall performance of electrical
systems.

► ACTIVE AND REACTIVE POWER CONCEPTS

Active and reactive power are two key components of electrical power in AC circuits, and
they play crucial roles in energy transmission and utilization. Below is a detailed explanation:

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 1. Active Power (Real Power, P)
Active power is the actual power that performs useful work in an electrical system. It is the
energy consumed by resistive components of a circuit, such as heaters, lights, and motors, to
produce output like heat, light, or mechanical work.
Unit: Measured in Watts (W) or kilowatts (kW).
Formula: P = V.I.cos(Φ)
Where , V= RMS voltage , I = RMS current
Φ = Phase angle between voltage and current
Characteristics:
Active power flows from source to load.
It contributes to the energy consumed and billed by utilities.
2. Reactive Power (Q)
Reactive power is the power used to establish and maintain electric and magnetic fields in
inductive and capacitive components of a circuit, such as inductors, transformers, and motors.
Unit: Measured in Volt-Ampere Reactive (VAR) or kilovolt-ampere reactive (kVAR).
Formula: Q = V.I.sin(Φ)
Characteristics:

 Reactive power oscillates between the source and reactive

components.
 It causes no net energy transfer over a complete cycle
► AC-DC CONVERTER AND ITS WORKING

Working of a Full-Wave AC-DC Converter Using MOSFET Switches with Body Diodes :
A full-wave AC-DC converter using MOSFET switches and their body diodes rectifies AC
voltage into DC voltage. The body diodes in MOSFETs act as unidirectional pathways for
current when the MOSFET switches are off, ensuring continuous conduction during both
halves of the AC cycle. Below is a detailed explanation:

Figure 3: Schematic diagram of AC-DC converter with a R L load

An AC-DC converter structure for supplying DC LOAD

 Basic Structure-
 Components:
A. Input AC Source: Supplies the alternating current.
B. MOSFETs with Body Diodes: Four MOSFET switches (Q1, Q2, Q3, Q4)
arranged in an H-bridge configuration.
 Each MOSFET has an internal body diode that allows current flow in
one direction when the MOSFET is off.
C. Load: The DC load (e.g., resistor or motor) connected across the DC output.
D. Filter Circuit: A capacitor or LC filter smooths the pulsating DC output.

Topology:

 The AC input is connected to the bridge circuit, and the load is connected
across the DC output.

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 Figure 4: Full wave bridge converter (MOSFET with body diode) output

B. Working Principle
The circuit utilizes both the body diodes and the MOSFET switches to rectify the AC input
into DC output. Here’s how it works for each half- cycle of the AC waveform:

A. Positive Half-Cycle
i. Input Voltage Polarity:
 During the positive half-cycle of the AC source, the top terminal is positive,
and the bottom terminal is negative.
ii. Switching States:
 Q1 and Q4 are turned ON (active conduction).
 Q2 and Q3 are OFF.
 iii. Current Flow:
 The current flows through:Positive terminal of AC → Q1 (MOSFET switch)
Load
→ Q4 (MOSFET switch) → Negative terminal of AC.
iv. Role of Body Diodes:
 If a MOSFET fails to switch ON immediately, the corresponding body
diode (e.g., Q1 or Q4) allows current flow to prevent disruption.

v. Output Voltage:
 A positive voltage appears across the load.

 A. Negative half cycle

ii) output voltage polarity:

 During the negative half-cycle, the top terminal of the AC source is
negative, and the bottom terminal is positive.
iii) Switching States:
 Q2 and Q3 are turned ON (active conduction).
 Q1 and Q4 are OFF.
iv) Current Flow:
 The current flows through:
 Positive terminal of AC → Q3 (MOSFET switch) → Load → Q2
(MOSFET switch) → Negative terminal of AC.
v) Role of Body Diodes:
 If a MOSFET fails to switch ON immediately, the corresponding body
diode (e.g., Q2 or Q3) conducts the current until the MOSFET switches
ON.
vi) Output Voltage :
 The polarity of the output voltage remains the same as the rectified DC voltage.
Vii) Filtering :

 The rectified output is pulsating DC.

