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Maximum Power Point Tracking for Solar Power Applications with Partial
Shading
By
Brian G. Finan
Scoil na hInnealtoireachta
Ollscoile na hEireann
Gallimh
Professor Gerard Hurley
A thesis submitted to the National University of Ireland in fulfilment of the
requirement for the degree of Bachelor of Energy Systems
Engineering (Electrical).
April 2013
This project is dedicated to my family,
Without whom I would not have come this far.
“go raibh maith agaibh"
i
Abstract
The title of this project is “Maximum power point tracking for solar power applications with
partial shading”. In simple terms this project’s objective is to have a solar panel outputting its
maximum possible power all of the time, this occurs when the panel has access to the
maximum amount of solar irradiance possible resulting in its output voltage and current being
at their maximum possible values. This study consists of examining solar energy as a viable
option and obtaining the maximum amount from the ‘green’ energy source, this means
getting the maximum power from a solar array at any given time. This is obtained by keeping
the solar array at its Maximum Power Point (MPP) continually. On researching this, it has
been found that some major factors come into account when the MPP is trying to be located
continually. These factors include partial shading of the solar array, which may be due to
clouds, location of the solar arrays, branches of trees etc. This study looks at issues of
Maximum Power Point Tracking (MPPT) under Partially Shaded Conditions (PSC), and
comes up with a valid solution to overcome the problem and obtain the MPP without
interruption. To achieve MPPT there are a number of options available to date, these are the
Perturb and Observe (P&O) MPPT method and Incremental Conductance (IC) MPPT
method. Extensive research has been carried out on these two MPPT methods and a detailed
account of the findings is documented in this report. It has been found that solar arrays under
PSC’s can have power losses as high as 70% [1]. Also this report gives details on the direct
relationship between power output and sunlight and temperature levels.
ii
Declaration of Originality
I declare that this thesis is my own original work except where stated.
Signature
………………………………………….
Date
………………………………………….
iii
Acknowledgements
I would like to express my sincere appreciation and thanks to my supervisor Professor Gerard
Hurley and Co-supervisor Mr Liam Kilmartin for all their guidance throughout this study and
in putting this thesis together.
I am grateful to the National University of Ireland, Galway for allowing me to use the
Electrical/Electronic Engineering Laboratories during the course of my work. I would also
like to express my sincere thanks to Martin Burke, Myles Meehan and Jun Zhang for their
technical help during this project.
iv
Table of Contents
Abstract i
Declaration of Originality ii
Acknowledgements iii
List of Tables vi
List of Figures vi
Glossary vii
Chapter 1: Introduction 1
1.1 Overview ..................................................................................................................... 1
1.2 Objectives .................................................................................................................... 2
1.3 Structure of thesis ........................................................................................................ 2
Chapter 2: Literature Review 4
2.1 Discussion ................................................................................................................... 4
2.2 Solar Power ................................................................................................................. 5
2.2.1 Background .......................................................................................................... 6
2.2.2 Photovoltaic Solar Cell ........................................................................................ 8
2.2.3 BP350 Solar Panel Characteristics ..................................................................... 10
2.2.4 Calculations for Outputs Characteristics of a Solar Panel ................................. 11
2.2.5 Solar Panel Costs ............................................................................................... 17
2.2.6 Investments in Solar Energy .............................................................................. 17
2.2.7 Mechanical and Electrical Tracking .................................................................. 18
2.2.8 Advantages and Disadvantages .......................................................................... 18
2.3 Maximum Power Point Tracking .............................................................................. 19
2.3.1 Perturb and Observe (P&O) method of MPPT .................................................. 19
2.3.2 Incremental Conductance method of MPPT ...................................................... 22
2.4 Modelling and Simulation of MPPT ......................................................................... 24
2.4.1 MATLAB Simulink Modelling ......................................................................... 24
Chapter 3: Proposed P&O Technique 26
3.1 Theory ....................................................................................................................... 26
v
3.1.1 Partial Shading ................................................................................................... 26
3.2 Experimental Setup ................................................................................................... 28
3.2.1 Parallel and Series Connected Solar Arrays ...................................................... 29
Chapter 4: Demonstration MPPT Circuitry 31
4.1 Hardware Circuits ..................................................................................................... 31
4.1.1 Current Sensor Circuit ....................................................................................... 31
4.1.2 Voltage Sensor Circuit ....................................................................................... 32
4.1.3 DC-DC Converter .............................................................................................. 32
4.2 Software Circuits ....................................................................................................... 36
4.2.1 Arduino Microcontroller .................................................................................... 38
4.2.2 Digital to Analogue Converter (DAC) ............................................................... 41
Chapter 5: Practical Procedures 42
5.1 PSpice Simulations .................................................................................................... 42
5.1.1 Background ........................................................................................................ 42
5.1.2 Use of Pspice...................................................................................................... 42
5.2 Building the Project ................................................................................................... 43
Chapter 6: Discussion and Results 45
Chapter 7: Conclusions and Recommendations 47
Chapter 8: Bibliography 48
Appendix A1 – Data Sheets 51
Appendix A2 – Excel Files 86
vi
List of Tables
Table 1: Solar Panel Characteristic Equations ......................................................................... 13
Table 2: Example of P&O workings ........................................................................................ 21
Table 3: Values used in designing Buck Converter ................................................................. 34
Table 4: Buck Converter Power Losses ................................................................................... 35
List of Figures
Figure 1: Solar Cell, Module, Array .......................................................................................... 5
Figure 2: Global Solar Radiation ............................................................................................... 6
Figure 3: Global Temperature Distribution ............................................................................... 7
Figure 4: Percentage losses if sun is misaligned. ....................................................................... 7
Figure 5: Photovoltaic Cell ........................................................................................................ 9
Figure 6: I vs V graph for July. ................................................................................................ 13
Figure 7: P vs V graph for July. ............................................................................................... 14
Figure 8: I vs V for different Irradiance levels ........................................................................ 15
Figure 9: P vs V for different Irradiance levels ....................................................................... 15
Figure 10: I vs V for different Temperatures. .......................................................................... 16
Figure 11: P vs V for different Temperatures. ......................................................................... 16
Figure 12: P&O Algorithm ...................................................................................................... 20
Figure 13: P&O Tracking Oscillations .................................................................................... 22
Figure 14: Flow chart of IC method ........................................................................................ 23
Figure 15: Incremental Conductance method .......................................................................... 24
Figure 16: Partially shaded Solar panel ................................................................................... 26
Figure 17: Effect of one cell in a module being shaded .......................................................... 27
Figure 18: Partial shading of a PV module .............................................................................. 27
Figure 19: Effects of partial shading ........................................................................................ 28
Figure 20: Experimental Layout .............................................................................................. 28
Figure 21: P&O technique setup .............................................................................................. 29
Figure 22: Series & Parallel connected Array ......................................................................... 30
Figure 23: Current Sensor ........................................................................................................ 31
vii
Figure 24: 100K Potentiometer ................................................................................................ 32
Figure 25: Buck Converter Circuit .......................................................................................... 35
Figure 26: Arduino Microcontroller ........................................................................................ 38
Figure 27: Pin layout of the Arduino ....................................................................................... 39
Figure 28: PSpice Simulation Circuit ...................................................................................... 42
Figure 29: PSpice Simulation Results...................................................................................... 43
Figure 30: PWM at 4 Volts ...................................................................................................... 45
Figure 31: PWM at 3 Volts ...................................................................................................... 45
Figure 32: PWM at 2 Volts ...................................................................................................... 46
Figure 33: PWM at 1 Volt ....................................................................................................... 46
Glossary
o PV = Photovoltaic
o MPP(T) = Maximum Power Point (Tracking)
o P&O = Perturb and Observe
o IC = Incremental Conductance
o PSC = Partially Shaded Conditions
o P-V = Power versus Voltage
o I-V = Current versus Voltage
o PWM = Pulse Width Modulation
o DC = Direct Current
o AC = Alternating Current
o PID = Proportional-Integral-Derivative
1
Chapter 1: Introduction
1.1 Overview
In recent times the global energy demand has increased due to global growth and technology
advances. This as well as the depletion of natural energy resources, such as fossil fuels, has
resulted in the cost of energy becoming much more expensive and the increase in energy
consumption has resulted in an increase in greenhouse gas emissions. As result of this,
countries are been forced to look at employing more effective ways to generate energy which
costs less and also reduces the country’s carbon footprint. Ireland has a number of ‘green’
energy options available to it; these include wind generation, tidal power and solar energy or
photovoltaic energy. Improvements in Photovoltaic (PV) technology in recent times has
resulted in solar energy prices becoming near levels in which it can compete effectively with
widely used fossil fuel energy sources [2]. Solar power’s extraordinary energy potential has
been recognised and for solar energy to become a major player in the energy sector in the
near future, further improvements need to be made. This study concentrated on coming up
with a system which stabilises the power output of solar energy in a PV system and making
the power output easier to predict.
