A Report into the Effects that Orientation and Inclination
have on the Efficiency of Solar Photovoltaic Panels in the
South East of England
Matthew Roberts BSc
06 / Aug / 2012
Word Count: 10,993
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Contents
1.0 Abstract................................................................................................................................................. 4
2.0 Acknowledgements ............................................................................................................................ 4
3.0 Introduction ......................................................................................................................................... 4
3.1 Aims and Objectives ...................................................................................................................... 6
4.0 Methodology ........................................................................................................................................ 7
4.1 Experimental setup to test the effects of varying the angles of inclination and
orientation .............................................................................................................................................. 7
4.2 Calculating the power output of the solar PV array .............................................................. 8
5.0 Results ................................................................................................................................................... 9
5.1 Orientation ...................................................................................................................................... 9
5.2 Inclination ......................................................................................................................................... 9
5.3 Comparison of inclination and orientation............................................................................. 11
5.4 ANOVA Test Results .................................................................................................................. 11
6.0 Discussion ........................................................................................................................................... 12
6.1 Discussion of results .................................................................................................................... 12
6.1.1 Graphical Analysis................................................................................................................. 12
6.1.2 Statistical Analysis ................................................................................................................. 13
6.2 Solar photovoltaic panel efficiencies under test conditions and in the real world ........ 14
6.2.1 Why real world applications rarely reach laboratory based recorded efficiencies
and power output ........................................................................................................................... 15
6.2.2 The effects of shading .......................................................................................................... 17
6.3 Calculating the power from the solar photovoltaic array................................................... 18
6.4 Validation by and comparison of results using two accredited solar energy calculators
................................................................................................................................................................. 22
6.4.1 PVGIS ...................................................................................................................................... 22
6.4.2 Energy Saving Trust .............................................................................................................. 25
6.5 Assumptions made in estimating energy production from solar panels in the report . 29
6.6 Uncertainties and assumptions made by the accredited solar energy calculators ........ 31
6.7 Calculating the optimal orientation and inclination of the solar photovoltaic array ..... 33
6.7.1 Correct Inclination ............................................................................................................... 33
6.7.2 Correct Orientation ............................................................................................................ 37
6.7.3 PVGIS suggested optimal inclination and orientation ................................................... 39
6.8 Shortcomings of and Improvements to the Laboratory based Experiment .................... 41
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7.0 Conclusion .......................................................................................................................................... 42
8.0 Appendix ............................................................................................................................................. 44
8.1 Calculations.................................................................................................................................... 44
8.2 Experiment Results ...................................................................................................................... 45
8.3 Risk Assessment ........................................................................................................................... 46
9.0 References .......................................................................................................................................... 47
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1.0 Abstract
An experiment was conducted into determining the affects that altering the angles of
orientation and inclination had on power output, with the prediction that altering inclination
has a greater effect than altering orientation on power output. Further research was
conducted into the expected energy returns from a 4kWp solar photovoltaic array situated
in the South East of England. Finally, it was suggested that the latitude and longitude could be
used to determine the optimal angles of inclination and orientation. An optimal inclination
was calculated as being 35° and an optimal orientation as being Due South, which could be
calculated using the Latitude and Longitude to a reasonable degree of validity. The solar PV
array was estimated at producing 3719 kWh/year and it was shown that the array could be
orientated ±27.5° away from Due South before the power output dropped below 95% and
the array inclined away from the optimal inclination of 35° by ±13° before the power output
dropped below 95%.
2.0 Acknowledgements
I would like to thank the hard working people of the Abbots Mill Project for their help
3.0 Introduction
The use of solar photovoltaic panels for domestic and commercial energy generation has
seen a recent surge in interest due to government incentives such as the Feed-In-Tariff, a
reduction in material costs and increased levels of efficiency seen under laboratory
conditions. However, the efficiencies which are recorded in the laboratory are rarely seen
in real world situations, and this is due to several reasons. Some aspects, such as
temperature and light dissipation in the atmosphere due to clouds and particulates, are
uncontrollable and vary day to day. Other aspects, such as the orientation and inclination of
the solar photovoltaic panel towards the sun, are controllable, and therefore achieving the
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optimal positioning should produce the highest efficiencies possible in the given conditions
on the day.
The driving factor behind the development of this report is the Abbot’s Mill Project, a
proposed urban hub of environmental and social excellence in the heart of Canterbury,
powered using renewable and sustainable sources, one of which will be a 4 kWp solar
photovoltaic panel array. As a demonstration test bed for cutting edge environmental
science and newly emerging sustainable technologies, it is important for the Abbot’s Mill
Project to utilize the renewable energy devices to their utmost potential, demonstrating to
the public that the technologies work and providing accurate information for those
interested in the technical details. Furthermore, achieving the maximum possible efficiency
of the solar photovoltaic panels will generate more energy, which will in turn produce
greater levels of revenue from the Feed-In-Tariff and help keep costs down.
To generate the optimal amount of power, a solar photovoltaic panel would ideally be
angled directly perpendicular to the sun and thus would track the sun’s trajectory
throughout the day. It is suggested that the angle of inclination plays a greater role than that
of orientation, with a comparatively large range that the solar panel could be orientated at
before any significant drop in efficiency is detected. Due South is considered optimally
orientated, but such is the variance that angling the solar photovoltaic panel to the SouthEast or South-West is not seen as being significantly detrimental to the efficiency. Boyle
(2004). Tracking the suns trajectory throughout the day is an unfeasible option for most
roof mounted solar arrays, mainly due to limited space, greater cost and over shadowing,
despite the fact that the power generated when tracking the sun’s trajectory is increased by
over 30 percent. Rizk and Chaiko (2008). Inclination, as previously mentioned, plays a
greater role than orientation. Previous studies indicate that the solar panels should be
inclined such so that they match the latitude of the position of where they are located,
minus the declination of the sun, which is the angle between the sun and the equator.
