Modelling and Analysis of Water Cooled Photovoltaics

Modelling and Analysis of Water Cooled Photovoltaics
Modelling and Analysis of Water Cooled Photovoltaics
Efstratios Chaniotakis
MSc Energy Systems and the Environment 2001
Department of Mechanical Engineering
University of Strathclyde
Acknowledgements
I would like to express my gratitude to my supervisor Dr Nick Kelly for his
help and support given for this project
Many thanks to my family for their moral support
Finally, thanks to the people of the class of ’00
1. Introduction
1
1.1 Overview
1
1.2 General about PV
3
1.3 Aims of the project
4
2. Technology review
5
2.1 General theory of PV cells
6
2.2 Four main types of PV cells
7
2.3 Structure of the solar cell
9
2.4 Panel position
20
2.5 Heat transfer
21
2.5.1 Conduction
21
2.5.2 Convection
22
2.5.3 Radiation
23
2.6 The stack effect
23
2.7 Cooling medium
24
2.8 Air cooled PV panel
26
2.9 Water cooled PV panel
35
2.10 Comparison of the two systems
39
3. Developing a Model of a Water Cooled PV panel
42
4. Parametric analysis of the Water Cooled panel
48
5. Quantification
54
6. Example of a PV in a Greek house
60
7. Discussion
69
7.1 General about the project
69
7.2 Main work
69
7.3 The model of the water cooled PV
70
7.4 Quantification analysis
70
7.5 Example of a PV in a Greek house
71
8. Conclusions
72
9. Recommendations for future work
74
10. Appendices
75
11.1 Appendix 1: Nomenclature
75
11.2 Appendix 2: The excel spreadsheet
77
12. References and bibliography
79
Abstract
Abstract
The project is focused on modelling and analyzing modern photovoltaics. Two types of PV are
presented and analyzed: the water cooled PV and the air cooled PV. The former uses water in
order to cool the panel while the latter uses air as the coolant. Naturally ventilated panels and
water cooled panels can provide higher efficiencies than conventional ones. The aim of the
project is to analyze - model both systems and compare them in order to reveal the most
promising. Furthermore, by altering various physical parameters of the heat exchanger in the
water PV system, the maximum efficiency is aimed. This information can be used in
maximizing the efficiency of any collector design. Various important characteristics that a
conventional PV can provide, such as the power, are calculated and compared to those of a
water cooled PV. Finally another aim of the project is to investigate whether a PV is able to
provide energy to a typical house and what is the autonomy of it.
In order to model the water cooled panel an excel spreadsheet was constructed. By using this
spreadsheet all the important physical parameters from the heat exchanger as well as from the
panel were altered and the results were analyzed. The impact every change had on the
effectiveness as well as the normal operation of the system could then be recorded. By the use
of the spreadsheet, the maximum efficiency of the panel can be achieved. This information
could be very important in designing-constructing collectors. Another method used in the
project was the direct comparison of both air cooled and water cooled systems in order to
reveal advantages and disadvantages. A real life scenario was created and all the important
characteristics of a PV panel were calculated in order to see if such a panel can provide
sufficient energy to a house. Finally a quantification analysis was performed in order to see
what is the maximum power a PV can provide and compare it with the one from the water
cooled panel.
The results of the project showed that the most efficient and promising system is the water
cooled photovoltaic. Apart form higher efficiency it can provide extra heat which can be used
in the house. Such a system proved to be feasible. Furthermore it was clearly shown that
altering various parameters of the system has as a result different efficiencies-output. Finally
the real life scenario of a PV installed in a Greek house demonstrated that the whole
configuration is feasible and that the energy supplied is sufficient to meet the daily demand of
a modern house.
Introduction
1. Introduction
1.1 Overview
Nowadays, most of the world’s energy (80%) is produced from fossil fuels. Massive
exploitation is leading to the exhaustion of these resources and imposes a real threat to the
environment, apparent mainly through global warming and acidification of the water cycle.
The distribution of fossil fuels around the world is equally uneven. Middle East possesses more
than half of the known oil reserves. This fact leads to economical instabilities around the world
which affect the whole geopolitical system.
The present system as it is cannot be maintained for more than two generations. The impact it
has on the environment as well to the humans cannot be disputed. Firstly there is the
greenhouse effect. This effect is the capacity of the atmosphere to retain heat. Seen from space,
the earth radiates energy at wavelengths characteristic of a body at -18°C. However, the
average surface is some 33°C higher, due to the presence of gases that are relatively
transparent to solar radiation but opaque to the infrared radiation given off by the earth. These
gases effectively trap the heat between the surface and mid atmosphere. Carbon dioxide CO2 is
particularly important in this respect. The burning of fossil fuels, coal in particular inevitably
produces atmospheric emissions of CO2.
It should be said here that a doubling of CO2 concentration (expected by 2035-2055) will
cause an average temperature rise of 3 to 5°C. This equals the rise between the coldest period
of the last ice age, 18000 years ago and the presence moment. Such heating is going to have
disastrous consequences for humanity. Major parts of polar ice caps will melt and the sea level
will increase covering big areas of the earth. Many ecosystems will be destroyed, unable to
adapt to the change.
Figure 1. Global temperature changes
1
Introduction
Furthermore, the combustion of fossil fuels is responsible of the production of nitric acid and
sulfuric acid. These elements are creating the phenomenon called acid rain. It harms plant life
and contributes to global pollution. Furthermore, once incorporated in the seawater is very
difficult to eliminate. [20]
Moreover, there is a danger arising from the increase of the energy use from the countries of
the Third World. It is expected that these countries will try to increase their standard of living
which is at the minimum level for decades. This will have as a result the increase of the
depletion of the limited stock, creating an even more severe ecological problem. These
countries even today, cannot afford the cost of protecting the environment. Consequently they
will increase the rate of combustion of oil and coal, will accelerate the deforestation or they
will turn to nuclear energy.
Keeping the above in mind as well as the fact that oil is running out fast, alternatives should be
adopted. Renewable energy is one of the most promising alternatives to the above problems.
Photovoltaic panels in particular can provide a good source of producing clean electricity. The
photovoltaic effect was first discovered by the physicist Edmund Becquerel in 1839. Despite
that, this technology is considered to be a very recent one. The first cell which could be
considered as PV was constructed in 1941 with an efficiency of 1%.
Present photovoltaic technology has been well developed since 1941. PV panels are used as the
primary electricity source in space missions and satellites. The cost of producing electricity for
house applications has dropped dramatically and PV panels are becoming more and more
economic viable. New materials have been developed and new technology has created PV
panels at efficiencies of 20% in many cases.
One relative new type of PV panel is the hybrid PV panel. This type of panel converts the sun’s
radiation to electricity while providing heat to the system for other purposes. This can be done
by either air or a fluid coolant. The cooling medium apart from conducting heat is cooling the
panel making it more efficient. The most widely used fluid is water.
2
Introduction
1.2 General about PV
The conversion of solar energy to electrical and thermal energy has been practiced for many
years. In order to convert the solar energy to electrical, photovoltaics are used. Photovoltaic
modules use the photoelectric effect in order to directly perform the above conversion. This
technology has been practiced for many years. The widely used heat collection systems are
flat-plate collectors and solar cells for thermal and electrical applications respectively.
Figure 2. Picture of a PV panel
Photovoltaic panels convert solar radiation to electricity with efficiencies in the range of 5% to
20%, depending on the type of the cell. Polycrystalline silicon solar cells offer the highest
range of possibilities for applications. This is a consequence of their modest price relative to
the monocrystalline silicon cells, and their considerable stability and efficiency (about 15%).
Furthermore, these cells are sold in the form of panels having dark blue appearance which is
aesthetically pleasant.
When the temperature of a photovoltaic module is increased, the efficiency drops. This can
typically result in an efficiency drop off of 0,5% per °C increase in the cell operating
temperature. The operating temperature is increased because a large part of the solar radiation
is not converted to electricity but is absorbed by the panel as heat. Natural circulation of air is
the easiest and cheapest way to remove this heat from the panel and consequently increase the
efficiency.
Another, more efficient way is to use a liquid as the coolant of the panel. This is the general
philosophy of hybrid photovoltaic-thermal collectors. In these systems the natural or forced
3
Introduction
circulation of a heat removing fluid can be used not only for PV cooling, but also for heat
generation. This heat can be used to preheat the hot water for applications in the building.
As said before the hybrid PV thermal systems are still under development. Nevertheless,
various experiments and publications have been made producing interesting results. Hendrie
[1] used both air and liquid as the coolant while Florschuetz [2] has presented an extension of
the Hotter-Whiller1 model to analyze the PV/T collectors by assuming a liner correlation
between efficiency of cell and temperature. Single and double air heaters were used by
Chandra et al [3] while Agarwal and Garg [4] carried out experiment on air and water-cooled
photovoltaic systems.
The IT Power and Newcastle Photovoltaic Application center has recently carried out a study
on the PV hybrid system, commissioned by the Joint Research Center at ISPRA. Finally,
various other works have been published by Garg and Adhikari [5], Brinkworth and Marshall
[11] on model of naturally ventilated PV claddings.
1.3 Aims of the project
As previously stated, naturally ventilated PV panels as well as water-cooled photovoltaics offer
higher electrical efficiencies as well as useful heat. The studies above, and others, show the
potential of these relative new systems as well as the general interest on the topic.
The current project, will present a model of air-cooled PV panel as well as a water-cooled
panel. Then, a comparison between the two systems will reveal the most efficient. A
spreadsheet will be presented in order to see how the physical properties of the heat exchanger
at the water-cooled PV can change the output of the system as well as the efficiency of it.
Various parameters will be tested and compared. All the above will be done in order to
optimize the PV component and to provide some useful information for designers.
Furthermore, a quantification analysis will be performed. This analysis will be done in order to
see what is the maximum power a PV panel can provide and compare it with the one using
water as the coolant.
1
This model will be discussed in the chapter “Technology review”.
4
Introduction
Finally at the end of the project, an example of how a PV system is installed and how it can
contribute to the energy demand of a typical Greek house is presented. This part of the
thesis is done in order to see if a PV system is able to produce enough electrical energy for
a house as well as to calculate various important parameters associated with a real life
scenario. The number of batteries used, the area needed by the PV panels as well as
collectors tilt and other parameters are investigated. Finally a discussion is performed as to
see if the thermal energy produced by a hybrid model can be used inside the house.
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Technology review
2. Technology review
2.1 General theory of PV cells
The conversion of the energy carried by electromagnetic radiation into electrical energy is a
physical phenomenon known as the photovoltaic effect. Solar cells are without doubt the most
important type of device for carrying out such conversion. When sunlight falls on semiconductor
materials (e.g. silicon), the photons making up the sunlight can transmit their energy to the
valence electrons.
Silicon is representative of the diamond crystal structure. Each atom is covalently bonded to
each of its four nearest neighbors. That is, each silicon atom shares its four valence electronic
with the four neighboring atoms, forming four covalent bonds. Silicon has atomic number 14,
and the configuration of its 14 electrons is 1s22s22p63s23p2 [6]. The core electrons, 1s2, 2s2
and 2p6, are very tightly bound to the nucleus and, at real-world temperatures, do not
contribute to the electrical conductivity. At absolute zero, as N silicon atoms are brought
together to form the solid, two distinct energy bands are formed-the lower, "valence" band and
the upper, "conduction" band. The valence band has 4N availability energy states and 4N
valence electrons and is therefore filled. Conversely, the conduction band is completely empty
at absolute zero. Thus the semiconductor is a perfect insulator at absolute zero.
As the temperature of the solid is raised above absolute zero, energy is transferred to the
valence electrons, making it statistically probable that a certain number of the electrons will be
raised in energy to such an extent that they are free to conduct electrical charge in the
conduction band. These electrons are called intrinsic carriers. The amount of energy necessary
to bridge the valence and conduction bands is referred to as the forbidden gap or energy gap
E.g., which is 1.12 eV at room temperature for silicon.