The characteristics of a solar panel show that when power is plotted against voltage there is a
voltage value corresponding to the MPP and normally this point is a function of the solar
light level. The maximum power transfer theorem shows that the maximum power is
transferred when the load resistance matches the output resistance of the panel [3]. A DC-DC
converter usually in the form of a buck converter is used to match the impedance of the load
to the panel by varying the duty cycle; this is MPPT. The duty cycle is the ratio of output
voltage to input voltage. When the solar panel is partially shaded the power versus voltage
2
characteristics shows a global peak and local peaks for the shaded section, this is a major
disadvantage as it results in severe power losses. The purpose of this project is to identify the
most suitable approach to MPPT and to modify it to take account of partial shading.
1.2 Objectives
The objective of this study is to:
o Look at the viability and technical feasibility of MPPT, looking in to the background
of solar power globally and giving details on the different methods of MPPT.
o Design a DC-DC converter solution to connect the solar panel to the load. This will
have the ability to output a constant voltage when partial shading effects a solar
powered system.
o Develop a model of a partially shaded PV system, being able to demonstrate how
partial shading of the solar panel result in solar panel output losses.
o Demonstrate the modified MPPT for partial shading. Partial shading will the effect
the outputs from the solar panel but the load output will be effected minimally when
the system is implemented.
o Implementation of a new algorithm for a microcontroller to deal with the issues
suppounding MPPT. Such an algorithm will have the ability to read the current and
voltage which the solar panel is producing, perturb these values and have the ability to
vary the duty cycle in the DC-DC converter which will result in a overall constant
output power being produced.
1.3 Structure of thesis
Chapter Two contains a literature review of topics pertaining to the study. These include
details of studies on the background of solar energy which have been carried out, studies
3
which have been carried out in relation to MPPT, discussing different possible methods of
coming up with a solution to the problem, and also discussing the possibility of modelling
this project in MATLAB using Simulink. The advantages and disadvantages of the use of
solar energy, the performance and emissions from this ‘green’ energy source are also
included in this review.
Chapter Three discusses the purposed method for MPPT, giving details of how the method
will be implemented to achieve MPPT, taking account of the issue of PSC in solar
applications. The layout of the circuitry is shown here. Also discussed is the way in which
solar panels are connected to output the current and voltage which gives the MPP and hence
results in maximum output power being obtained.
Chapter Four contains details of the circuit which was used, this included the hardware and
software used in the demonstration. Each component’s role in the circuit and how they work
is discussed, as well as some difficulties that arose when the circuits were being
implemented. The role of the software is detailed step by step with the code used to
implement these steps shown. This goes into details of the taught process in which went into
writing the code for the software to implement the algorithm.
Chapter Five discusses the work which was carried out on certain parts of the circuit and the
simulations which were carried out on the PSpice computer program, to simulate components
inside parts of the circuitry.
Chapter Six discusses the results which were found from this study.
Chapter Seven draws a conclusion to the study of MPPT for Solar Power Applications with
Partial Shading and gives recommendations for going forward, looking at better possible
ways of implementing a more effective algorithm that was discovered during the course of
this study
4
Chapter 2: Literature Review
2.1 Discussion
To gain a greater level of knowledge about the subject of solar power applications and
MPPT, a major literature review took place. Reading papers, journals and websites provided
a greater insight into the purpose of the project and answered many questions which arose on
first glance of this project. The journals and papers which were chosen to review were
obtained from the IEEE Xplore [4] section of the NUI Galway library website and from my
supervisor. The literature review gave a clear theoretical framework about the subject in
which this study was based.
The challenge of ensuring Ireland has the energy it needs after the depletion of existing non-
renewable global energy is an issue that has been addressed in recent years with the
development of renewable energy sources such as solar and wind. This was an important step
in ensuring that energy provision problems do not arise for future generations. Figure 1 [5]
shows the difference between a solar cell, module and array. The figure shows that a module
is made up of a number of cells and an array is made up of a number of modules.
5
Figure 1: Solar Cell, Module, Array
2.2 Solar Power
Solar power is an alternative energy source which is widely available to this country. This
renewable energy is being explored in greater depths and in recent years its development has
grown rapidly due to the large amount of funding it has received. This energy source is
receiving large amounts of funding due to its renewable appeal, its inexhaustible capacity and
its non-polluting attractive nature [6]. Solar powers evolution in the past ten-fifteen years has
been gratefully accepted, but further work will ensure the performance of PV cells will
transform from the subpar status which they currently hold. A system to optimize the
interaction between cells and other components would also be a major development in solar
power becoming a major player in the energy sector [7].
6
2.2.1 Background
o Solar energy has become much more important globally in recent years due to the
global energy crisis the world faces.
o Solar panels use light energy from the sun to generate electricity through the
photovoltaic effect.
o Photovoltaic is a method of generating electrical power by converting solar radiation
into Direct Current (DC) electricity, using semiconductors that exhibit the PV effect.
o A connected assembly of solar cells is known as a PV panel. Solar energy is said to be
very reliable as it is easy to predict how much energy can be produced with PV solar
panels. Countries nearer the equater have a lot more potential enegry available to
them due the temperature & radiation levels being higher than countries further away
from the equater. Figure 2 [8] shows the global average solar radiation and figure 3
[9] shows the global average temperature. These show that the solar power potential is
the greatest just north and south of the equater line due to the highest solar radiation
levels and temperatures being available in these regions.
Figure 2: Global Solar Radiation
7
Figure 3: Global Temperature Distribution
o Solar panels do not emit any greenhouse gases in operation unlike conventional
sources of energy i.e. fossil fuels.
o Solar tracker applications are widely used to maximise the angle of incident between
the incoming light of the sun and the panel. This angle should always be kept as near
as possible to 90 degrees. Figure 4 [10] shows how much potential power is lost if the
angle of the solar array differs from 90 degrees.
Figure 4: Percentage losses if sun is misaligned.
8
o Driven by advances in technology and increase in manufacturing scale and
sophistication, the cost of solar energy has declined steadily since the first solar cells
were manufactured.
o Solar cell efficiencys depend on many factors such as temperature of the sun, isolation
level, spectrial characteristics of sunlight [11], dust lying on the solar panel and
shading effects.
2.2.2 Photovoltaic Solar Cell
Photovoltaic effect is a phenomenon in which solar energy is converted directly into
electrical energy through the use of a solar cell [12] [7]. A PV cell is made of silicon, which
is purified, melted and then crystalized. The majority of the cell has a slightly positive
electrical charge, with a thin layer, at the top, having a slightly negative charge. A thin grid of
metal is placed on the top of the cell which allows adequate amounts of sunlight to be
admitted but also had the ability to carry electrical energy. Sunlight, sometimes described as
particles called ‘photons’, hits the PV cell and move into the cell [13]. Photons strike
electrons and dislodge them, these then become loose and start to move to the top of the cell.
The greater the amount of photons that are admitted by the cell results in a greater flow of
electrons towards the top of the cell. These then flow into the external electrical circuit
through the grid of metal placed on top of the cell. The electric fields in the solar cell put
these free electrons in directional current, from which the metal contacts on top of the cell
can generate electricity. Figure 5 shows a photograph of a solar panel, the silver lines in the
photograph is the metal grid, whose purpose has been clearly outlined.
Therefore, cells produce current and voltage, the amount of current produced depends on the
area of the cell whereas the amount of voltage produced does not depend on the cells area.
Both the voltage and current are affected by the resistance of the circuit the cell is present in.
