MAXIMUM POWER POINT TRACKING SYSTEM FOR SOLAR HIGHWAY IN
CALIFORNIA
Shailja Raval
B.E., C.U.Shah College of Engineering & Technology, India, 2007
Krupen Amin
B.E., C.U.Shah College of Engineering & Technology, India, 2005
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
ELECTRICAL AND ELECTRONIC ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL
2009
MAXIMUM POWER POINT TRACKING SYSTEM FOR SOLAR HIGHWAY IN
CALIFORNIA
A Project
by
Shailja Raval
Krupen Amin
Approved by:
__________________________________________________, Committee Chair
Dr. John C. Balachandra
___________________________________________________, Second Reader
Dr. Fethi Belkhouche
________________________________
Date
ii
Students: Shailja Raval
Krupen Amin
I certify that these students have met the requirements for format contained in the
university format manual and that this project is suitable for shelving in the library and
credits to be rewarded for the Project.
_______________________________, Graduate Coordinator
Dr. Preetham B. Kumar
iii
_______________
Date
Abstract
of
MAXIMUM POWER POINT TRACKING SYSTEM FOR SOLAR HIGHWAYS IN
CALIFORNIA
by
Shailja Raval
Krupen Amin
This project is about generation of power through the solar panels in Californian
highways and storing it in a storage system. The plan is to build up charging stations for
electric vehicles on highways and this stored form of energy can be used in these
charging stations which would be helpful in charging of hybrid and electric cars that pass
through the highways. It would boost the usage of electric vehicles. We could also use
the generated electricity to light the interchange at night as it was implemented by the
Oregon Solar Highway Project. A lot of energy saving could be done if we implement the
installation of the solar panels on the highways. Our main focus in this project would be
to determine the solar insolation levels for different targeted areas, getting estimates on
the generation of electricity on the basis of different conditions prevailing in those
areas and on the maximum power point tracking system for the PV (Photovoltaic) cells in
different conditions which helps to maximize the power output of the solar panel. We
iv
would be using Matlab for doing our simulations for the solar insolation and Maximum
Power Point Tracking System. We would also be using the NREL data for our
Calculations for different areas to determine the estimates.
_________________________________________________ , Committee Chair
Dr. John C. Balachandra
_______________________
Date
v
TABLE OF CONTENTS
Acknowledgements…………………………………………………………………….. vi
List of Figures…………………………………………………………………………...viii
List of Tables…………………………………………………………………………...... x
Chapters
1.
INTRODUCTION……………………………........................................................ 1
1.1 Basics Of Solar Cells………………………………………………….3
1.2 Physics Of Solar Cells………………………………………………...7
1.3 Solar Array’s…………………………………………………………10
2.
CHARACTERISTICS OF A PV MODULE…………………………………….. 12
2.1 Types Of Solar Panels………………………………………………. 12
2.2 Electrical Connections Of The Modules……………………………..15
2.3 Tilt Angle And Orientation…………………………………………. 16
2.4 Sun Tracking Concentrator System………………………………… 17
2.5 Shading……………………………………………………………... 18
3.
CALCULATIONS AND SIMULATIONS…………………………………….. 20
3.1 Calculation Of Solar Power Output On Highways Of California……20
3.2 Solar Insolation Calculation………………………………………… 21
3.3 Simulation Results For Solar Insolation………………………...….. 22
3.4 Estimations For The Favorable Site For Building Solar Panels…..... 26
3.5 Maximum Power Point Technique…………………………………. 32
vi
3.6 P&O Simulation Results For Different Values Of Insolation……… 34
3.7 P&O Simulation Results For Different Value Of Temperature…….. 38
3.8 Array Size Calculation……………………………………………… 40
4.
SIMULATION CODES AND RESULTS……………………………………... 43
4.1 MATLAB Code For I-V Characteristic Of Solar Cell For Different
Values Of Insoaltions And Temperature…………………………… 43
4.2 Matlab Code For Maximum Power Point Tracking system……….. 45
4.3 MATLAB Code For Solar Insolation…………………….……….... 47
4.4 Results………………………………………………………….…… 48
References………………………………………………………………………. 50
vii
LIST OF FIGURES
Page
1. Figure 1 Oregon Solar Highway……………………………………………….... 2
2. Figure 2 Formation of a solar array……………………………………………… 3
3. Figure 3 Photovoltaic cell showing surface contact patterns……………………. 4
4. Figure 4 A solar module and its connection in series……………………………. 4
5. Figure 5: Solar Cell equivalent to a battery……………………………………… 6
6. Figure 6: Cross section of a p-n homojunction cell……………………………… 8
7. Figure 7: Generation and movement of free carriers in a p-n junction solar cell…9
8. Figure 8: Insolation graph for Sacramento region……………………………… 22
9. Figure 9: Insolation graph for Fresno region…………………………………… 23
10. Figure 10: Insolation graph for San Diego Region……………………………... 24
11. Figure 11: Insolation graph for Daggett Region ……………………………….. 25
12. Figure 12: P&O algorithm……………………………………………………… 33
13. Figure 13: Plot of Voltage Vs Power for insolation = 250W/m² and
Temp = 25ºC……………………………………………………………………. 34
14. Figure 14: Plot of Voltage Vs Power for insolation = 500W/m² and
Temp = 25ºC…………………………………………………………………… 35
15. Figure:15 Plot of Voltage Vs Power for insolation = 750W/m² and
Temp = 25ºC…………………………………………………………………… 36
16. Figure:16 Plot of Voltage Vs Power for insolation = 1000W/m² and
Temp = 25ºC………………………………………………………………….. 37
17. Figure 17 Plot of Voltage Vs Power for insolation = 250 W/m² and
Temp = 25ºC………………………………………………………………….. 38
viii
18. Figure 18 Plot of Voltage Vs Power for insolation = 250 W/m² and
Temp = 50ºC………………………………………………………………….. 39
19. Figure 19 Plot of Voltage Vs Power for insolation = 250 W/m² and
Temp = 75ºC …………………………………………………………………. 40
ix
LIST OF TABLES
Pages
1. Table 1 Comparison between solar cell and conventional battery………………. 6
2. Table 2 PV System Specification for all regions……………………………….. 27