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Technology review
Each time a photon breaks a bond, an electron becomes free to roam through the lattice. The
absent electron leaves behind a vacancy, or hole, that can also move through the lattice as
electrons shuffle around it. The movement of the electron and holes in opposite directions
generates an electric current in the semiconductor. The current can carry on through an external
circuit, allowing the energy absorbed from the light to be dissipated in some useful way. To
separate the electrons from the holes and prevent the bonds from reforming, an electrical field is
used. It provides a force propelling the electrons and holes in opposite directions. The result is a
current in the direction of this field.
The main characteristics that distinguish photovoltaics from other renewables are:
•
Direct production of electrical energy, even in very small scale of few Watt or mWatt
•
They are easy to use. In certain small applications they can be installed directly from the
user
•
They can be installed in city centers without offending aesthetically the environment
•
They can be combined with other sources of energy (hybrid systems)
•
They can be expanded in order to meet higher demands
•
Their operation has minimum noise production as well as no emissions
•
Their operation life can be large with minimum maintenance
•
They require high investment cost
2.2The four main types of silicon photovoltaic cells
The four general types of silicon photovoltaic cells [17] are:
•
Single-crystal silicon.
•
Polycrystalline silicon (also known as multicrystal silicon).
•
Ribbon silicon.
•
Amorphous silicon (abbreviated as "aSi," also known as thin film silicon).
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Single-crystal silicon
Most photovoltaic cells are single-crystal types. To make them, silicon is purified, melted, and
crystallized into ingots. The ingots are sliced into thin wafers to make individual cells. The cells
have a uniform color, usually blue or black
Polycrystalline silicon
Polycrystalline cells are manufactured and operate in a similar manner. The difference is that a
lower cost silicon is used. This usually results in slightly lower efficiency, but polycrystalline
cell manufacturers assert that the cost benefits outweigh the efficiency losses. The surface of
polycrystalline cells has a random pattern of crystal borders instead of the solid color of single
crystal cells.
Ribbon silicon
Ribbon-type photovoltaic cells are made by growing a ribbon from the molten silicon instead of
an ingot. These cells operate the same as single and polycrystalline cells.
The anti-reflective coating used on most ribbon silicon cells gives them a prismatic rainbow
appearance.
Amorphous or thin film silicon
The previous three types of silicon used for photovoltaic cells have a distinct crystal structure.
Amorphous silicon has no such structure. Amorphous silicon is sometimes abbreviated "aSi"
and is also called thin film silicon.
Amorphous silicon units are made by depositing very thin layers of vaporized silicon in a
vacuum onto a support of glass, plastic, or metal.
Since they can be made in sizes up to several square yards, they are made up in long rectangular
"strip cells." These are connected in series to make up "modules.
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2.3 Structure of the solar cell
In conventional solar cells, the electrical field is created at the junction between two regions of
crystalline semiconductor having contrasting types of conductivity (Figure 3). If the
semiconductor is silicon, one of these regions (the n-type) [6] is doped with phosphorus, which
has five valence electrons (one more than silicon). This region (the p-type) is doped with boron,
having three valence electrons (one less than silicon). Here the concentration of holes is greater.
The large difference in concentrations from one region to the other causes a permanent electric
field directed from the n-type region towards the p-type region. This is the field responsible for
separating the additional electrons and holes produced when light shines on the cell.
Figure 3: The p-n junction (from Duffie [6]).
Nearly all cells currently available have a p-n junction of this type. In silicon cells (the most
common type of cell) the junction is obtained by diffusing a layer of phosphorus into a wafer of
silicon previously doped with boron. The junction is very shallow, typically only about 0,2 to 0,5
m deep. This layer is called the emitter. The electrical contact with the illuminated side of the
cell (the side where the diffusion occurs) has to leave most of the surface uncovered, otherwise
light cannot enter the cell. However, the electrical resistance of the contact must not be too high.
Furthermore, the electrical contact on the dark side of the cell covers the whole surface of the
cell.
The processes going on inside the cell can be described as follows:
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•
Photons that reach the interior of the cell and have energy equal to or greater than the
band-gap are absorbed in the bulk of the semiconductor, generating electron-hole pairs
that can function as carriers of current.
•
The electric field, or potential difference, produced by the p-n junction is responsible for
separating the carriers before they have a chance to recombine. The result is a potential
difference and current in the external circuit including the load.
•
The presence of a potential difference produces the phenomena of injection and
recombination of electron-hole pairs. In the solar cells these amount to losses. The extent
of the losses depends on this potential difference.
Major parts of a PV
1. PV panel
The voltage and the power of PV cells are very small in order to supply a device. For this reason,
many cells are combined together in a PV panel with common electrical output.
One of the main features of the panel is the peak power. The peak power is the power from the
photovoltaic when the solar irradiance is 1000 W in every square meter, when the temperature is
25 ƒ C. it is obvious that the power from the panel depends on the area of the panel, the type and
its operation temperature. The maximum power is given from the manufacturer.
The operating voltage is another important characteristic of the panel. Most photovoltaics today
are constructed in a way that they produce power higher than 12 V in order to charge the 12 V
batteries. Apart from the voltage, the operating current is another parameter. It is the current
which is determined from the maximum power from the panel and the voltage created, when the
irradiance is equal to 1000W/m2. For a panel with peak power equal to 40 W and operating
voltage 17 V, the operating current would be equal to:
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40 W/ 17 V=2,3A
For bigger PV systems, panels with operating voltages equal to 24 V or even 48 V are used.
The short circuits current (Isc) as well as the open circuit voltage (Voc) are other important
parameters. The short circuit current is the current from the PV when it is connected with a cable
of minimum resistance. The open circuit voltage is the voltage of the PV when it is measured by
a cable with infinite resistance. Both of the above are two of the main parameters of the PV cell.
In every curve, represented in the diagram, there is a point where the voltage and the current
have such values that the electrical power (P=VxI) has the maximum value. It is obvious that for
that particular point, the rectangle that is created has the maximum area of all possible ones
created. That point is called point of maximum power and the following formula can be written:
Pmax=ImaxxVmax
where: Pmax is the maximum power
Imax is the maximum current
Vmax is the maximum voltage
When R (resistance) is equal to zero or infinity, the electrical power is zero, since in the first
case the voltage is zero, and in the second the current reaches zero. In intermediate cases, the
electrical power is gaining values which are represented in figure below:
Figure 4: Power as a function of voltage (from T.E.I Han [17])
Therefore for given solar irradiances, the biggest power the PV can provide depends on the
appropriate choice of the system’s resistance. The above holds for constant irradiance and
temperatures.
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For different irradiances, a group of transposed curves is created. This represented n the figure
below:
Figure 5: Current vs. voltage (from T.E.I Han [17])
2. Voltage regulator or controller
This device controls the current flux from the PV to the batteries. When the battery is fully
charged, the voltage regulator decreases the current not to overcharge the battery. When the
battery is overcharged, the operational life is decreased.
3. Battery
The electrical energy is stored to the batteries in order to be provided in intervals with minimum
solar irradiance (during nights, cloudy days). Generally the batteries used for PV systems are the
same as the ones used in cars. The most common type is the battery with lead electrodes (poles)
in a sulphuric acid solution. This type is the most economic viable for PV systems. In cases were
there is large temperature variations, alkaline Ni-Cd (nickel-cadmium) batteries are used.
Every battery has various characteristics which should be taken into consideration before
connecting it to a PV system:
•
Total capacity: it represents the total load, in Ah, stored in the battery
•
The battery voltage: it depends on the type of the electrolyte as well as the number of the
elements
•
The discharge depth: it is the level of discharge that the battery can reach daily, in order
to be maintained in good condition and retain the normal operational life.
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•
The cost per KWh: in order to calculate the total electrical energy that the battery will
provide during it’s life cycle, the useful capacity Cx , the voltage V and the total number
of charge-discharge (N) should be used in the following formula:
Etot= Cx xVxN
When the cost of the battery is divided with Etot, the cost for every KWh is found. It is obvious
that this cost should be kept low.
•
Operating temperature: the capacity of the battery is decreasing with decreasing
temperatures. Many manufactures provide, among other specifications, the correction
curve of the battery. An example is given below:
Figure 6: Capacity vs. temperature (from T.E.I Han [17])
From the figure above, it can be seen that for discharge rate of C/5, and minimum temperature 0
°C, the corrected capacity is 73 Ah. Rate of discharge of C/5 means that the battery can provide
20 A and has capacity of 100 Ah.
•
Operational life of the battery: the operational life of the battery depends on many factors
such as the rate of charging and discharging, the number of charges, and the extreme
operating temperatures. In a PV system, a common lead battery has an operational life no
more than 5-6 years. On the other hand, nickel-cadmium batteries last longer when they
are operating in similar conditions.
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4.Load
The term load indicates the total number of electrical appliances that they will be operated with
the electrical energy provided by the PV. For a PV system to be well designed, the electrical
energy that these appliances consume in a time interval of one month, should be equal or less to
the energy produced by the system in the same time interval. For every electrical appliance,
various parameters should be known before connecting them the PV system:
•
The type of the operational current: It could be either direct or alternate. In the second
case, the frequency should de known as well.
•
The value of the operational voltage
•
The power dissipated during its operation.
The PV systems and the battery, provide direct current. In order to minimize losses from the
conversion from D.C. to A.C., appliances which operate with D.C. would be preferable.
Nevertheless, due to the use of the A.C. from the power stations most of the appliances work in
that type of current.
4.Inverter
This device converts D.C to A.C. in order for many devices to operate. One type of an inverter is
the centrifigular one. At this type, the D.C. current rotates a motor which provide power to a
A.C. generator. This type of inverter is rare today, since there are types with no moving parts.
The efficiency of the later is higher and their maintenance small.
Depending on the type of the photovoltaic, there is the appropriate inverter. A stand-alone PV is
connected to a converter which operates with the electrical energy from the PV and converts
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D.C. to A.C. In the case where the PV is connected to the grid a converter is connected which
operates with the energy from the grid and again transforms D.C. to A.C.
The table below represents the various costs associated to a complete PV system.
COST FACTOR
CONTRIBUTION
TO THE TOTAL
COST
PV panels
65%
PV panel support and cabling of the PV elements
5%
Batteries
15%
Voltage, power controllers arrangement and protection control
12%
Auxiliary generator
3%
Table 1. Example of various costs of a stand-alone PV system
As said before, the main parameters which characterize the photovoltaic cell are: the open circuit
voltage (Voc), the short circuit current (Isc), the voltage at maximum power point (Vmax) and
the current at maximum power point (Imax). Furthermore, another important parameter is the
Fill Factor (FF) which is also a measure of the quality of the silicon cells conversion ability. All
the above are described below:
Isc
Maximum power point
Isc(max)
Vo
Voc (max)
Figure 7: Characteristics of a PV module
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The Fill Factor [7] is an important parameter and can be described as follows:
)) =
9 PD[∗ ,PD[
9RF∗ ,VF
The Fill Factor varies little among devices and takes values in the range of 0,7 to 0,8 for many
crystalline semiconductor cells (Si, GaAs, InP).
Figure 8: Fill Factor (from T.E.I Han [17])
The energy-conversion efficiency of a solar cell is defined as the ratio between the maximum
electrical power that can be delivered to the load and the power input. Therefore:
η=
90 ∗ , 0 )) ∗92& ∗ , 6&
=
3LQSXW
3LQSXW
This efficiency and the maximum power output are obtained only if the resistance of the load
has the right value of VM/IM.