9
The light level and the temperature available to the cell affect the amount of current and
voltage produced respectively, which will have a direct effect on the power output.
Figure 5: Photovoltaic Cell
2.2.2.1 Grid-Connected PV System
This is a system which connects the PV panels directly to the national grid, exporting it
directly as power is being produced. The grid therefore acts as a storage system for the
producer of the power, where the electricity is sold to the grid when there is no demand for it
by the producer and then bought back from the grid when it is required. This system needs an
inverter to transfer the power from DC, which the PV system produces, into AC at which the
grid operates. When the PV system is producing power and the producer is using power in
their home/business etc., power is fed directly from the PV system. When the full demand of
power is not being produced by the PV system, electricity is used from the grid. If the system
is reversed and the PV system is producing more power than there is required, the surplus is
sold to the national grid. The payment which people receive for supplying power to the grid
is usually much less than the cost of buying power from the grid. The highest prices are paid
when the national electricity usage peaks. These systems require very little maintenance and
can result in big cost savings if the building where the PV system is located uses the power
produced directly, and there is an incentive to make money by selling power to the grid if the
10
building is a low consumer of electricity, therefore energy saving techniques may pay
dividend if implemented [14] [15].
Connecting a source of electrical energy such as a Solar PV system to operate in parallel with
ESB networks LV system involves a number of steps and conditions. The system must be
rated up to and including 25 amperes at low voltage of 230 volts when the connection is
single phase and 16 amperes at low voltage of 230/400 volts when connection is three phase.
There is no cost of connecting such a system to the grid provided it complies with conditions
stated in the European standards EN50438 [16].
2.2.2.2 Stand-Alone PV System
This is a system which is not connected to the national grid but a system which allows the
producer to use the power produced directly. The power is usually stored in batteries when
production levels exceed demand levels. This type of system is particularly useful in areas of
the world which do not have a national grid such as in the developing world for water
pumping, schools and hospitals. This system has also become very common in this country in
recent years for the running of street lighting and warning lights along the roadside. This
system usually involves the use of a much smaller panel compared to the panels used in a
grid-connected PV system due to the power demand being significantly lower [14] [15].
2.2.3 BP350 Solar Panel Characteristics
The BP350 solar panel is the solar panel that is being modelled in this project. This is a 50
Watt photovoltaic module using cells with silicon nitride (SiN) coating. The BP350 has a
nominal output voltage of 12 volts. This panel is supplied with a performance warranty of a
minimum power output of 45 watts or 90% power output over 12 years and 80% power
output over 25 years. The voltage and current at maximum power measures at 17.3 volts and
2.89 amps respectively [17] [18].
11
Each BP350 module contains 72 photovoltaic cells. A study was carried out in paper [7],
which concentrate on the output power of the panel, showed that peak power points degrade
from 21.48 W to 15.44 W when one of the 72 cells on this module is shaded. Degraded
module output is the result of shading effects, which occur because the current of the series-
connected string in the module is affected.
2.2.4 Calculations for Outputs Characteristics of a Solar Panel
The following section shows a detailed study into the output voltage vs. output current and
output voltage vs. output power for solar radiation levels in Galway for the month of July as
well as a study into the output voltage vs. output current and output voltage vs. output power
for different solar irradiance levels and different temperatures. The solar panel used in these
calculations is HIP photovoltaic module, HIP-210NH1-BO-1; the data sheet for this PV
module is included in Appendix A1. All calculations and graphs for this section were
calculated and created using Microsoft Excel. All Microsoft Excel calculations are also
shown in Appendix A2.
Solar Panel Characteristic Equations
Q Charge on an electron q = 1.6022 x 10-19
C
K Boltzmann constant K=1.38*10-23
m².kg.s-2
°K
N Ideality factor n=1.5
I Output current (to be calculated)
Iph Photo-generated current (to be calculated)
Isat Saturation current (to be calculated)
V Output Voltage (0 to open circuit voltage,
Voc)
12
Ns Number of cells in series 100
Rs Series resistance Rs= 0.004Ω
Tcell Solar Panel temperature Tcell=15°C
The output current is given by:
The photo generated current Iph is given by:
The saturation current, Isat, is given by:
Iscref**
Short circuit current at standard conditions,
25°C & 1000W/m2 (Iscref=5.57A)
S
Solar radiation (S=429.67W/m2, maximum
average solar radiation for July in Galway)
Sref Reference solar irradiance (Sref=1000W/m²)
isc**
Short circuit current temperature
coefficient (isc = 0.00167A/°C, from
solar panel data sheet)
Tref
Reference temperature at standard conditions
(Tref=25°C)
The open circuit voltage, Voc, is given as:
Vocref**
Open circuit voltage at standard operating
conditions (Vocref=50.9V)
voc** Open circuit voltage temperature coefficient
13
(voc =-0.127V/°C)
VD The range of VD is from 0 to Voc
The voltage range, VD, is given as:
V
VD = V+I.Rs
Output Voltage
The output voltage, V, is given as: V= VD - I.Rs
P Output Power
The output Power, P, is given as: P= V*I
**: Details given in solar panel data sheet.
Table 1: Solar Panel Characteristic Equations
The graphs below are Microsoft Excel graphs which document all the information calculated
in the Microsoft Excel file. All values of current, voltages and powers are displayed in amps,
volts and watts respectively.
Figure 6: I vs V graph for July.
0
0.5
1
1.5
2
2.5
0 5 10 15 20 25 30 35 40 45 50 55
C
u
r
r
e
n
t
Voltage
I vs V
I vs V
14
Figure 6 shows the current versus voltage for the solar irradiance level measured in Galway
in the month of July; this was found to be 429.67W/m2. The temperature of the cell was taken
at as 15°C to generate this graph.
Figure 7: P vs V graph for July.
Figure 7 shows the power versus voltage. This graph also takes the solar irradiance level
measured in Galway in the month of July and the maximum output power was found to be
92.4W. This value relates directly to the knee of the curve in figure 6, where the current and
voltage were found to be 2.2A and 41.99V respectively.
0
20
40
60
80
100
0 5 10 15 20 25 30 35 40 45 50 55
P
o
w
e
r
Voltage
P vs V
P vs V
15
Figure 8: I vs V for different Irradiance levels
Figure 9: P vs V for different Irradiance levels
Figure 8 and figure 9 show the Current versus Voltage and Power versus Voltage graphs
respectively for different solar irradiance levels. For these graphs the cell temperature is taken
0
1
2
3
4
5
6
0 5 10 15 20 25 30 35 40 45 50 55
C
u
r
r
e
n
t
Voltage
I vs V for different Irradiance levels
800W/m2
600W/m2
400W/m2
200W/m2
1000W/m2
0
20
40
60
80
100
120
140
160
180
200
220
0 5 10 15 20 25 30 35 40 45 50 55
P
o
w
e
r
Voltage
P vs V for Different Irradiance levels
800W/m2
600W/m2
400W/m2
200W/m2
1000W/m2
16
as 15°C. The highest irradiance level of 1000W/m2 gives out a power of 214.98W while the
lowest irradiance level of 200W/m2 gives out a power of 43.01W.
Figure 10: I vs V for different Temperatures.
Figure 11: P vs V for different Temperatures.
0
0.5
1
1.5
2
2.5
0 5 10 15 20 25 30 35 40 45 50 55
C
u
r
r
e
n
t
Voltage
I vs V for Different Temperatures
288K
298K
308K
318K
328K
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30 35 40 45 50 55
P
o
w
e
r
Voltage
P vs V for Different Temperatures
288K
298K
308K
318K
328K
17
Figure 10 and figure 11 show the Current versus Voltage and Power versus Voltage graphs
respectively for different temperatures. For these graphs the solar irradiance level is taken as
429.67W/m2 and the reference solar irradiance level taken as 1000W/m
2. The highest
temperature of 55°C gives out a power of 84.3W while the lowest temperature of 15°C gives
out a power of 92.4W.
It is clear from all of the above calculated date that a higher irradiance level is more
beneficial than higher temperatures when it comes to power output. Ideal conditions would
have a very high irradiance level and low temperature, but unfortunately such scenarios are
very hard to achieve anywhere in the world as solar irradiance levels and solar temperatures
are very much so dependent on each other.
