Photovoltaic Charge Controller

A Project Report on
“PHOTOVOLTAIC CHARGE CONTROLLER”
Submitted for partial fulfillment of requirement of award of
BACHELOR OF TECHNOLOGY
Degree
In
Electrical & Electronics Engineering
By
Akanksha Roll No. 0906321008
Prashant Verma Roll No. 0906321068
Sukriti Ranjan Rao Roll No. 0906321110
Avinav Prince Roll No. 0906321027
SESSION: 2012-13
G.L.A. INSTITUTE OF TECHNOLOGY AND MANAGEMENT, MATHURA

CERTIFICATE
This is to certify that the project entitled “Photovoltaic Charge Controller” is
the bonafide work of Akanksha, Prashant Verma, Sukriti Ranjan Rao, and Avinav
Prince submitted in partial fulfillment of the requirements for the award of the
degree of Bachelor of Technology (B.Tech.) in Electrical and Electronics (EN) by
GBTU, Lucknow, U.P. during the academic year 2012-2013.
Signature
(Mr. Subhash Chandra)
Project Supervisor

ACKNOWLEDGEMENT
We would like to express our gratitude towards all the people who have
contributed their precious time and efforts to help us in completing this project,
without whom it would not have been possible for us to understand and analyze
the project.
We would like to thank Mr. Subhash Chandra, Department of Electrical
Engineering, and our Project Supervisor, for his guidance, support, motivation and
encouragement throughout the period this work was carried out. His readiness for
consultation at all times, his educative comments, his concern and assistance have
been invaluable.
We are also grateful to Dr. S. Basu, Professor and Head, Department of Electrical
and Electronics Engineering, for providing the necessary facilities in the
department.
We would also like to thank Mr. Sanjay Maurya, Department of Electrical and
Electronics Engineering, our Project Incharge, for consultation and support
throughout the length of the project.

TABLE OF CONTENTS
CHAPTER PAGE
TITLE i
CERTIFICATE ii
ACKNOWLEDGEMENT iii
TABLE OF CONTENT iv
LIST OF TABLES vii
LIST OF FIGURES viii
1. INTRODUCTION
1.1 Background 1
1.2 Objectives 2
1.3 Scope of Project 2
2. LITERATURE REVIEW
2.1 Need of Renewable Energy. 3
2.2 Different Sources of Renewable Energy 3
2.3 Renewable Energy Trends across the globe 5
2.4 Why Solar Energy? 5
2.5 Recent Data on Solar Power in India 5
3. PHOTOVOLTAIC POWER TECHNOLOGY
3.1 Photovoltaic Cell 6
3.2 PV Module 8
3.3 PV Modelling 8
3.4 PV Charge Controller 8

4. DC-DC Converter
4.1 Buck (Step-Down) Converter 11
4.1.1 Basic Modes of Operation Buck Converter 12
4.1.2 Simulink Model of Buck Converter 15
4.1.3 Output Waveform Scope 16
4.2. Boost (Step-Up) Converter 17
4.2.1 Basic Modes of Operation Boost Converter 18
4.2.2 Simulink Model of Boost Converter 21
4.3 Mathematical analysis of Boost Converter 23
4.4 Variation in Duty Cycle for constant output Voltage 23
4.5 Variation between Input Voltage and Duty Cycle 24
4.6 Matlab Script Code for Boost converter 25
4.7 Case Study 26
4.8 Pulse Width Modulation (PWM) 27
5. BUCK-BOOST CONVERTER
5.1 Introduction 28
5.2 Modes of Operation Buck-Boost Converter 29
5.2.1 Simulink Model of Buck-Boost Converter 32
5.2.2 PWM Controller Subsystem 33
6. COMPONENTS
6.1 Introduction to MATLAB™ and SIMULINK™ 35
6.2 Components Used 38
6.1.1 MOSFET 38
6.1.2 Inductor 39
6.1.3 Capacitor 40
6.1.4 Diode 41
6.1.5 Pulse Generator 42

6.1.6 Resistor 43
6.1.7 Repeating Sequence 44
6.1.8 Scope 44
6.1.9 Power GUI 45
REFERENCES 46

List of Table:
4 (i) Boost Converter Output for Constant Duty Cycle
4 (ii) Boost Converter Output for Constant Input Voltage
4 (iii) Graph showing variation between Duty Cycle and Input Voltage
4 (iv) RLC values for 8-24V

List of Figures:
4.a. Circuit Diagram of Buck Converter
4.b. Buck Converter in ON state
4.c. Buck Converter in OFF state
4.d. Simulink model of Buck Converter
4.e. Scope of Buck Converter
4.f. Circuit Diagram of Boost Converter
4.g. Boost Converter in ON state
4.h. Boost Converter in OFF state
4.i. Boost Converter in OFF state (Both transistor and diode OFF)
4.d. Simulink model of Boost Converter
4.e. Scope of Boost Converter