 A filter circuit (capacitor or LC filter) smooths the output voltage by reducing ripple,
providing a stable DC voltage for the load.

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i. Advantages of Using MOSFETs with Body Diodes
1. Simplified Design: No need for additional freewheeling diodes, as the body diodes
handle reverse current.
2. High Efficiency: When MOSFETs are ON, they have lower conduction losses
compared to the body diodes.
3. Fast Switching: MOSFETs allow high-frequency operation, reducing the size of
the filter components.
4. Uninterrupted Operation: Body diodes ensure current continuity during switching transitions.

ii. Applications
 Power supplies for electronic devices.
 Battery charging systems.
 Motor drives.
 Renewable energy systems like solar inverters.

 Waveforms
Input Voltage: A sinusoidal AC waveform.
Output Voltage: A pulsating DC waveform, which becomes a smooth DC after
filtering.
Current Waveform: Follows the switching pattern, showing continuous conduction.

The full-wave AC-DC converter using MOSFETs with body diodes is a highly efficient and
reliable method for rectification. The MOSFETs provide low-loss switching, while the body
diodes ensure seamless operation during transitions, making it suitable for high-performance
power electronics applications
2. SINUSOIDAL PULSE WIDTH MODULATION (SPWM)

Sinusoidal Pulse Width Modulation (SPWM) is a widely used technique in power

electronics for generating an AC output from a DC source, particularly in inverters. It
involves modulating the width of pulses in a switching signal to replicate a sinusoidal
waveform at the output.

► Principle of SPWM :

 Carrier Signal: A high-frequency triangular waveform is used as the carrier signal.

 Reference Signal: A low-frequency sinusoidal waveform (the desired output
waveform) is used as the reference signal.
 Comparison:

 The reference sinusoidal waveform is continuously compared with the triangular

carrier waveform.
 Whenever the sinusoidal waveform's value is higher than the triangular waveform,
the output of the comparator is high (logic 1).
 Whenever the sinusoidal waveform's value is lower than the triangular waveform,
the output of the comparator is low (logic 0).
 Pulse Generation:

 The high and low comparator outputs correspond to turning ON and OFF the
switches in the inverter.
 The resulting output is a series of PWM pulses with varying widths that
emulate the sinusoidal waveform.

 Working of SPWM :
1. Inverter Operation:

 SPWM is implemented in a full-bridge or half-bridge inverter.

 The PWM pulses control the ON/OFF states of the power electronic
switches (e.g., MOSFETs, IGBTs).
2. Output Waveform:

 The output of the inverter is a series of PWM pulses.

 These pulses are filtered (using an LC filter) to smooth out the waveform,
producing a sinusoidal AC voltage.

21 | P a g e
Figure 5: SPWM generation waveform

In model we compare a triangular signal with frequency 5khz with sinusoidal wave (pulse
rating) with frequency of 50 Hz to produce spwm and by providing delay in triangular wave
producer we are creating the lagging angle ‘a’.This image represents Sinusoidal Pulse Width
Modulation (SPWM) used in three-phase inverter control.

 Carrier signal:
A high-frequency triangular waveform (Vc).

 Modulation signals:
Three sinusoidal waveforms (Vm) spaced 120° apart.
The pulse width varies based on the comparison of carrier and modulation signals.

 Line voltage waveform:

Shows how the line voltage builds a stepped waveform, which approximates a sinusoidal
form.
 Advantages Of SPWM :

1. Reduced Harmonics:
 By closely emulating a sinusoidal waveform, SPWM minimizes harmonic distortion.

2. High Efficiency:
 Switching losses are reduced as switches operate only during specific intervals.

3. Amplitude Control:
 By varying the modulation index, the amplitude of the output waveform can be
controlled.

4. Wide Application:
 Used in motor drives, inverters, and renewable energy systems like solar PV
inverters.

 Waveforms in SPWM :

1. Carrier Wave (Triangular): High-frequency waveform.

2. Reference Wave (Sinusoidal): Desired low-frequency output waveform.
3. Generated PWM Pulses: Varying-width pulses based on the comparison.
4. Filtered Output: A sinusoidal AC waveform after passing through an LC filter.

