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DEVELOPMENT OF A POWER FACTOR CORRECTION
BUCK CONVERTER IN SINGLE PHASE RECTIFIER
USING FUZZY LOGIC
ASMAWI BIN MUDA@OTHMAN
A project report submitted in partial fulfillment of
the requirement for the award of the Master of
Electrical Engineering
Faculty of Electrical and Electronic Engineering
Universiti Tun Hussein Onn Malaysia
JULY, 2013
v
ABSTRACT
Power Factor Correction (PFC) circuits are widely used in single-phase rectifiers in
order to emulate a linear resistive behavior. The buck PFC is still the most popular
configuration due to its simplicity, but it suffers from high voltage stresses across the
power electronic devices. This thesis presents to development buck converter in
single phase rectifier used the fuzzy logic.
The methodology integrates fuzzy logic controlling the output voltage of DC-DC
converter and to improve performance of the buck converter during transient
operation. Instead of generating fast pulse-width-modulated (PWM) signal, the
digital signal processor is required to generate a slow- varying dc signal only for
determining the PWM ramp function. A model for power factor correction has been
formed by using the MALTAB software. The simulation and experimental results
show that output voltage of buck converter can be control according to the value of
duty cycle. The advantage of using the Buck Converter in power factor correction
circuit is that better line regulation is obtained with appreciable power factor.
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ABSTRAK
Litar faktor kuasa (PFC) digunakan dengan meluas dalam pelurus satu fasa supaya
mencontohi satu tingkah laku berintangan linear. Penukar Buck PFC adalah paling
popular digunakan
disebabkan kesederhanaannya, tetapi nilai voltan meningkat
tinggi apabila merentasi alat kuasa elektronik . Projek ini adalah membangunkan
penukar buck dalam penerus fasa tunggal menggunakan kawalan fuzzy logic.
Kaedah mengintegrasikan fuzzy logic mengawal voltan output penukar AT-AT dan
memperbaiki prestasi penukar Buck semasa operasi. Daripada isyarat pulse-widthmodulated (PWM) , pemproses isyarat digital dikehendaki untuk menjana isyarat
yang boleh ubah secara pelahan-lahan untuk menentukan rangkap fungsi PWM. Satu
model bagi pembetulan faktor kuasa telah ditubuhkan dengan menggunakan perisian
MALTAB. Simulasi dan hasil percubaan menunjukkan voltan output penukar buck
boleh mengawal nilai kitar kerja. Kelebihan menggunakan penukar buck di litar
pembetulan faktor kuasa adalah peraturan talian lebih baik diperolehi berbanding
faktor kuasa ketara.
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TABLE OF CONTENTS
TITLE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF SYMBOLS
xiii
CHAPTER 1 INTRODUCTION
1
1.1
Project background
1
1.2
Problem statement
2
1.3
Project objective
3
1.4
Project scope
3
1.5
Thesis overview
3
CHAPTER 2 LITERATURE REVIEW
5
2.1
Introduction
5
2.2
Buck converter
6
2.2.1 Modes of operation
9
2.2.1.1 Continuous conduction mode (CCM)
10
2.2.1.2 Discontinuous conduction mode (DCM)
10
viii
2.2.2 Critical component value
11
2.2.3 Mathematical modeling of Buck Converter
14
2.2.3.1 State-space representation
14
2.2.3.2 Average state-space representation
17
2.2.4 Advantages of buck converter for power
2.3
2.4
factor correction
17
Power factor correction (PFC)
18
2.3.1 Need of PFC
18
2.3.2 Types of power factor correction
19
2.3.2.1 Passive power factor correction
19
2.3.2.2 Active power factor correction
20
Fuzzy logic controller
CHAPTER 3 METHODOLOGY
21
25
3.1
Project design
25
3.2
Parameter for buck converter
27
3.3
Fuzzy logic controller design
27
3.3.1 Fuzzification interface
27
3.3.2 Rule base
31
3.3.3 Fuzzy logical decision making
35
3.3.4 Deffuzzifier
35
CHAPTER 4 RESULTS AND ANALYSIS
36
4.1
MATLAB software
36
4.2
Simulation results
36
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4.3
Simulation for reference voltage (ref)
equal 115V
4.4
Output voltage for reference voltage 110V,
100V, 90V and 80V
4.5
4.6
37
41
Power factor for reference voltage 110V, 100V,
90V and 80V
43
Analysis for buck converter
47
CHAPTER 5 CONCLUSION AND RECOMMENDATION
5.1
Conclusion
48
5.2
Recommendation
49
REFERENCES
50
x
LIST OF TABLES
3.1
Parameter for Buck Converter
27
3.2
Rules for error and change of error
31
4.1
Analysis of power factor for reference voltage set to 115V,
110V, 100V, 90V and 80V
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xi
LIST OF FIGURES
2.1
Circuit diagram for Buck Converter
6
2.2
Waveform for Buck Converter
7
2.3
(a) Turn on switch “Circuit Diagram Buck Converter”
7
2.3
(b) Turn off switch “Circuit Diagram Buck Converter”
8
2.4