The power absorbed by the collector is given by:
4S = *$τ Fα S
where:
Qp= absorbed power (W)
G= total irradiance (W/m2)
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A= area of solar collector (m2)
τc= transmission factor of cover
αp= absorptance factor of collector plate
The power loss from the collector is given by:
4/ = 8$7F − 7D where:
QL= power loss from the collector (W)
U= collector U value (W/m2K)
Tc= temperature of collector plate (K)
Ta= ambient air temperature (K)
The useful power supplied by a solar collector (Qs) can be derived from the above equations
which forms the basis of the Hotter-Whiller equation:
4V = 4S − 4/
4V = *$τ Fα S − >8$7F − 7D @
In the case of the PV module the above equation becomes:
4V = *$τ Fα S − >8$7F − 7D @ − *$ε (
where:
εE: efficiency of electrical conversion
The factors affecting the performance as well as the Fill Factor are:
•
Cell operating temperatures
•
Atmospheric conditions
•
Band gap of semiconductor
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•
Solar intensity
•
Cell materials
The cell operating temperature and the cell conversion efficiency has an inverse linear
relationship. As the cell temperature increases, the efficiency decreases. This can typically
result in an efficiency drop of 0,5% per °C increase in cell operating temperature. As the cell
heats up, its bandgap decreases, allowing more electrons to jump into the conduction band.
This provides a small increase in Isc. However, the increased temperature also means increased
kinetic energy on a molecular level. The influence of the electric field at the p-n junction is
reduced for the faster-moving electrons, allowing them to recombine more easily with holes.
This reduces Voc considerably.
Figure 9: Current as a function of voltage for various temperatures
(from Tripanagnostopoulos [9])
As the Voc decreases over the increase of Isc, a rise in the cell temperature decreases the
power of the PV panel. This is illustrated above.
As mentioned before, the atmospheric conditions affect the FF as well as the efficiency. This
refers to the condition of the environment where the PV is used. Dust on the panel as well
pollution from cars affect the cell performance of the module.
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The bandgap of the semiconductor affects the FF and efficiency. Band gap is the energy
difference between the valence and conduction bands in a semiconductor. Each band gap
responds best to a particular spectral distribution, so the cell cover is manufactured to ensure
that the favored light reaches the cell.
The solar intensity is another very important parameter. The intensity varies with different
locations around the earth. Normally, the PV panel will operate more efficient with higher
solar intensities.
Finally another important parameter is the material used. Single-crystal silicon has been the
material of choice for high-performance, highly reliable solar cells since the successful
deployment of silicon photovoltaic systems for space power. Most of the terrestrial
photovoltaic power systems sold today are also crystalline silicon. The need to lower the cost
of terrestrial photovoltaic power has focused research efforts on alternative materials as well as
on less expensive means of producing solar-grade silicon.
Crystalline silicon is made by growing large cylindrical single crystals, called boules. The
boules are sliced into thin wafers, from which photovoltaic devices are made. Slicing is an
expensive and material-wasteful process. Several approaches have been investigated to
minimize the cost of the original silicon material and to eliminate the slicing step.
A less expensive material, polycrystalline silicon, bypasses the expensive and energy-intensive
crystal growth process. The molten silicon is instead cast directly into either cylindrical or
rectangular ingots. The polycrystalline material has a large number of crystallites separated by
grain boundaries [19]. The material has poorer crystalline quality, and light-induced electronhole pairs can recombine at the grain boundaries without producing current in the external
circuit. Although polycrystalline materials result in less efficient solar cells than crystalline
silicon, they are sufficiently cheaper that they are commercially viable. The cast material must
still be sliced, however, leading to a loss of about half of the material. Improvements in sawing
techniques such as multiple-wire saws continue to reduce the loss in producing thinner wafers.
The lowest-cost approach would be to minimize the required amount of semiconductor
material. Thin films have been developed that are only a few micrometers thick. Such films are
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produced by a number of vapor-deposition approaches carried out with in-line, highly
automated systems. The techniques are adaptable to a number of semiconductor materials that
are optimized for solar cell operation. It has been shown that silicon, with its bandgap of 1.12
eV, I s not optimal. Materials with bandgaps nearer to 1.5 eV, such as GaAs and CdTe, have
higher theoretical efficiencies. Thin films are cheaper than crystalline structures but typically
have lower efficiencies. Ultimately, however, thin films will be necessary for producing lowcost electricity, because the bottom line-the cost per watt-is more important than efficiency.
2.4 Panel position
The position of the photovoltaic panel is very important to its effective function. In order for
the PV to produce the maximum amount of energy, it should intercept the highest possible
flux. This occurs when the panel is perpendicular to the sun’s incoming rays.
Summer solstice
Solar cell module/Panel
tilted to angle of latitude
Vernal and autumnal equinoxes
Winter solstice
23,5°
Latitude
,
Figure 10: Sun’s position at local noon on a fixed south-facing surface at
various times of year
The above figure shows the position of the sun at solar noon relative to a PV panel oriented to
the South and tilted at the latitude angle. The maximum variation of the sun’s angle in this case
is ± 23,5°. The reason many designers select the latitude angle is to get the most energy for the
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Technology review
whole year from the fixed flat-plate arrays. As indicated by Figure 2.4, the average position of
the sun angle relative to the plane of the panel occurs at the two equinoxes. The optimum tilt
angle is site-dependent and calculation of this angle requires a solar irradiance prediction
computer programme. There is a common agreement that for the higher latitudes the optimum
tilt angle is usually 10 to 15° lower than the latitude angle. [21] Hence, a general rule of thumb
for the tilt angle of PV panels is to choose an angle which is zero to 15° lower than the site
latitude angle.
2.5 Heat transfer
Photovoltaic panels absorb energy and convert it to electricity. Not all this energy is converted
to electricity since the panels are not 100% efficient. Most of this energy is converted to heat.
This heat can be transferred away by conduction, convection and radiation.
2.5.1 Conduction
Conduction [8] is the transfer of heat from one part of a substance to another part of the same
substance, or form one substance to another in physical contact with it. In the case of the PV
panel, energy is absorbed by the silicon cell and heat is conducted to the back and front of the
panel via the intervening layers. Fourier’s law for steady state, one-dimensional applications
states that:
4 = − λ$
GW
G[
where:
Q is the heat flow
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Technology review
is the thermal conductivity of the material
A the area of the section at right angles
dt/dx the change of temperature with respect to the length of the path of the heat flow.
For a single plane slab of thickness L, the equation becomes:
4 = − λ$
7 − 7 /
and for a composite slab consisting of two materials is:
4= $
7 − 7 / /
+
. .
This is the equation used in the case of the PV panels. Furthermore, after the heat has reached
the surface, it is transferred to the surroundings by a mixture of convection and radiation.
2.5.2 Convection
Convection is the transfer of heat within a fluid by mixing of one portion of the fluid with
another. The movement of the fluid may be caused by differences in density resulting from the
temperature differences as in natural convection (or free convection), or the motion can be
produced by mechanical means as in forced convection.
Convective heat transfer is described using correlations between certain dimensionless
parameters. Such parameters are the Nusselt, Reynolds and Prandtl numbers. These parameters
are used in order to determine the value of h for each case:
4 = K$7V − 7I Newton’s Law of cooling is then used in order to calculate the convective heat transfer.
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Technology review
2.5.3 Radiation
Radiation is the means of heat transfer between distant surfaces. Energy is carried by
electromagnetic waves.
The equation below is used in this case:
4=
σ$7 + 7 ε − + ε − − where 1 is the Stefan-Boltzman constant
A the area of the surface
T1, 2 are the surface temperatures
01, 2 are the surface emissivities
2.6 The stack effect
An important part of the theory of the photovoltaic panels is the phenomenon called stack
effect. This phenomenon causes the air to be driven up the duct by the buoyancy of the warmth
of the inside air relative to that outside. It is a very important parameter in determining the
efficiency of a naturally ventilated system.
The pressure difference Ps is given by:
3V =
J3D
>7F − − 7K − @K − K 5D
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Technology review
where: Pa is the atmospheric pressure
Ra is the air constant
Th,c are the temperatures at heights h2,1
g the acceleration due to gravity
in a stack effect the flow rate of the air is determined by that pressure difference. By looking at
the equation, if the temperature or the height is increased, the flow rate will be increased. This
flow rate is determined by the general equation:
4D = F 3V Q
where c, n constants
2.7 Cooling medium
The cooling fluid passing through the tubes of the heat exchanger should have the properties
below:
•
high thermal transmittance for a given speed of the fluid and for given tube diameters
•
high heat capacity in order not to provide increased flow
•
small viscosity in order to provide small amounts of energy for it’s transport
•
it should not be oxidised in order to avoid rustiness inside the tubes
•
non toxic
•
non erosive-corrosive
•
it’s steam pressure should be as low as possible in order to use in lower pressures
•
inexpensive
Water
The thermo physical properties of water establish it as a good cooling medium. The coefficient
of thermal transmittance between metal and fluid is very good and can be improved under
boiling. Nevertheless, its use under liquid form in high temperatures involves higher pressures.
For this reason it cannot be used in temperatures higher than 320 ° C (150 bar) [16]. Another
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Technology review
disadvantage is that it provides oxidation. Finally, in freezing point, it can produce damages to
the system.
Oils
There are various types of oils, synthetic or mineral, that can be used as cooling mediums.
These products can cover a wide area of temperatures, even more than 400 ° C. Their thermal
capacity is not as good as the capacity of water, but they can be used under low-pressure
conditions. Their viscosity is a function of temperature and for this reason liquids which are
used in high temperatures, cannot be circulated in low temperatures. Due to the fact that they
are flammable, they should not come in contact with air.
Special liquids
The use of mixture of salts is done in higher temperatures (500° C-600° C) because below the
melting point (140° C) for the mixture NO3K, NO2Na, NO3Na (53%, 40%, 7 %) the mixture
is solidifying. Mercury can also be used in the temperature range between 360 and 540 ° C but
it is toxic and very expensive.
Gases
They can be used in very high temperatures between 500° C-1000° C for air under pressure. A
major disadvantage is that they have small heat capacities and the energy needed for their
circulation is high. Therefore it is needed a special design for the whole configuration.
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Technology review
As mentioned before at the introduction of the project, two ways of cooling the photovoltaic
module will be presented and discussed. The first one is a steady state simulation of a PV/T air
heating collector and the second one is a water cooled PV/T. Various results will be explained
and the main similarities and differences discussed. Finally, by comparison of the results, the
most efficient way of cooling the panels will be presented. This comparison is obtained from
the literature review.
Between the two systems discussed above, the project is more concentrated on the water
cooled PV which is the main topic of discussion-analysis. This system provides a wide area of
analysis and simulation. It can be combined in such a way in order to provide extra heat to a
house as well as electricity. It can work on higher efficiencies and can operate as a hybrid
system. Furthermore, the analysis is done in order to see the feasibility of such a system and
what factors affect its efficiency and operation. The above reasons justify the option selected.
Apart from the actual developed systems discussed above, the general theory behind them will
be discussed for a better understanding of the systems.
2.8 Air cooled photovoltaic panel
One way of cooling the photovoltaic unit is by using air. Of course in this particular case air is
used to absorb the heat from the unit and consequently to cool it. The heat absorbed by the air
can be used for providing warm air inside the building.
G
hg-a
Tg
Transparent cover
hp-g
hs-g
Ts
Tp
Ti
Solar cell
hp-f
Absorber plate
To
hb-f
Rear plate
Insulation
Tb
Ub
Figure 11: Schematic configuration of a conventional PV/T air heating collector
along with the associated energy transfer mechanism
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Technology review
The above figure shows the PV configuration along with associated flows for a PV/T air
heating system. This PV system includes the transparent cover, a metallic black absorbing
surface and a well-insulated rear plate. The latter has a gap between the absorber so air is able
to pass through. In the actual model, the solar cells are pasted 1 m wide on the absorber plate at
equal distances along the surface.