Sinusoidal Pulse Width Modulation (SPWM) is an effective method for generating sinusoidal
AC waveforms from a DC source with high efficiency and low harmonic distortion. Its
ability to control amplitude and frequency makes it ideal for modern power electronics
applications.

23 | P a g e
2.1 ROLE OF SPWM IN POWER FACTOR IMPROVEMENT OF AN AC-DC CONVERTER

Sinusoidal Pulse Width Modulation (SPWM) is a widely used technique in AC-DC

converters (rectifiers) for improving the power factor by controlling the switching of power
electronic devices. The key role of SPWM lies in ensuring the input current waveform closely
follows the shape of the input voltage waveform, reducing harmonic distortion and improving
power factor. Below is a detailed explanation of how SPWM achieves this:

 Role of SPWM in Power Factor Improvement

SPWM enhances power factor by addressing harmonic distortion and phase alignment in AC-
DC converters. Here’s how:

a) Current Waveform Shaping

 SPWM generates a PWM signal for controlling the switching of power electronic
devices (e.g., MOSFETs, IGBTs) in the AC-DC converter.
 The SPWM technique ensures that the input current waveform is sinusoidal and in
phase with the input voltage.
 Effect: Reduces reactive power and improves power factor by minimizing phase
difference between voltage and current.

b) Harmonic Reduction
 Traditional rectifiers (e.g., diode-based rectifiers) introduce high harmonic distortion,
leading to a poor power factor.
 SPWM minimizes harmonics by generating a high-frequency switching pattern that
produces a smooth sinusoidal input current after filtering.
 Effect: Lower harmonic content reduces Total Harmonic Distortion (THD),
improving the displacement power factor.
 C ) Modulation Index Control

 The modulation index () in SPWM is adjustable, allowing precise control of the input
current amplitude and phase.
 By matching the modulation index to the input voltage profile, SPWM ensures
optimal current waveform shaping.
 Effect: Aligns current with voltage, further enhancing the power factor.

D ) Bidirectional Control (In Active Rectifiers)

 In active rectifiers (e.g., boost-type converters), SPWM enables bidirectional control

of the switches.
 This allows the converter to absorb reactive power and
dynamically compensate for power factor issues in the grid.
 Effect: The AC-DC converter acts as a power factor correction (PFC) unit.

► Practical Implementation in AC-DC Converters

 Switching Devices: SPWM is applied to control MOSFETs or IGBTs in the
converter.
 Controller: A microcontroller, DSP, or FPGA generates SPWM signals based on
input voltage and current feedback.
 Filters: LC filters are used to smooth the modulated signals, ensuring sinusoidal
current flow.
 Feedback Mechanism:
 A feedback loop monitors the input current and voltage to adjust SPWM
parameters in real time for optimal performance.

► Benefits of Using SPWM in Power Factor Improvement

1. Higher Efficiency:
 Improved power factor reduces energy losses in the system.

2. Lower Harmonics:
SPWM minimizes harmonic currents, ensuring compliance with standards like IEEE 519.

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 3. Better Grid Performance:
 Improved power factor reduces the burden on the power grid, enhancing
voltage stability.
4. Dynamic Compensation:
 SPWM enables dynamic adjustment for varying loads, maintaining a

► Applications -

 Industrial Power Supplies: High-efficiency rectifiers for motors and drives.

 Renewable Energy Systems: AC-DC converters in solar and wind energy
applications.
 Electric Vehicle Chargers: For maintaining grid stability during charging.

SPWM plays a crucial role in improving the power factor of AC-DC converters by ensuring that
the input current waveform is sinusoidal and in phase with the input voltage. By reducing
harmonics and reactive power, SPWM enhances the efficiency and reliability of power
conversion systems while minimizing the impact on the electrical grid.
2.2 HOW THIS SPWM TECHNIQUE TARGETS THE OPTIMUM POWER FACTOR
ACHIVEMENT

When we change the vale of a (lagging or leading angle of Vg to Vc) the shape of the SPWM
wave from changes as this change happen this effect the vale of cos(Φ)) and as well as the
value of THD now to varying this to our model find the optimum point for the best Power
factor possible ,as the wave form changes an and bn does vary so the power factor also vary.