3. Table 3 Sacramento Area Readings…………………………………………….. 28
4. Table 4 Fresno Area Readings………………………………………………….. 29
5. Table 5 San Diego Area Readings……………………………………………… 30
6. Table 6 Daggett Area Readings………………………………………………… 31
7. Table 7 Current Values defined for different value of Insolation………………. 48
8. Table 8 Current Values defined for different value of Insolation (2)……………. 49
x
xi
1
Chapter 1
INTRODUCTION
Scarcity of energy resources is a burning topic in today’s time. Due to extensive use of
energy resources there has arouse a need to use natural methods to create energy to
protect the extinct of energy resources and also help in reducing pollution. Our project is
targeting to one such renewable method. The project is about generation of power
through the solar panels in Californian highways and storing it in a storage system. The
plan is to build up charging stations for electric vehicles on highways and this stored
form of energy can be used in these charging stations which would be helpful in charging
of hybrid and electric cars that pass through the highways. Doing this would increase the
usage of electric cars for even longer runs. It would boost the usage of electric vehicles
and henceforth the consumption of fuel would be decreased. This produced energy could
also be used to light up the highway at nights and that can save a lot of electricity being
used. There is much more that could be extracted from this power plant. Our main focus
in this project would be to determine the solar insolation levels for the targeted areas,
getting estimates on the generation of electricity on the basis of different conditions
prevailing in those areas and on the maximum power point tracking system for the PV
(Photovoltaic) cells in different conditions which helps to maximize the power output of
the solar panel.
2
California is blessed with abundant sunlight and we should make efficient use of that
energy available. In 2008, the Oregon Department of Transportation (ODOT) completed
the nation’s first solar photovoltaic project in the highway. It used the energy to light the
interchange at night. The innovative idea of using that energy in building a charging
station is being proposed to increase the usage of electric vehicles so they can be used for
longer commute. The solar panels would be builded alongside the highway. Below is an
image of one such solar power plant that was built in Oregon.
Figure1: Oregon Solar Highway [12]
3
1.1 Basics Of Solar Cell
We would be digging into the basics of solar array’s and would explore that how is it
possible to generate power from them. The basic part of the solar array is a solar cell.
Solar cells are made of semiconductor material, such as silicon. A number of solar cells
electrically connected to each other and mounted in a support structure or frame is called
a photovoltaic module. The term photovoltaic system is from Greek word of light
“Photo” and the physicist “Volta” (the inventor of electric battery). It is applied to direct
conversion of light into energy by means of solar cells. These modules supply electricity
at a certain voltage. The current produced is directly dependent on how much light strikes
the module.
Figure2: Formation of a solar array [1]
4
Multiple modules can be wired together to form an array. The larger the area of a module
or array, the more electricity would be produced. These arrays would be used in building
up solar panels on the highways.
The solar cell is the basic building block of solar photovoltaics. Solar cell is a two
terminal device. We can consider it just as a diode in the dark and it is in its active state
when it’s in sunlight. It generates a photo voltage when it is charged by sun. It is
basically a thin slice of semiconductor material around 100 cm2 in area. It appears dark
blue or black in color. A pattern of metal contacts is imprinted on the surface to make
electrical contact; this unit is shown in fig (3). When this unit is charged by sun it
generates a dc photo voltage of 0.5 to 1 volt and when it is in short circuit mode it is
Figure 3 : Photovoltaic cell showing surface
contact patterns [2]
Figure 4 : A solar module and its
connection in series [2]
able to generate around ten’s of milliamps per cm2. The voltage acquired from this cell is
too small for many applications to run and hence these cells are connected together in
5
series and encapsulated into modules. A module generally contains 28 to 30 cells in
series and this module would be able to generate around 12V in standard illumination
conditions (fig 4). Now according to the power demanded by the application, these
modules can now be connected in parallel or series to form an array to obtain larger
voltage and current output. [2]
In simple electric terms the solar cell can take place of a battery. In the dark its just like
Figure 5: Solar Cell equivalent to a battery [2]
Fig (a) and does nothing. When light falls, the solar cell gets switched and behaves like
fig (b) creating voltage and e.m.f, analogous to the e.m.f to the battery. The voltage
developed when the terminals are isolated (infinite load resistance) is known as the open
circuit voltage (Voc). When the terminals are connected together a current is developed
which is known as the short circuit current (Isc). Hence for any load resistance Rl the cell
develops a voltage V between Voc and 0 and is capable of delivering current I based on
V=IRl. Thus we can determine both I and V depending on the intensity of illumination
and the load. [2]
6
We discussed the basic behavior of the solar cell. According to that aspect at this point it
would come in everyone’s mind that solar cell and conventional battery are both similar.
But that is not true; we would briefly describe the differences between a solar cell and a
conventional battery.
SOLAR CELL
CONVENTIONAL BATTERY
Solar cell derives its e.m.f from a
temporary change in electrochemical
potential caused by light.