There are various assumptions taken into consideration:
•
Steady-state energy transfer
•
Temperatures of various components vary along the direction of the flow only
•
The heat capacity of the transparent is neglected (very small)
•
There is no leakage of air from the system
•
Side losses are negligible
Theory
(The nomenclature for the theory below can be found in Appendix 1)
In order to calculate the heat removed as well as the coefficients we must introduce the
following formulae:
for the transparent cover:
D * + KS − J 7S − 7J + KV− J 7V − 7J = KJ − D 7J − 7D (a)
for solar cell:
D * = KV − S 7V − 7J + KV − J 7V − 7J + ( 7V where
(b)
( 7V = − D D Vη V $5*
for the absorber plate:
D * + KV− S 7V − 7S = KS − J 7S − 7J + KS −E 7S − 7E + KS − I 7S − 7I for rear plate:
27
(c)
Technology review
KS −E 7S − 7E = KE − I 7E − 7I + 8E 7E − 7D (d)
and for working fluid (which is air):
•
P& I G7I
= KS − I 7S − 7I + KE − I 7E − 7D %
G[
(e)
The fraction of energy absorbed by different components of the system is defined as:
D = − 5J D J
D = − 5J − D J D V
D = − 5J − D J − D V − $5 D S
where AR is the ratio of collector area to the area covered by solar cells.
Solving equations (a)-(d) for the temperature of the transparent cover, solar cell, absorber plate
and rear plate and substituting these values into equation (e), the following linear differential
equation is obtained:
G7I [
G[
+ S7I [ = T
At this point we have to solve the above for the fluid (air) temperature. In order to do that we
will use the initial boundary condition:
7I [ = 7L DW [ = we can obtain:
7I [ =
T
T
+ 7L − H − S[
S
S
The fluid temperature can be averaged over collector length and can be calculate as:
−
7
I
=1/Lœ7f(x)dx
substituting we have:
−
7
I
=1/L
œ
7I [ =
Solving the above integral:
28
T
T
+ 7L − H − S[
S
S
Technology review
−
T
T
7 = S + S/ 7 − S − H
L
− SO
Now, applying the boundary condition
7I [ = 7 DW [ = /
we can calculate the outlet temperature as follows :
7 =
T
T
+ 7L − H − SO
S
S
Various performance parameters
The thermal efficiency can be calculated by:
QW =
while the solar cell efficiency:
P& I 7R − 7L *
QV = Q I > − β U 7V − 7U @
where
β U = 7V − 7U The electrical efficiency:
QH = QV $5 − 5J − 5J − D J − D J and the system efficiency:
Q7 = QW + QH
A simulation model
The above is the general theory used in order to perform various calculations for a simulation
model. The model below discussed is done by Garg and Adhikari [5].
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Technology review
Figure 12: Testing curves of PV/T air heating collectors (from Garg [9])
Figure 12 represents the thermal efficiencies curves for fixed duct depth, collector length, mass
flow rate and different solar densities 0 and 10 *10m2, corresponding to the absorber with and
without selective coating. The two different values of the solar density represent the absorber
without solar cells (conventional air heater) and the absorber fully covered with solar cells
respectively. As it can be seen from the figure, the thermal efficiency of the system is higher
when the absorber is not fully covered with solar cells.
Figure 13: Solar cell efficiency (from Garg [9])
As it can be seen from the figure above, the solar cell efficiency calculated and plotted,
decreases as the temperature of the panel increases. Keeping in mind the theory presented in
the previous chapters, this phenomenon was expected.
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Technology review
Figure 14: Thermal efficiency as a function of duct depth (from Garg [9])
The above figure represents how the thermal efficiency of the system changes with the increase
in duct depth. The depth was varied from 0,01 m to 0,1 m. Apart from the duct depth, the
length was also varied. The maximum efficiency was 67,5 % for duct depth equal to 0,01 m
and length of 8m. The minimum efficiency was 57% for duct depth equal to 0,1 m and length
2m. Therefore the thermal efficiency of the system drops with increasing duct depth.
Nevertheless when the length is decreased the efficiency is also decreased. These
characteristics can be attributed to the decreasing absorber to air heat transfer coefficients.
Therefore the system efficiency, which is a sum of thermal and electrical efficiencies, also
decreases with increase in duct depth and decrease in collector length.
Figure 15: Solar cell efficiency and system efficiency as a function of duct depth (from
Garg [9])
The above statement is graphically represented by Figure 15. The left one represents the solar
cell efficiency and the right one the system efficiency.
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Technology review
Figure 16: Thermal efficiency (from Garg [9])
Figure 16 represents the variation of performance parameter as a function of duct depth and
cell density. The thermal efficiency is observed to be decreasing with increase in duct depth
and cell density.
Figure 17: System efficiency and solar cell efficiency as a function of duct depth and
number of solar cells (from Garg [9])
However solar cell efficiencies are observed to be almost equal. This is due to the fact that the
conversion of transmitted solar irradiance into electrical energy is more and more as cell
density increases by reducing the thermal energy fraction. Increasing cell density results in
very large values of electrical efficiency and therefore the system efficiency observed to
increase with cell density, although thermal efficiency is lower for a larger value of cell
density.
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Technology review
Figure 18: Thermal efficiency as a function of number of solar cells and
collector length (from Garg [9])
The above figure represents graphically how the thermal efficiency of the system is altered
with changes in collector length as well as the number of cells. The thermal efficiency is
increasing with the increase of the length, and decrease with the increase of number of cells.
Figure 19: System efficiency and solar cell efficiency as a function of number of solar cells
and collector length (from Garg [9])
The system efficiency is increased with collector length increases, as well as with increases in
the number of solar cells. The solar cell efficiency however has not been changed greatly. The
collector length seems to be a more important parameter in this case.
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Technology review
Figure 20: Thermal efficiency as a function of mass flow rate and duct depth, collector
length respectively (from Garg [9])
As it can be seen from the above figures, the thermal efficiency drops with increased duct
depth but is increased with increased flow rates. On the other hand, the efficiency is increased
with increased length and increased flow rates. The impact the thermal efficiency has on the
system efficiency for both cases, is represented in the figure below.
Figure 21: System efficiency as a function of mass flow rate and duct depth, collector
length respectively (from Garg [9])
The system efficiency in both cases follows the behaviour of the thermal efficiency presented
above. It decreases on the left diagram and increases on the right.
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Technology review
2.9 Water cooled photovoltaic panel
As said before, instead of air as the coolant of the panel, water can be used in order to absorb
more heat and to cool the panel more effectively. This system which is using a fluid as the
coolant, is called hybrid. It transforms the sun’s radiation to electrical energy and
simultaneously absorbs the heat from the panel. By this way, the panel is working in lower
temperatures (higher efficiency), and the heat produced can be used for covering a part of
thermal requirements of a building, for example preheating the water used for hot water
applications.
Figure 22: Hybrid system
As it can be seen from the figure, the hybrid system is constructed by a PV panel “A”, a heat
exchanger “B” consisting of pipes “C” with fins “D” in contact with the backside of the
module, ant thermal insulation around and back of the heat exchanger. The fluid “F” passes
inside the pipes of the heat exchanger. The whole configuration can include a system which
can monitor and control the inlet temperature of the water.
The cold water can be stored in a tank which is connected to a pump in order to circulate the
water around the panel. Another tank is used in order to store the warm water leaving the heat
exchanger. Cold water is entering the first tank by the supply network. Considering the fact
that the water is continuously entering from the supply network, the temperature of the first
tank is kept at low levels for better PV cooling.
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Technology review
Various performance parameters-theory
Again the theory of calculating various parameters is the same as in the case of the air-cooled
panel.
A simulation model
As an example of such a hybrid system, the experiment done by Trypanagnostopoulos [9] was
used. The PV model used was a pc-Si panel with an absorber surface area of 0,4 m2. The
maximum PV temperature values without water circulation were measured in the range of
40°C to 70°C, depending on the incident solar radiation, ambient temperature and wind
velocity.
Figure 23: Experimental results of electrical and thermal efficiency
The above graph presents the electrical efficiency of the module for solar radiation intensity I
of about 900 W/m2 as well as the thermal efficiency of the system. As it can be seen from the
graph on the left, for once more the electrical efficiency drops rapidly when the temperature is
increased. At the temperature range of 30°C the electrical efficiency ne equals to 13% while at
60 ne drops to 9,5%.
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Technology review
Furthermore, the right graph presents the thermal efficiency of the heat exchanger. In this
case, the water circulation through the PV heat exchanger can extract heat with thermal
efficiency of 55%. ∆Τ/Ι represents (Ti-Ta)/I where Ti, Ta are the input water temperature and
the ambient temperature respectively.
Once again, the effect of temperature on the efficiency was the declining of the latter. It is
clearly obvious the necessity of operating the whole system at lower temperatures. This, in
combination with the fact that the thermal efficiency reaches the value of 55%, shows that the
presence of the heat exchanger is beneficial to the system. In order to prove that
experimentally, the following graph is presented:
Figure 24: Variation of temperatures, solar radiation and electrical efficiencies
The results presented in the above graph were taken during the experiment done in the time
8:00 to 17:00 for a typical daily operation of a simple PV module and the module with the heat
exchanger. Where
I
: the incoming solar radiation intensity
TPV1
: the operating temperature of the PV1 (with heat exchanger)
TPV2
: the operating temperature of the PV1
Ta
: the ambient temperature
Tw
: the water temperature of the tank T1
ne, 1
: the electrical efficiency of PV1
ne, 2
: the electrical efficiency of PV2
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Technology review
As it can bee seen from the graph, the operating temperature of the system including the
cooling system (PV1) is lower than the temperature of PV2. At the region with the highest
incoming solar radiation intensity, that is between 11:00 and 14:00, the difference between
these temperatures is approximately 20°C. Considering the effect of high temperatures to the
system this is a very big value. Consequently the electrical efficiency of the PV1 is higher than
PV2. The efficiency of PV1 is 15% higher.
In order to determine the time interval on the limited effective operation of the system without
water circulations, various experiments were carried out [9]. These tests without continuous
water circulation were performed in several time intervals. Temperature data from
photovoltaics PV1 and PV2 were recorded in order to remark and estimate this cooling
procedure. These tests showed that a cold water circulation for 5 minutes through the heat
exchanger of PV1 with flow rate of 60 lt/h, can be considered sufficient to operate the nest 5
minutes without water circulation keeping the PV1 mean temperature under 35°C (for
I=900W/m2. Ta=20°C and Tw=20°C). For lower water flow rate or longer time than 5 minutes
without water circulation, PV1 mean operating temperature increases and the electrical
efficiency gain decreases. The above can be used in order to optimise the best effective
operation of the hybrid system, reducing the working time of the pump circulating the water.
As said before the water leaving the heat exchanger has gained heat from the PV module. This
water can be stored in well-insulated tanks for use in hot water applications. The water
produced cannot cover the needs for hot water for the whole building but it can be used for
preheating applications.
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Technology review
Applications of hybrid systems
As said before the hybrid systems can produce electrical energy as well as thermal energy for
application in a building. It is very important during the installation of such systems to keep
certain distances in-between the modules in order to avoid shading of the PV. The latter can
decrease the efficiency of the modules.
Dmin
Figure 25: PV panel position
Figure 25 shows an example of the minimum distance between the modules in order to avoid
shading. The distance in-between can be used if the hybrid systems are combined with diffuse
reflectors installed at the bottom of the panels in order to increase the electrical as well as the
thermal efficiency.
2.10 Comparison of the two systems
In the last two paragraphs two PV systems were described. The first one was the air cooled PV
module and the second the water-cooled PV module. During this part, the two systems will be
compared in order to see which one is the most promising.