I (t) = I o + ∑ C n cos (nωt +φ n ¿ )¿

1

bn
C n=√ (a ² ¿ ¿ n ¿ +b ²n )¿ ¿ , tan φn=(− a ) n

Software used for experiment : Here we used Simulink and MATLAB software for modeling
the circuit and analysis.

 Design and Implementation

Designing and implementing an SPWM-based AC-DC converter involves a systematic

approach to ensure efficient power conversion, harmonic reduction, and power factor
improvement. The key components and design considerations are outlined below.
1. Key components :

( i) Power Electronics Switches.

• MOSFET or IGBTs- used for switching in the converter

(A)Selection Criteria:
• High switching speed (especially for MOSFETs).
• Low on-state resistance () or low conduction losses. Vo
• Voltage and current ratings matching the system requirements.

(B)Freewheeling/Body Diodes:
▪ Provide paths for current during switching transitions or when the switches are off.
▪ Fast recovery diodes are often preferred to minimize switching losses.

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 (ii)Control Unit

▪ Controller (Microcontroller, DSP, or FPGA):

• Generates SPWM signals to control the switches.
• Implements feedback loops for current and voltage control.
• Example: Microcontrollers like TI’s C2000 series or ARM-based processors.

(iii)LC Filter

▪ Purpose: Smooth the output waveform and reduce high- frequency harmonics
▪ Design Parameters:
• Cutoff frequency: Should block switching frequency components.
• Inductor and capacitor ratings: Chosen to handle peak currents and voltages.

(iv) Heat Sinks

▪ Purpose: Dissipate heat generated by power switches.

▪ Consideration:Design
• Adequate thermal management to prevent overheating.

2. Design Considerations:

(i)SPWM Generation

▪ Carrier Frequency:
• Typically much higher than the fundamental frequency of the output AC waveform.
• Common range: 5–20 kHz.
▪ Reference Signal:
• Represents the desired sinusoidal waveform.
• Frequency determines the output AC frequency.

(ii) Switching Frequency

◦ Trade-offs:
▪ Higher switching frequency reduces output harmonics but increases switching losses.
▪ Optimal choices efficiency and harmonic performance.

(iii) Harmonic Reduction

◦ Filter Design:
▪ LC filter parameters chosen to suppress high- frequency components in the output.
◦ Compliance:
▪ Designed to meet harmonic standards like IEEE 519.

(iv) Efficiency

◦ Switching Losses:
▪ Minimized by selecting switches with low switching energy.
◦ Conduction Losses:
▪ Reduced by optimizing the conduction path and using low-loss components.

1. Implementation Steps -
 a. Circuit Design:
o Create the circuit topology, incorporating switches, diodes, and LC
filters.

b. SPWM Signal Generation:

o Use a microcontroller or DSP to generate SPWM signals by
comparing a sinusoidal reference with a triangular carrier wave.

c. Simulation:
o Test the design using simulation software (e.g., MATLAB/Simulink,
LTSpice) to analyze waveforms, harmonics, and power factor.

d. Prototyping:
o Build a prototype circuit using power switches, controllers,
and sensors.
2. Challenges -

o Switching Losses: High-frequency operation increases losses; addressed by

selecting efficient components.
o Harmonics: Requires well-designed filters to ensure compliance with standards.
o Thermal Management: High-power converters need effective cooling systems.

The design and implementation of an SPWM-based AC-DC converter require careful selection of
components and a well-optimized control strategy. By focusing on SPWM generation, feedback
control, harmonic reduction, and thermal management, the converter can achieve high efficiency,
improved power factor, and reliable performance for various applications.

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3. SIMULATION ANALYSIS

We developed a model using Simulink software in MATLAB, below the circuit are shown and
explained-

Figure 6: Simulation model

Here the total main circuit is shown there MOSFET Converter circuit SPWM generator and
power factor measuring block and current converter subsystems are made.