Power delivered by the solar cell is
dependent on incident light intensity and
not primarily on the load.
Solar cell is never exhausted, as it can be
continually recharged with light.
The solar cell is characterized on the
illumination source and hence Isc and Voc
must be quoted for a known spectrum. It is
modeled electrically as a current generator.
The e.m.f of a battery is due to the
permanent
electrochemical
potential
difference between two phases in the cell.
Power delivered by the battery to a
constant load resistance is relatively
constant.
Battery is completely discharged when it
reaches the end of life.
The battery is characterized by its e.m.f, its
charge capacity and by a polarization curve
(determines how e.m.f varies with current)
and is modeled electrically as a voltage
generator.
Table 1: Comparison between solar cell and conventional battery
7
1.2 Physics Of Solar Cells:
As we all now know that solar cells are made up of silicon. When silicon is stripped of all
impurities it makes an ideal neutral platform for the transmission of electrons. Silicon
also has some atomic level properties which make it more attractive for the creation of
solar panels. Silicon atoms have room for 8 electrons in the outer band, but carry only
four in their natural state hence it has room for four more electrons. If one silicon atom
contacts another silicon atom, each receives the other atom’s four electrons. This
eventually creates a strong bond, there is no positive or negative charge present because
the eight electrons satisfy the atom’s needs. Silicon atoms can combine for years to result
in a large piece of pure silicon. This is the material which is used to form the plates of
solar panels. Just two plates of silicon are not able to generate electricity because they do
not possess positive or negative charge. Hence they are created by combining silicon with
other elements that do have positive or negative charges like for example phosphorous
and boron.
The solar cells contain a junction between two different materials across which has a
‘built-in’ electric field. When light is absorbed by the solar cell, they create mobile
electrons and holes. They flow in opposite directions across the junction. In this manner
the flow of absorbed photons is then converted into a flow of DC power from the
illuminated cell. The solar cell is made up of a large area of p-n junction made from
silicon. Usually the solar cells are made by diffusing an n-type do pant into one side of a
p-type wafer (or vice versa).
8
If p-type silicon and n-type silicon are placed in intimate contact with each other then a
diffusion of electrons occurs from n-type side of junction because it is has high electron
concentration into p-type side of junction because it has a low electron concentration.
When the electrons diffuse across the p-n junction, they recombine with holes on the ptype side. An electric field is created by the imbalance of charge immediately on either
side of the junction and hence the diffusion of carriers does not happen indefinitely. The
electric field established across the p-n junction creates a diode that promotes charge
flow, known as drift current, and it eventually balances the diffusion of electron and
holes. The region where electrons and holes have diffused across the junction is called
the depletion region because it no longer contains any mobile charge carriers. It is also
known as the space charge region. The structure as a whole remains electrically neutral,
but the junction region contains an electric double layer, consisting of two space-charge
regions or depletion regions as shown in the fig 6. The depletion regions are typically less
than a
Figure 6: Cross section of a p-n homojunction cell [3]
9
Micron thick and the chares they contain are those of the ionized dopants. The generation
and movement of free carriers in a p-n junction solar cell is shown in the fig below, it
shows the working of an illuminated c-Si cell. The absorption of photons of energy
Figure 7: Generation and movement of free carriers in a p-n junction solar cell [3]
greater than the band-gap energy of silicon promotes electrons from the valence band to
the conduction band, creating hole-electron pairs throughout the illuminated part of the
cell, which in c-si cells extends well into the base layer. In c-Si and most other
semiconductors, these hole-electron pairs quickly dissociate into ‘free’ carriers – mobile
holes and electrons that move independently of each other. Those free carriers that
approach the junction come under the influence of the built-in electric field, which
sweeps electrons from the p to the n side, and holes from the n to the p side. [3]
10
1.3 Solar Array’s:
A solar array also known as photovoltaic array is a linked collection of photovoltaic
modules. These modules are made up of a collection of solar cells. The cell converts solar
energy into direct current electricity via the photovoltaic effect. The electrical
requirements of a home or a business can be taken care of by one such module, hence the
modules should be linked together to form an array to support huge demands. Most PV
array’s use an inverter to convert the DC power produced by the modules by the
alternating current so that it could be plugged into the existing infrastructure to power
lights, motors and other loads. The modules in a PV array are usually first connected in
series to obtain the desired voltage. Then they are connected in parallel to allow the
system to produce more current. The measurement of solar arrays is done by the peak
electrical power they produce, in watts, kilowatts or even megawatts. [7]
Solar arrays are the best source of creating renewable energy resource. PV is the second
fastest growing energy technology in the world. But as every coin has its two sides it
does have a few drawbacks. The first being its intermittence and seasonality of sunlight.
It would be able to generate power only when sunlight is available. The lack of
inexpensive and efficient methods to store electrical energy, and the poor match between
the solar and electrical demand peaks in many locations and applications, are the main
hurdles for PV. The other aspect is its low power density. The solar power received at
Earth’s surface, averaged over day and night, winter and summer varies from around 100
W m-s in temperate locations to about 300 Wm-2 in Sunbelt regions. The solar
technologies hence require areas to be covered by solar converters or by optical
11
concentrators coupled to solar converters, for substantial amounts of power to be
generated. Hence it brings us to another drawback of solar energy is its cost. Manufacture
of most cell types requires careful control of semiconductor growth and purity and many
processing steps. The PV systems are expensive. The high costs for PV- generated
electricity are often compared unfavorably with typical retail prices for grid electricity
which make them a better choice than PV because it seems expensive in locations with
immediate access to the grid, where distribution costs are subsidized. The PV system is
an emerging technology its ignorance is one of its main drawback. Even if customers are
aware of the benefits of the benefits of PV they seldom take it into consideration and end
up in buying the regular category of products that uses conventional electricity. [3]
12
Chapter 2
CHARACTERISTICS OF A PV MODULE
Effects Of Temperature On Solar Panels
2.1 Types Of Solar Panels:
All the solar Panels are affected by temperature. By all it means there are different kinds
of solar panels available in the market. The three most common types of solar panels
available are Monocrystalline, Polycrystalline and Amorphous. We would go in a little
bit detail for these types of solar panels.