2.2.5 Solar Panel Costs
A 1.2 kW solar PV system is available to buy online for €2350 + VAT [19]. This system
requires a lot of roof space as it is made up of five 240 Watt PV panels. The system also
comes with an inverter which makes this system suitable for grid connection. A power output
guarantee comes with this product as well as a manufactures warranty. The capital costs for
introducing a system like this are quite high which results in a long payback period for the
irradiance levels which are experienced in this country, with many payback periods being
very close to the lifespan of the product itself.
2.2.6 Investments in Solar Energy
Solar energy has been heavily researched area in recent years, with over seventy five projects
having taken place in Universities around the country between 2004 and 2010. These projects
cost the state €24 million in total. €14 million of this investment was invested in the area
Solar PV systems, with particular attention being paid to the development of new materials
and to incorporate devices which capture the steps involved in natural photosynthesis [20].
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2.2.7 Mechanical and Electrical Tracking
Mechanical tracking looks at the position of the sun in the sky relative to the location of the
solar panel, from dawn until dusk. A mechanical tracker twists and tilts the panel so it is in
the best position and at 90° to the sun, all the time. This results in the solar panel having the
maximum possible solar irradiation available to it which results in the solar panel performing
very efficiently and outputting the maximum possible power all of the time. Dual axis
trackers are widely available to purchase and are well worth looking at if a solar PV system is
being installed.
Electrical tracking in solar PV systems aims to keep the output of a solar panel constant all of
the time. The solar panel may not be receiving full solar irradiance due to clouds in the sky or
branches of trees blocking the suns path towards the panel, but the system still outputs the
same current & voltage and therefore the power output remains the same as if the solar panel
was receiving full solar irradiance.
2.2.8 Advantages and Disadvantages
Advantages:
o This is a renewable energy source.
o Solar level are high enough in 75-80% of the world to implement this system.
o Low maintenance costs [1].
o Pollution-free energy conversion process [1].
Disadvantages:
o In a 24 hour day, sunlight is only available for a limited time and depends heavily on
weather conditions [7].
o Solar panels are prone to nonideal conditions including partial shading, dust
collection, and photovoltaic ageing [7].
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o High initally capital costs and there payback period is long [1].
2.3 Maximum Power Point Tracking
This is a method used in Solar PV arrays to expose uniform solar irradiance and maintain a
maximum power output for a period of time. In figure 7 the maximum power output can
clearly be seen at the ‘knee’ of the curve. This is the position that is most sought after and is
achieved when maximum voltage and maximum current are achieved at the same time.
MPPT is a method to ensure that maximum voltage and maximum current is reached as much
as possible and overall to make maximum utilization of PV modules and minimise the power
failure due to environmental conditions [13]. This is done by having the solar array track the
path of the sun and also by making sure that none of the solar array becomes partially shaded
at any stage due to cloud, branches of trees etc., and if this does occur a system is in place to
adjust the panel and get it back to output the maximum current and voltage and hence the
maximum output power. Details of the two methods used to track the MPP are given below;
the method that is being used in this project is the Perturb and Observe (P&O) method.
If irradiance levels differ throughout the solar array, this results in multiple local maxima
points being produced. This results in nonlinearity of the PV characteristic curves, which
means there is more than one ‘knee’ in the P-V curve. Multiple local maxima are not good for
tracking as it reduces the effectiveness of the tracking system, and these results in overall loss
in power output.
2.3.1 Perturb and Observe (P&O) method of MPPT
This is an algorithm which is used as a method of MPPT. The P&O tracking process is
carried out by observing the array output power and determining the next action, either to
increase or decrease the array operating voltage. In recent times this method has been widely
used to achieve the maximum amount of power from a solar panel. The presence of multiple
20
local maximum power points, these occur when an entire PV array do not receive uniform
solar irradiance, due to partial shading, reduce the effectiveness of this method greatly [21]. If
the operating voltage of a PV array is perturbed in a given direction and if the power drawn
from the PV array increases, this means that the operating point has moved towards the MPP
and therefore, the operating voltage must be further perturbed in the same direction.
Otherwise, if the power drawn from the PV array decreases, the operating point has moved
away from the MPP and therefore, the direction of the operating voltage perturbation must be
reversed. This is explained in the form of a flowchart below in figure 12, and in table 2,
showing the workings of the method.
Figure 12: P&O Algorithm
21
Perturbation Change in Power Next Perturbation
Positive Positive Positive
Positive Negative Negative
Negative Positive Negative
Negative Negative Positive
Table 2: Example of P&O workings
If the system increases the operating voltage and the power output increases, the system will
continue to do this until the power output decreases. Then the voltage is decreased to get back
to the system outputting its maximum power output. This continues indefinitely which results
in the power output value oscillating up to the MPP continually and never stabilizing.
Usually the P&O algorithm uses fixed iteration step sizes, but this has been a limitation of the
system as it is impossible to provide performance requirements of fast dynamic response and
good accuracy during the steady state at the same time. The reasons for this are, if the step
size is too big, the oscillations around the MPP will increase during steady state and this will
result in lost power generation, if the step size is too small the highest generation cannot be
restored quickly enough during changing operation conditions [22]. Figurer 13 shows the
oscillation about the MPP when the P&O method is in operation. Variable step sizes are now
being implemented to overcome this problem.
The advantages of this method include [23] [24]:
o Very simple and easy to implement and does find true MPP.
o It can be taken as either an Analog or Digital technique of MPPT.
o Most commonly used so information is widely available.
22
o Provides predictive and accurate solutions to MPPT under PSC.
o No oscillation during tracking and steady state operations
The disadvantages of this method include:
o Under rapidly varying irradiance & load conditions the system can track in the wrong
direction.
o The size of the change in operation voltage chosen determines the speed &
convergence of the MPP and the range of oscillation.
Figure 13: P&O Tracking Oscillations
2.3.2 Incremental Conductance method of MPPT
This method always adjusts the array terminal voltage according to the MPP voltage. This
method computes maximum power and directly controls the extracted power from the PV
cell. This method uses a DC-DC converter which is controlled by an Incremental
Conductance (IC) algorithm. This system offers great performance under quick changing
circumstances and can be implemented using low cost microcontrollers. The method can
track the maximum power points accurately at high speeds and greatly increase the power
output of a solar array under Partially Shaded Conditions. Figure 43 [25] shows the IC MPPT
23
algorithm in the form of a flow chart. It can be seen from this that the algorithm is much more
complex than the P&O algorithm. If this MPPT method was used in this study, a complex
microcontroller would be required to implement the algorithm.
Figure 14: Flow chart of IC method
This method computes the maximum power point by comparing (ΔI/ΔV) (Incremental
conductance) to (I/V) (array conductance) [13]. Figure 15 [25] shows the basic idea of the IC
method on the P-V curve, the MPP occurs when the slope of the curve is zero, with the slope
becoming greater than zero to the left and less than zero to the right hand side of where the
slope is equal to zero. Therefore the aim of the algorithm is to keep the slope of the curve at
zero all of the time. Simulation results are given in [25] for this algorithm, where the tracking
efficiency is calculated to be 96.8%. This method of MPPT is a digital method of medium
complexity [23].
24
Figure 15: Incremental Conductance method
2.4 Modelling and Simulation of MPPT
Modelling the performance and output of a solar system is a very important procedure which
allows the user to become familiar the system as well as interactions with utility grids.
Models may be used to investigate the effects with the conditions which give out the best
results and conditions which are best suited to of partial shading and module mismatching of
a solar panel. Particular focuses are paid to the modelling and simulation of models in [26],
with modelling approaches based on PSIM simulation circuit and MATLAB - SIMULINK
based simulations being discussed. This paper shows the importance of detailed
parameterization when trying to create a PV model or simulation. A generalized approach is
needed to create a simulation which may be used for long-term operations of different PV
systems.