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Technology review
As said before the air-cooled panel uses the air in order to cool the panel. Natural ventilation of
air passing through the gaps of the system absorbs the heat from the panel. It has been recorded
tat the overall efficiency of the system is higher than the efficiency of a PV module with no
ventilation at all. As it can bee seen from Figure 13 for a mass flow rate of air 100Kg/h m2 and
irradiance of 900W/m2 the efficiency of the panel has a maximum value of 8,4 % when the
temperature was 67°C which was the minimum temperature value. The temperature range was
from 67°C to 98°C where the efficiency was 7%.
On the other hand the water-cooled PV uses water as the coolant medium. It was operating in
the range of 25°C to 30°C. Comparing these temperatures it is obvious that the PV/W is
operating in lower temperatures. Consequently the overall efficiency of the system was higher.
The maximum value of the efficiency was 12,5 % at 27°C. Therefore the difference between
these systems is about 4,1 % in solar cell efficiency.
Furthermore, the main advantage of the water-cooled system is that the heat absorbed can be
used for various applications. This system can produce electricity at higher efficiencies than
the PV/T (air cooled) but simultaneously can use the absorbed heat to warm the water for
preheating applications.
It should be said here that the air-cooled PV system is less efficient than the water one, but the
cost of the former is lower. The heat exchanger used by the PV/W, the water tanks used as well
as the whole tube configuration can result in an expensive system. Furthermore, proper
insulation must be used which can be proved costly. If a choice between these two systems
should be done, an economic analysis should be performed in order to calculate the payback
period for both systems. This analysis is beyond the scope of the project and it is suggested as
future work.
Concluding, the water-cooled photovoltaic proved to be more efficient than the air-cooled PV.
Nevertheless, the latter proved to be more efficient than a normal operating photovoltaic
module.
40
Model of a Water Cooled PV panel
3. Developing a Model of a Water Cooled PV panel
As said before in previous chapters, a spreadsheet was developed in order to investigate how
various parameters affect the overall efficiency of the system. The whole spreadsheet was
based on the water-cooled PV panel which is the most promising one. At this part of the
project various graphs of the spreadsheet are presented and discussed. Nevertheless, the whole
theory behind the calculations should first be presented.
The general configuration of the water-cooled system follows the one presented in Figure 22 in
previous chapters.
Figure 26: The PV/W model
For the figure above:
C is the cover of the system
S is the solar panel
A is the absorber
/
is the thickness of the absorber
D diameter of tube
W distance of two tubes
F fluid passing through tubes
B is the heat exchanger
T represents each tube
Model of a Water Cooled PV panel
Between the heat exchanger’s tubes there is the absorber with thickness δ. Furthermore this
water cooled PV has a cover on top of the solar cell in order to be more realistic. Each of the
above components is characterized by various importance parameters. These are the
absorbance α(λ), emissivity ε(λ), reflectivity ρ( λ) and transmittance τ(λ). These generally
obey ρ(λ)+α(λ)+τ(λ)=1 and α(λ)= ε(λ). As described in the general theory of PV, energy can
be exchanged by conduction, convection and radiation. The conductive and convective terms
are linear in the temperature difference. They are characterized by the generalized
conductances Uxy between the components x and y. For example, USA is the conductance
between the solar cell and the absorber while UAa is the sum of edge and bottom losses due to
conductance and convection.
Energy conservation in steady state for the area above the tubes gives [8]:
for the fluid:
T'− + 8 )D 7 − 7D = 8 $) 7$ − 7 for the absorber:
B
8 $) 7$ − 7 + 8 $D 7$ − 7D + ^ ε $ α $` σ 7$ = 86$ 76 − 7$ + ^ ε Vα $` 56 + ^ ε Fτ Vα $` σ7F + ^ τ Fτ Vα $` ( + T I '−
and for the solar cell:
B
376 + 86$ 7V − 7$ + 86& 76 − 7& + ^ ε 6 α 6 ` 56 = ^ τ &α 6 ` ( + ^ ε &α 6 ` σ7& + ^ ε $α 6 ` σ7$ where
q
is the heat per length in the fluid direction y
D
is the diameter of one tube
σ
is the Stefan’s Boltzmann’s constant
P(Ts) is the electric power per area that can be drawn from the solar cell,
the total irradiance E.
qf
is the heat per length that it is bought to the tube from the fin
Rs
is the radiation from the solar cell
under
Model of a Water Cooled PV panel
The above formulae contain terms in curly braces. These terms represent geometric series due
to multiple reflections and transmissions [5]. The table below lists the most important ones.
B
^ ε $ α $` = ε $ −
^ ε $D V ` = ε $D V α $ ρ V − ρ V ρ F + τ V ρ F
− ρ V ρ F − ρ V ρ $ − τ V ρ $ρ F
− ρ VρF + τ V ρF
− ρ V ρ F − ρ V ρ $ − τ V ρ $ρ F
^ τ Fτ V D $` = τ Fτ V D $ ^τ F D V` = τ F D V − ρ V ρ F − ρ V ρ $ − τ V ρ $ρ F
− ρ Vρ $ + τ V ρ $
− ρ V ρ F − ρ V ρ $ − τ V ρ $ρ F
For reasons of simplicity some approximations have been made in the balance equations:
1. the heat transport normal to the collector plane is independent of the heat transport
in the plane
2. all material properties are presumed to be independent of temperature and equal on
both sides
3. the components are further through to be thin enough to allow for neglecting
temperature gradients through them
4. the ambient temperature is taken to be equal on all sides of the collector
5. all radiation in and out of the fluid is neglected
Furthermore, the calculations followed in the spreadsheet are complicated and in order to
simplify them the term UFa(T-Ta) is neglected supposing that the fluid is properly isolated from
the ambiance. The Rs terms can also be neglected because the solar cell radiation is small. An
effective heat conductivity USa is further introduced instead of USC and the radiative cover
effects are included in this term.
In order to find the transport of heat qf from the fin to the tube, an infinitesimal segment with
width ∆x is considered. The energy balance equation for this segment is:
Model of a Water Cooled PV panel
B
8$D 7$I − 7$∆[ + ^ε $ α $`σ7$I ∆[ = 86$7V − 7$I ∆[ + ^τ Fτ Vα $` (∆[ −κδ
G7$I
G[
+κδ
[
G7$I
G[
[+G[
where TAf is the x-dependent temperature of the absorber on the fin , k is the thermal
conductivity and δ is the thickness of the absorbing fin. The solar cell temperature may be
found from the balance equation (3). This yields the differential equation:
Nδ
G 7$I
G[
= 8 $D
′ 7$I − 7D + )5σ7$I − 6
where the following notation has been used:
8 $D
′ = 8 $D +
8 6$ 8 6D − F( 8 6$ + 8 6D − F(
B
B
8 6$^ ε $α 6 `
)5 = ^ ε $ α $` −
8 + 8 − F(
6$
6 = ^ ε $α $` −
6D
8 6$ ^ τ Fα 6 ` − η (
8 6$ + 8 6D − F(
where
U’Aa
is the loss factor from the absorber when the loss through the solar cells is
accounted
for
FR
is the radiation loss factor
S
is the part of the insolation that is useful for the absorber
Due to the radiation term the differential equation has no analytical solution and an
approximation should be done. Around TAf=Ta the right hand side is almost linear in (TAf -Ta),
and a Taylor expansion is quite accurate:
κδ
G 7$I
G[
≈ )5σ7D − 6 + 8 $D
′′ 7D 7$I − 7D Model of a Water Cooled PV panel
the modified loss factor is :
8 $D
′′ 7D = 8 $D
′ + )5σ7 D
which also accounts for radiation losses. In combination with the boundary conditions:
G7$I
=
G[
[= 7$I : − ' = 7$
where W is the width of one unit ,this gives:
FRVKω[
6 − )5σ7D
6 − )5σ7D
7$I [ = 7D +
− 7$ +
− 7$ FRVKω : − '
8 $D
8 $D
′′ 7D ′′ 7D ω = 8 $D
′′ 7D κδ −
where :
The heat brought to the tube from the two half fins is thus
T ) = −κδ
G7$I
G[
=
: − ' ) I 6 − )5σ7D − 8 $D
′′ 7D 7$ − 7D [ = : − '
where the fin factor Ff is defined as:
)I =
WDQKω : − ' ω : − ' The fin factor is a measure on how effectively the heat is transported from the fin to the tube
via the absorber.
Having found the heat from the two half fins, it is straightforward to solve the balance
equations (1)-(4) to find the following expression for the generalised heat:
T 7 = :) 7> V − )5 7σ7 − 8 / 7 − 7D @
the collector efficiency factor F(T) is given by:
Model of a Water Cooled PV panel
'
:− '
+
)I :
'
) 7 =
:− '
+ 8 / +
) I + )5σ7 8 $)
'
the effective radiation loss factor as
: − ' 7D
)I +
'
7 )
)5 7 =
5
:− '
+
)I '
and the total conductive loss factor as :
8/ =
:− '
) I 8 $D
′′ 7D '
:− '
+
)I '
8 $D
′ +
In order for the performance of the absorbed to be maximized, the efficiency factor should be
as close to unity as possible, whereas the total conductive loss factor and the effective radiation
loss factor should be as low as possible.
The rate of heat that it is drawn from the system is
47 P& S 7/ − 7L where the outlet temperature TL is the fluid temperature at y=L. the thermal efficiency, most
conveniently defined as the ratio of the generated heat to the incoming insolation, is given by:
Q$ =
P& S
T 7D T ′7D /
47
7D − 7L −
− H[S
=
T ′7D (/: (/:
P&
S
where
T ′7D =
GT
G7 7 = 7D
which is the differentiated heat. After calculations the differentiated heat was found to be:
T′7D =:)′7D 6−:σ>)′7D )57D 7D + )7D )5′7D 7D +)7D )57D [email protected]−:8/ 7D −7D )′7D Model of a Water Cooled PV panel
In order to find the above, we have to find the differentiated collector efficiency factor F´(Ta)
as well as the differentiated effective radiation loss factor. After some relatively complex
calculations:
)5σ7D
'
:− '
+
) I :
'
8 $)
) ′7D = −
:− '
8 / +
) I + )5σ7D
'
+>
@
8 $)
)5′ 7D =
:− '
−
) I 7D '
:− '
+
)I
'
− )5
Now the equation (4) can be solved. All the above were used in order to construct the
spreadsheet in the Excel package and it is presented in the Appendix [2].
Parametric Analysis of the Water Cooled Panel
4. Parametric analysis of the Water Cooled Panel
The parametric analysis of the water cooled photovoltaic is performed in order to determine the
most important parameters which affect the operation of the PV panel. These parameters can
either be the physical properties of the heat exchanger connected to the panel as well as the
flow of water inside the tubes. After determining these factors and their importance on the
efficiency of the system, the latter can be maximized. The information gained by the analysis
can be used in order to maximize the efficiency of any collector design which is the main aim
of the project. All the graphs presented below are related to the model presented to the previous
chapter.
A said before the basic spreadsheet is presented in Appendix [2]. The upper part of the sheet
contains the numbers which are constants. These values were found by a review of relevant
literature (Sizmann 1991, Lampert 1987,Bogaerts 1983). The lower one contains the functions
used to find the thermal efficiency.
The first graph was constructed by using the following data: W held constant and equal to
0,01m, D= 0,01, Ti=280 K, m=0,0003 kg/s. The other parameters were taken as follows:
{τcαs }=0,7 {εAαΑ }=0,1 {τcτsαΑ }=0,15 {εΑαs}=0,05 , E= 800W/m2, n0=0,125 , c=5*10-4,
Ta=293K, UAa=1W/m2 K-1, UAF=200 W/m2K-1, USA=100W/m2K-1, USa= 6 W/m2K-1, k=385
W/mk ( for copper),Cp=4200J/KgK (water), δ=5*10-4 m ,L=1 m.