Monocrystalline: These are made from a single large crystal and are cut from ingots.
They are considered as most efficient and along with that are the most expensive. They
are better in low light conditions.
Polycrystalline: These are cast blocks of silicon which contain many small crystals.
These are the most common types in the market at this point. They are less efficient than
a single crystal but when they are put together with other cells rounding up to around 35
or more cells the actual difference between watts per square foot is not that much.
Amorphous: These are also known as thin film. They consist of large plates or flexible
laminates and silicon is directly spread on those. They are less efficient and are very
cheap compared to the other types and hence this sums up to use more panels of
amorphous to derive the same power. Uni solar is one example. [4]
Hence the effect of temperature in all these would be different according to the type of
the solar cell. But the operation for all of these remains the same.
13
We would now dig deep into the role played by the temperature in the solar panels. The
solar cells are encapsulated into a PV module. One of its unwanted characteristics is that
due to the encapsulation disturbs the heat flow into and out of the PV module which
increases the operating temperature of the PV module. The increase in temperature in
turn reduces the voltage and eventually lowers the output power. Due to the increase in
temperature stresses associated with thermal expansion increases and it increases
degradation rates by a factor of about two for each 10 C increase in temperature. We can
determine the operating system of a module by equilibrium between the heat produced by
the PV module, the heat lost to the environment and the ambient operating temperature.
The heat produced by the module depends on the operating point of the module, the
optical properties of the module and solar cells, and the packing density of the solar cells
in the PV module. The heat lost can proceed via one of the three mechanisms;
conduction, convention and radiation. These mechanisms depend on the thermal
resistance of the module materials, the emissive properties of the PV module and the
ambient condition in which the module is mounted. [5]
We would now see how heat is generated into the PV modules. As we all are aware when
a PV module is exposed to electricity it produces both heat and electricity. For a
commercial PV module operating at its maximum power point, only 10 to 15% of the
incident sunlight is converted into electricity and the remainder gets converted into heat.
The factors that affect the heat of the module are: [5]

The electrical operating point of the module :
14
The fraction of light that is generated into electricity in a solar module is the electrical
operating point or the efficiency of the PV module. If the module is operating in short
circuit current or open circuit voltage than all power generated by the module is
converted into heat and no electricity is produced.

The packing density of the solar cells
The design of solar cells is done as such they can absorb maximum solar radiation.
The cells would generate heat usually higher than the module encapsulated and rear
backing layer. Therefore, a higher packing factor of solar cells increases the generated
heat per unit area.

Absorption of low energy (infrared) light in the module or solar cells
Light can be of different type, the one that has an energy below that of the band gap
of the solar cells is not able to contribute to electrical power. When this light is
absorbed by solar cells it would contribute in heating. The aluminum present at the
rear of the solar cells usually absorbs this infrared light and in the solar cells which do
not have this coverage the infrared passes through the solar cells and exits from the
module.

The reflection from the top surface of the module
The sunlight that is reflected from the front surface of the module is not helpful in
generating electrical power. We need to minimize such light as it contributes to the
electrical loss mechanism. The reflected light does not contribute to the heating of the
modules. We can calculate the maximum power rise by multiplying incident power and
15
reflection. Usually we have a glass top surface on the PV modules adding that factor the
reflected light contains about 4% of the incident energy.

Absorption of sunlight by the PV module in regions which are not covered by
solar cells:
The amount of light absorbed by the parts of the module other than the solar cells also
is a contributor to the generation of heat. The amount of light absorbed and reflected
is determined by the color and material of the rear backing layer of the module.[5]
2.2 Electric Connection Of The Modules [6]:
A number of modules can be connected in series string to increase the voltage level,
in parallel to increase the current level or in a combination of two. The current and
voltage requirements of the load circuitry fed by the system output decide the exact
configuration. If we match the interconnected modules in respect with their outputs
we can maximize the efficiency of an array. One shaded module in a series connected
string could act as a load in the same manner a shaded solar cell in a module can act
as a load. Considering it within the cell, the damage can take place due to the heat
produced by the current that flows through the module. As such the severity of the
problem does vary according to the number of the modules in the string and also the
partial shading of the string depending on the system design and location. The
damage caused by the shading situation can be overcome by inserting by pass diodes.
The bypass diode is connected in parallel with the module and if a module is shaded
the current flows through the diode rather than through the module.
16
The addition of bypass diodes adds cost and also reduces the output of the string by a
small amount due to the voltage that is dropped across the diode. If there are large
modules the bypass diodes are incorporated in the manufacturing stage by placing
several diodes protecting different sections. This reduces the need for extra wiring but
it becomes an issue to replace the diode in a case of a failure. In systems where
shading reduces the output of one of the strings substantially below that of the others,
they normally include a blocking diode connected in series with each string. This
prevents the current from the remainder of the array being fed through the shaded
string and causing damage. Including blocking diodes reduces the output of the
system but provides protection. The design of the system, protection from shading
and many other aspects decide whether the use of blocking or bypass diodes is
beneficial.