1
Chapter 1
Introduction
1.1 Background
Photovoltaic or in short term PV is one of the renewable energy resources that
recently has become broader in nowadays technology. PV has many benefits
especially in environmental, economic and social. In general, a PV system
consists of a PV array which converts sunlight to direct-current electricity, a
control system which regulates battery charging and operation of the load, energy
storage in the form of secondary batteries and loads or appliances. A charge
controller is one of functional and reliable major components in PV systems. A
good, solid and reliable PV charge controller is a key component of any PV
battery charging system to achieve low cost and the benefit that user can get from
it.
1.a. Block diagram of PV system
The main function of a charge controller in a PV system is to regulate the
voltage and current from PV solar panels into a rechargeable battery. The
minimum function of a PV charge controller is to disconnect the array when the
battery is fully charged and keep the battery fully charged without damage. A
charge controller is important to prevent battery overcharging, excessive
discharging, reverse current flow at night and to protect the life of the batteries in
a PV system. A power electronics circuit is used in a PV charge controller to get
highest efficiency, availability and reliability. The use of power electronics
circuits such as various dc to dc converters topologies like buck converter, boost
Solar
Energy
Photovoltaic
cell
Photovoltaic
Charge
Controller
Battery
System

2
converter, buck-boost converter and others converter topology as power
conditioning circuitry to provide a desired current to charge battery effectively.
1.2 OBJECTIVES
(i) To design Photovoltaic (PV) Charge Controller by using Pulse Width
Modulation as a switching controller.
(ii) To maintain constant output voltage for the variable input voltage of the
Photovoltaic Cell and to charge a battery.
1.3 SCOPE OF PROJECT
(i) The PV charge controller that designed in this project will be implement
Pulse Width Modulation (PWM) controller in it.
(ii) This project concentrates on DC-DC Converter.
(iii) This project will use PWM controller to control the voltage and current at
certain values that have been set which act as an input to the gate junction
of mosfets, which results in constant output voltage of this photovoltaic
charge controller.

3
Chapter 2
LITERATURE REVIEW
2.1 Need for Renewable Energy
Renewable energy is the energy which comes from natural resources such as
sunlight, wind, rain, tides and geothermal heat. These resources are renewable and
can be naturally replenished.
Many forms of energy that we have grown dependent on are from non-
renewable energy sources. This means that when the energy has been consumed,
the supply has gone and cannot be replaced. An example of this is coal. Coal is
known as a fossil fuel and is the largest source of energy for the generation of
electricity worldwide. When coal has been mined and burnt, it cannot be replaced.
Finding alternative energy sources, ideally from renewable sources, will decrease
our dependency on fossil fuels and other non-renewable energy sources.
Therefore, for all practical purposes, renewable resources can be considered
to be inexhaustible, unlike dwindling conventional fossil fuels.
2.2 Different sources of Renewable Energy
2.2.1 Wind power
Wind turbines can be used to harness the energy available in airflows. Current day
turbines range from around 600 kW to 5 MW of rated power. Since the power
output is a function of the cube of the wind speed, it increases rapidly with an
increase in available wind velocity. Recent advancements have led to aerofoil
wind turbines, which are more efficient due to a better aerodynamic structure.

4
2.2.2 Solar power
The tapping of solar energy owes its origins to the British astronomer John
Herschel who famously used a solar thermal collector box to cook food during an
expedition to Africa. Solar energy can be utilized in two major ways. Firstly, the
captured heat can be used as solar thermal energy, with applications in space
heating. Another alternative is the conversion of incident solar radiation to
electrical energy, which is the most usable form of energy. This can be achieved
with the help of solar photovoltaic cells or with concentrating solar power plants.
2.2.3 Small hydropower
Hydropower installations up to 10MW are considered as small hydropower and
counted as renewable energy sources. These involve converting the potential
energy of water stored in dams into usable electrical energy through the use of
water turbines. Run-of-the-river hydroelectricity aims to utilize the kinetic energy
of water without the need of building reservoirs or dams.
2.2.4 Biomass
Plants capture the energy of the sun through the process of photosynthesis. On
combustion, these plants release the trapped energy. This way, biomass works as
a natural battery to store the sun’s energy and yield it on requirement.
2.2.5 Geothermal
Geothermal energy is the thermal energy which is generated and stored [9] within
the layers of the Earth. The gradient thus developed gives rise to a continuous
conduction of heat from the core to the surface of the earth. This gradient can be
utilized to heat water to produce superheated steam and use it to run steam turbines
to generate electricity. The main disadvantage of geothermal energy is that it is
usually limited to regions near tectonic plate boundaries, though recent
advancements have led to the propagation of this technology.

5
2.3 Renewable Energy Trends across the Globe
Due to the increasing demand for the energy there are some methods that can be
used to store energy.
 From sun, solar power is radiated it is energy and can be stored in a
 From the movement of huge quantity of water a hydropower is come from it.
 One way is geothermal power; in this way energy from hot water and steam
can be produced on earth’s surface.
 Wind power is usually used by big turbines same as that of the windmills that
are roiled by the atmospheric winds.
Among these applications Solar Energy is the most efficient, easy and practical
method to be acceptable for the production of electricity.
2.4 Why Solar Energy?
The Earth receives 174 petawatts (PW) of incoming solar radiation (insolation) at
the upper atmosphere.Approximately 30% is reflected back to space while the rest
is absorbed by clouds, oceans and land masses.
2.5 Recent Data on Solar Power in India
 Total development of Solar PV system in India has exceeded 1040 MW.
 Under first phase of Jawahar lal Nehru National Solar Mission (JNNSM) to
be implemented between 1st
april 2010 and 31st
march 2013, 200MW
capacity equivalent off grid Solar PV systems and 7 million square meteres
solar thermal collector are to be installed in the country. As an feb 2011, the
achievement figures are 38.5MW for off grid PV system and 1.2 lakh
square meter solar thermal collecter area.
 A 214 MW solar park was installed recently at Charanka (Gujarat).
 By the end of 2011, a total of 67.4 GW had been installed, sufficient to
generate 85 TWh/year. And by end of 2012, the 100 GW installed capacity
milestone was achieved.