Rakovec et al (2011). This still requires some form of vertical plane tracking or year round
manual adjustment, which on roof mounted solar photovoltaic arrays, such as the one which
will be mounted on the Abbots Mill Project; will not be possible. Therefore a fixed position
which produces the optimal power as a yearly average is needed. The Solar Trade
Association (2012) recommends an angle inclination of 30°, which concurs with findings
from The University of Strathclyde (2010), but who go to say that the photovoltaic panels
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should be angled at approximately the same angle of latitude as the location they are
situated at. Another factor which must be taken into account when determining the correct
angle of inclination, is the type of solar radiation which is predominant at the location, as the
sun’s radiation reaches earth in two different forms, direct and diffuse, direct radiation being
that which has reached the earth’s surface directly and diffuse radiation being that which is
diffused in the atmosphere by clouds and particulates and then reflected onto the earth’s
surface. DEFRA (2012). Due to the nature of diffuse radiation and the fact that it is reflected
onto the earth’s surface through a multitude of angles; a solar panel inclined at an acute
angle (relative to the ground) would be able to receive more diffuse radiation than one
placed at an obtuse angle. SEAI (2010). MacKay (2009) suggests that on average the U.K
receives direct solar radiation for only one third of the day between dawn and dusk, and for
the other two thirds of the day, it is diffuse radiation that is predominant. This is especially
noteworthy as diffuse radiation is only one tenth the intensity of direct radiation. Another
consideration which may affect which angle the solar photovoltaic panel is inclined at is
deciding whether to maximise generation at certain times of the year.
3.1 Aims and Objectives
The aim of the project is to identify the optimum orientation and inclination for a solar
photovoltaic panel array in the South East of England and to observe the effects of altering
the orientation and inclination on power output.
The objectives of the project are;
To conduct a laboratory based experiment into the effects of varying the orientation and
inclination of a solar panel, to observe how this effects power output and determine how
precisely a solar panel has to be aligned to still achieve 95% of the optimal power generated.
To acquire the precise latitude and longitude of the Abbot’s Mill Project and use these to
calculate the optimal orientation and inclination, taking into account both direct and indirect
irradiation, estimated sun hours and cloud coverage.
Calculate the likely power output of the array and compare this with two accredited online
solar power calculators and evaluate the findings.
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4.0 Methodology
The calculations that have been conducted within this report are based upon the use of a
precise location so that the maximum efficiency can be achieved for the specific solar panel
array. Additional calculations for other locations were used to compare the optimal angles
and hence draw a conclusion on whether achieving a precise optimal angle provides
noticeable increase in efficiency over that of the suggested thirty six degree inclination and
southerly orientation.
4.1 Experimental setup to test the effects of varying the angles of
inclination and orientation
A laboratory based experiment has been conducted into the effects of adjusting the
orientation of a Solar Photovoltaic Panel in relation to a fixed light source and the impact
this has had on power production.
To first examine how orientation affects the power output, the following experiment has
been carried out.
The experiment has been conducted in a blackout room to eliminate the possibility of light
other than that coming from the 500W bulb affecting the recordings. The 500W bulb was
also switched off after every recording so that the solar panel was not exposed to the heat
given off by the bulb for an extended duration, which will affect the efficiency of the solar
panel.
The solar panel was positioned perpendicular to a 500W bulb, at a distance of 0.4m and
positioned so that it is orientated ‘portrait’, i.e. so that it is taller than it is wider. The solar
panel was then connected to two multi-meters, one to record voltage and the other to
record current, the readings of which were used to calculate power. A variable resistance
box has also been included in the circuit, which was set to match the internal resistance of
the solar panel. The solar panel was then rotated around its central vertical axis point from
0° to 90° at 10° intervals, with 0° representing the solar panel directly facing the 500W
bulb, and 90° representing the solar panel positioned side on to the 500W bulb. At each 10°
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adjustment of the orientation, the current and voltage was measured on the multi-meters
and the power calculated from the two. Power was then plotted against orientation on a
scatter graph.
To examine how inclination will affect power output the same experiment was carried out
but with an alteration to the point of axis on which the solar photovoltaic panel was pivoted
on, and this was changed from vertical to horizontal.
Each of the experiments was repeated three times to ensure validity of the results.
4.2 Calculating the power output of the solar PV array
The third objective to calculate the power produced by the solar photovoltaic array was
achieved by first deciding on a likely peak power for the Abbot’s Mill project solar
photovoltaic array.
The next step referred to the MET Office’s Solar Radiation Map to determine how much
solar irradiation the Abbot’s Mill Project would receive on a horizontal incline. As two
figures are given, one for summer and one for winter, an average of the two was taken.
To determine how much irradiation the solar photovoltaic array would receive and convert
from a horizontal incline to an optimally angled incline, two equations were needed. The
first was to calculate the optimal incline:
βopt = 3.7 + 0.69│Ø│
The second is to transpose the irradiation received on a horizontal incline to the irradiation
received on an optimally angled incline using the figure derived from the first equation for
the optimal angle.
G(βopt) = G(0) / (1 - 4.46X10-4 X βopt - 1.19X10-4 X β²opt)
Once the irradiation captured by the solar photovoltaic array was calculated, the losses
which occur within the whole solar photovoltaic system were calculated and then the two
combined. This is achieved using the following equation:
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Eout = Annual average irradiation x Efficiency of solar cell x Efficiency of inverter x Efficiency
of cables
This calculates an electrical energy output in kilowatt hours per meter squared per year. To
calculate how much electrical energy the whole array would produce, this was multiplied by
the area of the solar cells in the module.
5.0 Results
5.1 Orientation
Graph 1 shows the effects on power output as the orientation is varied. An orientation of
0° represents the solar PV panel facing perpendicular to the lamp and an orientation of 90°
represents the solar PV panel facing in-line with the lamp. As can be seen, there is only a
slight drop in power output as the orientation changes from 0° to 30°. A much more
significant reduction in power output occurs once the orientation is more than 50° with
almost no power being produced at 90°.
Graph 1. Power output of solar PV panel against varying orientations.
5.2 Inclination
Graph 2 shows the effects on power output as the inclination is varied. Altering the
inclination of the solar PV panel has a minimal effect on power output up until it is adjusted
past 20°. Once the solar PV panel has been rotated past 20° then the reduction in power
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output becomes severe before the curvature of the slope becomes less steep as a significant
proportion of the power output has already been lost.
Graph 2. Power output of solar PV panel against varying inclinations.
Graph 3. Comparison of the effects of inclination and orientation on power output.