2.3 Tilt Angle And Orientation [6]:
The intensity of the sunlight falling on a modules surface can be measured by the
orientation of the module with respect to the direction of the sun. The tilt angle and
the azimuth angle are the two main parameters that describe this factor. The tilt angle
is the angle between the plane of the module and the horizontal and the Azimuth
angle is the angle between the plane of the module and due south (or sometimes due
north depending on the definitions used). We can determine the correction of the
direct normal irradiance to that on any surface using the cosine of the angle between
the normal to the sun and the module plane.
17
The optimum array orientation depends on the latitude of the site, prevailing weather
conditions or the loads to be met. For low latitudes the maximum annual output is
obtained when the array tilt angle is roughly equal to the latitude angle and the array
faces due south (in the northern hemisphere) or due north for the southern
hemisphere. The optimum tilt angle is affected by the proportion of diffused radiation
in the sunlight, since diffuse light is only weakly directional. For locations with a high
proportion of diffuse sunlight, the effect of tilt angle is reduced. If a constant or
reasonably constant load is to be met or particularly if the winter load is higher than
the summer load, then the best tilt angle may be higher in order to boost winter
output. The incorporation in the support structure plays an important role in deciding
on the array orientation. It is necessary to trade off the additional output from the
optimum orientation against any additional costs that might be added to accomplish
this. The aesthetic issues must also be considered.
2.4 Sun Tracking/Concentrator Systems [6]:
The flat plate array uses a configuration of a fixed array with no change of orientation
during operation. Some arrays are designed to track the path of the sun. We can track
two axis to capture the sun’s movement fully and can only track in one axis from east
to west to track the sun partially.
By using a flat-plate array and single-axis tracking we can have an increase in an
output up to 30% for a location with predominantly clear sky conditions. In two axis
tracking where the array follows both the daily east-west and north-south movement
of the sun, can provide a further increase of about 20%. For locations where frequent
18
overcast conditions prevail the benefits of tracking are considerably less. It is more
economical to install a larger panel with locations of less than about 3000 hours of
direct sunshine per annum. For both the cases, the additional output from the system
must be compared to the additional cost of including the tracking system, which
controls the control system and the mechanism of moving the array.
For concentrator systems the system should be able to track the sun to maintain the
concentrated light falling onto the cell. As the concentration ratio increases it
increases the cost of tracking system and the accuracy of tracking.
2.5 Shading [6]:
Shading in any part of the array would reduce its output. The output of any cell or
module that is shaded would be reduced according to the reduction of the light
intensity falling on it. If the shaded cell or module is electrically connected to other
cells and modules which are unshaded then due to a mismatch situation it reduces the
performance. For example, if a single module of a series string is partially shaded its
current output would be reduced and it would dictate the operating point of the whole
string. If there are several modules that are shaded the string voltage may be reduced
to a point where the open circuit voltage of that string is below the operating point of
the rest of the array, and then that string would not contribute to the array output. As
discussed earlier we can include a blocking diode for this kind of string protection.
The reduction in output from shading of an array can be significantly greater than
the reduction in illuminated area, because it results from:

The loss of output from shaded cells and modules.
19

The loss of output from illuminated modules in any severely shaded stings that
cannot maintain operating voltage; and

The loss of output from the remainder of an array because the strings are not
operating at their individual maximum power points.
In the case of an open environment in the case of the highway solar panels, shading
would not that be such an issue as unlike in city areas it would not be obstructed by
buildings and any other structures. The only hindrance it would cause would be the
natural shading occurred due to the clouds and other aspects.
20
Chapter 3
CALCULATIONS AND SIMULATIONS
3.1 Calculation Of Solar Power Output On The Highways Of California
Now we are well versed with the working and the characteristics of the solar panels.
As California has abundant of sunlight energy available we are targeting 4 areas for
our calculations to make fair estimates in respect with the solar insolation and the cost
of generating electricity in these areas and then after analyzing the results we can
come to a conclusion of where would be the best place to install the solar panels. The
areas were we would be doing our calculations are Sacramento, Fresno, San Diego
and Daggett. The first step to our calculation would be to have reliable solar
insolation data for these locations. Once we have the solar insolation data we would
be able to calculate through our code as to what amount of power output would be
generated so we could come to a conclusion as to which area is most suitable for
building up the solar panels.
The solar insolation data could be analyzed by the simulations carried out on the basis
of the geographical parameters of each area and taking their latitude into
consideration.
21
3.2 Solar Insolation Calculation:
I = S cos Z
I = Solar Insolation
S = 1000 W/m² = Clear day solar insolation on a surface perpendicular to
incoming solar radiation. This value actually varies greatly due to atmospheric
variables.
Z = Zenith Angle
(Zenith Angle is the angle from the angle from the zenith (point directly overhead
to the sun’s position in the sky.) The zenith angle is dependent upon latitude, solar
declination angle and time of the day.
Z = cos‾¹ (sin Ø sin C + Cos Ø Cos C Cos H)
Ø = Latitude
H = Hour Angle (Angle of radiation due to time of day)
= 15º x (Time -12)
Time is given as the hour of the day from midnight
C = Solar Declination Angle
Solar Declination Angle for the northern Hemisphere
Vernal Equinox Mar. 21/22
C = 0º
Summer solstice Jun 21/22
C = +23.5º
Autumnal Equinox Sept 21/22
C = 0º
Winter Solstice Dec 21/22
C = -23.5º [11]
22
3.3 Simulation Results For Solar Insolation:
The simulation results show us the solar insolation data on an hourly basis and as
summer is the peak time for the highest solar energy available we would be taking it
into consideration.