6
Chapter 3
Photovoltaic Power Technology
3.1 Photovoltaic Cell
A photovoltaic cell or photoelectric cell is a semiconductor device that converts
light to electrical energy by photovoltaic effect. If the energy of photon of light is
greater than the band gap then the electron is emitted and the flow of electrons
creates current.
However a photovoltaic cell is different from a photodiode. In a photodiode
light falls on n-channel of the semiconductor junction and gets converted into
current or voltage signal but a photovoltaic cell is always forward biased.
The photovoltaic (pv) power technology uses semiconductor cells (wafers),
generally several square centimeters in size. The cell is basically a large area p-n
diode with the junction positioned close to the top surface. The cell converts the
sunlight into direct current electricity. Numerous cells are assembled in a module
to generate required power..
Typically a solar cell can be modelled by a current source and an inverted
diode connected in parallel to it. It has its own series and parallel resistance.
Series resistance is due to hindrance in the path of flow of electrons from n to p
junction and parallel resistance is due to the leakage current.
3.a. Single diode model of a PV cell

7
Where I is the reverse saturation current of the diode, q is the electron charge, Vd
is the voltage across the diode, k is Boltzmann constant (1.38 * 10-19
) J/K) and T
is the junction temperature in Kelvin (K)
3.b. I-V characteristics of PV cell

8
3.2 PV Module
Usually a number of PV modules are arranged in series and parallel to meet the
energy requirements. PV modules of different sizes are commercially available
(generally sized from60W to 170W). For example, a typical small scale
desalination plant requires a few thousand watts of power.
3.3 PV Modelling
A PV array consists of several photovoltaic cells in series and parallel
connections. Series connections are responsible for increasing the voltage of the
module whereas the parallel connection is responsible for increasing the current
in the array. Typically a solar cell can be modeled by a current source and an
inverted diode connected in parallel to it. It has its own series and parallel
resistance. Series resistance is due to hindrance in the path of flow of electrons
from n to p junction and parallel resistance is due to the leakage current.
The relationship between volts, amps, and watts. Solar panels are typically
marketed based on their peak power production, measured in watts.
Watts = Volts x Amps
2.4 Photovoltaic Charge Control
In general, a PV system consists of a PV array which converts sunlight to direct-
current electricity, a control system which regulates battery charging and
operation of the load, energy storage in the form of secondary batteries and loads
or appliances. A charge controller is one of functional and reliable major
components in PV systems. A good, solid and reliable PV charge controller is a
key component of any PV battery charging system to achieve low cost and the
benefit that user can get from it.
The main function of a charge controller in a PV system is to regulate the
voltage and current from PV solar panels into a rechargeable battery. The
minimum function of a PV charge controller is to disconnect the array when the
battery is fully charged and keep the battery fully charged without damage. A
charge controller is important to prevent battery overcharging, excessive

9
discharging, reverse current flow at night and to protect the life of the batteries in
a PV system. Efficiency, size, and cost are the primary advantages of switching
power converters when compared to linear converters. Switching power converter
efficiencies can run between 70-80%, whereas linear converters are usually 30%
efficient. These converters are generally either hard-switched PWM or soft-
switched resonant link types.
The hard-switched PWM converters operate with a fixed-frequency,
variable duty cycle. This type of signal is called Pulse Width Modulated signal
(PWM), depending on the duty cycle, they can operate in either continuous current
mode (CCM) or discontinuous current mode (DCM). If the current through the
output inductor never reaches zero then the converter operates in CCM; otherwise
DCM occurs.
The output voltage will be equal with the average value on the switching
cycle of the voltage applied at the output filter. Due to the losses on the ON or
OFF state of the ideal transistor are zero, the theoretical efficiency of the switching
mode converters is up to 100%. But, considering the real switches, with parasitic
elements, the efficiency will be a little bit lower, but higher than linear regulators.
Another advantage of switching mode converters consist in the possibility
to use the same components but in other topology in order to obtain different
values of the output voltages: positive or negative, lower or higher than input
voltage.
There are various analysis methods of DC-DC converters. While demands
for portable power electronics have grown significantly during the last a few
years, end users are more concerned about the battery run-time. Extending the
battery run-time becomes the top priority for the system designers. This project
overviews three commonly used DC-DC conversion topologies suitable for
battery operated systems:
 Buck converter,
 Boost converter,
 Buck-Boost converter.
In this approach, the differential equations that describe the inductor current
and capacitor voltage are determined and are solved according with the boundary

10
conditions of the switching periods. The values of currents and voltages at the end
of a period become initial conditions for the next switching period. This method
is very accurate and produces a set of equations that require extensive
computation.