48
Parametric Analysis of the Water Cooled Panel
7KHUPDOHIILFLHQF\YV:'IRUP .JV
Q$
:'
Figure 27: The thermal efficiency as a function of WD-1
The thermal efficiency of the system is plotted in the above figure. The dependence W/D (with
W constant) is plotted in order to show how the relative size of the fin influences the
performance. D was changed from 0,01 m to 0,1 m. As it can be seen, the thermal efficiency of
the system drops from 63,77% at W/D 1,25 to 56,19 % at W/D equal to 10. This efficiency
reduction is due to the conduction and radiation losses from the fin, because the latter is at
higher temperatures. The mass flow rate of water in this case was equal to 0,0003Kg/s. This
value is slightly increased when the tube diameter is decreased, but this effect is small enough
not to alter the efficiency greatly.
49
Parametric Analysis of the Water Cooled Panel
7KHUPDOHIILFLHQF\YV:'IRUP .JV
Q$
:'
Figure 28: The thermal efficiency as a function of WD-1 (m=0,001kg/s)
The above graph represents the thermal efficiency with respect to W/D when the flow rate of
water is increased from 0,0003 kg/s to 0,001 kg/s. The effect of such a big increase in m on the
efficiency, is a small increase of the latter. In this case the highest value of nA was 64,19%
while the smallest value was 49,23%. It obvious that the flow rate of water doesn’t play a very
important role on the system’s thermal efficiency. To illustrate this better, the following figure
is presented.
7KHUPDOHIILFLHQF\YV:'
Q$
P P :'
Figure 29: Thermal efficiency as a function of W/D
50
Parametric Analysis of the Water Cooled Panel
The figure above represents the thermal efficiency of the system when W/D is varied for
m=0,0003 kg/s and m=0,001 kg/s. as it can clearly be seen, the two graphs are almost identical.
A small increase of the efficiency can be shown when m is larger and W/D reaches 1. As
mentioned earlier, despite that the flow rate has been increased greatly, the efficiency didn’t.
Another very important parameter of the system apart from the tube diameter and the flow rate
is the inlet temperature of the water entering the heat exchanger.
Q$
7KHUPDOHIILFLHQF\YV7LQOHW
7L.
Figure 30: Thermal efficiency as a function of the inlet temperature
The inlet temperature of the water to the heat exchanger varied from 280 K to 320 K in order to
see how the thermal efficiency is altered. As it was expected the efficiency dropped with
increasing temperature. The interesting point is that the variations in temperature change were
large, nevertheless the efficiency decreased slightly.
Keeping in mind that PV panels transform the sun’s energy to electricity it can be said that one
fundamental parameter is the solar irradiance E. This parameter plays a very important role on
the whole system’s efficiency. In order to investigate on the above, the solar irradiance E was
varied, and various values of the thermal efficiency were recorded. The results of this
spreadsheet are presented in the graph which follows. It should be said here that the designer
has not control over this parameter. Nevertheless, for a better understanding of PV systems the
thermal efficiency of the system as a function of the irradiance is presented.
51
Parametric Analysis of the Water Cooled Panel
7KHUPDOHIILFLHQF\YV,UUDGLDQFH
Q$
,UUDGLDQFH(:P
Figure 31: Thermal efficiency as a function of the irradiance
The irradiance was changed from 600 W/m2 up to 1400W/m2 which is considered to be two
extreme values. Nevertheless the importance of E on the PV panel is well illustrated above. At
600 W/m2 the efficiency was 48,25% while on 1400 it was 50,66%. The difference between
these values is 2,41% which is considered to be high. The above graph represents a
phenomenon which was totally expected from the start of the project. Nevertheless it makes
clear how the efficiency is dependent on the solar irradiance.
Once again another parameter of the system was changed in order to gain some results on the
efficiency. This time the length was changed. The length of the absorber was changed and
various values of the efficiency were recorded. The minimum length was 1 m while the
maximum value was 2.1 m. consequently the efficiency dropped from 49,19% to 49,12%. It is
clear therefore the fact that the thermal efficiency of the system is not highly dependent on the
fin size. If the fin size is doubled, the thermal efficiency of the PV only increases by 0,06 %.
52
Parametric Analysis of the Water Cooled Panel
7KHUPDOHILLFLQHF\YV$PELHQWWHPSHUDWXUH
QD
7HPSHUDWXUH.
Figure 32: Thermal efficiency as a function of ambient temperature
The above graph represents the thermal efficiency of the cell with respect to the ambient
temperature. The efficiency drops when the ambient temperature increases. The maximum
value of the efficiency was 49 % at 293 K and the minimum was 48% at 307 K. Therefore, for
a change of 14ºC the efficiency drops about 1%.
It should be made clear at this point that the above spreadsheet was developed in order to
investigate how various parameters of the PV/W affect the thermal efficiency of the system.
This efficiency is completely different with the electrical efficiency of the panel as well as the
overall one. The relationship between them has been investigated in previous chapters.
Furthermore, the graphs presented in the technology review show how the electrical and cell
efficiency are varied when the thermal efficiency is altered.
53
Quantification
5. Quantification
In this part of the project, the quantification of the photovoltaic module is presented in
order to see how much energy the module can produce. The characteristics of the
photovoltaic are presented below. The data set used was chosen for a typical PV
system at STC.
The module’s characteristics at Standard Test Conditions are:
Tmodule= 25°C
G=1000W/m2
Voc=14,6V
Vmax=12,6A
Isc=4,9A
Imax=4,1 A
Using the above data, firstly the fill factor can be calculated. The formula used is
presented in the theory of the project and is:
9PD[ , PD[
9RF , VF
=
= )) =
As said before, the Fill Factor is an indication of the quality of the silicon (0,72 is
considered to be good).
The electrical power generated from the module is to be calculated next. The module
is considered to have a drop off due to temperature =0,22 W/°C and it is consisted of
2500 modules. In order to calculate the power generated, the data below will be used.
54
Quantification
time
9:00-10:00
10:00-11:00
11:00-12:00
12:00-13:00
13:00-14:00
14:00-15:00
15:00-16:00
16:00-17:00
Gb
50
300
710
880
720
410
250
30
Gd G(Sum) Tmod(k)
180
230
295
150
450
311
130
840
341
110
990
359
130
850
343
150
560
327
170
420
311
190
220
303
Table.2
Gb and Gd are the beam solar irradiance and the diffuse solar irradiance respectively.
The total irradiance incidental on a surface is
Gsum= Gb+ Gd
Tmod is the temperature of the module at that particular time interval.
The power drop off due to temperature was described in previous chapters. In this
case this value is 0,22 W/°C. This has to be converted to %/°C. So:
6R 3PD[ = 9PD[ , PD[
= = DQG
=
= &
3PD[ This is the power drop off expressed in %/°C. Now using
3R S = 3PD[
55
*
Quantification
and table 2, the table below can be constructed:
time
9:00-10:00
10:00-11:00
11:00-12:00
12:00-13:00
13:00-14:00
14:00-15:00
15:00-16:00
Po/p
11,88
23,25
43,39
51,14
43,91
28,93
21,70
Table.3
It can be seen from the table that the highest power output occurs between 12:00 and
13:00 where there is the highest irradiance. Now using Table 3 and
3WHPS = 3R S > − 3GURSRII 7FHOO − @
the nest table is constructed:
time
9:00-10:00
10:00-11:00
11:00-12:00
12:00-13:00
13:00-14:00
14:00-15:00
15:00-16:00
16:00-17:00
Ptemp
12,03
21,96
35,46
37,88
35,51
25,36
20,50
11,12
Table.4
Table 4 represents the power from the system for every hour, including the power
drop of due to temperature effects. Now in order to calculate the total power delivered
form the system the following formulae will be used: Pdel=Ptemp*No
56
Quantification
where N o is the number of modules. The power delivered is then:
time
9:00-10:00
10:00-11:00
11:00-12:00
12:00-13:00
13:00-14:00
14:00-15:00
15:00-16:00
16:00-17:00
Pdel
30083,23
54906,51
88660,18
94711,18
88782,55
63410,07
51246,07
27809,22
Table 5.
It can be seen from table 5 that the maximum power delivered by the module occurs
during 12:00 to 13:00. In order to calculate the effectiveness of the module the
formula below is used
HIIHFWLYHQHVV =
3WHPS
3PD[
in combination with Table 4 :
time
effectiveness
9:00-10:00
10:00-11:00
11:00-12:00
12:00-13:00
13:00-14:00
14:00-15:00
15:00-16:00
16:00-17:00
0,233
0,425
0,686
0,733
0,687
0,491
0,397
0,215
Table 6
Again the maximum effectiveness is during the same time interval. The above table is
graphically presented by figure 34 below.
57
Quantification
(IIHFWLYHQHVVYV7LPH
(IIHFWLYHQHVV
7LPH
Figure 33: Effectiveness as a function of time
The effectiveness of the panel is gaining it’s maximum value at the time 12:00 to
13:00. After that it starts declining again until it reaches almost the initial minimum
value.
As said in the start of the quantification analysis, the PV module had a power drop off
due to temperature equal to 0,22W/°C. The power associated with these losses is
Ptemp and it is represented at the figure 35 below. Po/p is the power of the system if
the temperature of the module did not affect the performance. It can bee seen that the
bigger difference is during periods with high solar irradiance and consequently high
operating temperatures. At the start of the operation of the PV the two power outputs
are almost the same, and it is the same case at the end of the operation. During these
time intervals the operating temperature of the module is not high.
The case where the operating temperature does not affect the performance is achieved
when a water PV panel is used. It should be said that again in this case, high
58
Quantification
temperatures affect the performance of the system but the water is cooling the panel
providing minimized temperatures.
3RSDQG3WHPSYVWLPH
3RZHU
3RS
3WHPS
7LPH
Figure 34: Po/p and Ptemp as a function of time
59
Example of a PV system in a Greek house
6. Example of a PV system in a Greek house
This system can either be a simple or a more complex one. As said before in previous
chapters of the project, there are various configurations of photovoltaic systems.
Before analyzing the one for the house, a general description is performed.
The simplest type of the PV is the one that it is consisted from the panels which
provide energy directly to the house without storing energy or regulating the voltage.
This system can provide energy only when there is illumination to the panels.
A more complex system is the one that comprises a battery for the storage of the
energy from the PV. In this case the energy is provided to the various devices and the
remaining is stored in the battery. This system is described below:
Figure 35: A stand alone PV comprising an accumulator, [17]
The size of the panels should be the appropriate not to overcharge the batteries. A
regular examination of the battery should be performed otherwise the service life
can be minimized. For better operation of the whole system, a voltage regulator is
used. This device regulates the voltage between the panels and the batteries. The
regulator is needed in a PV system which is not regularly monitored. Such systems
are being used in remote areas but also in houses where the monitoring of the
operation of the battery is difficult.
60
Example of a PV system in a Greek house
As said before in the theory chapter, in the case where alternate current is used, the
D.C to A.C. converter is being used. This device is putted between the battery and
the devices of the house. If there is a device working in D.C. the battery is
supplying energy directly.
Figure 36: Figure of a stand alone PV comprising an accumulator and converter.
The battery is supplying energy directly to the D.C. devices, [17]
If the power needed to supply the house is very large, the PV and the stored energy
could be insufficient to meet the demand in the house. In these cases, like a cloudy
period with no sunshine or an unexpected fault in the system, an auxiliary diesel
generator and a battery power supply is used. This system is described below:
61
Example of a PV system in a Greek house
Figure 37: Stand alone PV with auxiliary generator and charging power supply,
The auxiliary generator is a way of coping with large unexpected demands. By this way
there is no need of using other PV panels which would be useful only in extreme cases
of low solar irradiance. It should be said here that the generator is an auxiliary device of
the PV system and it is used rarely to charge the batteries. Most, or usually all the
energy needed is provided form the PV panels. Only in the case where the needed
power exceeds 1 KW the auxiliary generator is used.