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5.3 Comparison of inclination and orientation
As can be seen from the above amalgamation of the two sets of results in Graph 3, the
effects of inclination on power output is greater than the effects of orientation on power
output. Power output does not drop below 0.06 W until the solar PV panel is orientated to
60°, however the same drop in power output occurs once the solar PV panel has been
inclined by 30°.
5.4 ANOVA Test Results
Table 1. Results of ANOVA statistical analysis for varying angles of orientation.
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Table 2. Results of ANOVA statistical analysis for varying angles of inclination.
6.0 Discussion
6.1 Discussion of results
6.1.1 Graphical Analysis
Comparison of the two graphs show that a change in the angle of inclination has a greater
affect on power output compared to changing the angle of orientation. The findings from
the experiment correlate with empirical evidence gathered from other studies and as such
the results have been as predicted. Direct comparison of the results, which are displayed in
Graph 3, show that the starting power output differs between the orientation and
inclination and this is likely to have arisen from a fault in the experiment set up. However, it
can still be seen that the power output for inclination not only starts to decrease before the
power output for orientation but also at a much faster rate which is demonstrated in the
steepness of the curvature of the trendline.
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6.1.2 Statistical Analysis
One-way Analysis of Variance (ANOVA) has been used to compare the means of the three
power measurements from each of the two experiments. The ANOVA test was selected
due to the number of mean averages that were compared simultaneously, i.e. three, and this
therefore rules out such statistical tests as the t-test and the z-test which could cause false
conclusions to be drawn due to an increase in the likelihood of making a Type 1 or Type 2
error. Spector and Levine (1987). ANOVA was also chosen as the data from the
experiments are normally distributed and have homogeneity of variance. The homogeneity
of variance is tested by dividing the largest variance by the smallest variance. This figure is
then correlated with an Fmax table and if the figure is less than the critical figure in the Fmax
table then there is homogeneity of variance. The calculation for homogeneity of variance is
displayed below:
Fmax Critical Value: 87.5 (3 samples, 2 degrees of freedom)
Orientation
Largest variance: 0.000594
Smallest variance: 0.000500
0.000594 / 0.000500 = 1.19
1.19 < 87.5 = homogeneity of variance
Inclination
Largest variance: 0.000869
Smallest variance: 0.000760
0.000869 / 0.000760 = 1.14
1.14 < 87.5 = homogeneity of variance
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The ANOVA results in Table 1 and Table 2 show that there isn’t a significant difference
between the mean averages of either the orientation or the inclination power output results
as both F values, 0.358 and 0.242 respectively, are below the F critical value of 3.3541. This
implies that as there is no significant difference between the three mean averages of either
the inclination or orientation power outputs that all three are suitable for use in calculating
an average power output for every increment of the angle (0°-90°).
Using the forecast function in Excel the angles at which power output would still be at 95%
were calculated. The orientation angle which would still provide 95% power output was
27.5° and the angle of inclination which would still provide 95% of the power output was
13°. (Table 3 in Appendix).
6.2 Solar photovoltaic panel efficiencies under test conditions and in the
real world
To ensure that efficiencies which are measured in laboratories, where optimal conditions
are conducive to achieve the maximum possible performance from solar PV panels, are kept
uniform and so that the efficiencies recorded in one laboratory are comparable to another;
a set of rules or Standard Test Conditions (STC) exist. These are conditions that all solar
PV panels are subjected to and affects the rated power of the panel as well as the efficiency.
Solanki (2011) states that the STC are;
1.5 Air Mass (AM)
Temperature of 25°C
Irradiation of 1000 W/m²
Wind speed of 1 m/s
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6.2.1 Why real world applications rarely reach laboratory based recorded
efficiencies and power output
The efficiency of the Solar PV panel is directly affected by the temperature, whether it is
from the ambient weather conditions or from the collection of solar irradiance. Katkar,
Shinde and Patil (2011) suggest that as the temperature of the solar PV panel rises, the
efficiency of the solar PV panel drops, to the effect that for every temperature increase of
1°C the efficiency drops by 0.4% for mono and polycrystalline silicon cell solar PV panels.
Furthermore, by the time the solar panel had reached 58 °C the efficiency had dropped to
2.3% down from 12% at 36°C, demonstrating the significant impact temperature has on
solar panel efficiency. As the temperature of the solar panel is unlikely to be at a constant
25°C such as is in the STC and is often likely to be above this, then the performance of the
solar panel is likely to be reduced.
The amount of irradiation that the solar panel receives also fluctuates during the day and
during the year, peaking at the solar noon of each day and peaking during the summer
months. Figure 1 shows the daily insolation for Manchester, as well the insolation for four
different months of the year. As can be seen in Figure 1, the insolation levels only reach
1000 W/m² in July and possibly a few months either side, whereas the rest of the year is
considerably lower and therefore the actual solar panel efficiencies will not meet the
efficiencies stated in the STC.
Figure 1. Average daily insolation for Manchester at different time of the day and year. BRE
(2006).
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The term Air Mass (AM) is a technical expression used to denote the number or amount of
atmosphere that the source of the irradiation (the sun) has to pass through before it
reaches the solar panel. An AM of 1 represents the amount of atmosphere at the equator
when the sun is directly overhead and therefore an AM of greater than 1 means that the
irradiation has to pass through more atmosphere before it reaches the solar panel. Magee
(2010). Şen (2008) suggests that the amount of atmosphere that the irradiation has to pass
through is significant as the proportion of diffuse irradiation compared to direct irradiation
increases due to scattering as the AM increases. The importance of the ratio of diffuse to
direct irradiation will be discussed in greater detail later on in the report, but it has a direct
effect on power output and the optimal angle on inclination. As with irradiance, AM varies
throughout the day and the year, and as such the Air Mass for the Abbot’s Mill Project in
summer will be AM 1.15 and in winter AM 4, as the Air Mass can be calculated using the
solar altitude (see Appendix). Thus, the Air Mass will be more than the STC Air Mass of AM
1.5 for a significant part of the day and the year and the solar PV array efficiencies will
reflect this.
Dust deposition is an often overlooked factor concerning the reduction in efficiency of a
solar PV array. Whilst the problems associated with dust deposition are more commonly
associated with arid regions, all solar PV installations suffer from some form of particulate
build-up in varying degrees. Dust deposition arises from a number of different sources such
as construction works, landscaping or debris from trees. Figure 2 shows dust deposition
from three sources; limestone, carbon and cement, in various particle sizes and the effect
they have on reducing solar intensity.