We also use a two scope two see the current and voltage signals and compare them, a free wheel
diode is used parallel to the load to support the freewheeling action of inductor. Here we are
using a current chopping switch(MOSFET device) in gate terminal of which we are applying
SPWM .
 Figure 7: Subsystem of SPWM generator

► This Simulink model represents the Sinusoidal Pulse Width Modulation (SPWM) technique.

 Component used :

1. Triangle Generator: Produces a high-frequency triangular waveform used as the carrier signal.

2. Constant 1 (Sinusoidal o/p of full wave rectifier): Represents a sinusoidal reference signal, typically the output of a
full-wave rectifier.

3. Add Block: Adds the triangle signal and the constant (sinusoidal) signal together.

4. Relational Operator ("<"): Compares the sinusoidal signal with the triangle signal to generate the PWM signal.
The output is high (1) when the sinusoidal input is less than the triangle waveform.

5. Scope: Used to display the resulting PWM waveform.

 Purpose:

This model generates a PWM signal whose duty cycle varies sinusoidally, which is essential for producing AC
waveforms from a DC source in inverters.

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 Figure 8: MOSFET block parameter

 AC-DC Converter using MOSFET Switches with parasitic Diode

► This block models a MOSFET (Metal-Oxide-Semiconductor Field-Effect
Transistor) with an internal diode in parallel with a series RC snubber circuit. Here's a
breakdown of each parameter:

1. FET resistance (Ron):

Value: 0.1 ohms.
Represents the on-resistance of the MOSFET when the gate is driven, which occurs when
the MOSFET is conducting.
2. Internal diode inductance (Lon):
Value: 0 (for most applications).
this parameter models the inductance of the internal diode. For most applications, it is
typically set to zero.
3. Internal diode resistance (Rd):
Value: 0.01 ohms.
Represents the resistance of the internal diode when it is in the conducting state.
4. Internal diode forward voltage (VF):
Value: 0V.
This parameter represents the forward voltage drop of the internal diode
5.Initial current (Ic):
Value: 0A.
Specifies the initial current through the MOSFET at the beginning of the simulation.
6. Snubber resistance (Rs):
Value: Zero , this parameter would represent the resistance in the snubber circuit, used for
damping high-frequency oscillations that might occur during switching events.
In

Figure 9: Power Factor measuring block internal diagram

MATLAB, MOSFET switches can be modeled using Simulink or the Simscape Electrical
toolbox, which provides prebuilt models for power electronics components like MOSFETs,
diodes, and more. Here's an overview of how to use MOSFET switches in MATLAB for
simulation purposes:
 Using MOSFETs in Simulink
Library: Simscape Electrical → Semiconductors

This Simulink model represents a power measurement block, designed to compute real power
(or active power) from a given voltage and current signal using RMS and phase angle
calculations.
 Component used :
1. Fourier Voltage & Current Blocks:
Extract the fundamental magnitude and phase angle (∠u) of voltage and current signals
using Fourier analysis.
2. RMS Blocks:
Calculate the Root Mean Square (RMS) values of voltage and current signals.
3. Sqrt and Constant Blocks:
Multiply RMS values by 0.707 (≈ 1/√2) to relate them to peak values in sinusoidal signals.
4. Phase Angle Difference:
Phase difference between voltage and current is calculated.
Converted from degrees to radians using π/180.
5. Cosine Block:
Takes the cosine of the phase angle difference to find the power factor (cos φ).
6. Final Power Calculation:
Real Power = V_RMS × I_RMS × cos(φ)
Achieved using a series of product (×) blocks combining voltage, current, and power factor.

 Purpose:
This block calculates the active (real) power by:
Measuring RMS values,
Computing the phase angle difference,Multiplying voltage, current, and cos(φ).

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 Figure 10: Converter block

This Simulink model illustrates a converter block implemented using IGBTs (Insulated Gate Bipolar
Transistors), commonly used in power electronic applications such as AC-DC or DC-DC
converters.