When a stand alone PV is to be installed, the use of electrical appliances that produce
heat should be minimized because such devices produce high demand for electrical
energy. The electrical devices connected to the PV should be of high efficiency. If there
are old appliances should be replaced by new, more technologically advanced, which
offer the same or better results.
In general the dissipation of the electrical energy should be minimized in order not to
use the auxiliary generator which uses gas and needs maintenance. Furthermore, such a
device produces noise and cannot store the energy produced by the PV. Therefore,
before installing a PV to a house, careful and precise calculations should be performed,
which is not the case for a PV connected to the grid. The latter can be manufactured to
62
Example of a PV system in a Greek house
provide higher amounts of energy than the amount needed for the house, since the rest
of the energy can be provided to the grid.
Concluding, the stand alone PV should produce energy such as firstly to meet the
demand in the house while the rest to be provided to the batteries for use during nights.
Design for usual consumption
A usual consumption for a residential installation can be taken as 7 KW per day during
winter and summer and lower during autumn and fall.
Device
Power
Operation
time
Electrical
consumption
Lights
:
3,0 h
3,0 KWh
Refrigerator
0,3 KW
9,0 h
2,7 KWh
Television
0,2 KW
4,0 h
0,8 KWh
Hoover
0,6 KW
0,5 h
0,3 KWh
Hair drier
0,4 KW
0,5 h
0,2 KWh
Toaster
1,25KW
0,2 h
0,3 KWh
Washing machine
3,25KW
0,2 h
0,7 KWh
Total
7 KW
8,0 KWh
Table 7.Daily electrical consumption of various devices in a house
It is obvious that if the PV system is installed to meet the demand for winter where the
sunshine could be limited, it will certainly meet the demand for other seasons. It is
supposed at this point that a converter with efficiency of 90% will be installed with
losses to the cables of around 5%. The energy that should reach the entrance of the
converter is:
E=7000Wh / 0,85 per day
E= 8235 Wh per day
63
Example of a PV system in a Greek house
Therefore the energy at the converter’s exit will be 7000Wh. If the panels are orientated
due 3+15° (for Greece 3=38°) [17],where 3 is the latitude, then the maximum power
from the panels will be :
8235Wh/day / 3,5 H/day = 2353 W
PANEL ORIENTATION: -+15°
3$1(/25,(17$7,21--15
HOURLY CONSUMPTION / DAY
HOURLY CONSUMPTION / DAY
WINTER
AUTUMN
SUMMER
FALL
3,5
5,0
5,5
4,5
WINTER
AUTUMN
SUMMER
FALL
3,0
6,0
7,5
4,5
Table 8.
HOURLY CONSUMPTION / DAY
WINTER
AUTUMN
SUMMER
FALL
3,0
6,0
7,5
4,5
Table 9.
If the converter used is operating with entrance voltage of 48 V (D.C.) the current from
the panels will be:
Current=Voltage /Power
Current= 2353W / 48V= 49 A
If the panels used have the following characteristics:
Voltage equal to 12 V and current 2,3 A, under solar irradiance of 1000W/m2 then it
is obvious that every row of panels should be consisted of 4 panels in order to provide
4 x 12 V =48V in total.
64
Example of a PV system in a Greek house
The number of rows that will be connected in parallel is defined by the current provided
by each row and the total current which should be produced by the panels in order to
meet the demand.
No of rows = 49A/2,3 A / row = 21,3 rows
Therefore:
4 x 22= 88 panels
these panels will produce electrical energy per day:
22 x 48V x 2,3A x 3,5h= 8500,8 Wh
The energy produced exceeds the value of 8235 Wh which is needed for the house per
day.
The ampere hours produced by the system under 48 V are:
22 x 2,3A x 3,5h= 177,1 Ah
which are more than
7000Wh / 145 Ah = 48 V
that the house is needed per day. For the prediction of the number of batteries which
will be needed in order to store the energy, the number of days with no sunshine should
be taken into consideration. For these days, electrical energy should be stored in order
to be provided to the system. With the storage of energy for 3 cloudy days the use of
the generator can be totally avoided.
In order to have sufficient energy for the house, the batteries used should have enough
energy stored for 7 days without sunshine [17] . As said before the daily energy
production from the PV is 8500,8 Wh. Therefore :
8500,8Wh / 48 = 177,1 Ah
in order to meet the demand ,the amount of stored energy in the batteries should be:
177,1Ah x 3 = 531,3 Ah
and for 7 days:
177,1 Ah x 7 =1239,7 Ah
65
Example of a PV system in a Greek house
It is supposed at this point that the battery used has the following characteristics:
voltage equal to 12 V, capacity equal to 140 Ah with safe level of discharge of 80%
.That means that the useful capacity is 140 Ah x 0,8=112 Ah and that is the load of the
battery every time is discharged.
Since the system’s voltage is 48V, the batteries should be connected in rows, parallel to
each other and every row to be consisted of 4 batteries. Therefore:
4 x 12 V= 48 V
For 7 days of storage the number of rows needed is
1239,7 Ah / 112 Ah/row = 11,1 rows.
11 rows of batteries consist 11 x 4 =44 batteries can store energy for 7 days with no
sunshine. It is left to see if such a system can meet the demand for 7 days in the
production of kilowatts-hours.
As seen before, the electrical energy needed by the system is
8235Wh x 7= 57645 Wh
Every row of batteries with level of discharge of 80%can give
48V x 112Ah = 537 Wh
For 11 rows:
537Wh x 11 = 59136 Wh which can meet the 57645Wh demand for the week
At the system described above, the generator wasn’t used at all. In the case where the
cloudy days were much more than 7, the stored energy in the batteries wouldn’t be
sufficient to meet the demand. Under these conditions the use of the generator would be
essential in order to provide energy to the house.
In order to find the area of the panels that would be used for the example described
above, the following procedure should be done. The electrical energy produced by a PV
system is:
E=G * * A
where G is the solar irradiance, is the efficiency , G is the solar irradiance and A the
total area needed. [17]
therefore for the example above : A=E/(G*) m2
66
Example of a PV system in a Greek house
Keeping in mind the values from table 7 and in the case where the efficiency of the
panels about 12% placed at an angle of 45° for January, it holds:
A=8(KWh/d) / {3,32(KWh/m2d)*0,12}=20,08 m2
In order to have a more realistic model in the analysis, it is assumed that the electrical
losses of the system (accumulators, converters), is about 30 % of the energy produced.
Therefore, the coefficient of performance of the system from the exit of the PV panel,
to the end of the system (inside the house) is 0,7
So the area is 20,08/0,7=28,68 m2
That is the total area of the PV needed to supply electrical energy to the house.
The hybrid PV model
The above analysis was for a conventional PV system. In the case where a hybrid
system was installed, apart from the electrical energy produced, the thermal energy
produced could be used as well.
As seen form previous chapters, the hybrid PV system can produce electrical energy as
well as thermal energy which is used to warm the cooling medium. The example above
shows how a PV system can meet the daily demand for electrical energy for a house. So
the hybrid model can be considered as two different mechanisms. One that provide
electrical energy described and analyzed above, and another that produce heat,
therefore thermal energy.
As said before, there are various cooling mediums which can be used. In the case where
water is used, the thermal energy can be used as follows. Water is passing through the
tubes of the heat exchanger connected to the PV panel (described in chapter 4). The
heat from the panel is absorbed by the tubes and the water is warmed up. In order to
have warm water inside the house, usually a boiler is used. This device uses electrical
energy or gas in order to warm up the water for hot water applications.
The tubes from the heat exchanger can be connected to that boiler providing the tank
with preheated water. For example, instead of warming the water from 15° C, which is
67
Example of a PV system in a Greek house
the normal temperature for water, the boiler will start warming the water from 30 ° C to
its final temperature. By this way, energy will be saved. The heat recovered from water
is not sufficient to warm completely the water for direct use in the house. Nevertheless
it can be used as preheated water inside the boiler’s tank.
If other cooling mediums are used, such as oils, their use inside the house is becoming
more complex. They cannot be used for the hot water applications and they cannot be
used inside the boiler. The heat gained by the panel is not sufficient for other uses. For
example the hot fluid could be circulated inside the radiators providing heat to small
rooms in the house. In the hybrid system, the thermal energy is small for this kind of
application.
68
Discussion
7. Discussion
7.1 General about the project
Once the project begun it was rapidly realized that the topic area was interesting but
the work done on it was scarce. The main theory of photovoltaics as well as the
general history about them could be easily found in books but modern air-cooled and
especially water-cooled PV panel theory was very difficult to find. Various
publications and periodicals were found which provided precious help.
7.2 Technology review
During this part of the project two photovoltaic panels were described and compared.
The theory presented was identical for both cases and various graphs were given. The
two models were constructed by different authors each one trying to achieve different
goals. That was the main problem in directly comparing them. Nevertheless, a decent
comparison between them was made, with valuable conclusions.
The air cooled model proved to be simpler in operation than the PV/W. The air
passing through the panel does provide cooling of the system improving the
efficiency. The hot air from the panel could be used as a warm air inside the building
providing heat. This phenomenon was not described fully because it was beyond the
scope of the analysis. The overall performance proved to be less efficient than the
water-cooled PV, but it should be kept in mind that the whole cost of the system is
smaller than the cost of the latter.
On the other hand, PV/W proved to be more efficient in operation than the PV/T.
Furthermore, the useful heat produced could be used for preheating the water inside
the building. The cost however of such a system is higher than PV/T and should be
analyzed as well.
69
Discussion
The cost analysis and payback period methods were not performed in this work since
they are beyond the scope of the project. Nevertheless if a conclusion is to be made on
which system is the most favorable, the above should be done. By this way, not the
most efficient but the most economic system, which will provide cheaper electricity,
will be revealed.
7.3 The model of the water cooled PV
This model was done in order to see how various physical parameters could change
the performance of the system. Since the water PV was the main interest, it was
chosen for the simulation. It should be said here that the theory behind the spreadsheet
was difficult and various complex calculations were made. Furthermore, various
parameters were very difficult to find in bibliography and precious time was spent on
it. All the above made the spreadsheet, a time consuming task. On a more positive
note, the above simulation proved that various physical parameters have an impact on
the performance of the system.
7.4 Quantification analysis
This analysis was done in order to see what is the maximum power that a PV can
provide and compare it with the PV/W. The general theory of photovoltaic was used
in combination with an Excel spreadsheet. The analysis provided some values on
power output and showed for once more that the water PV could provide higher
power.
70
Discussion
7.5 Example of a PV system in a Greek house
At this part of the thesis an example of a stand alone photovoltaic system installed in a
Greek house was presented. This analysis was done in order to see various parameters
of such a system in a real life scenario. The total energy produced was calculated and
an analysis was performed to see if it can meet the total energy demand.
The number of PV panels as well as the area needed in order to operate was also
calculated. For the days with no sunshine, the use of an auxiliary generator and
various batteries were also discussed. Finally, it was discussed whether the thermal
energy produced by the photovoltaic can be used for application inside the house.
Depending on the cooling medium used, the heat gained can become useful or not.
71
Conclusions
8. Conclusions
From the work done and presented the main conclusions drawn are:
•
An increase in the operating temperature of the panel affects the solar cell
efficiency of the system. This conclusion was expected from the literature
research of the project. Nevertheless the detailed effect of the temperature was
presented and discussed.
•
The water cooled photovoltaic panel is more efficiently cooled than a thermal
photovoltaic panel, and the thermal efficiency of the former is higher
•
An increase in the duct depth of the system has as a result the minimization of
the thermal efficiency.