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Figure 2. Dust deposition from limestone, cement and carbon in varying particle sizes and
their effect on reducing solar intensity. Mani and Pillai (2010).
As it can be seen, the build up of even a small amount of dust can have a significant effect on
reducing solar intensity. Sulaiman et al suggests that a reduction in peak power of 18% can
be attributed to dust deposition and therefore the build up of any dust should be of concern
and the removal of such, paramount to ensuring continued maximum possible performance.
6.2.2 The effects of shading
It can be argued that the shading created by trees, dirt and bird droppings has a much
greater effect on reducing the efficiency of a solar panel than not achieving the optimal
angles of inclination and orientation. Xiao, Ozog and Dunford (2007) suggests that shading
drastically reduces the peak power point of a solar photovoltaic panel; the point on a
Current/ Voltage (I/V) curve where the maximum power is produced, which in turn has a
knock-on effect to other modules connected in series to the one being shaded, thus
reducing the efficiency of part or all of the solar PV array. Not only is shading significantly
detrimental to the efficiency of the solar photovoltaic array, but Ramaprabha and Mathur
(2009) suggest that partial shading of a module can lead to a problem known as hot-spotting,
where one cell in the module is generating less current than the cells in the string around it,
and this can cause permanent damage to the module. The knock-on effect of shading that
was explained earlier can be seen in Figure 3, where the shading of just one cell of the
whole module has effectively reduced the peak power point by half. Hanitsch, Schulz and
Siegfried (2001).
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Figure 3. The effects of shading on a solar PV module with just one cell shaded can be seen
on the I/V curve. Hanitsch, Schulz and Siegfried (2001).
6.3 Calculating the power from the solar photovoltaic array
To achieve the third objective of calculating the expected power output of the solar
photovoltaic array that will be mounted on the roof of the Abbot’s Mill Project building, the
size or peak kilowatt rated power of the array must first be known. Whilst an array size has
not been officially decided upon, it is likely to be 4kWp as this is the upper limit of the
highest Feed-In-Tariff (FIT) band and will therefore generate the greatest amount of income
at 15.44p/kWh, without being large enough to be in the band below and therefore receive a
lower FIT. Energy Saving Trust (2013b).
The next step was to calculate the solar radiation that the Abbot’s Mill Project solar
photovoltaic array will receive. The MET Office (2013) suggests that a horizontal solar array
will receive between 2.5 MJ/m² and 19 MJ/m² daily depending on the time of year. Using a
3.6 MJ to 1 kWh conversion this equates to an irradiance of between 0.69 kWh/m²and 5.23
kWh/m² daily. Taking an average of 2.96 kWh/m²/day, this gives a yearly horizontal
irradiation of 1080 kWh/m², which is corresponds with the annual horizontal irradiation
figures seen in PVGIS (2007).
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An optimally inclined and orientated solar photovoltaic array will receive more irradiation
than a horizontally inclined solar photovoltaic array due to receiving more direct irradiation
which has more energy than diffuse irradiation as diffuse irradiation has been scattered and
reflected and is therefore less concentrated than direct irradiation. Balfour, Shaw and
Jarosek (2011). To convert from solar irradiation received on a horizontal incline to solar
irradiation received on an optimal incline, Luque and Hegedus (2011) suggest two
calculations, the first of which attempts to establish an optimal incline and the second of
which converts irradiation received on a horizontal incline to irradiation received on an
optimal incline.
The first calculation for a suggested optimal incline is:
βopt = 3.7 + 0.69│Ø│
Where βopt is the optimal incline, and │Ø│ is the latitude of the Abbot’s Mill Project solar
photovoltaic array. The Abbot’s Mill Project is situated at latitude 51°, which when entered
into the formulae gives:
βopt = 3.7 + 0.69 │51│
βopt = 3.7 + 35.19
βopt = 38.89°
The second calculation for converting irradiation received on a horizontal incline to
irradiation received on an optimal incline is:
G(βopt) = G(0) / (1 - 4.46X10-4 X βopt - 1.19X10-4 X β²opt)
Where G(βopt) is the annual solar irradiation on the optimally inclined solar photovoltaic
array, G(0) is the annual solar irradiation on a horizontal incline and βopt is the optimal
incline. The solar irradiation on a horizontal incline for the Abbot’s Mill project is 1080
kWh/m² and the suggested optimal incline for the solar photovoltaic array is 38.89°, which
when entered into the formulae gives:
G(βopt) =
1080 / ((1 - 4.46X10-4 X 38.89 - 1.19X10-4 X 1512.4)
G(βopt) =
1080 / 0.80
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G(βopt) =
1345.5 kWh/m²/year
The expected irradiation on an optimally inclined solar photovoltaic array at the Abbot’s
Mill Project of 1345.5 kWh/m²/year compares favourably with the predicted irradiation for
the same location seen in Figure 4, which displays the yearly sum of global irradiation for the
United Kingdom on an optimally inclined photovoltaic module.
Abbot’s Mill
Project
Figure 4. Global irradiation and solar electricity potential for an optimally inclined
photovoltaic module in the United Kingdom. PVGIS (2012a)
Once the estimated annual solar irradiation for the Abbot’s Mill Project has been
determined, then the efficiencies of the solar photovoltaic array and the associated losses
that occur throughout the system need to be considered to establish the estimated energy
output. Green et al (2012) suggests that modern polycrystalline silicon photovoltaic modules
can reach efficiencies of over 20% in standard test conditions. The solar photovoltaic
modules under consideration for use on the Abbot’s Mill Project are the Sharp 250W
Polycrystalline modules, which have a rated efficiency of 15.2%. Sharp (2012). However, for
reasons previously mentioned, solar photovoltaic module efficiencies very rarely reach the
stated maximum efficiency and therefore a more practical real world efficiency for the Sharp
250W polycrystalline modules is 12%. The proposed Inverter for the solar photovoltaic
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array is the Sunny Boy 4000TL RPC, which has a maximum efficiency of 97%. SMA (2013).