11
Chapter 4
DC-DC Converters
4.1 BUCK (Step-Down) CONVERTER
A buck converter is called a step-down DC to DC converter because the
output voltage is less than the input. Its design is similar to the step-up boost
converter, and like the boost converter it is a switched-mode power supply that
uses two switches (a transistor and a diode) and an inductor and a capacitor.
Most buck converters are designed for continuous-current mode operation
compared to the discontinuous-current mode operation. The continuous-current
mode operation is characterized by inductor current remains positive throughout
the switching period. Conversely, the discontinuous-current mode operation is
characterized by inductor current returning to zero during each period.
The figure below shows the basic of buck converter circuit. The switches
alternates between connecting the inductor to source voltage to store energy in the
inductor and discharging the inductor into the load with at a rate of PWM
switching frequency.
The output that results is a regulated voltage of smaller magnitude than
input voltage. The converter operation will be analyzed function of switches state.
4.a. Circuit diagram of Buck Converter

12
4.1.1 Basic modes of Operation of Buck Converter:
A) THE FIRST TIME INTERVAL: Transistor is in ON state and diode is OFF.
During this time period, corresponding with duty cycle of PWM driving signal,
the equivalent diagram of the circuit is presented below:
4.b. Buck converter in ON state
When the switch is in ON state, diode become as reversed biased and the inductor
will deliver current and switch conducts inductor current. With the voltage (Vin -
Vo) across the inductor, the current rises linearly (current changes, ΔiL). The
current through the inductor increase, as the source voltage would be greater then
the output voltage and capacitor current may be in either direction depending on
the inductor current and load current.
When the current in inductor increase, the energy stored also increased. In
this state, the inductor acquires energy. Capacitor will provides smooth out of
inductor current changes into a stable voltage at output voltage and it’s big enough
such that V out doesn’t change significantly during one switching cycle.
For this equivalent circuit will write the equations that describe the
converter operation:

13
𝑑𝑢𝑜
𝑑𝑡
𝑖𝐿
𝑢𝑜
𝑅 𝐶
;
𝑑𝑖𝐿
𝑑𝑡
𝐸
𝑢𝑜
𝐿
;
B) THE SECOND TIME PERIOD: The transistor is OFF and diode is ON.
In the moment when the transistor switch in OFF state, the voltage across the
inductor will maintains current to load. Because of inductive energy storage, iL
will continues to flow. While inductor releases current storage, it will flow to the
load and provides voltage to the circuit. The diode is forward biased. The current
flow through the diode which is inductor voltage is equal with negative output
voltage. The equivalent diagram of the circuit is presented below:
4.c. Buck Converter in OFF state
For this operation period, the output voltage u0 and the current through the
inductor iL satisfy the following equations:

14
𝑑𝑢𝑜
𝑑𝑡
𝑖𝐿
𝑢𝑜
𝑅 𝐶
;
𝑑𝑖𝐿
𝑑𝑡
𝑢𝑜
𝐿
;

15
4.1.2 Simulink Model of Buck Converter:
4.d. Simulink Model of Buck Converter

16
4.1.3 Output Waveform Scope :
4.e. Scope of Buck Converter

17
4.2 BOOST (Step-Up) CONVERTER
The boost (or step-up converter), contains a capacitor and an inductor with role of
energy storing, and two complementary switches. In the case of the boost
converter, the output voltage is higher than the input voltage. The switches are
alternately opened and closed with at a rate of PWM switching frequency. As long
as transistor is ON, the diode is OFF, being reversed biased. The input voltage,
applied directly to inductance L, determines a linear rising current. When
transistor is OFF, the load is supplied by both input source and LC filter. The
output that results is a regulated voltage of higher magnitude than input voltage.
The converter operation will be analyzed according with the switches states.
4.f. Circuit Diagram of Boost Converter.
‘

18
4.2.1 Modes of Operation
A) THE FIRST TIME INTERVAL: The transistor is in ON state and
diode is OFF.
the equivalent diagram of the circuit is presented below. In this time period the
inductance L store energy.
3.g. Boost Converter in ON State
inductor iL satisfies the following equations:
𝑑𝑢𝑜
𝑑𝑡
𝑢𝑜
𝑅𝐶
;
𝑑𝑖𝐿
𝑑𝑡
𝐸
𝐿
;

19
B) THE SECOND TIME PERIOD: The transistor is OFF and diode is
ON.
inductor will change the polarity and diode will switch in ON state. The equivalent
diagram of converter during this period is shown in the bellow figure:
4.h. Boost Converter in OFF state
inductor iL satisfy the following equations:
𝑑𝑢𝑜
𝑑𝑡
𝑖𝐿
𝑢𝑜
𝑅 𝐶
;
𝑑𝑖𝐿
𝑑𝑡
𝐸
𝑢𝑜
𝐿
;

20
C) THE THIRD OPERATION MODE: The both transistor and diode
are OFF.
If the inductor current becomes zero before ending the diode conduction period,
both the transistor and the diode will be in OFF state. Due to the diode current
becomes zero, the diode will naturally close, and the output capacitor will
discharge on the load. This operation regime is called discontinuous current mode.
The equivalent diagram of this operation regime is shown below:
4.i. Boost Converter in OFF state (both transistor and diode are OFF)
inductor iL can be calculated from the following equations:
𝑑𝑢𝑜
𝑑𝑡
𝑢𝑜
𝑅𝐶
;
𝑑𝑖𝐿
𝑑𝑡
0;

21
4.2.2 Simulink Model of Boost Converter:
4.j. Simulink Model of Boost Converter.