 Component used :
1. IGBT Switches:
The circuit includes four IGBT switches: IGBT, IGBT1, IGBT2, and IGBT3.
Each IGBT has a gate signal input (g, g1, g2, g3) that controls its switching behavior.
2. Power Terminals:
Terminals labeled E, E1, E2, and C represent electrical connection points (possibly representing
emitter, collector, or input/output terminals of the converter).
3. Connections:
The IGBTs are connected in a configuration that suggests controlled power flow between E, E1, E2,
and C.
This is likely part of a switching converter topology (e.g., inverter, buck/boost converter, or AC-DC
converter), depending on the input/output configuration.
Functionality:
Gate signals (g, g1, g2, g3) are used to turn ON/OFF the IGBTs based on a control logic (not shown
here but likely part of a larger system).
The converter controls the direction and form of the electrical power—either converting AC to DC,
DC to AC, or regulating DC voltage levels.

 Purpose:
This block forms the core switching unit in a power electronic system. By appropriately switching
the IGBTs, the system can regulate:
Output voltage and current,
Power flow direction,
Harmonics and waveform shape (in case of modulation techniques like SPWM).

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 Figure 11: Sinusoidal output of full wave rectifier
This Simulink model represents a Sinusoidal Pulse Width Modulation (SPWM) control scheme used for
generating the output waveform of a full wave rectifier.
 Component used :
1. Sine Wave Function:
Represents the reference sine signal for generating SPWM pulses.
Multiplied with the output of Pulse Generator2 to produce one half of the modulated signal.
2. Pulse Generators (Pulse Generator1 & Pulse Generator2):
Generate square wave signals (PWM pulses).
Used to modulate the sine wave signal by switching it ON/OFF, enabling rectification.
3. Sine Wave Function1:
Another sine reference (likely phase-shifted) for symmetrical modulation.
Works with Pulse Generator1 to produce the second half of the rectified output.
4. Product Blocks:
Used to multiply (modulate) the sine wave signals with the corresponding pulse signals.
5. Add Block (Add2):
Adds the two modulated waveforms from both halves of the rectifier to generate the full wave SPWM
output.
6. Out1:
Final output terminal that gives the modulated sine wave, representing the full-wave rectified signal
using SPWM technique.

 Purpose:
This model simulates how SPWM technique is used to generate a smooth sinusoidal output
from a full-wave rectifier, which is common in inverter or AC power control systems. The
modulation helps in:
Improving output waveform quality.
Reducing harmonics.

3.1 SIMULATION RESULTS

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Figure 12: SPWM chopped voltage waveform for 30% duty cycle
[ Output voltage (Y-axis ) VS time ( X-axis ) ]

This is the simulation result which we have build in the MATLAB ,the output
graphs which is shown in this figures is the result of SCOPE2 [ Fig - 6 ]

Figure 13:SPWM chopped voltage waveform for 50% duty cycle

[ Output voltage (Y-axis ) VS time ( X-axis ) ]

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3.2 TABLE : CALCULATION OF THE PF USING SIMULATION RESULTS

LOAD ANGLE “a” (in PF with SPWM PF without

degree) SPWM

R=10 ohm
70 0.9552 0.6367
L=0.2 Henry

50 0.9582

60 0.9580

45 0.9570

R= 20 ohm
L = 0.001 Henry 90 0.9685 0.7511

110 0.9681

120 0.9688

140 0.9700

R=10 ohm
L=0.001Henry 70 0.9790 0.6823

80 0.9840

90 0.9884

110 0.9780

INTERPRETATION: As the R/L value is increased , the value of angle ‘a’ becomes
positive.

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 Figure 14: Variation of Power Factor with lag angle for different loads in same plot

Now we are check ,how the lag angle ( a ) for the maximum power factor vary
with the variation of duty cycle ( D ). The table is shown below -

D ( Duty cycle) a (lag angle) Power Factor

10 140 0.5520

40 90 0.9969

30 110 0.9736

 Formula development using Curve fitting technique -

Here we are trying to express the lag angle ( a ) the function of R ( Load
resistance) , L (Load inductance ) , D (Duty cycle ) .