As previously mentioned, inverters operate at near maximum efficiency, so a working
efficiency of 95% has been accepted as plausible. Whilst efficiency losses imparted through
the cabling are expected to be minimal, a resistance is present and therefore a 1% reduction
in efficiency has been allowed which falls well within the acceptable boundaries. Therefore
to calculate the predicted energy produced from the solar photovoltaic array per square
meter, Tiwari (2006) suggests the following formula is used:
Eout = Annual average irradiation x Efficiency of solar cell x Efficiency of inverter x Efficiency
of cables
Annual average irradiation = 1345. 5 kWh/m²/year
Efficiency of solar cell = 12%
Efficiency of inverter = 95%
Efficiency of cables = 99%
Eout = 1345.5 x 0.12 x 0.95 x 0.99
Eout = 151.9 kWh/m²/year
The Sharp 250W Polycrystalline solar panels are made up of 60 individual cells, each one
measuring 156.5mm² or 0.1565m². Sharp (2012). The area of the solar photovoltaic panel is
therefore:
Area = 0.1565 x 0.1565 x 60
Area = 1.47m²
The Abbot’s Mill Project Solar photovoltaic array will have a peak kilowatt rated power of
4kWp and therefore be comprised of 16 Sharp 250W Polycrystalline solar photovoltaic
panels. Therefore the total area of the Abbot’s Mill Solar photovoltaic array will be:
Individual solar photovoltaic panel area = 1.47m²
Number of Panels = 16
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Total area = Panel area x Number of panels
Total area = 23.52m²
Finally to calculate the predicted total energy produced by the Abbot’s Mill Project solar
photovoltaic array the predicted energy per square meter and the total area of the solar
photovoltaic array are multiplied.
Predicted energy per m² = 151.9 kWh/m²/year
Total area of array = 23.52m²
Total energy produced by solar PV array = Predicted energy per m² x Total area of array
Total energy produced by solar PV array = 151.9 x 23.52
Total energy produced by solar PV array = 3572.7 kWh/year
6.4 Validation by and comparison of results using two accredited solar
energy calculators
To validate the predictions made about the energy produced from the Abbot’s Mill Project
solar photovoltaic array, two accredited solar photovoltaic energy calculators have been
utilised.
6.4.1 PVGIS
The first solar energy calculator is the Photovoltaic Geographical Information System
(PVGIS), which is part of the European Commission’s Joint Research Council Institute for
Energy and Transport solar research project. PVGIS has been developed to provide a
comprehensive inventory of the solar irradiation and electricity generation potential of
photovoltaic systems via a map based resource, which covers Europe, Africa and South
West Asia. PVGIS (2012c). The calculator incorporates the map based resource into the
program through correlating a user determined location for the solar photovoltaic array
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with the solar irradiation inventory to establish the predicted solar irradiation the array will
receive.
Once the location and the predicted solar irradiation have been determined, the user is
required to enter details about the solar photovoltaic array which relate to the PV
technology or type of material the module cells are made from, the rated peak power of the
array in kW, the estimated system losses as a percentage, whether the panels are standalone or building integrated, the slope or inclination of the array in degrees, the azimuth or
orientation in degrees, tracking options and output options.
The type of PV technology used in the array is Crystalline Silicon, the rated Peak Power of
the array is 4kWp, the estimated system losses from the inverter, cabling and dirt build up
are estimated at 9% to remain in line with previous calculations. The Abbot’s Mill Project
solar photovoltaic array will be mounted on the roof, so the building integrated option was
selected for ‘mounting position’. The slope or incline of the array was input at 36° and the
azimuth or orientation at 0°, which equates to due south. These figures were selected as
they are often quoted as being correct for the U.K, notably by the following government
and recognised bodies; Strathclyde University (2002), National Energy Foundation (2012),
Energy Saving Trust (2012a), Highlands and Islands Energy (2013). As the array will be fixed
in position, then no tracking information is required and the designated output option for
the results is that they are displayed on a web page.
Figure 5 shows the first stage of the solar photovoltaic energy calculation, where on the left
hand side of the image it can be seen that the location of the Abbot’s Mill Project is depicted
using a pink marker. The right hand side of the image shows the system specifications that
have been entered by the user. Figure 6 shows the second stage of the solar photovoltaic
energy calculation, where the results and some of the assumptions made about system
losses are displayed. Whilst the average sum of global irradiation per square meter per year
is almost identical to the one calculated above, PVGIS’s figure of 4140 kWh/year for
electricity generated by the solar photovoltaic array is significantly higher, suggesting that
the array is assumed to have a greater surface area than the one calculated and/or a higher
efficiency of solar module.
23
Figure 5. Stage one of PVGIS Solar PV energy estimator: system specifications and location.
PVGIS (2012b).
Figure 6. Stage 2 of PVGIS Solar PV energy estimator: predicted energy and irradiance.
PVGIS (2012b).
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6.4.2 Energy Saving Trust
The Energy Saving Trust is a social enterprise with charity status, which collaborates with
government and industry to provide information and advice on carbon reduction and energy
saving technologies and techniques to the general public. The Energy Saving Trust’s solar
energy calculator is the U.K Government’s recommended resource for estimating energy
production from solar photovoltaics, and therefore should produce the most valid results as
it is presumed that the solar energy calculator’s methodology has been vetted by experts
before such a recommendation could be made. Gov.uk (2013).
The Energy Saving Trust solar energy calculator is made up of three steps. The first step is
imputing the location of the solar photovoltaic array and the Energy Performance Certificate
(EPC) rating of dwelling. The second step is imputing the specifications of the solar array,
such as peak rated power, orientation and inclination, shading and the monthly electricity
demand for the dwelling. The third step is where the results are displayed showing the
estimated tonnes of carbon dioxide reduced through using solar photovoltaics to produce
electricity as opposed to buying electricity off the national grid. The annual income
generated and the amount of electricity generated by the array is also displayed in step
three. Energy Saving Trust (2013c).
The Energy Performance Certificate (EPC) rating of the dwelling is as yet unknown,
however, as the Abbot’s Mill Project will be a new build with sustainability and energy
efficiency as key aspects, it is likely to be a band D or better. The Energy Performance
Certificate (EPC) rating is a measure of the buildings energy efficiency and environmental
impact and is the result of a Standard Assessment Procedure (SAP), which is endorsed by
the U.K Government as a means of determining an energy rating for a building. The banding
runs from G to A, G being the worst and A the best. Poel, Van Cruchten and Balaras
(2007). A postcode rather than a latitude and longitude is used to determine the location of
the solar photovoltaic array for the Energy Saving Trust solar energy calculator. Figure 7
shows the first step of the solar energy calculator with the upper EPC banding selected and
the postcode for the Abbot’s Mill Project entered as CT1 2BF.