2.4.1 MATLAB Simulink Modelling
The creation of a MPPT system may be modelled using the MATLAB based simulator,
Simulink. This is implemented using the SimPower systems toolbox of the
MATLAB/Simulink model. A Simulink model of a PV system under different temperatures
and irradiation is created in [6] by adjusting the duty cycle of the DC-DC converter. The
purposed system in this paper discusses the implementation of an algorithm to find and
25
maintain peak power. The modified version of the IC method is used to do this, the system
contains an internal regulator to minimise the error where the regulator output is equal to the
duty cycle correction. The digital controller in the system can directly control the duty cycle
of the converter current which makes it possible to find the MPP. This paper presents results
which prove that the modified IC method of MPPT reaches the intended MPP. This is a
representation that MATLAB/Simulink simulations can be accurately used to simulate the
outcome of MPPT in a PV system.
26
Chapter 3: Proposed P&O Technique
3.1 Theory
This project involves, the ability to find the MPP through the use of the P&O method of
MPPT and then varying the duty cycle of the buck converter which causes the output voltage
to remain constant as Vo=Vin*D. These tasks are carried out using software within the
complete experimental setup and implemented using a microcontroller. Figure 12 shows a
very simple flowchart representation of the P&O algorithm used in the software.
3.1.1 Partial Shading
Partial shading occurs when the entire array does not receive uniform isolation. An example
of this is shown in figure 17 [27].
Figure 16: Partially shaded Solar panel
This causes the power output of the array to become distorted due to the voltage and current
output being reduced, with the array sometimes displaying multiple peaks. Only one of a
number of peaks is a global peak with the others being local peaks, these are all clearly
described in [7]. Figure 18 [7] shows the current vs voltage curve for a module with one cell
shaded compared to the module with no shading.
27
Figure 17: Effect of one cell in a module being shaded
Figure 19 [28] shows a solar array partially shaded. Figure 20 [28] shows the effect of the
partially shaded conditions of the array on the current vs voltage graph and the power vs
voltage graph. Local maximum points can be seen clearly in the power vs voltage graph
which occurs due the sudden drops in currents on the current vs voltage graph. Local
maximum power points are a direct result of partial shading and are not a true representation
of the MPP. The global power point is the correct maximum power point which should be
tracked and maintained.
Figure 18: Partial shading of a PV module
28
Figure 19: Effects of partial shading
3.2 Experimental Setup
Figure 21 shows the experimental setup of the project with all parts is described in more
detail later in this report. The testing of different components in this setup was carried out
with the use of a power supply, a signal generator, a multimeter and an oscilloscope in the
Labourites of the college.
Figure 20: Experimental Layout
The experimental setup was based on a system which was found to be very well
implemented, figure 22 [24] shows a P&O experimental setup from a journal. The figure
shows that the main part of the setup is software based, while the hardware part of the setup
29
differs from the purposed setup as a boost converter is used rather than a buck converter. The
software here includes a discrete PI controller, low pass filter, P&O Algorithm and another PI
controller
Figure 21: P&O technique setup
3.2.1 Parallel and Series Connected Solar Arrays
Connecting solar cells in series means you connect the positive terminal of one solar cell to
the negative terminal of another. This results in the voltages of the cells being added together
while the amps stay the same. Connecting solar cells in parallel means you connect the
positive terminal of one cell to the positive terminal of another and the negative terminal of
one cell to the negative terminal of another. These results in the voltage remaining the same
but the currents of the cells will be added together. When an array of solar cells is connected
30
in series and parallel, significant problems exist with parallel connections. Shadow effects
can shut down the weaker parallel string (string that experience partial shading) which would
cause a big power loss and some damage to the weaker string. This damage is caused by
excess reverse bias applied to the shadowed cell by the cells which are receiving full solar
irradiance.
In an array like the one shown below in figure 23, each solar cell has a specific maximum
voltage and maximum current. In the array shown each solar cell has a current of 3 amps and
a voltage of 6 volts, therefore this gives us a system with a voltage of 24 volts and a current
of 6 amps. If one of these paths becomes blocked due to partial shading or some other factor,
this will have a major effect.
Figure 22: Series & Parallel connected Array
31
Chapter 4: Demonstration MPPT Circuitry
4.1 Hardware Circuits
In this section all aspects of the hardware will be discussed, which will explain the role in
which they play overall in the PV system. Data sheets for all hardware components used are
in Appendix A1. These give operational data as well as limitations of the products and best
conditions at which the product operates. The data sheets were very important reference to
ensure circuits were being setup correctly.
4.1.1 Current Sensor Circuit
The current sensor chip used is the ACS712 produced by Allergo Micro Systems. This will
measure the current provided by the solar panel. This current will also be put into the MPPT
digital controller. This sensor can handle a current between -5A and +5A and it outputs the
current as a voltage of between 0 and 5 volts corresponding to the measured current. This
voltage, from pin 4, is then fed into an analogue pin of the Arduino. The connection diagram
for the current sensor is shown in figure 24. In practice pins 1 and 2 are joined internally as
are pins 3 and 4 so only one of each needs to be connected. The 5V supply is supplied from
the 5V power source on the Arduino.
Figure 23: Current Sensor
32
4.1.2 Voltage Sensor Circuit
The voltage sensor is a simple voltage divider that steps down the voltage of the power
amplifier to something between 0V and 5V so that it can be fed into one of the analogue
inputs of the Arduino. This will measure the voltage provided by the solar panel. A 100k
potentiometer is used to achieve this. To calibrate it, 30V was fed into it and a multimeter
took a voltage reading from the wiper. The potentiometer was then adjusted until the
multimeter read 4V. Figure 25 shows a clear image of the potentiometer. Pin 1 is connected
to ground, pin 2 in the new output voltage which is connected to pin 3 of the Arduino, while
pin 3 is the original input voltage. The gold twistable component on top of the device is used
to adjust the output voltage of pin 2.
Figure 24: 100K Potentiometer
4.1.3 DC-DC Converter
This is a power electronics circuit that convert a DC voltage to a different DC voltage level
and often provides a regulated output. Switch mode DC-DC converters operate by storing the
input energy temporarily and then releasing that energy to the output at a different voltage
and current. A DC-DC converter could be compared to a transformer as they both carry out
much the same role changing input energy into a different impedance level, with some energy
being used by the converter when it is being passed through it. DC-DC converters are
33
commonly found in many electronic devices such as mobile phones and laptops. The
converter presents an electrical load to the solar panel that varies as the output voltage of the
panel varies. This load variation in turn causes a change in the operation point (current and
voltage characteristics) of the panel. Thus by intelligently controlling the operation of the
DC-DC converter, the maximum possible output power may be achieved.
A Boost converter are used to step up the input voltage resulting in a higher output voltage
and a Buck converter are used to step down the input voltage resulting in a lower output
voltage, while a Buck-Boost converter is used when the output voltage is required to be either
higher or lower than the input voltage.
4.1.3.1 Buck converter
The buck converter is used in this circuit which steps down the input voltage giving a steady
output voltage but one which is always less than the input voltage. The inductor, capacitor,
load resistance & MOSFET values must be worked out for this circuit to be built.
Determining a value for the output voltage is a key step in finding the value of components
required. An online source [29] was used in determining these values of components used.
Buck Converter Design
Duty Cycle Minimum, Dmin: 0.2
Duty Cycle Maximum, Dmax: 0.8
Frequency, ʄ (Hz): 10,000
Inductance, L (H): To be calculated
Capacitance, C (F): To be calculated
Inductor Current, Imax (A): To be calculated
Diode used: Schottky diode
MOSFET used: IRF820, 500V & 2.5A
34
MOSFET driver chip: IRS2003
Vin (V): 24
Iin (A): 2
VoMin (V): Vin (V)* Dmin= 4.8 Volts
VoMax (V): Vin (V)* Dmax= 19.2 Volts
Vo (V): 15
Resistance, R (Ω): R=
: 7.5 Ω
Inductance: L= ( )
: 500µH
Capacitance: C=
( ) 10µF
Inductor Current, max: Imax= Vo(
+
) 3.2 Amps
Inductor Current, min: Imax= Vo(
-
) 1.92 Amps
Table 3: Values used in designing Buck Converter
Table 3 shows the calculations which were carried out to find the correct value of
components needed.
The inductor which was used is a EPCOS product with model number B82721-K with an
inductance of 400µH. The diode used in the circuit is a schottky diode; this is a low forward
voltage drop and a fast switching action. The capacitor which was used has a value of10µ
(10-6
) Farad, as calculated above. A MOSFET is used in this circuit which acts as a switch.