22
4.2.3 Output Waveform Scope:
4.k. Scope of Boost Converter.

23
4.3 MATHEMATICAL ANALYSIS OF BOOST CONVERTER:
S.No Input Voltage Duty Cycle Output Voltage
1 10 85 12.86
2 12 85 15.43
3 14 85 18
4 16 85 20.57
5 18 85 23.14
6 20 85 25.71
7 22 85 28.28
3(i) Boost converter output for constant duty cycle
4.4 VARIATION IN DUTY CYCLE FOR CONSTANT OUTPUT
VOLTAGE
S.No. Input Voltage Duty Cycle Output Voltage
1 10 85.84 15
2 10.5 85.554 15
3 11 85.304 15
4 11.5 85.074 15
5 12 84.86 15
6 12.5 84.66 15
7 13 84.47 15
8 13.5 84.29 15
9 14 84.116 15
10 14.5 83.954 15
4 (ii) Boost Converter output for constant output

24
4.5 VARIATION BETWEEN INPUT VOLTAGE AND DUTY
CYCLE:
4(iii) Graph shoeing variation between duty cycle and input voltage
The above graph shows variation between Input Voltage and Duty Cycle. The
Negative Slope indicates that increase in input voltage results in decrease in duty
cycle.
83
83.5
84
84.5
85
85.5
86
10 10.5 11 11.5 12 12.5 13 13.5 14 14.5
Input Voltage
DUTYCYCLE

25
4.6 BOOST CONVERTER CODING (for user interface) :
clc;
Vin=input('enter the input voltage:');
Vout=input('enter the output voltage:');
I=input('enter the maximum output current:');
f=input('enter the switching frequency:');
D=1-(Vin/Vout);
di=I*D;
L=Vin/(f*di);
dv=0.5;
C=((I-di)*D)/(f*dv);
R=Vout/I;
disp('DUTY CYCLE:');
D=D*100;
D
disp('INDUCTOR VALUE:');
L
disp('CAPACITOR VALUE micro farad:');
C
disp('RESISTOR VALUE:');
R

26
4.7 CASE STUDY:
INPUT RANGE: 8-24V
OUTPUT VOLTAGE: 30V
Vin Vout R L C
8 30 15 0.1091 0.0156
10 30 15 0.1500 0.0178
12 30 15 0.2000 0.0192
14 30 15 0.2625 0.0199
16 30 15 0.3429 0.0199
18 30 15 0.4500 0.0192
20 30 15 0.6000 0.0178
22 30 15 0.8250 0.0178
24 30 15 1.2000 0.0156
4 (iv) R L C Values for 8-24 V
 For constant values of
Resistance (R) = 12 Ω
Inductance (L) = 1 H
Capacitance (C) = 0.04 µF
 Input Voltage (Vin) = 15 V
Output Voltage (Vout) = 30 V
Maximum output current (Imax) = 3 A
Switching frequency (f) = 50 Hz

27
4.8 Pulse Width Modulation (PWM)
Pulse Width Modulation (PWM) controls adjusts the duty ratio of the
switches as the input changes to produce a constant output voltage. The DC
voltage is converted to a square-wave signal, alternating between fully on and
zero. By controlling analog circuits digitally, system costs and power
consumption can be drastically reduced. In nowadays implementation, many
microcontrollers already include on-chip PWM controllers making
implementation easy. In a nutshell, PWM is a way of digitally encoding analog
signal levels.
PWM control can be used in two ways: voltage-mode and current-mode. In
voltage-mode control the output voltage increases and decreases as the duty ratio
increases and decreases. The output voltage is sensed and used for feedback. If it
has two-stage regulation, it will first hold the voltage to a safe maximum for the
battery to reach full charge. Then it will drop the voltage lower to sustain a "finish"
or “trickle" charge. Two-stage regulating is important for a system that may
experience many days or weeks of excess energy (or little use of energy). It
maintains a full charge but minimizes water loss and stress. The voltages at which
the controller changes the charge rate are called set points.
When determining the ideal set points, there is some compromise between
charging quickly before the sun goes down, and mildly overcharging the battery.
The determination of set points depends on the anticipated pattern of use, the type
of battery, and to some extent, the experience and philosophy of the system
designer or operator.

28
Chapter 5
BUCK BOOST CONVERTER
5.1 BUCK BOOST CONVERTER
A buck-boost converter provides an output voltage that may be less than or greater
than the input voltage hence the name „‟ buck-boost’’; the output voltage polarity
is opposite to that of the input voltage. This converter is also known as an
inverting regulator. The circuit arrangement of a buck-boost convertor is shown
in figure below:
5.a. Circuit Diagram of Buck-Boost Converter
The switches are alternately opened and closed with at a rate of PWM switching
frequency. As long as the transistor is ON, the diode is OFF, being reversed biased.
The input voltage, applied directly to inductance L, determines a linear rising
current. The capacitor is discharged on the load circuit. When the transistor is
OFF, the load is supplied by LC filter. The output that results is a regulated voltage
of smaller or higher magnitude than input voltage, depending on the value of duty
cycle, but it has a reverse polarity. The converter operation will be analyzed
according with the ON or OFF state of switches.