Inductor current waveform of PWM converter
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2.5
(a) Mode 1
14
2.5
(b) Mode 2
14
2.6
Structure of fuzzy logic controller
22
3.1
Block diagram of the Power Factor CorrectionBuck Converter in
single phase rectifier using fuzzy logic
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3.2
Flowchart of the project
26
3.3
FIS editor
29
3.4
(a) Membership function of input variable ‘input 1’
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3.4
(a) Membership function of input variable ‘input 2’
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3.4
(c) Membership function of output variable
30
3.5
(a) Show the rule base
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3.2
(b) Rule views for Fuzzy Logic Controller using Fuzzy Logic Toolbox
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4.1
Block diagram of Buck Converter in single phase rectifier using
Fuzzy Logic Controller
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4.2
Input voltage (Vin) for reference voltage (Vref) equal 115V
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4.3
Output current (Iout) for reference voltage (Vref) equal 115V
38
4.4
Output voltage (Vout) for reference voltage (Vref) equal 115V
39
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4.5
Power Factor (PF) for reference voltage (Vref) equal 115V
40
4.6
(i) Output voltage (Vout) for Vref equal 110V
41
4.6
(ii) Output voltage (Vout) for Vref equal 100V
41
4.6
(iii) Output voltage (Vout) for Vref equal 90V
42
4.6
(iv) Output voltage (Vout) for Vref equal 80V
42
4.7
(i) Power factor for Vref equal 110V
43
4.7
(ii) Power factor for Vref equal 100V
44
4.7
(iii) Power factor for Vref equal 90V
45
4.7
(iv) Power factor for Vref equal 80V
46
xiii
LIST OF SYMBOLS
Symbol
Vo
Output voltage
Vi
Input voltage
Vref
Reference voltage
R
Resistor
C
Capacitor
L
Inductor
CCM
Continuous Conduction Mode
DCM
Discontinuous Conduction Mode
PWM
Pulse Width Modulation
DC
Direct Current
AC
Alternating Current
IL
Inductor Current
f
Frequency
T
Period
PFC
Power Factor Correction
e
Error
ce
Change of Error
ΔQ
change of charge
Cmin
Minimum Capacitor
D
Duty Cycle
Q
Transistor
NB
Negative Big
NM
Negative Middle
NS
Negative Small
Z
Zero
PS
Positive Small
PM
Positive Middle
PB
Positive Big
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CHAPTER 1
INTRODUCTION
1.1
Project background
With
rapid
development
in
power
electronic
technology,
power
semiconductor technology, modern control theory for dc to dc converter such as
buck converter and manufacturing technology for step down voltage in industry,
buck converter have been widely used in many fields. Step down buck converter are
integral to modern electronic [1]. Step down converter transfer small packets of
energy using a switch, diode, an inductor and several applications. Through
substantially larger and noisier than their linear regulator counterparts, buck
converters offer higher effiency in most cases.
The general, DC-DC converter consists of power semiconductor devices
which are operated as electronic switches. Operation of the switching devices causes
the inherently nonlinear characteristic of DC-DC converter including one known as
the Buck converter. Consequently, this converter requires are controller with a high
degree of dynamic response.
The study about fuzzy logic quickly developed in the past few decades in the
control system has made great progress. The fuzzy logic approach has been proposed
to converters. Its major advantage is that expert knowledge can regulate the output
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voltage of the switching DC–DC Buck Converter be incorporated into the fuzzy
controller using simple linguistic rules to achieve the control objective without
involving the converter’s mathematical models. [2][3] The Fuzzy logic controller are
designed based on dimensional rule table using voltage error and change in voltage
error as input variables and change in duty cycle as control output. [4]
1.2
Problem Statement
The DC-DC converters such as Buck converter which is capable to stepdown the output voltage produce higher current ripple. This will influenced and
decreased the output voltage regulation and efficiency of the converter. These
weaknesses can be overcome by Buck converter which exhibit low input and output
current ripple.
The Fuzzy control is a practical alternative for a variety of challenging
control applications because Fuzzy logic control is nonlinear and adaptive in nature
that gives it a robust performance under parameter variation and load disturbances.
Fuzzy logic controller used in buck converter single phase rectifier circuit is