The MOSFET used is a 2.5A, 500V n-channel MOSFET with model number IRF 820. This
requires a gate driver circuit, which incorporates a way to drive the gate voltage about the
source. The driver chip used to do this is a half bridge driver, IRS2003, which outputs 10-20
volts which is perfect to drive the MOSFET.
35
Figure 25: Buck Converter Circuit
Figure 26 shows the buck converter which was used, two 15Ω power resistors are used in
parallel which gives the required 7.5Ω resistance.
Buck Converter Losses
Component Losses
MOSFET 0.0195
MOSFET Driver 0.625
Diode 0.96
Inductor 0.2048
Capacitor 0.4608
Total Losses (Watts) 2.2701
Output Power of Buck Converter (Watts) 30
Efficiency (%) ((30-2.2701) / 30)*100 = 92.43%
Table 4: Buck Converter Power Losses
Table 4 shows the losses which occur when power is passed through the Buck Converter, and
its efficiency is found to be 92.43%.
36
4.2 Software Circuits
The software in this study takes up a major part of the circuit. Much research went into
finding the proper effective way of carrying out the task at hand [24]. The software in this
project carries out the following:
o Reads in the array current and array voltage from the solar panel.
o The array current and array voltage is then filtered to reduce noise and to get a more
accurate sample, the array output power is then calculated using the filtered signals.
o The change in the array output power within the sample span is calculated for
smoothing purposes. This value will be large at the start and then reduce.
o The variation in power is treated using a proportional-integral-derivative controller
(PID controller), and ulitized to generate the perturb value for the array reference
voltage.
o Calculate the error between the reference and actual array voltage.
37
o Vary the duty cycle in the buck converter to output the same power continually which
deals with partially shaded conditions, and read out a Pulse Width Modulation
(PWM) waveform.
o Implements the P&O algorithm.
o Initialise all arrays to zero.
38
4.2.1 Arduino Microcontroller
The microcontroller to be used to implement the required algorithm is the Arduino. The
decision to use this microcontroller was made after carrying out research on it and also on the
8051 microcontroller. The Arduino is relatively simple and is perfectly able to implement the
type of algorithm that is used. On researching the 8051 microcontroller it was found that it is
a lot more complicated than the Arduino and may prove hard to implement the algorithm, if it
was chosen. An image of the Arduino Uno microcontroller is shown in figure 27.
Figure 26: Arduino Microcontroller
The main reasons for choosing the Arduino is:
o Inexpensive, most Arduino starter kits cost between €50-70.
o The Arduino will work on Windows, Mac and Linux.
o Simple clear and open source programming environment. Software for the
programming of the Arduino can be obtained online for free and the programming
environment is relatively simple with the languge being a mix of C and C++.
Some characteristics of the Arduino:
o 6 analogue inputs.
39
o Operating voltage of 5 volts.
o DC current i/o pin 40mA.
o Flash memory of 32kb (0.5kb used by the boot loader).
o Input voltage maximum of 6-20 volts, recommended to use 7-12 volts.
o 14 digital outputs, 3 of which are pulse width modulators (providing 8 bit pulse width
modulation).
o Board can be powered by the USB port from a computer, 2.1mm centre positive plug
in the board, or the 5 volt and the 3.3 volt connection on the board.
o Clock speed of 16MHz.
Figure 27: Pin layout of the Arduino
Figure 28 shows the pin layout of the Arduino. Logic expressions such as &&, ||, ! which are
AND OR and NOT logical operators respectively, were used in when writing the code to
program the microcontroller. Operators such as these saved time and cut down on the amount
of code written. These operators were learned in the Fundamentals of Electrical & Electronic
Engineering in first year of college.
40
4.2.1.1 Limitations of the Arduino Microcontroller
Algorithms like the one employed in this project can sometimes be difficult to implement
using the Arduino due to inner workings not being exposed. The Arduino’s relatively
inaccurate timer’s means that systems have to be ran for a greater number of samples to get
accurate results. Interrupt commands in the Arduino are hard to implement successfully and
the open identification of variables between loops can sometimes cause confusion when the
microcontroller is being programmed. For the program that was used in this study, initially
arrays of 100 samples were taken to get accurate readings, on testing the software it was
found that the code would only run correctly up to a certain point. After much research and
reading of the Arduino website [30] it was found that the SRAM (Static RAM) part of the
memory, which is used to store these arrays, has a limit of 2k. The arrays in the code were
101 elements with each element being a float of 4 bytes long, therefore each array is 404
bytes. The SRAM has a limit of 2k which is equal to 2048 bytes. Therefore after the fifth
array, an error would occur due to the capacity of the memory being used up. The code is
made up of 9 arrays as well as other variables, so it was decided to decrease the number of
samples taken to 10 samples. This provides a less accurate solution but solves the problem
with the memory’s capacity. Another possible solution to the problem was found on the
website, this was using the flash program memory, where the Arduino sketch is stored instead
of SRAM, where the Arduino sketch creates and manipulates variables when it runs. This is
done using the PROGRAM keyword as the variable modifier, for this the library in which the
PROGRAM is part of must first be included by including at the top of the sketch:
#include <avr/pgmspace.h>
And then putting whatever data required to go into the flash memory into it, using the
following form:
41
dataType variableName[] PROGMEM = dataInt0, dataInt1,
dataInt3...;
Where dataType is the memory variable type and variableName is the name of the array the
is required to be put in the alternative memory.
4.2.2 Digital to Analogue Converter (DAC)
This is used to convert digital code to an analogue signal, binary code to current, voltage or
electric charge. There is a DAC built into the Arduino Uno which is being used. This is used
to convert the voltages read into the analogue pins to a decimal between 0 and 1023.
42
Chapter 5: Practical Procedures
5.1 PSpice Simulations
5.1.1 Background
PSpice is a computer circuit simulator used to simulate various levels of devices and
components. Probe is a graphical postprocessor program which accompanies PSpice and the
waveform of ay current or voltage in a circuit can be shown graphically using this. This
allows the circuit’s behaviour to be viewed prior to the circuit being physically built. Probe is
also capable of mathematical computations involving current and/or voltage [31].
5.1.2 Use of Pspice
PSpice simulations were used to simulate the DC-DC converter that is used in this study. This
simulation has the ability to predict the dynamic behaviour of a DC-DC converter for changes
in the source voltage or load current. Figure 29 shows the setup of the Buck converter using
PSpice. All components in the circuit are shown with their values displayed beside them.
Figure 28: PSpice Simulation Circuit
43
Figure 30 shows the results of the Buck converter when the simulation is ran. The output
voltage of the DC-DC converter is shown in red, and the inductor current is shown in green.
The simulation runs for 2 milliseconds, the output voltage oscillates about 14 volts, 14 volts
is achieved due to the input voltage being 24 volts and the duty cycle, D, is set to 0.5833333
as Vo=Vin*D. The inductor current is oscillating about 1.8 Amps continuously with Imax being
2.7A and Imin being 1A.
Figure 29: PSpice Simulation Results
5.2 Building the Project
This project consisted of a considerable amount of software, with the complete algorithm
implemented using the Arduino. The Arduino code takes the current and voltage readings of
the solar panel from the current sensor and potentiometer respectively, it uses these to then
calculate the power output of the solar panel. The voltage value is then perturbed positively
by an offset value and if this results in an increase in power it is continued, otherwise the
value is perturbed negatively, and this system is shown in figure 12. The hardware is made up
44
mainly by the buck converter which required a driver chip to drive the MOSFET, with the
help of the components data sheets and making reference to [31], this worked perfectly.
45
Chapter 6: Discussion and Results
The PWM waveforms got from the Arduino for different voltages show the difference in
switching times as the voltage varies, with the width of the pulse when it is on being much
wider at higher voltages rather than at lower voltages. A number of voltages were chosen to
show this with the reference voltage being 5 volts.
Figure 30: PWM at 4 Volts
Figure 31: PWM at 3 Volts
46
Figure 32: PWM at 2 Volts
Figure 33: PWM at 1 Volt
It can be seen from the above results that the duty cycle is greatly reduced as the input
voltage is decreased.