Figure 8: Insolation graph for Sacramento region
23
Figure 9: Insolation graph for Fresno region
24
Figure 10: Insolation graph for San Diego Region
25
Figure 11: Insolation graph for Daggett Region
From the simulation graphs we come to a conclusion that the solar insolation
available in these areas is nearly close to each other and is ranging between 960 and
980. So it would not be a fair estimate to judge the locality on the basis of the solar
insolation of each areas, we should dig in more into the details like insolation on a
yearly basis, cost effectiveness of each area, maximum power tracking system,
environmental challenges and then come to a wise conclusion.
26
3.4 Estimations For The Favorable Site For Building Solar Panels:
“NREL National Renewable Energy Laboratory is the nation’s primary laboratory for
renewable energy and energy efficiency research and development (R&D)” [8] . It
has undergone many researches in all renewable resources. It also has an extensive
database to carry out researches based on the solar energy. We contacted NREL and
came across a PVWATT calculator used by them in order to specify the estimates of
building up the solar photovoltaic systems in the desired area. The calculator uses the
meteorological year weather data and determines the solar radiation incident on the
PV array and the PV cell temperature for each hour of the year. . The calculator
works by creating hour-by-hour performance simulations that provide estimated
monthly and annual energy production in kilowatts.[8] As we had targeted these 5
areas we would develop calculations based on the PVWATT calculator and come
with the numbers and a conclusion as to which area would be the best to install the
solar panels. We would be listing the charts below based on the areas:
We are assuming 1000kW output to be generated. A 2-Axis tracking system for all
calculations as it gives the highest performance the only drawback it has is that it is
costly. The PV specification for all the system remains the same as we are doing a
comparative analysis. The cost of electricity in the whole of California remains the
same being 12.5¢/kwh so the calculations for the cost measurement are done on this
fixed rate. The PV specifications are also listed below:
27
PV System Specification
DC Rating
1000.0kW
DC to AC Derate Factor
0.770
AC Rating
770.0kW
Array Type
2-Axis Tracking
Table 2: PV System Specification for all regions
28
Station Details
City
Sacramento
Latitude
38.52° N
Longitude
121.50º W
Elevation
8m
Sacramento Area Readings
Results
Month
Solar Radiation
(kWh/m²/day)
AC Energy
(kWh)
Energy Value
($)
1
3.14
72363
9045.38
2
5.02
103707
12963.38
3
6.61
151904
18988.00
4
8.64
189468
23683.50
5
10.11
222264
27783.00
6
11.15
234329
29291.12
7
11.25
239928
29991.00
8
10.53
22497
28121.75
9
9.22
191823
23977.88
10
7.16
156535
19566.88
Year
7.55
1954444
244305.50
Table 3: Sacramento Area Reading
29
Station Details
City
Fresno
Latitude
36.77° N
Longitude
119.72º W
Elevation
100m
Fresno Area Readings
Results
Month
Solar Radiation
(kWh/m²/day)
AC Energy
(kWh)
Energy Value
($)
1
3.52
79975
9996.88
2
5.49
112704
14088.00
3
7.38
165857
20732.12
4
9.39
202560
25320.00
5
10.64
230984
28873.00
6
11.30
230769
28846.12
7
11.64
241589
30198.62
8
10.80
221863
27732.88
9
9.27
187147
23393.38
10
7.69
165371
20671.38
Year
8.00
2031522
253940.24
Table 4: Fresno Area Reading
30
Station Details
City
San Diego
Latitude
32.73° N
Longitude
117.17º W
Elevation
9m
San Diego Area Readings
Results
Month
Solar Radiation
(kWh/m²/day)
AC Energy
(kWh)
Energy Value
($)
1
6.13
138172
17271.50
2
6.74
136814
17101.75
3
7.54
170694
21336.75
4
8.72
188541
23567.62
5
7.88
176924
22115.50
6
8.16
175258
21907.25
7
8.62
189038
23629.75
8
8.89
192983
24122.88
9
7.53
158404
19800.50
10
7.41
164388
20548.50
Year
7.52
1968866
246108.24
Table 5: San Diego Area Readings
31
Station Details
City
Daggett
Latitude
34.87° N
Longitude
116.78º W
Elevation
588m
Daggett Area Readings
Results
Month
Solar Radiation
(kWh/m²/day)
AC Energy
(kWh)
Energy Value
($)
1
7.26
165202
20650.25
2
7.85
156764
19595.50
3
9.50
214221
26777.62
4
11.21
241118
30139.75
5
11.42
247078
30884.75
6
12.14
148975
31121.88
7
11.59
240178
30022.25
8
10.84
225358
28169.75
9
10.17
207169
25896.12
10
8.93
194040
24255.00
Year
9.61
2459570
307446.24
Table 6: Daggett Area Reading
32
From the calculations so far Sacramento seems to be the most promising as it is having
the solar radiation of 7.55 Kwh/m²/day on a yearly basis and the most important factor is
that it is the most cost effective from all the other areas. The availability of huge
highways is also a benefit for the Sacramento region.
3.5 Maximum Power Point Technique:
The selection of the site is being done. Now our major concern would be as to how we
can get maximum output from the solar panels in each and every condition. To make this
happen we have the Maximum Power Point Technique in the picture to give us a clear
idea.