29
5.2 Modes of operation
Phase Mosfet 1 Mosfet 2 Operating modes
1 OFF OFF BUCK
2 OFF ON OFF
3 ON OFF BUCK-BOOST
4 ON ON BOOST
5(i) Modes of operation of Buck-Boost Converter
A) THE FIRST TIME INTERVAL: The transistor is in ON state and
diode is OFF.
the equivalent diagram of the circuit is presented below. In this time period the
inductance L stores energy. The load current is assured by the output capacitor.
5.b. Buck Boost Converter in ON state.
inductor iL are given by the following equations system:
𝑑𝑢𝑜
𝑑𝑡
𝑢𝑜
𝑅𝐶
;

30
𝑑𝑖𝐿
𝑑𝑡
𝐸;
B) THE SECOND TIME PERIOD: the transistor is OFF and diode is
ON.
inductor will change the polarity and diode will switch in ON state. The energy
stored in the inductor will supply the load. The equivalent diagram of converter
during this period is shown in the figure below:
5.c. Buck Boost Converter in OFF state.
For this operation period, the following equations for the output voltage u0 and the
current through the inductor iL can be written as:
𝑑𝑢𝑜
𝑑𝑡
𝑖𝐿
𝑢𝑜
𝑅 𝐶
;
𝑑𝑖𝐿
𝑑𝑡
𝑢𝑜
𝐿
;

31
C) THE THIRD OPERATION MODE: The both transistor and diode
are OFF.
If the inductor current becomes zero before ending the diode ON period, both the
transistor and the diode will be OFF. Due to the diode current becomes zero, the
diode will naturally close, and the output capacitor will discharge on the load.
This operation regime is called discontinuous current mode. The equivalent
diagram of this operation regime is shown below:
5.d. Buck-Boost Converter in OFF state (both transistor and diode are OFF)
For this operation mode, the output voltage u0 and the current through the inductor
il can be calculated from the following differential equations:
𝑑𝑢𝑜
𝑑𝑡
𝑢𝑜
𝑅𝐶
;
𝑑𝑖𝐿
𝑑𝑡
0 ;

32
5.2.1 Simulink Model of Buck-Boost Converter for PV array of 50-
200V output:
5.e. Simulink Model of Buck-Boost Converter

33
5.2.2 PWM Controller Subsystem Simulink Diagram
5.f. Simulink Model of PWM Controller

34
5.2.3 Output Waveform Scope:
a) For Vin = 75 V Vout = 100.5 V
5.f. Scope of Buck-Boost Converter

35
Chapter 6
COMPONENTS
6.1 MATLAB® AND SIMULINK®
MATLAB® Version R2009a 7.8.0 (64 bit)
6.1.1 Overview of the MATLAB Environment
The MATLAB high-performance language for technical computing
integrates computation, visualization, and programming in an easy-to-use
environment where problems and solutions are expressed in familiar mathematical
notation. Typical uses include
 Math and computation
 Algorithm development
 Data acquisition
 Modeling, simulation, and prototyping
 Data analysis, exploration, and visualization
 Scientific and engineering graphics
 Application development, including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that
does not require dimensioning. It allows you to solve many technical computing
problems, especially those with matrix and vector formulations, in a fraction of
the time it would take to write a program in a scalar non-interactive language such
as C or FORTRAN.
The name MATLAB stands for matrix laboratory. MATLAB was originally
written to provide easy access to matrix software developed by the LINPACK and

36
EISPACK projects. Today, MATLAB engines incorporate the LAPACK and
BLAS libraries, embedding the state of the art in software for matrix computation.
MATLAB has evolved over a period of years with input from many users.
In university environments, it is the standard instructional tool for introductory
and advanced courses in mathematics, engineering, and science. In industry,
MATLAB is the tool of choice for high-productivity research, development, and
analysis.
MATLAB features a family of add-on application-specific solutions called
toolboxes. Very important to most users of MATLAB, toolboxes allow you to
learn and apply specialized technology. Toolboxes are comprehensive collections
of MATLAB functions (M-files) that extend the MATLAB environment to solve
particular classes of problems. You can add on toolboxes for signal processing,
control systems, neural networks, fuzzy logic, wavelets, simulation, and many
other areas.
6.1.2 The MATLAB System
The MATLAB system consists of these main parts:
 Desktop Tools and Development Environment
This part of MATLAB is the set of tools and facilities that help you use and
become more productive with MATLAB functions and files. Many of these tools
are graphical user interfaces. It includes: the MATLAB desktop and Command
Window, an editor and debugger, a code analyzer, browsers for viewing help, the
workspace, and files, and other tools.
 Mathematical Function Library
This library is a vast collection of computational algorithms ranging from
elementary functions, like sum, sine, cosine, and complex arithmetic, to more
sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions,
and fast Fourier transforms.