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 We build up 2nd degree polynomial model and included the corresponding
equation as part of the analysis -

[ a = K₁ / L + K₂ R + K₃ D + K₄ R ² + K₅ D² + K₆ R D + K₇ ]

This function :
i. Still keeps 1/L because L has a strong inverse effect .
ii. Adds quadratic and interaction terms in R and D for finer fitting .

 Data points -

L R D a
0.2 10 30 50

0.01 10 30 90

0.001 10 30 110

0.001 20 30 140

0.001 10 10 140

0.001 10 40 90

We are now using this data in Microsoft Excel and applying the curve fitting
technique. So finding the values of k₁ , k₂ , k₃ , k₄ , k₅ , k₆ , k₇ .We got the
final equation .

► Final equation from using curve fitting technique -

[ a= 0.04505 / L + 4.109 R + 6.010 D + 0.597 R² – 0.0256 D² – 0.640 RD + 0.613 ]

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 3.3 Study of Harmonics in the current waveform of AC DC Converter

We used FFT ( fast Fourier transform ) tools from Power Gui . Before that , we logged the
output from the scope at source end . Then, we used the FFT tool to analyze the harmonics
components in the current waveform.
To mitigate the impact of 5th harmonic , an RC filter was implemented at the load end of our
developed circuit.

Table I – where L is taken 0.2 Henry , and R is taken as 50 ohm

L (H ) R ( ohm ) 3rd harmonics 5th harmonics THD R (f ) C (f)

0.2 50 64.36 23.74 151.1% 0.01 100

0.2 50 53.33 18.35 140.23% 0.1 100

0.2 50 51.9 17.95 142.75% 1 100

0.2 50 51.83 18.42 143.05% 10 10

0.2 50 52.11 21.80 144.69% 100 1

Table II – where L is taken 2 Henry , and R is taken as 10 ohm

L ( H) R (ohm ) 3rd harmonics 5th harmonics THD R (f ) C (f )
2 10 64.34 23.52 151.38% 0.01 100

2 10 53.22 18.32 142.69% 0.1 100

2 10 51.57 17.86 142.74% 1 100

2 10 43.67 17.67 142.02% 10 10

2 10 43.41 17.27 141.13% 100 1

Table III– where L is taken 0.2 Henry , and R is taken as 10 ohm

L ( H) R (ohm ) 3rd harmonics 5th harmonics THD R (f ) C (f )
0.2 10 44.62 19.53 141.88% 100 100

0.2 10 44.74 19.58 141.91% 100 100

0.2 10 44.61 19.52 141.84% 100 100

0.2 10 50.21 18.33 142.13% 10 1

0.2 10 50.62 18.31 142.56% 10 0.1

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 This FFT analysis was performed on a current waveform using MATLAB Power GUI FFT
tool. The signal was taken from Scope Data1 at the source end, starting from 4 seconds over
one cycle. The results are shown below.

Figure 15: FFT analysis result 1

The analysis shows:

Fundamental frequency: 50 Hz
Total Harmonic Distortion (THD): 142.74%, indicating a high level of harmonics
Dominant harmonics: Significant amplitudes are observed at the 3rd, 5th, 7th, and higher-
order harmonics
This indicates that the waveform is highly distorted and would require harmonic mitigation
(e.g., filtering), especially to reduce the impact of the 5th harmonic.

Figure 16:FFT analysis result 2

 The analysis shows:

Fundamental frequency: 50 Hz
Total Harmonic Distortion (THD): 142.02%

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 Figure 17:FFT analysis result 3

 The analysis shows:

Fundamental frequency: 50 Hz
Total Harmonic Distortion (THD): 142.23%

► Curve fitting summary :

Based on the given data -

L (H ) R (ohm) R’ C’
0.2 50 1 100
2 10 10 10
0.2 10 10 1

We are now using this data in Microsoft Excel and applying the curve fitting
technique. So finding the values of R’ and C’ . We got the result which is
shown below-

R’ = 269.2 * R -1.431 and C’ = 0.0069 * (R 2.861 / L)

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3.4 ADVANTAGES AND DISADVANTAGES OF USING THIS SPWM METHOD

 Advantages of SPWM (Sinusoidal Pulse Width Modulation):

1. Power Factor Improvement:

SPWM allows better shaping of the input current to be in phase with the input voltage, reducing phase
difference and improving the power factor.