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Figure 7. Step 1 of Energy Saving Trust Solar Energy Calculator: Building efficiency rating
and location by postcode. Energy Saving Trust (2013c).
The Energy Saving Trust solar energy calculator does not allow for precise adjustment of
the inclination and instead increases in increments of five degrees. Therefore an angle of
thirty five degrees was selected as this was the closest option to the desired suggested angle
of 36 degrees. The postcode entered into the calculator in step 1 is then converted into a
precise location displayed upon a map, where the orientation of the solar photovoltaic array
can then be altered by the user. To maintain consistency with the two previous calculations
and the suggested optimal angles, the orientation was kept facing due south. Shading is
assumed to be none existent as the Abbot’s Mill Project building and thus the solar
photovoltaic array, will be positioned in such a manner as to avoid this. The installation size
is the same as the previous two calculations at 4kWp. The monthly electricity bill is assumed
to be £0 as the Abbot’s Mill Project will also be incorporating a hydroelectric waterwheel
into the its design and this will provide all of the electricity needs for the buildings. Figure 8
shows the relevant details entered into Step 2 of the solar energy calculator. Note that the
actual location of the Abbot’s Mill Project is situated ten to twenty meters to the right of
the position indicated on the map.
26
Figure 8. Step 2 of Energy Saving Trust Solar Energy Calculator: orientation, inclination,
size and demand of system. Energy Saving Trust (2013c).
Figure 9 shows Step 3 of Energy Saving Trust solar energy calculator where the results are
displayed. There are two options in the results section that relate to the different cut off
points for the Feed-In-Tariff (FIT), the first of which is inapplicable to the Abbot’s Mill
Project as the solar photovoltaic array will not be installed and operational before the 30th
of April 2013. The second option has been selected as the one with the greater likelihood of
being met, however the cut off date for installation of the solar photovoltaic array is the 31st
of July 2013 which may mean this is missed too, but as these options refer to projected
income and are only a guideline estimate of the likely Feed-In-Tariff, then it is not a matter
of great importance. Figure 9 also displays the projected electricity that the solar
photovoltaic array could produce, which is estimated at 3446 kWh/year, a similar figure to
the one calculated in the report previously, although considerably less than the figure
calculated by PVGIS. The final piece of information that is of interest is the carbon dioxide
saving for the life time of the solar photovoltaic system (the panels and components such as
27
cabling and the inverter), which is estimated at 41 tonnes of CO₂. The life time of the solar
photovoltaic system is suggested to be twenty five years, but research from the Centre for
Alternative Technology (2013) and Zweibel (2010) suggest that the majority of the
components are likely to last longer than the estimated time frame without serious
degradation (<1% per year) and that it is only the inverter which will need maintenance or
replacing before the twenty five year life time expectancy.
Figure 9. Step 3 of Energy Saving Trust Solar Energy Calculator: Estimated income and
electricity generated. Energy Saving Trust (2013c).
The PVGIS solar energy calculator uses a number of data sets and computational models
within its own calculations to produce the energy predictions. Whilst some of the data sets
can be considered current, others use information gathered from over thirty years ago and
therefore are likely to be out of date and contain a certain amount of errors, which calls
into question the validity of the estimations made by the PVGIS solar energy calculator.
Further compounding the validity of the PVGIS solar energy calculator is that some of the
data sets are less well represented than others, in so much as the number of ground station
measurements varies between data sets and therefore some data sets require a greater
number of interpolations to be made, thus reducing the accuracy of the final energy
estimate. It has been found that the PVGIS solar energy calculator overestimates the annual
solar irradiation on an inclined plane by 3.2% when compared to actual ground station
measurements in at least one location and it can therefore be assumed that other variations
28
between actual and predicted solar irradiation measurements exist elsewhere. Suri et al
(2007).
The Energy Saving Trust solar energy calculator lacks the same degree of precision that the
PVGIS solar energy estimator does, as it is more focused on the needs of the average
household owner and the lack of some of the more technical options that are available in
the PVGIS solar energy estimator alludes to this. The Energy Saving Trust solar energy
calculator only allows the user to select increments of 5° when selecting the pitch angle and
therefore the inclination angle of the solar PV array, and also does not suggest an optimal
inclination angle such as the PVGIS solar energy estimator does. This would suggest that an
optimal angle of inclination is not necessary for a small scale (4kWp and under) solar PV
array or that the average household will not go to the trouble of aligning the solar PV array
to the correct optimal angle and will merely use the pitch of the roof. The final report
produced by the Energy Saving Trust solar energy calculator is also not as in-depth as the
PVGIS solar energy estimator report, but does however give a predicted saving of tonnes of
CO₂, which for the purposes of calculating the energy produced by the solar PV array is
irrelevant, but could provide the Abbot’s Mill Project with further green credentials and
information for visitors to the centre.
6.5 Assumptions made in estimating energy production from solar panels
in the report
Various assumptions have been made in all three solar energy calculations; by PVGIS, by the
Energy Saving Trust, and the calculations made in the report. Some assumptions invariably
have to be made when making predictions of any sort and predicting energy production is
no different. Many variables exist within the calculations due to unknown or unforeseeable
elements, whose predictions are based on past observed measurements, often utilising one
or more data sets, which are then extrapolated to estimate a figure or value for the variable.
While testing shows that this can be an accurate method of prediction, the models for doing
so are less than one hundred percent accurate and anomalies do occur. Thornton and
Running (1999).
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The elements about which assumptions need to be made can be divided into two categories;
those that affect efficiency before the solar photovoltaic array and those which affect
efficiency within or after the photovoltaic system (which includes the solar array, cables and
inverter).
The variables that affect efficiency before the solar photovoltaic array are; variations in the
shading profile from vegetation, the proportion of direct and indirect sunlight the solar array
receives, build up of dirt, leaves and animal matter on the solar photovoltaic array,
temperature fluctuations, and reflectance.