37
 The Language
The MATLAB language is a high-level matrix/array language with control
flow statements, functions, data structures, input/output, and object-oriented
programming features. It allows both "programming in the small" to rapidly create
quick programs you do not intend to reuse. You can also do "programming in the
large" to create complex application programs intended for reuse.
 Graphics
MATLAB has extensive facilities for displaying vectors and matrices as
graphs, as well as annotating and printing these graphs. It includes high-level
functions for two-dimensional and three-dimensional data visualization, image
processing, animation, and presentation graphics. It also includes low-level
functions that allow you to fully customize the appearance of graphics as well as
to build complete graphical user interfaces on your MATLAB applications.
 External Interfaces
The external interfaces library allows you to write C and Fortran programs
that interact with MATLAB. It includes facilities for calling routines from
MATLAB (dynamic linking), for calling MATLAB as a computational engine,
and for reading and writing MAT-files.
6.2 SIMULINK®
Simulink® software models, simulates, and analyzes dynamic systems. It
enables you to pose a question about a system, model the system, and see what
happens.
With Simulink, you can easily build models from scratch, or modify
existing models to meet your needs. Simulink supports linear and nonlinear
systems, modeled in continuous time, sampled time, or a hybrid of the two.
Systems can also be multirate—having different parts that are sampled or updated
at different rates.

38
Thousands of scientists and engineers around the world use Simulink to model
and solve real problems in a variety of industries, including:
 Aerospace and Defense
 Automotive
 Communications
 Electronics and Signal Processing
 Medical Instrumentation
6.3 COMPONENTS USED
6.3.1 MOSFET
6.a. MOSFET symbols in Simulink
The metal-oxide semiconductor field-effect transistor (MOSFET) is a
semiconductor device controllable by the gate signal (g > 0). The MOSFET device
is connected in parallel with an internal diode that turns on when the MOSFET
device is reverse biased (Vds < 0) and no gate signal is applied (g=0). The model

39
is simulated by an ideal switch controlled by a logical signal (g > 0 or g = 0), with
a diode connected in parallel.
The MOSFET device turns on when a positive signal is applied at the gate input
(g > 0) whether the drain-source voltage is positive or negative. If no signal is
applied at the gate input (g=0), only the internal diode conducts when voltage
exceeds its forward voltage Vf.
With a positive or negative current flowing through the device, the
MOSFET turns off when the gate input becomes 0. If the current I is negative and
flowing in the internal diode (no gate signal or g = 0), the switch turns off when
the current I becomes 0.
The on state voltage Vds varies
 Vds = Ron*I when a positive signal is applied at the gate input.
 Vds = Rd*I-Vf +Lon*dI/dt when the antiparallel diode is conducting (no
gate signal).
The Lon diode inductance is available only with the continuous model. For most
applications, Lon should be set to zero for both continuous and discrete models.
The MOSFET block also contains a series Rs-Cs snubber circuit that can
be connected in parallel with the MOSFET (between nodes d and s).
6.1.2 Inductor
An inductor (also choke, coil, or reactor) is a passive two-terminal electrical
component that stores energy in its magnetic field. For comparison,
a capacitor stores energy in an electric field, and a resistor does not store energy
but rather dissipates energy as heat.
Any conductor has inductance. An inductor is typically made of a wire or
other conductor wound into a coil, to increase the magnetic field. When the
current flowing through an inductor changes, a time-varying magnetic field is
created inside the coil, and a voltage is induced, according to Faraday’s law of

40
electromagnetic induction, which by Lenz's law opposes the change in current that
created it. Inductors are one of the basic components used in electronics where
current and voltage change with time, due to the ability of inductors to delay and
reshape alternating currents.
The effect of an inductor in a circuit is to oppose changes in current through it by
developing a voltage across it proportional to the rate of change of the current. An
ideal inductor would offer no resistance to a constant direct current; however,
only superconducting inductors have truly zero electrical resistance.
The relationship between the time-varying voltage v(t) across an inductor with
inductance L and the time-varying current i(t) passing through it is described by
the differential equation:
𝑡 𝐿
𝑑𝑖 𝑡
𝑑𝑡
6.1.3 Capacitor
A capacitor (originally known as condenser) is a passive two-terminal electrical
component used to store energy in an electric field. The forms of practical
capacitors vary widely, but all contain at least two electrical conductors separated
by a dielectric (insulator). The capacitor is a reasonably general model for electric
fields within electric circuits. An ideal capacitor is wholly characterized by a
constant capacitance C, defined as the ratio of charge ±Q on each conductor to the
voltage V between them.
𝐶
Sometimes charge build-up affects the capacitor mechanically, causing its
capacitance to vary. In this case, capacitance is defined in terms of incremental
changes:

41
𝐶
𝑑
𝑑
6.1.4 Diode
The most common function of a diode is to allow an electric current to pass in one
direction (called the diode's forward direction), while blocking current in the
opposite direction (the reverse direction). Thus, the diode can be viewed as an
electronic version of a check valve. This unidirectional behavior is called
rectification, and is used to convert alternating current to direct current, including
extraction of modulation from radio signals in radio receivers—these diodes are
forms of rectifiers.
However, diodes can have more complicated behavior than this simple on–off
action. Semiconductor diodes begin conducting electricity only if a certain
threshold voltage or cut-in voltage is present in the forward direction (a state in
which the diode is said to be forward-biased). The voltage drop across a forward-
biased diode varies only a little with the current, and is a function of temperature;
this effect can be used as a temperature sensor or voltage reference.
Fig 3.8 diode symbol.