2. Reduced Harmonics:
The high switching frequency and sinusoidal nature of SPWM reduce low-order harmonics, improving
power quality and reducing THD (Total Harmonic Distortion).

3. Controlled Output Voltage:

SPWM enables precise control over the output DC voltage by adjusting the modulation index (ratio of sine
wave amplitude to carrier amplitude).

4. Better Efficiency:
With proper filtering, SPWM reduces losses due to harmonics, enhancing the overall converter efficiency.

5. Flexibility:
It can be easily implemented using digital controllers (like microcontrollers, DSPs) and adapted to various
applications including inverters and rectifiers.

6. Improved Dynamic Response:

Fast response to load variations is possible due to the modulation strategy.

 Disadvantages of SPWM(Sinusoidal Pulse Width Modulation):

1. Complex Control Circuit:

Generating SPWM requires precise timing and fast digital signal processing, making the controller design
more complex and costly.

2. High Switching Losses:

Due to frequent switching at high frequency, switching losses in power devices (MOSFETs/IGBTs)
increase, especially in high-power applications.

3. Electromagnetic Interference (EMI):

High-frequency switching can generate EMI, requiring additional filtering and shielding.

4. Need for Filters:

To smooth out the output waveform and reduce ripple, bulky LC filters are often needed, increasing size
and cost.

5. Reduced Reliability:
Continuous high-frequency switching stresses semiconductor devices and may reduce their lifespan if not
managed proper

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 CONCLUSION

The implementation of the Sinusoidal Pulse Width Modulation (SPWM) technique in an AC-
DC converter demonstrates significant improvements in power factor and overall system
efficiency. The SPWM technique effectively reduces harmonics in the input current, bringing
it closer to a sinusoidal waveform.

SPWM is highly effective for power factor correction in AC-DC converters, offering better
waveform quality and control. However, it comes at the cost of increased complexity,
switching losses, and design effort. Proper design of control and filtering is essential to fully
benefit from the technique.

This results in a power factor closer to unity, minimizing reactive power and improving
power delivery efficiency. By modulating the input signal with SPWM, the system achieves a
lower THD, which ensures better compliance with power quality standards and reduces stress
on electrical components, employing the SPWM technique in AC-DC converters is an
effective approach to improve power factor, reduce harmonic distortion, and enhance the
overall performance of power electronic systems.

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 REFERENCES

1. K.Georgakas, A. Safacas, "Efficiency and Power Factor Investigation of Characteristic Converter Topologies via
Simulation", ICEMS, Conference Nanjing, China, September

2. K.Georgakas, A. Safacas, I. Georgakopoulos, "Determination of the Optimum Power Factor and Efficiency Values of a
Single Phase Converter Supplying a DC Drive via Simulation", ICEM, Conference Chania, Greece, September 2-5. 2006,
Proceedings, paper No.307

3. Nabil A. Ahmed, Kenji Amei, Masaaki Sakui, "AC chopper voltage controller-fed single-phase induction motor
employing symmetrical PWM control technique", Elsevier Sciences, Electric Power System Research, 55(2000), pp. 16-20

4. BOR-REN, "High Power Factor AC/DC/AC Converter With Random PWM, IEEE TRANSACTIONS ON
AEROSPACE AND ELECTRONIC SYSTEMS, VOL 35, NO.3 July 1999, pp. 935-943.

5. Mohan, Undeland, Robbins, "POWER ELECTRONICS Converters Applications and Design", John Wiley and Sons,
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6. Dr. P. S. Bimbhra Power Electronics",Khanna publication [ 2022 - 7th edition ]

7. M. D. Singh & K. B. Khanchandani ,"Power Electronics", The M C Grah hill companies [2019 - 2nd edition ]

8. https://www.wikipedia.org/

9. https:www.researchgate.netpublication264894259_A_Study_of_ACDC_Converter_with_I
mproved_Power_Factor_and_Low_Harmonic_Distortion

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