•
The physical properties of the heat exchanger in the water cooled photovoltaic
can alter greatly the efficiency of the system. Using the spreadsheet developed,
various physical parameters of the system were tested in order to see the effect
on the efficiency of the PV. In more detail, the width and the length of the
tubes are very important parameters. Altering them has as a result a different
value of thermal efficiency. The water flow rate is also another parameter
which was analyzed. The results showed that increasing the flow rate, the
efficiency is also increased. All the above, which are fully described in the
results section, can be used from a designer for optimal use of a PV.
•
Apart from the properties of the heat exchanger, the inlet water temperature as
well as the ambient temperature plays an important role on the system’s
operation. As it was diagrammatically shown in the parametric analysis
chapter, when the water inlet temperature is small the thermal efficiency is
high. Consequently, when the inlet temperature of the coolant gets higher, the
efficiency drops. A similar result stands for the ambient temperature case.
72
Conclusions
•
The power gained from a conventional system is less than the one from a
cooled panel (either thermal or water cooled).
•
The section “Example of a PV in a Greek house” provided important
theoretical and design information about a stand alone photovoltaic system.
The analysis showed that a conventional PV system can provide electrical
energy to a usual house and meet the daily demand. Various other parameters
such as the area needed by the panels and the number of batteries used for
energy storage were calculated and proved that such a system can be installed.
The results of this section showed that, for the proposed PV system, the
autonomy of it in terms of sunshine is 7 days. After that time interval, the
auxiliary generator could be used. The use of such a generator as well as its
electrical consumption was not calculated since it was beyond the scope of the
analysis. Finally, the hybrid model could provide apart from electrical energy,
thermal energy to the house.
In summary:
In summary it could be said that the water-cooled photovoltaic has a good potential in
providing electricity as well as warm water for preheating applications. Water as a
coolant medium is extracting heat more efficiently than air. Nevertheless, the whole
configuration is more complex and the cost of such a system can be very large. The
comparison between the two systems showed an advantage of the PV/W over the
PV/T in areas such as thermal, electrical and cell efficiency. Despite that, the quality
of the products has not been investigated and a comparison between these systems in
that area would be very interesting.
Furthermore, the hybrid PV/W system is greatly dependent on the properties of the
heat exchanger. It was proved that every change in the latter has an influence on the
system’s efficiency. Apart from the physical properties such as the tube diameter and
length, the water flow rate and the temperature are also very important. The designer
of such a system should take into consideration all the above in order to develop the
optimal system.
73
Recommendations for future work
9. Recommendations for future work
•
Cost analysis and payback period method for both systems in order to see
which one is more preferable
•
Investigation in the quality of the electricity and heat produced by both
systems
•
Implementation of both systems in real life conditions and monitoring of their
performance
•
Large scale experiments, as well as experiments in a more controlled
environment to determine which of the many physical processes involved has
the greatest influence on the optimization of the systems
•
In the PV/W case, is alternative coolant than water can be used and what are
the results of such a change?
•
Determination of the impact of the stack effect on the system
•
Demand-side studies on the buildings for which water cooled photovoltaics
are proposed.
74
Appendices
10. Appendices
Appendix 1:
area m2
duct dept, m
duct width, m
specific heat, J/kg°C
electrical energy produced by solar cell,W
solar iradiance,W/m2
heat transfer coefficient,W/m2°C
collector length,m
mass flow rate kg/h m2
cell density, per m
coefficients of linear differential equations for fluid temperature
reflectivity
temperature
heat loss coefficient W/m2°C
A
D
B
C
E
G
h
L
m
N
p,q
R
T
U
Appendix 2:
Cp
D
E
F
Ff
FR
k
L
m
q
qf
Rs
S
T
Ta
TA
TAf
Tc
Ti
TL
Ts
Nomenclature for simulation model 1
Nomenclature for spreadsheet
heat capacity for the fluid (J kg-1K-1)
diameter of one tube (m)
irradiance (Wm-2)
collector efficiency factor
fin factor
radiation loss factor
thermal conductivity (Wm-1K-1)
length of the absorber (m)
mass transport (kg s-1)
heat per length in the fluid direction (Wm-1)
heat per length brought to the tube from the fin (Wm-1)
radiation from the solar cell (W m-2)
the part of the insolation that is useful for the absorber
temperature of the fluid (K)
temperature of the ambience (K)
temperature of the absorber (K)
temperature of the absorber on the fin (K)
temperature of the cover (K)
inlet fluid temperature (K)
outlet fluid temperature (K)
temperature of the solar cell (K)
75
Appendices
UMN
U´Aa
UL
W
/
0M
nA
!
1
2
generalized conductance between components M and N (Wm-2K-1)
modified loss factor (Wm-2K-1)
total conductive loss factor (Wm-2K-1)
width of one unit (m)
thickness of the absorbing fin (m)
emmisivity of component M
thermal conversion efficiency
reflectance of component M
Stefan-Boltzmann’s constant (5,67 x 10-8Wm-2K-4)
transmittance of component Greek letters
α
ε
η
absorptivity, fraction of energy absorbed
emissivity
efficiency
Subscripts
a
b
f
g
g1
g2
i
o
p
r
s
ambient
rear plate
working fluid (air)
transparent cover
upper transparent cover
lower transparent cover
inlet
outlet
absorber plate
reference
solar cell
76
Appendices
Appendix 2:
w/d
The excel spreadsheet
10
5
3
3
2
2
1
(W-D)/D
9,00E+00
4,00E+00
2,33E+00
1,50E+00
1,00E+00
6,67E-01
4,29E-01
W
1,00E-01
1,00E-01
1,00E-01
1,00E-01
1,00E-01
1,00E-01
1,00E-01
D
1,00E-02
2,00E-02
3,00E-02
4,00E-02
5,00E-02
6,00E-02
7,00E-02
Ti
2,80E+02
2,80E+02
2,80E+02
2,80E+02
2,80E+02
2,80E+02
2,80E+02
m
3,00E-04
3,00E-04
3,00E-04
3,00E-04
3,00E-04
3,00E-04
3,00E-04
Tcas
7,00E-01
7,00E-01
7,00E-01
7,00E-01
7,00E-01
7,00E-01
7,00E-01
EAaA
1,00E-01
1,00E-01
1,00E-01
1,00E-01
1,00E-01
1,00E-01
1,00E-01
TcTsaA
1,50E-01
1,50E-01
1,50E-01
1,50E-01
1,50E-01
1,50E-01
1,50E-01
Eaas
5,00E-02
5,00E-02
5,00E-02
5,00E-02
5,00E-02
5,00E-02
5,00E-02
E
8,00E+02
8,00E+02
8,00E+02
8,00E+02
8,00E+02
8,00E+02
8,00E+02
n0
1,25E-01
1,25E-01
1,25E-01
1,25E-01
1,25E-01
1,25E-01
1,25E-01
c
5,00E-04
5,00E-04
5,00E-04
5,00E-04
5,00E-04
5,00E-04
5,00E-04
Ta
2,93E+02
2,93E+02
2,93E+02
2,93E+02
2,93E+02
2,93E+02
2,93E+02
UAa
1,00E+00
1,00E+00
1,00E+00
1,00E+00
1,00E+00
1,00E+00
1,00E+00
UAF
2,00E+02
2,00E+02
2,00E+02
2,00E+02
2,00E+02
2,00E+02
2,00E+02
USA
1,00E+02
1,00E+02
1,00E+02
1,00E+02
1,00E+02
1,00E+02
1,00E+02
USa
6,00E+00
6,00E+00
6,00E+00
6,00E+00
6,00E+00
6,00E+00
6,00E+00
k
3,85E+02
3,85E+02
3,85E+02
3,85E+02
3,85E+02
3,85E+02
3,85E+02
Cp
4,20E+03
4,20E+03
4,20E+03
4,20E+03
4,20E+03
4,20E+03
4,20E+03
δ
5,00E-04
5,00E-04
5,00E-04
5,00E-04
5,00E-04
5,00E-04
5,00E-04
L
T
Ta
1,00E+00
2,85E+02
2,93E+02
1,00E+00
2,80E+02
2,93E+02
1,00E+00
2,80E+02
2,93E+02
1,00E+00
2,80E+02
2,93E+02
1,00E+00
2,80E+02
2,93E+02
1,00E+00
2,80E+02
2,93E+02
1,00E+00
2,80E+02
2,93E+02
77
Appendices
F(T)
7,40E-01
8,48E-01
8,93E-01
9,19E-01
9,35E-01
9,46E-01
9,54E-01
FR
5,27E-02
5,27E-02
5,27E-02
5,27E-02
5,27E-02
5,27E-02
5,27E-02
S
q(T)
Ff
F(Ta)
FR(T)
UL
σ
U"Aa
U""(Ta)
ω
q(Ta)
F"(T)
FR"(T)
F"(Ta)
FR"(Ta)
FR(Ta)
q"(Ta)
nA
5,56E+02
4,34E+01
9,77E-01
7,40E-01
5,82E-02
6,57E+00
5,60E-08
6,30E+00
6,60E+00
5,86E+00
3,94E+01
-1,28E-05
-6,64E-04
-1,35E-05
-6,45E-04
5,27E-02
-2,96E-03
4,92E-01
5,56E+02
5,25E+01
9,82E-01
8,48E-01
6,10E-02
6,54E+00
5,60E-08
6,30E+00
6,60E+00
5,86E+00
4,50E+01
-1,33E-05
-6,00E-04
-1,46E-05
-5,73E-04
5,27E-02
-5,88E-03
5,62E-01
5,56E+02
5,53E+01
9,86E-01
8,93E-01
6,00E-02
6,51E+00
5,60E-08
6,30E+00
6,60E+00
5,86E+00
4,74E+01
-1,36E-05
-5,24E-04
-1,49E-05
-5,01E-04
5,27E-02
-8,82E-03
5,92E-01
5,56E+02
5,69E+01
9,90E-01
9,19E-01
5,89E-02
6,48E+00
5,60E-08
6,30E+00
6,60E+00
5,86E+00
4,88E+01
-1,37E-05
-4,49E-04
-1,50E-05
-4,30E-04
5,27E-02
-1,18E-02
6,09E-01
5,56E+02
5,79E+01
9,93E-01
9,35E-01
5,79E-02
6,45E+00
5,60E-08
6,30E+00
6,60E+00
5,86E+00
4,97E+01
-1,38E-05
-3,75E-04
-1,51E-05
-3,58E-04
5,27E-02
-1,47E-02
6,20E-01
5,56E+02
5,86E+01
9,95E-01
9,46E-01
5,68E-02
6,42E+00
5,60E-08
6,30E+00
6,60E+00
5,86E+00
5,04E+01
-1,38E-05
-3,00E-04
-1,51E-05
-2,87E-04
5,27E-02
-1,77E-02
6,28E-01
5,56E+02
5,91E+01
9,97E-01
9,54E-01
5,58E-02
6,39E+00
5,60E-08
6,30E+00
6,60E+00
5,86E+00
5,08E+01
-1,38E-05
-2,25E-04
-1,51E-05
-2,15E-04
5,27E-02
-2,06E-02
6,34E-01
nA%
49,19%
56,19%
59,21%
60,92%
62,03%
62,80%
63,36%
78
References
11. References and Bibliography
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2. Florschuetz, L.H., Extension of the Hottel-Whiller bliss model to the analysis
of combined Photovoltaic/Thermal flat plate collectors, ICSE Solar Energy
Meeting, Winnipeg,Canada, 15-20 August 1979
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two-pass PV/T air collector, Proc. SESI, Baroda, 15-18 Dec. 1983, 63-69
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circulation flat plate solar water heater with solar cells, Energy
Convers.Mgmt, 1995, 36(2),87-99
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6. Duffie, JAB , Beckman ,WA, Solar energy thermal processes, Whiley (1974)
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8. Eastop & McConkey, Applied thermodynamics for engineering technologists,
Longman, 1193, 5th edition
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80
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