42
6.1.5 Pulse Generator
6.b. Pulse Generator Symbol in simulink
The Pulse Generator block generates square wave pulses at regular
intervals. The block's waveform parameters, Amplitude, Pulse Width, Period, and
Phase Delay, determine the shape of the output waveform. The following diagram
shows how each parameter affects the waveform.
The Pulse Generator can emit scalar, vector, or matrix signals of any real
data type. To cause the block to emit a scalar signal, use scalars to specify the
waveform parameters. To cause the block to emit a vector or matrix signal, use
vectors or matrices, respectively, to specify the waveform parameters. Each
element of the waveform parameters affects the corresponding element of the
output signal. For example, the first element of a vector amplitude parameter
determines the amplitude of the first element of a vector output pulse. All the
waveform parameters must have the same dimensions after scalar expansion. The
data type of the output is the same as the data type of the Amplitude parameter.
Depending on the pulse's waveform characteristics, the intervals between
changes in the block's output can vary. For this reason, a time-based Pulse
Generator block has a variable sample time.

43
6.1.6 Resistor
A resistor is a passive two-terminal electrical component that implements
electrical resistance as a circuit element. The current through a resistor is in direct
proportion to the voltage across the resistor's terminals. This relationship is
represented by Ohm's law:
𝑅 𝑜 𝑡
Where I is the current through the conductor in units of amperes, V is the potential
difference measured across the conductor in units of volts, and R is the resistance
of the conductor in units of ohms.
Resistors are common elements of electrical networks and electronic circuits and
are ubiquitous in electronic equipment. Practical resistors can be made of various
compounds and films, as well as resistance wire (wire made of a high-resistivity
alloy, such as nickel-chrome). Resistors are also implemented within integrated
circuits, particularly analog devices, and can also be integrated
into hybrid and printed circuits.
6.c. various types of resistors.

44
6.1.7 Repeating Sequence:
6.d. Repeating Sequence symbol in Simulink
It generates arbitrarily shaped periodic signal.
The Repeating Sequence block outputs a periodic scalar signal having a waveform
that you specify. You can specify any waveform, using the block dialog's Time
values and Output values parameters. The Times value parameter specifies a
vector of sample times. The Output values parameter specifies a vector of signal
amplitudes at the corresponding sample times. Together, the two parameters
specify a sampling of the output waveform at points measured from the beginning
of the interval over which the waveform repeats (i.e., the signal's period). For
example, by default, the Time values and Output values parameters are both set to
[0 2]. This default setting specifies a sawtooth waveform that repeats every 2
seconds from the start of the simulation and has a maximum amplitude of 2. The
Repeating Sequence block uses linear interpolation to compute the value of the
waveform between the specified sample points.
6.1.8 Scope
6.e. Scope Symbol in Simulink.
The Scope block displays its input with respect to simulation time.

45
The Scope block can have multiple axes (one per port) and all axes have a
common time range with independent y-axes. The Scope block allows you to
adjust the amount of time and the range of input values displayed. You can move
and resize the Scope window and you can modify the Scope's parameter values
during the simulation.
If the signal is continuous, the Scope produces a point-to-point plot. If the
signal is discrete, the Scope produces a stair-step plot.
6.1.9 Power GUI
The Powergui block allows you to choose one of the following methods to solve
your circuit:
 Continuous method, which uses a variable step Simulink solver
 Ideal Switching continuous method
 Discretization of the electrical system for a solution at fixed time steps
 Phasor solution method
The Powergui block is necessary for simulation of any Simulink model containing
SimPowerSystems blocks. It is used to store the equivalent Simulink circuit that
represents the state-space equations of the model.
Place the Powergui block at the top level of diagram for optimal performance.
However, you can place it anywhere inside subsystems for your convenience; its
functionality will not be affected.
 You can have a maximum of one Powergui block per model
 You must name the block powergui

46
REFERENCES
1) Design and Modeling of Standalone Solar PhotovoltaicCharging System
By-Mathur B.L, Professor, Department of EEE, SSN College of
Engineering
2) Modelling of DC-DC converters
Ovidiu Aurel Pop and Serban Lungu
Technical University of Cluj-Napoca
Romania
3) www.mathworks.in
4) Irving M. Gottlieb, Power Supplies, Switching Regulators, Inverters, &
Converters, New York: McGraw-Hill, 1993, pp. 132-141.
5) Paper on PHOTOVOLTAIC CHARGE CONTROLLER
By: NOOR JUWAINA AYUNI BT. MOHD
6) Comparison of Photovoltaic array maximum power point tracking
technique - Patrick L Chapman, Trishan Esram
7) Texas Instruments papers
8) Power Electronics by Muhammad H. Rashid
9) Power Electronics by P. S. Bhimra
10) Development of a dc-dc buck boost converter using fuzzy logic control by
fathi shaban jabber
11) F. Liu, S. Duan, F. Liu, B. Liu, and Y. Kang, ―A variable step size INC
MPPT method for PV systems,‖ IEEE Trans.Ind.Electron., vol. 55, no.
7,pp. 2622–2628, Jul. 2008.

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