acquiring value power factor correction around 0.9 (90%) to almost 1.0 (100%).
Fuzzy logic is suited to low-cost implementations and systems of fuzzy can
be easily upgraded by adding new rules to improve performance or add new features.
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1.3
Project objective
The major objectives of this project are:
1.
To develop, describes and simulate the designed, use and analysis of Buck
Converter for power Factor Correction.
2.
To develop and simulate the designed single phase rectifier using the fuzzy
logic controller for variable output voltage DC-DC buck converter.
1.4
Project scope
The scopes of this project is to simulate the proposed method of power factor
correction buck converter in single phase rectifier using using fuzzy logic controller
with MATLAB Simulink software. The analysis only covered the output voltage and
power factor correction only.
1.5
Thesis Overview
This project report is organized as follows;
a) Chapter 1 briefs the overall background of the study. A quick glimpse of
study touched in first sub-topic. The heart of study such as problem
statement, project objective, and project scope is present well through this
chapter.
b) Chapter 2 covers the literature review of previous case study based on fuzzy
logic controller background and development. Besides, general information
about Buck Converter and theoretical revision on fuzzy logic control system
also described in this chapter.
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c) Chapter 3 presents the methodology used to design open loop Buck
Converter and fuzzy logic controller. All the components that have been used
in designing of fuzzy logic controller are described well in this chapter.
d) Chapter 4 shows the analysis for fuzzy logic controller will be with helps
from set of figures and tables.
e) Chapter 5 a conclusion for this project and recommendation for future study.
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CHAPTER 2
LITERATURE REVIEW
2.1
Introduction
Energy storage elements including capacitors and inductors are used for
energy transfer and work as a low-pass filter. The buck converter and the boost
converter are the two fundamental topologies of switch mode DC-DC converters.
Most of the other topologies are either buck-derived converter, because their
topologies are equivalent to the buck converters [5].
A thorough literature overview was done on the usage of fuzzy logic
controller as applied DC-DC Buck Converter.
M. Bayati Poodeh, S. Eshtehardiha, M. R. Zare (2007), proposed an
application of fuzzy logic to control the DC – DC converter using
MATLAB/SIMULINK software. This paper demonstrated the effectiveness of the
fuzzy controller applied to the state space averaging DC – DC converter using
MATLAB.
M. J Yusoff, N.F Nik Ismail, Ismail Musirin, N. Hashim, D. Johari (2010),
proposed a comparative study of fuzzy logic controller and proportional integral
derivative controller on DC – DC buck converter using MATLAB simulation
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software. Fuzzy logic controller has advantages in fast response controlled with
higher accuracy. FLC has a potential to improve robustness of DC – DC converter.
Based on those related work, the researchers make a great efforts to propose
the good to overcome the DC-DC Converter problems. Their applications of each
method differ, thus the further investigation of this controller is needed.
2.2
Buck Converter
The step-down dc-dc converter, commonly known as buck converter, it
shown in fig. 2.1. This consists of dc input voltage source Vs, controlled switch S,
diode D, filter inductor L, filter capacitor C and load resistance R. Typically
waveform in the converter are shown in fig 2.2, under assumption that the inductor
current is always positive. The state of the converter in which the inductor current is
never zero for any period of time is called the Continuous Conduction Mode (CCM).
[4][13].
Figure 2.1 : Circuit Diagram for Buck Converter
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Figure 2.2: Waveform for Buck Converter
It can be seen from the circuit that when the switch S is commanded to the on state,
the diode D is reverse biases, which can be shown in figure 2.3(a). When the switch
is off, the diode conducts to support an interruption current in the inductor, which
can be shown in figure 2.3(b) .
Figure 2.3 (a) : Turn on switch “Circuit Diagram Buck Converter”
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Figure 2.3 (b) : Turn off switch “Circuit Diagram Buck Converter”
When the switch S1 is on and D is reverse biased, the dynamics of inductor current iL
abd the capacitor voltage Vc are:
(2.1)
When the switch S1 is off and D is forward biased, the dynamics of the are
(2.2)
When the switch S1 is off and D is also not conducting,
(2.3)
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The state space representation for converter circuit configuration can be expressed
as:
(2.4)
Where X = [x1, x2]T = [Vc , iL]is the state vector and A’s and B’s are the system
matrices.
The state matrices and the input vectors for the ON and OFF periods are.
(2.5)
And U = Vin 0
2.2.1 Modes of Operation
The operation of dc-dc converters can be classified by the continuity of
inductor current flow. So dc-dc converter has two different modes of operation that
are:
(a) Continuous conduction mode (CCM) and
(b) Discontinuous conduction mode (DCM).
A converter can be design in any mode of operation according to the requirement.
10
2.2.1.1 Continuous Conduction Mode (CCM)
When the inductor current flow is continuous of charge and discharge during
a switching period, it is called Continuous Conduction Mode (CCM) of operation
shown in figure 2.4(a). The converter operating in CCM delivers larger current than
in DCM.
2.2.1.2 Discontinuous conduction mode (DCM).
When the inductor current has an interval of time staying at zero with no
charge and discharge then it is said to be working in Discontinuous Conduction
Mode (DCM) operation and the waveform of inductor current is illustrated in figure
2.4(c). At lighter load currents, converter operates in DCM. The regulated output
voltage in DCM does not have a linear relationship with the input voltage as in
CCM.
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Figure 2.4: Inductor current waveform of PWM converter
(a) CCM (b) boundary of CCM and DCM (c) DCM
2.2.2 Critical Component Values
Since the inductor current magnitude at the end of the switching period must
equal the inductor current magnitude at the beginning of the next period at steady
state, the change in current over the switching period must equal zero.
Using this knowledge yields the following:
Δ l L.period = Δ l L.closed + Δ l L.open = 0
(2.6)
12
Substituting equations (2.1) and (2.6) into (2.7) and solving for D yields:
(2.7)
D = Vout
Vin
Now the average inductor current equals the average of the minimum and
maximum inductor current values, so the maximum inductor can be found using
equation (2.9) nothing that either Δ l L.closed or Δ l L.open can be used.
ILmax = IL + [Δ l L]
2
(2.8)
Using the rule known as amp-second balance, which states the average
current through a capacitor at steady state must equal zero, the average inductor
current must equal the average output current.
IL =
I out =
(2.9)
Vout
R
Substituting equations (2.6) and (2.9) into (2.8) and simplifying yields:
(2.10)
The minimum inductor current can be found in the same manner as the maximum
inductor current:
lLmin = IL - [Δ l L]
2
(2.11)
The minimum inductor current is an important value, because as mentioned
previously, it determines the mode of conduction. Since all previous equations were
derived using the assumption of CCM, for them to remain valid I
Lmin
can never go
below zero. So by setting equation (2.15) equal to zero and rearranging to solve for
L, the minimum inductor value can be found to keep the converter in CCM:
13
(2.12)
Once the inductor value is determined, the minimum capacitance to maintain
the desired output ripple voltage can be found. This can be done by finding how
much charge is supplied by the capacitor when the switch is on or off. By using ampsecond balance the average current through a capacitor must equal zero if the circuit
is in steady state.
Then by calculating the area under the current wave form either when the
switch is on or off will yield the change in charge. Since the current wave form is
triangular the area can be found by using the formula one half times the triangle’s
base times the triangles height. Where the height equals the change in current
divided by two, and the base is the switching period divided by two.
(2.13)
In this case the change of charge (ΔQ) is easier to calculate using the change
in current when the switch is off (Δ I
L,open).
Substituting equation (2.6) into (2.14)
and simplifying yields:
(2.14)
C
=
ΔQ
Δ Vout
(2.15)
14
Substituting equation (2.15) into equation (2.16) yields the equation for selecting the
minimum output capacitor for the desired output ripple voltage.
(2.16)
2.2.3 Mathematical Modeling of Buck Converter
2.2.3.1 State-Space Representations
The buck converter is nonlinear, time-dependent system and its operation is
described by the two modes, illustrated in Figure 2.5 (a) and (b). The system is
linearized through switch averaging method about a selected operating point, and