A maximum power point technique is a highly efficient DC to DC converter. It functions
as an optimal electrical load for a solar cell or an array. It then converts the power to a
voltage or current level which is the most suitable to the designed load system. This
system tracks the maximum value of current and voltage of the solar panel and gives the
maximum output. [10]
We are taking into consideration the P&O algorithm also known as pertube and observe
algorithm for the design of this system. P&O is the most efficient algorithm and also very
simple to implement on an industrial basis for the maximum power point tracking system.
It is known for its simple control structure and very few measured parameters.
33
P&O Algorithm:
We have made a P&O algorithm and is as below:
Input V, I
Power=V*I
YES
NO
Power_New>Power
YES
NO
NO
Vref_new>V
Vnew=Vref_
new+a
YES
Vref_new>V
Vnew=Vref_
new-a
Vnew=Vref_
new-a
END
Figure 12: P & O Algorithm
Vnew=Vref_
new+a
34
3.6 P&O Simulation Results For Different Values Of Insolation:
Figure 13: Plot of Voltage Vs Power for insolation = 250W/m² and Temp = 25ºC
35
Figure 14: Plot of Voltage Vs Power for insolation = 500W/m² and Temp = 25ºC
36
Figure 15: Plot of Voltage Vs Power for insolation = 750W/m² and Temp = 25ºC
37
Figure 16: Plot of Voltage Vs Power for insolation = 1000W/m² and Temp = 25ºC
38
3.7 P&O Simulation Results for different value of Temperature:
Figure 17: Plot of Voltage Vs Power for insolation = 250 W/m² and Temp = 25ºC
39
Fig
ure 18: Plot of Voltage Vs Power for insolation = 250 W/m² and Temp = 50ºC
40
Figure 19: Plot of Voltage Vs Power for insolation = 250 W/m² and Temp = 75ºC
All the simulation results shown above give us the maximum power output in
different conditions like different value of insolation and different temperatures.
3.8 Array Size Calculation:
One of the major factors affecting to build up a solar power plant is to see how we can
determine the size of the solar system that would be able to power up the electrical needs.
In our case we would be having high electrical needs so a large number of panels should
be required. Oregon was one of the first ones to install the solar highways in USA. It
41
generates 112,000 kilowatt hours (ac) annually and had a project capacity of 104
kilowatts (dc). [12]
We would present a procedure of calculating the solar array size.
For our assumption if we are taking into consideration a 100 amp-hours/day current to
drive our load.
The steps for the calculation are listed below:

We multiply the current by 1.2 to account for the battery loss to the current
required.
100 x 1.2 = 120 amp-hours/day

Now assuming the Average sun hours per day = 3.07 kWh/hr

We divide the amp-hours/day with the average sun hours per day then we have
the total solar array amp required
120 ÷ 3.07 = 39.08. That is the total solar array amp required

Now ideally an 80 Watt module has around 4.5 amps

Therefore the total number of solar modules required in parallel are 39.08/4.5 =
8.68 that is equivalent to 9.

The number of module strings to provide DC battery voltage is equal to 4
modules.
42
Hence, total number of solar modules 4 x 9 = 36. That means that 36 modules would be
required in each series string to supply necessary DC battery voltage.
This method is useful in calculating the array size for our [9]
43
Chapter 4
SIMULATION CODES & RESULTS
4.1 MATLAB Code For I-V Characteristic Of Solar Cell For Different Values Of
Insoaltions And Temperature
function I= mysolar(V,G,Tc)
V= solar module voltage;
I= module current
G= Solar insolation (1G=1000W/m2);
Tc=Cell temperature;
% first define all the constant
A=1.2;
Vg=1.12;
Sc=36;
k=1.38e-23;
q=1.60e-19;
diode ideality factor
band-gap voltage
number of series cell
Boltzmann’s constant
electron charge
temp1=298;
Is_temp1=3.80;
Vo_temp1=21.06/Sc;
% temp. in Kelvin
temp2=348;
Is_temp2=3.92;
Vo_temp2=17.05/Sc;
% temp. in Kelvin
Tr=273+25;
Tw=273+Tc;
% reference temp
working temperature
Calculate light generated current
Il_temp1=Is_temp1*G;
a= (Is_temp2-Is_temp1)/Is_temp1;
b= 1/(temp1-temp2);
44
c= a*b;
Il=Il_temp1*(1+c*(Tw-temp1));
Vt_temp1=k*temp1/q;
Reverse Saturation Current At Different Temperature
A1= (exp (Vo_temp1/ (A*Vt_temp1))-1);
B1= (exp (Vo_temp2/ (A*Vt_temp1))-1);
Ir_temp1=Is_temp1/ A1
Ir_temp2=Is_temp2/ B1
d=Vg*q/A*k;
Ir=Ir_temp1*(Tw/temp1). ^ (3/A).*exp (-d.*(1./Tw-1/temp1));
X=Ir_temp1/ (A*Vt_temp1) * exp (Vo_temp1/ (A*Vt_temp1));
dvdi_Vo=-1.15/Sc/2;
Rseries=-dvdi_Vo-1/X;
Series Resistant
Vt_2=A*k*Tw/q;
Cell Voltage
Cv =V/Sc;
I=zeros(size(Cv));
temp=zeros(size(Cv));
Vtemp=zeros(size(Cv));
for j=1:20;
I=I-(Il-I-Ir.*(exp((Cv
1)).*Rseries./Vt_2)
+I.*Rseries)./Vt_2)-1))/(-1-(Ir.*(exp((Cv
+I.*Rseries)./Vt_2)-
45
temp(j)=I
end
plot(Vtemp,temp(j));