Overall it was found that the implementation of the algorithm used was very difficult to carry
out successfully due to the complexity of detail required to find the duty cycle offset value
and the current and voltage perturb value.
47
Chapter 7: Conclusions and Recommendations
This report has outlined the viability of solar power today and the importance of tweaking
solar power systems to improve their efficiency and cut down on costs. The technique which
is carried out in this paper is effective for MPPT of a partially shaded solar array. More
complex solutions are also widely available and have been discussed previously in this report.
The P&O algorithm that was implemented has the ability to track the MPP. Some difficulties
were discovered when implementing the algorithm as the duty cycle offset was very hard to
get correct, further work on this would result in the full implementation of the system. A
recommendation for further work in this area would be to implement the algorithm using a
different Microcontroller, as the relatively simple nature of the Arduino Uno were clear to
see, providing some technical issues which had to be worked around in this study.
The buck converter was a major part of this project, PSpice simulation were carried out on
this which showed its ability to step the varying input voltage down to a constant output
voltage over a period of time. The code which was written to control the Adruino
microcontroller was very time consuming and contains great details which are necessary for
it to work successfully. A copy of the entire code is attached on a CD.
Great research went into the background to solar power and the methods of dealing with the
problem which was faced. Papers, websites and books which have been made reference to
were studied in depth and findings from these have been clearly outlined. A greater
appreciation and understand of the very powerful, renewable solar energy source has been
achieved due to this study. The solar panel characteristics which were calculated and graphed
show the importance of radiation and temperature levels and their direct effect on the power
output of a solar panel.
48
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51
Appendix A1 – Data Sheets
Solar panel used in solar panel characteristic calculations:
52
53
Solar Panel used in experiment:
54
55
MOSFET used:
56
57
58
59
60
61
Driver Chip used:
62
63
64
65
66
Inductor used:
67
68
69
Schottky Diode used:
70
71
100k Potentiometer:
72
73
Current Sensor:
74
75
76
77
78
79
80
81
82
83
84
85
86
Appendix A2 – Excel Files
q= 1.60E-19 Iph= 2.3532944 4.3815848 3.2861886 2.1907924 1.0953962 5.476981
K= 1.38E-23 Voc= 52.17
n= 1.5 Isat= 1.92E-06 3.56819E-06 2.67614E-06 1.7841E-06 8.92048E-07 4.46024E-06
I= Iph-Isat*(e(q(V+I*Rs)/n*K*Tcell*Ns)-1)
V= 0
Ns= 100
Rs= 0.004
Tcell(K)= 288 298 308 318 328
Iscref= 5.57
Tref(K)= 298 .
Vocrer 50.9
S(W/m2)= 429.67
Sref(W/m2)= 1000 800 600 400 200
αish= 0.00167
αVoc= -0.127
87
V= Vd-I*Rs V V V V P P P P I I I I V I P
Vd I (Amps) V (Volts) P (Watts) 800W/m2 600W/m2 400W/m2 200W/m2 800W/m2 600W/m2 400W/m2 200W/m2 800W/m2 600W/m2 400W/m2 200W/m2 1000W/m2 1000W/m2 1000W/m2
0 2.353294426 -0.00941318 -0.02215198 -0.01752634 -0.01314475 -0.00876317 -0.00438158 -0.07679314 -0.0432 -0.0192 -0.0048 4.381585 3.286189 2.190792 1.095396 -0.021908 5.476981 -0.1199893
2 2.353293062 1.990586822 4.684434159 1.982473661 1.986855246 1.99123683 1.995618418 8.686371424 6.529177 4.362384 2.185992 4.381582 3.286187 2.190791 1.095396 1.9780921 5.47697783 10.833967
4 2.353290727 3.990586822 9.391010966 3.982473661 3.986855246 3.99123683 3.995618422 17.44951863 13.10154 8.743958 4.376778 4.381578 3.286183 2.190789 1.095394 3.9780921 5.47697239 21.787901
6 2.353286731 5.990586822 14.09756848 5.982473661 5.986855246 5.99123683 5.99561843 26.21262994 19.67387 13.12551 6.567556 4.38157 3.286178 2.190785 1.095393 5.9780921 5.47696309 32.74179
8 2.35327989 7.990586822 18.80408728 7.982473661 7.986855246 7.99123683 7.995618442 34.97566921 26.24615 17.50703 8.758316 4.381558 3.286168 2.190779 1.095389 7.9780922 5.47694717 43.69559
10 2.35326818 9.990586822 23.51053007 9.982473661 9.986855246 9.99123683 9.995618464 43.73856704 32.81832 21.88848 10.94904 4.381536 3.286152 2.190768 1.095384 9.9780923 5.47691992 54.649213
12 2.353248136 11.99058682 28.21682608 11.98247366 11.98685525 11.99123683 11.9956185 52.50119171 39.39029 26.26979 13.1397 4.381499 3.286124 2.190749 1.095375 11.978093 5.47687326 65.602495
14 2.353213825 13.99058682 32.92284233 13.98247366 13.98685525 13.99123683 13.99561857 61.2632957 45.96187 30.65085 15.33022 4.381435 3.286076 2.190717 1.095359 13.978093 5.47679341 76.555127
16 2.353155094 15.99058682 37.62833084 15.98247366 15.98685525 15.99123683 15.99561867 70.02441747 52.53271 35.03141 17.5205 4.381325 3.285994 2.190663 1.095331 15.978093 5.47665672 87.506533
18 2.353054563 17.99058682 42.33283242 17.98247366 17.98685525 17.99123683 17.99561886 78.7837023 59.10217 39.41105 19.71032 4.381138 3.285854 2.190569 1.095285 17.978094 5.47642275 98.455645
20 2.352882481 19.99058682 47.03550152 19.98247366 19.98685525 19.99123683 19.99561918 87.53957633 65.66908 43.78898 21.89929 4.380818 3.285613 2.190409 1.095204 19.978096 5.47602225 109.4005
22 2.352587921 21.99058682 51.73478894 21.98247366 21.98685525 21.99123683 21.99561973 96.2891559 72.23126 48.16377 24.08668 4.380269 3.285202 2.190135 1.095067 21.978099 5.4753367 120.33749
24 2.352083714 23.99058682 56.42786856 23.98247366 23.98685525 23.99123683 23.99562067 105.0271803 78.78478 52.53278 26.27119 4.379331 3.284498 2.189665 1.094833 23.978103 5.47416323 131.26005
26 2.351220646 25.99058682 61.10960433 25.98247366 25.98685525 25.99123683 25.99562228 113.7440892 85.32245 56.89123 28.45041 4.377724 3.283293 2.188862 1.094431 25.978111 5.47215455 142.15624
28 2.349743302 27.99058682 65.77069391 27.98247366 27.98685525 27.99123683 27.99562503 122.4225663 91.8313 61.23045 30.62003 4.374973 3.28123 2.187486 1.093743 27.978125 5.46871623 153.00443
30 2.347214483 29.99058682 70.39433976 29.98247366 29.98685525 29.99123683 29.99562974 131.031343 98.28787 65.53482 32.77221 4.370265 3.277698 2.185132 1.092566 29.978149 5.46283074 163.76555
32 2.342885819 31.99058682 74.95029222 31.98247366 31.98685525 31.99123683 31.99563779 139.514109 104.6499 69.77617 34.89288 4.362205 3.271654 2.181103 1.090551 31.978189 5.45275635 174.36927