with respect to the transistor duty cycle, k.
Figure 2.5: (a) Mode 1
Figure 2.5:
(b) Mode 2
Mode 1 of operation is described by two differential equations derived from the
circuit in Figure 2.5 (a) and consistent with transistor Q switch being turn on:
15
(2.17)
(2.18)
The state-space representation for mode 1 (transistor is on) is given by:
(2.18)
(2.19)
(2.20)
(2.21)
(2.22)
The corresponding state-space representation for mode 1 is:
(2.23)
(2.24)
During mode 2, transistor Q switch is turn off, and the voltage across diode is zero,
as illustrated in Figure 2.5 (b). Mode 2 is describe by a set of differential equations,
16
consistent with the transistor Q switch being turn off:
(2.25)
The state-space representation of mode 2 is obtained from mode 1 state-space
representation by setting all coefficients of Vg to zero:
(2.26)
(2.27)
(2.28)
(2.29)
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2.2.3.2 Average State-Space Representation
The two linear systems are averaged with respect to their time span during
the switching period [1]:
(2.30)
This system representation is an approximation of the time-varying system,
in which a new input variable is introduced: duty cycle k(t). Thus, a new input vector
u’(t) is defined:
(2.31)
The non-linear time-invariant system obtained, with state vector x(t), input
vector u’(t) and output y(t) is written in a general format as:
Defining the deviations from an operating point, a straight forward linearization is
applied:
(2.32)
2.2.4 Advantages of Buck Converter for Power Factor Correction
i. It requires only one transistor and is simple.
ii. It has high efficiency, more than 90%.
iii. The inductor limits the rate of change of load current.
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But, the input current is discontinuous and a smoothing input filter is required. Buck
converter provides one polarity of output voltage and unidirectional output current.
In systems such as universal line AC-DC converters [5], it is very difficult to
improve power factor where high efficiency is required throughout the entire line. A
Power Factor Correction circuit using Boost Converter possesses 1% to 3% lower
efficiency at 100 Volts than that at 230 Volts. This is due to increased input current
that produces higher losses in semiconductors and input filters. Also the high output
voltage of Boost Converter in 380-400 Volts range has a detrimental effect on its
switching losses and on the size and efficiency of the isolation transformer.
2.3
Power Factor Correction (PFC)
Power factor correction is the method of improving the power factor of a
system by using suitable devices. The objective of power factor correction circuits is
to make the input to a power supply behave like purely resistive or a resistor. When
the ratio between the voltage and current is a constant, then the input will be resistive
hence the power factor will be 1.0. When the ratio between voltage and current is
other than one due to the presence of non-linear loads, the input will contain phase
displacement, harmonic distortion and thus, the power factor gets degraded [7]. [12]
2.3.1 Need of PFC
The rise in the industrial, commercial and residential applications of
electronic equipment’s has resulted in a huge variety of electronic devices requiring
mains supply. These devices have rectification circuits, which is the prominent
reason of harmonic distortion. These devices convert AC to DC power supply which
causes current pulses to be drawn from the ac network during each half cycle of the
supply waveform. Even if a single device for example, a television may not draw a
lot of reactive power nor it can generate enough harmonics to affect the supply
19
system significantly, but within a particular phase connection, there may exist
several such devices connected to the same supply phase resulting in production of a
large amount of reactive power flow and harmonics in line current [8].
2.3.2 Types of Power Factor Correction
Power Factor Correction can be classified as two types:
i.
Passive Power Factor Correction
ii.
Active Power Factor Correction
2.3.2.1 Passive Power Factor Correction
In Passive PFC, in addition to the diode bridge rectifier, passive elements are
introduced to improve the nature of the line current. By using this, power factor can
be increased to a value of 0.7 to 0.8 approximately. As the voltage level of power
supply increases, the sizes of PFC components increase. The idea of passive PFC is
to filter out the harmonic currents by use of a low pass filter and only allow the 50
Hz power frequency wave to increase the power factor [7], [8].
a)
Advantages of Passive PFC :