end
4.2 Matlab Code For Maximum Power Point Tracking system.
function [out]= MPPT(V);
Calling the function from previous program
I=mysolar (V,.G,Tc);
Power=V*I;
a=0.5; % constant
temp1=zeros(1,40);
temp2=zeros(1,40);
Vref_new=V+a;
for i=1:40
I_new=mysolar(Vref_new,G,Tc)
Power_new=I_new* Vref_new
if (Power_new<Power)
if (Vref_new>V)
Vnew=Vref_new-a;
else
Vnew=Vref_new+a;
end
else
46
if (Vref_new>V)
Vnew=Vref_new+a;
else
Vnew=Vref_new-a;
end
end
% tenp1=Power_new
% temp2=Vref_new
Vref_new=Vnew
Power=Power_new
temp1(i)=Vnew
temp2(i)=Power_new
end
plot(temp1,temp2)
xlabel ('Voltage')
ylabel ('Power')
Vm=V;
Ia=I_new;
47
4.3 MATLAB Code For Solar Insolation
function [out]=New(latitude, hour, declination);
a=sin(latitude*pi/180) * sin(declination*pi/180);
b=cos(latitude*pi/180) * cos(declination*pi/180) * cos(15*(hour-12)*pi/180) ;
c=a+b;
I=1000*c
plot(hour,I);
xlabel (‘Hour’)
ylabel (‘Insolation W/m2)
end
48
4.4 Results:
Values of current that we derived from our code for different values of Insoaltion
Insolation (G) = 250 W/m²
i/p 
o/p Current
Voltage
(Amp)
(V)
0
0.9500
1
0.9500
2
0.9500
3
0.9500
4
0.9500
5
0.9500
6
0.9500
7
0.9500
8
0.9500
9
0.9499
10
0.9498
11
0.9495
12
0.9487
13
0.9467
14
0.9418
15
0.9300
16
0.9010
17
0.8311
18
0.6674
19
0.3089
19.5
0.0022
Insolation (G) = 500 W/m²
i/p 
o/p Current
Voltage
(Amp)
(V)
0
1.9000
1
1.9000
2
1.9000
3
1.9000
4
1.9000
5
1.9000
6
1.9000
7
1.9000
8
1.9000
9
1.8999
10
1.8997
11
1.8983
12
1.8974
13
1.8960
14
1.8902
15
1.8761
16
1.8414
17
1.7579
18
1.5624
19
1.1340
20
0.3185
20.29
0.0100
Table 7: Current Values defined for different value of Insolation
49
Insolation (G) = 750 W/m²
i/p 
o/p Current
Voltage
(Amp)
(V)
0
2.8500
1
2.8500
2
2.8500
3
2.8500
4
2.8500
5
2.8500
6
2.8500
7
2.8500
8
2.8500
9
2.8499
10
2.8497
11
2.8492
12
2.8481
13
2.8454
14
2.8387
15
2.8222
16
2.7819
17
2.6848
18
2.4574
19
1.9591
20
1.0107
20.73
0.01
Insolation (G) = 1000 W/m²
i/p 
o/p Current
Voltage
(Amp)
(V)
0
3.8000
1
3.8000
2
3.8000
3
3.8000
4
3.8000
5
3.8000
6
3.8000
7
3.8000
8
3.8000
9
3.7999
10
3.7996
11
3.7991
12
3.7979
13
3.7947
14
3.7871
15
3.7683
16
3.7223
17
3.6116
18
3.3523
19
2.7842
20
1.7028
21
0.1043
21.05
0.0220
Table8: Current Values defined for different value of Insolation (2)
50
REFRENCES
[1] How do photovoltaics work?
http://science.nasa.gov/headlines/y2002/solarcells.htm
[2] Physics of solar panels:
http://www.worldscibooks.com/etextbook/p276/p276_chap1.pdf
[3] Series of Photoconversion of Solar Energy -- Vol 1.
Clean electricity from photovoltaics By Mary D.Archer, Robert Hill
Imperial College Press
[4] Innovative Solar: http://www.innovativesolar.com/solar-modules-196/
[5] Photovoltaics CDROM Christiana Honsberg and Stuart Bowden:
http://pvcdrom.pveducation.org/index.html
[6] Photovoltaic Modules, Systems and Applications
Nicola M. Pearsall and Robert Hill
[7] http://en.wikipedia.org/wiki/Photovoltaic_array
[8] National Renewable Energy Laboratory: http://www.nrel.gov/
[9] AMECO: A Solar Energy source for Southern California Since 1974
http://www.solarexpert.com/Pvmodule.html
[10] http://en.wikipedia.org/wiki/Maximum_power_point_tracker
[11] http://edmall.gsfc.nasa.gov/inv99Project.Site/Pages/solar.insolation.html
[12] http://www.oregon.gov/ODOT/HWY/OIPP/docs/solar_factsheet.pdf
51
[13] Evaluating MPPT Converter Topologies using PV Models
http://www.itee.uq.edu.au/~aupec/aupec00/walker00.pdf
[14] Advance Algorithm of MPPT Control of Photovoltaic systems.
http://www.solarbuildings.ca/c/sbn/file_db/Advanced%20algorithm%20for%20MPPT.pd
f
[15]
http://www.wisegeek.com/how-do-solar-panels-work.htm
[16]
http://en.wikipedia.org/wiki/Solar_cell#The_p-
52