34 2.335476299 33.99058682 79.38420992 33.98247366 33.98685525 33.99123683 33.99565159 147.7697057 110.8416 73.90391 36.95675 4.348409 3.261307 2.174205 1.087102 33.978258 5.43551167 184.68922
36 2.322793174 35.99058682 83.59868939 35.98247366 35.98685525 35.99123683 35.99567521 155.6168114 116.7268 77.82736 38.91848 4.324795 3.243596 2.162397 1.081199 35.978376 5.40599338 194.49886
38 2.301083041 37.99058682 87.41949505 37.98247366 37.98685525 37.99123683 37.99571563 162.7310745 122.0624 81.38431 40.69695 4.284373 3.21328 2.142186 1.071093 37.978578 5.35546592 203.39298
40 2.263921075 39.99058682 90.53553231 39.98247366 39.98685525 39.99123683 39.99578482 168.533367 126.4139 84.28515 42.14737 4.215181 3.161386 2.107591 1.053795 39.978924 5.26897637 210.64801
42 2.200309686 41.99058682 92.39229492 41.98247366 41.98685525 41.99123683 41.99590326 171.9914231 129.007 86.01366 43.01161 4.096743 3.072558 2.048372 1.024186 41.979516 5.12092929 214.97413
44 2.091423929 43.99058682 92.00296593 43.98247366 43.98685525 43.99123683 43.99610599 171.2681786 128.4639 85.65115 42.83032 3.89401 2.920507 1.947005 0.973502 43.98053 4.86751211 214.07576
46 1.90504051 45.99058682 87.61393098 45.98247366 45.98685525 45.99123683 45.99645302 163.0990762 122.336 81.56508 40.78717 3.546984 2.660238 1.773492 0.886746 45.982265 4.4337294 203.87292
48 1.586001733 47.99058682 76.11315388 47.98247366 47.98685525 47.99123683 47.99704703 141.6906675 106.2777 70.85827 35.43343 2.952967 2.214725 1.476484 0.738242 47.985235 3.69120891 177.12353
50 1.039892311 49.99058682 51.98482686 49.98247366 49.98685525 49.99123683 49.99806383 96.77452938 72.58726 48.39575 24.20118 1.936169 1.452127 0.968085 0.484042 49.990319 2.42021158 120.98715
52.17 0 52.16058682 0 52.15247366 52.15685525 52.16123683 52.17 0 0 0 0 0 0 0 0 52.17 0 0
88
Voc Voc Voc Voc Voc T=15°C T=25°C T=35°C T=45°C T=55°C
Iph= 2.353294426 2.3932619 2.433229374 2.4731968 2.513164321 52.17 50.9 49.63 48.36 47.09 288 298 308 318 328
Isat= 1.91643E-06 4.33911E-06 9.3243E-06 1.911E-05 3.75186E-05 Vd Vd Vd Vd Vd V (Volts) V (Volts) V (Volts) V (Volts) V (Volts) P P P P P
I= 2.353294426 2.3932619 2.433229374 2.4731968 2.513164321 0 0 0 0 0 -0.00941 -0.00957 -0.00973 -0.00989 -0.01005 -0.02215 -0.022911 -0.0236824 -0.0244668 -0.02526
2.353293062 2.393258944 2.433223285 2.4731849 2.513141693 2 2 2 2 2 1.990587 1.990427 1.990267 1.990107 1.989947 4.684434 4.7636071 4.84276427 4.9219032 5.00102
2.353290727 2.393253976 2.43321322 2.4731654 2.513105416 4 4 4 4 4 3.990587 3.990427 3.990267 3.990107 3.989948 9.391011 9.5501052 9.70917077 9.8681953 10.02716
2.353286731 2.393245623 2.433196582 2.4731336 2.51304726 6 6 6 6 6 5.990587 5.990427 5.990267 5.990107 5.989948 14.09757 14.336563 14.5754977 14.814336 15.05302
2.35327989 2.39323158 2.433169079 2.473082 2.512954029 8 8 8 8 8 7.990587 7.990427 7.990267 7.990108 7.989948 18.80409 19.122942 19.4416714 19.760192 20.07837
2.35326818 2.393207973 2.433123616 2.472998 2.512804567 10 10 10 10 10 9.990587 9.990427 9.990268 9.990108 9.989949 23.51053 23.90917 24.3075558 24.705517 25.10279
2.353248136 2.393168286 2.433048466 2.4728613 2.51256496 12 12 12 12 12 11.99059 11.99043 11.99027 11.99011 11.98995 28.21683 28.69511 29.1729027 29.649876 30.12553
2.353213825 2.393101567 2.43292424 2.472639 2.51218084 14 14 14 14 14 13.99059 13.99043 13.99027 13.99011 13.98995 32.92284 33.480514 34.0372629 34.59249 35.14529
2.353155094 2.392989403 2.432718893 2.4722771 2.511565046 16 16 16 16 16 15.99059 15.99043 15.99027 15.99011 15.98995 37.62833 38.264925 38.8998298 39.531986 40.15981
2.353054563 2.39280084 2.432379451 2.4716884 2.510577848 18 18 18 18 18 17.99059 17.99043 17.99027 17.99011 17.98996 42.33283 43.047513 43.7591642 44.465954 45.16519
2.352882481 2.39248384 2.431818346 2.4707305 2.508995244 20 20 20 20 20 19.99059 19.99043 19.99027 19.99012 19.98996 47.03551 47.826781 48.612712 49.390191 50.15472
2.352587921 2.39195092 2.430890828 2.4691718 2.506458125 22 22 22 22 22 21.99059 21.99043 21.99028 21.99012 21.98997 51.7348 52.600035 53.4559613 54.297393 55.11695
2.352083714 2.39105501 2.429357622 2.4666357 2.502390798 24 24 24 24 24 23.99059 23.99044 23.99028 23.99013 23.98999 56.42788 57.362452 58.2809758 59.17492 60.03233
2.351220646 2.389548863 2.426823204 2.4625093 2.495870349 26 26 26 26 26 25.9906 25.99044 25.99029 25.99015 25.99002 61.10962 62.105431 63.0738454 64.000986 64.86771
2.349743302 2.387016825 2.422633761 2.4557951 2.485417231 28 28 28 28 28 27.9906 27.99045 27.99031 27.99018 27.99006 65.77073 66.81368 67.8102687 68.73814 69.56697
2.347214483 2.382760126 2.415708529 2.4448706 2.468659538 30 30 30 30 30 29.99061 29.99047 29.99034 29.99022 29.99013 70.3944 71.460094 72.4479133 73.322208 74.03541
2.342885819 2.375604037 2.404260984 2.4270952 2.441794801 32 32 32 32 32 31.99063 31.9905 31.99038 31.99029 31.99023 74.95039 75.996755 76.9132296 77.643484 78.11358
2.335476299 2.363573681 2.385337969 2.398173 2.398727171 34 34 34 34 34 33.99066 33.99055 33.99046 33.99041 33.99041 79.38438 80.339159 81.0787316 81.514876 81.53371
2.322793174 2.343349019 2.354057855 2.3511136 2.329684222 36 36 36 36 36 35.99071 35.99063 35.99058 35.9906 35.99068 83.59897 84.3386 84.7239164 84.617979 83.84692
2.301083041 2.309348619 2.302351212 2.2745434 2.218999493 38 38 38 38 38 37.9908 37.99076 37.99079 37.9909 37.99112 87.41998 87.733915 87.4681428 86.411954 84.30228
2.263921075 2.252189333 2.216879118 2.149956 2.041557637 40 40 40 40 40 39.99094 39.99099 39.99113 39.9914 39.99183 90.53634 90.067284 88.6555065 85.979752 81.64563
2.200309686 2.156096817 2.075592072 1.9472401 1.757095517 42 42 42 42 42 41.9912 41.99138 41.9917 41.99221 41.99297 92.39364 90.537471 87.1576347 81.768918 73.78566
2.091423929 1.994552259 1.842041815 1.6174013 1.301066149 44 44 44 44 44 43.99163 43.99202 43.99263 43.99353 43.9948 92.00516 87.744386 81.0362674 71.155195 57.24014
1.90504051 1.722973937 1.455978663 1.080721 0.569992416 46 46 46 46 46 45.99238 45.99311 45.99418 45.99568 45.99772 87.61735 79.244927 66.966539 49.708496 26.21835
1.586001733 1.266413927 0.817808704 0.2074892 0 48 48 48 48 47.09 47.99366 47.99493 47.99673 47.99917 47.09 76.11802 60.781453 39.2521426 9.959309 0
1.039892311 0.498874599 -4.4409E-15 0 2.513164321 50 50 49.63 48.36 49.99584 49.998 49.63 48.36 51.99029 24.942734 -2.204E-13 0
0.07896665 4.44089E-16 2.433229374 2.4731968 2.513164321 52.043 50.9 52.04268 50.9 4.109636 2.26E-14
0 52.044 0