It has a simple structure.

It is reliable and rugged.

The cost is very low because only a filter is required.

The high frequency switching losses are absent and it is not sensitive to
noises and surges.

b)
The equipment used in this circuit don’t generate high frequency
Disadvantages of Passive PFC :

For achieving better power factor the size of the filter increases.
20

Due to the time lag associated with the passive elements it has a poor
dynamic response.

The voltage cannot be regulated and the efficiency is low.

Due to presence of inductors and capacitors interaction may take place
between the passive elements and the system resonance may occur at
different frequencies.

Although by filtering the harmonics can be filtered out, the fundamental
component may get phase shifted thus reducing the power factor

The shape of input current is dependent upon what kind of load is connected
[7],[ 8].
2.3.2.2 Active Power Factor Correction
An active PFC is a power electronic device designed to control the amount of
power drawn by a load and obtains a power factor as close as possible to unity.
Commonly any active PFC design functions by controlling the input current in order
to make the current waveform follow the supply voltage waveform closely (i.e. a
sine wave). A combination of the reactive elements and some active switches
increase the effectiveness of the line current shaping and to obtain controllable
output voltage [7], [8].
The switching frequency differentiates the active PFC solutions into two classes.
i) Low frequency active PFC:
Switching takes place at low-order harmonics of the line-frequency and it is
synchronized with the line voltage.
ii) High frequency active PFC:

The switching frequency is much higher than the line frequency.
21

The power factor value obtained through Active PFC technique can be more
than 0.9. With a suitable design even a power factor of 0.99 can be achieved
easily. Active PFC power supply can detect the input voltage automatically,
supports 110V to 240V alternative current, its size and weight is smaller than
passive PFC power supply [7], [8].
a) Advantages of Active PFC :

The weight of active PFC system is very less.

The size is also smaller and a power factor value of over 0.95 can be obtained
through this method.

It reduces the harmonics present in the system.

Automatic correction of the AC input voltage can be obtained.

It is capable of operating in a full range of voltage [7], [8].
b) Disadvantages of Active PFC :

The layout design is somewhat more complex than passive PFC.

It is very expensive since it needs PFC control IC, high voltage MOSFET,
high voltage ultra-fast choke and other circuits [7], [8].
2.4
Fuzzy logic Controller
The most important specifications of fuzzy control method are their fuzzy
logical ability in the quality perception of system dynamics and the application of
these quality ideas simultaneously for power systems [9]. A simple block diagram of
a fuzzy system is shown in figure 2.6.
22
Knowledge Based /
Rule Base
input
Fuzzification
output
Defuzzifacition
Fuzzy Logical
Decision Maker
Figure 2.6: Structure of fuzzy logic controller
a)
Input
The inputs are most often hard or crisp measurement from some measuring
equipment is converted into fuzzy values for each input fuzzy set with the
fuzzification block. [10]
b)
Fuzzification
The fuzzification block performs the following tasks:

Measures the value of input variables.

Performs a scale mapping that transfers the range of values of input variables
into the corresponding universes of discourse.

Performs the function of fuzzification, which converts input data into suitable
linguistic values that may be viewed as labels of fuzzy sets.
23
c)
Knowledge based/rule base
The collection of rules is called a rule base. The rules are in “If Then” format
and formally the If side is called the conditions and the Then side is called the
conclusion. The computer is able to execute the rules and compute a control signal
depending on the measured inputs error (e) and change in error.(dE). In a rule based
controller the control strategy is stored in a more or less natural language. A rule
base controller is easy to understand and easy to maintain for a non- specialist end
user and an equivalent controller could be implemented using conventional
techniques. [10]
d)
Fuzzy logical
The fuzzy engine is the kernel of a fuzzy logic controller, which has
capability of simulating human decision making based on fuzzy concepts and of
inferring fuzzy control actions using fuzzy implication (fuzzy relation) and the rules
of inference in fuzzy logic. This means that the fuzzy inference engine handles rule
inference where human experience can easily be injected through linguistic rules.
e)
Defuzzication
Defuzzification is when all the actions that have been activated are combined
and converted into a single non-fuzzy output signal which is the control signal of the
system. The output levels are depending on the rules that the systems have and the
positions depending on the non-linearity’s existing to the systems. To achieve the
result, develop the control curve of the system representing the I/O relation of the
systems and based on the information; define the output degree of the membership
function with the aim to minimize the effect of the non-linearity.[10]
24
f)
Output
The output is output gain that can be tuned and also become as an integrator.
The output crisp value can be calculated by the centre of gravity or the weighted
average. [8]
50
REFERENCES
[1]
Mohan, Underland, Robbins “Power Electronics converters applications and
design” John Wiley & sons, inc. 2003 pp- 231-303.
[2]
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