Calculating the amount of shading a solar photovoltaic array will receive from vegetation can
be particularly challenging as the shading profile is constantly changing due to the growth
and direction of growth of the vegetation. The type of tree can impact the shading profile as
deciduous trees will shed their leaves in winter and let more irradiation through than a
coniferous tree which maintains roughly the same shading profile year round. Munzinger et
al (2006).
As previously mentioned, direct irradiation is more concentrated than diffuse irradiation and
therefore contains more energy per meter squared and so determining the likely ratio of
direct irradiation to diffuse irradiation can have a big impact on energy generated from the
solar photovoltaic array. Diffuse irradiation is the predominant from of irradiation when
there is cloud cover and direct irradiation is predominant when the sky is clear. To
accurately calculate which type of irradiation is likely to be predominant on any one day
requires a reliable prediction of the weather forecast, a complex procedure which is difficult
to correctly achieve and is often only useful in the immediate future. Whilst weather
conditions follow a similar pattern year on year and thus provide a good basis for making a
prediction, there is likely to be a degree of variability between years, partially due to
abnormal weather conditions. Peterson, Stott and Herring (2012) suggest that extreme
weather events are likely to become more frequent in future years to come, which by their
nature, are not only hard to predict their timing but also make predicting what effects the
weather event will have on electricity generation an unknown. As such, the greater the
extent of time the prediction is made for, the greater the uncertainty the prediction will be
correct. This is particularly poignant in the Energy Saving Trust solar energy calculator as
calculations are made for the lifetime of the solar photovoltaic system, which is estimated at
twenty five years. Energy Saving Trust (2013c). The assumption made in all three solar
30
energy calculations is that the irradiation will remain the same year on year and that the
irradiation figure is fixed. To provide a more accurate representation of the likely
irradiation, a maximum and minimum range is needed as this will reflect the possible
fluctuations.
The variables that affect efficiency within the solar photovoltaic system are; module
degradation, incorrect sizing of the inverter or losses which occur when irradiance is low
and cable losses.
6.6 Uncertainties and assumptions made by the accredited solar energy
calculators
The Energy Saving Trust Solar Energy Calculator makes several assumptions, the first of
which is that a building already exists for the solar PV array to be mounted on. Whilst this is
not overly problematic as a nearby building can be selected, it does mean that the precise
location of the Abbot’s Mill Project could not be used and the results do not completely
accurately represent the real world conditions. The second assumption is that the system
power performance will decline by 20% over the 25 year expected lifetime of the project as
stated in Energy Saving Trust (2013d). It does not however, mention which parts of the
system this includes and also does not take into account that inverters tend to have a much
shorter lifespan than the estimated 25 year lifespan given by the Energy Saving Trust. Harb
et al (2011).
The PVGIS solar energy estimator uses spatial interpolation to predict the levels of solar
irradiation for locations between measuring stations. Spatial interpolation uses known
locations where actual data has been gathered; in this case the measuring stations, and then
calculates and infers a value for anywhere between two or more of the measuring stations.
To be accurate, spatial interpolation relies on the measuring stations being in close
proximity to one another and the further away they are from one another, the greater the
uncertainty of the accuracy there is. PVGIS (2012d) suggests that the mean bias error for
the daily global horizontal irradiation compared using the yearly average is 0.3% and the
root mean squared error is 3.2% for the summer months and 7.8% for the winter months.
The PVGIS solar energy estimator only allows the user to choose from a small selection of
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generic solar PV panel technologies, i.e. Crystalline Silicon, Cadmium Telluride (CdTe) and
one or two others. This means that as the different sub categories of the solar PV panel
technologies, such as poly and mono crystalline silicon, are grouped together under the
same selection heading then a singular efficiency has been used as a representative efficiency
for the whole technology group. Figure 10 shows that there is a noticeable difference of 46% between the efficiencies of poly and mono crystalline solar PV panels as well a significant
difference in efficiencies between solar PV panel technologies which are grouped under the
‘other’ heading in the PVGIS solar energy estimator. Therefore, as a generic efficiency has
been used for several solar PV panel technologies, some uncertainty will exist as to the
precision of the results.
Figure 10. Advancement of solar PV panel technologies over time. Castellano (2010).
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6.7 Calculating the optimal orientation and inclination of the solar
photovoltaic array
Achieving the correct angle of inclination and orientation of a solar photovoltaic array is
paramount if the optimal performance of the solar photovoltaic array is to be achieved.
However, the correct angle of inclination and orientation varies between locations and what
is true for one solar photovoltaic array may not be true for an identical array located
elsewhere. There are several factors which influence the optimal angles such as location,
time of year and time of day. Li and Lam (2007). The Abbot’s Mill project solar photovoltaic
array will be fixed; in as such it will not track the progression of the sun across the horizon
and will not adjust depending upon the season, and therefore the angle of inclination and
orientation which is optimal for the entire year rather than at a certain time of year is
needed.
6.7.1 Correct Inclination
The angle of inclination is the angle between the horizontal plane and the solar photovoltaic
panel or array. The aligning of the angle on this axis is to capture the solar irradiation as the
solar altitude varies throughout the day and throughout the year. As the solar altitude is
continually changing throughout the year, so too is the amount of solar irradiation, due in
part to the thickness of the earth’s atmosphere the solar irradiation has to pass through,
known as the air mass ratio. The air mass ratio is less during summer and more during
winter. Goswami, Kreith and Kreider (2000). This is true for the amount of energy the solar
photovoltaic array will produce; more in summer, less in winter, and therefore the angle of
inclination for the solar photovoltaic array is not a straight forward split between the lowest
and the greatest solar altitude. As can be seen from Figure 11, the latitude angle of the
location where the solar PV array is sited affects not only how much solar irradiation the
array receives but at what times of year the peaks in solar irradiation occur. Burgess (2009).
For London, the peak in solar irradiation happens in the summer time when the solar
altitude is at its greatest angle and the days are at their longest. It therefore makes sense for
the solar PV array to be inclined as such that it can make use of the greatly increased solar
33
irradiation at this time of year and for that the angle of inclination needs to be flatter to
accommodate this.
Figure 11. Annual irradiation at three different latitudes. Burgess (2009).
It has been suggested that two optimal angles of inclination, one for summer and one for
winter, would produce more energy as the difference in maximum solar altitude of the sun
between winter and summer is significant, as the maximum solar altitude in summer for the
Abbot’s Mill Project is sixty two degrees and the maximum solar altitude in winter is fifteen
degrees. HM Nautical Almanac Office (2006). However despite the significant change in the
suns solar altitude between summer and winter, Huld, Suri and Dunlop (2008) found that an
optimally inclined solar photovoltaic panel compared to a solar photovoltaic panel which
was adjusted biannually, produced under one per cent less energy.
Nakamura et al (2001) has suggested that a correlation between the optimum angle of
inclination and the latitude angle exists and that an annual optimum angle of inclination can
be achieved for a fixed plane solar PV array if it is tilted at same angle of latitude. Their
findings showed that an optimal angle of inclination was approximately 30° for Hamamatsu,
Japan, which has a latitude angle of 34°. It should be noted that their experiments took place
over the winter months, September - February and therefore does not represent an annual
optimal inclination.
34
Agarwal, Vashishtha and Mishra (2012) have also conducted research into the correlation
between the optimum inclination angle and latitude angle. Their work compared four
different models; Liu and Jordan (1977), Hay (1979), Badescu (2002) and Reindl, Beckmann
and Duffie (1990) which were used to help predict the optimal inclination for each month
and the average annual optimal inclination. This showed that using the Badescu model
produced the closest optimal inclination, which for Chennai, India was 18°, which has a
latitude angle of 14°, therefore reinforcing the notion that optimal inclination and latitude
angle are closely linked. This is further verified by Ahmad and Tiwari (2009), who suggest
that monthly or seasonal adjustment of the angle of inclination will produce the best results,
however if a fixed angle of inclination is required, then the angle of latitude should be
adopted. It should also be noted that an annual optimal inclination produces only 13.4% less
power than a monthly adjusted optimal inclination. This is considered acceptable for small
scale PV arrays such as the one on the Abbot’s Mill Project. It should be noted that where
the latitude angle is advised for use as the optimal angle of inclination, the locations of the
solar PV arrays are relatively close to the equator (compared to the Abbot’s Mill Project),
and receive more sun hours and direct beam irradiation.
Further research into the correlation between latitude and optimal inclination has been
carried out by Cheng, Jimenez and Lee (2009) who suggest that the optimal inclination for a
Building Integrated Photovoltaic (BIPV) system such as the one on the Abbot’s Mill Project
can be calculated using the latitude angle for the location of the PV array. Their study, which
was conducted across fourteen different countries and compared predictions with actual
recorded data, showed that on average the latitude angle could be used to predict the angle
of inclination which would produce 98.6% of the maximum possible system performance.
However Beringer et al (2011), calls into question the need to establish an optimum
inclination at all, suggesting that over a range of different inclination angles (0°-70°) the
difference in energy output between the maximum values and the minimum values for the
summer months in Hannover, Germany, was 6% and in the winter months the difference
rose to 10%. Hannover shares an almost identical latitude to the Abbot’s Mill Project, 52°
and 51° respectively, and a similar weather pattern. Whilst no one optimal inclination is
given by Beringer et al (2011), Figure 12 displays the ratios of cumulative energy output
values annually and for the summer and winter months, which would seem to suggest that
an optimal angle which lies between 30° and 40° would be best. Whilst this angle of
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inclination is not the same as Hannover’s latitude angle, it is interesting to note that the
annual energy output values do not drop below 5% of the maximum for any of the
inclination angles used, suggesting that if the latitude angle was used the energy output
would be almost identical.
Figure 12. Ratios of cumulative values annually and for the summer and winter months.
Beringer et al (2011).
Bird and Riordan (1984) suggest that one aspect which may cause the angle of inclination to
be less than the latitude angle is that not all irradiation that the solar PV array receives is
direct beam irradiation, i.e. the irradiation which comes directly from the sun and hits the
surface of the solar PV array. Two other forms of irradiation are also collected and these
are diffuse and reflected irradiation. Diffuse irradiation occurs when the sun’s rays pass
through molecules and particles, such as cloud cover and is then scattered in all directions,
thus the diffuse irradiation that the solar PV array receives also comes from all directions.
Reflected irradiation is as the name suggests, the irradiation which has been reflected of a
surface and then is collected by the solar PV array.
Chang (2008) suggests that for direct irradiation, the use of the latitude angle is correct but
when diffuse and reflected irradiation make up a greater percentage of the total global
irradiation received, the optimal angle of inclination becomes much flatter. This is likely to
occur in countries that have a greater proportion of cloud cover or in cities which have high
levels of pollution. As the United Kingdom is known for its inclement weather conditions,
with Kent, U.K, only receiving an average annual 1649.9 sunshine hours and 117 days of
rainfall (MET Office, 2010), the proportion of cloud cover is likely to be much greater than
36
that of New Delhi, India, which receives nearly 3000 sunlight hours even with a monsoon
season. Garg and Garg (1985). Therefore the diffuse irradiation in Kent makes up a greater
proportion of the total global irradiation received by the solar PV array and the angle of
inclination needs to be adjusted accordingly to compensate for this.
Thomas and Fordham (2003) suggest that for any location in the U.K. the optimal angle of
orientation can be calculated using the latitude angle and subtracting 20° from that number.
Furthermore, their findings compare favourably with other research in the sense that solar
arrays that are not optimally inclined do not suffer from being so, also suggesting that there
is significant leeway before drops in performance fall below 95% due to suboptimal
inclination.
6.7.2 Correct Orientation
As has been previously mentioned, a south facing solar PV array is often quoted as being
optimally orientated for any location the Northern Hemisphere. This assumption stands to
good reason as can be seen in the simplified pictorial diagram of the sun’s path in Figure 13;
where the sun is at its highest when it is due south regardless of the time of year.
Figure 13. The sun’s position at different times of the year for the Northern Hemisphere.
Kalogirou (2009).
There is a significant amount of empirical evidence to back up the suggestion that a south
facing solar PV array is optimally orientated. Rakovec et al (2001) found that for a variety of
locations in Slovenia, which due to significantly varying topological and meteorological
conditions experiences substantial variations in irradiation from location to location, that
37
the optimal orientation for collection of the maximum amount of irradiation was due South.
Tovey and Turner (2008) conducted a study based in the U.K to determine where the best
energy yield ratios (the number of times a solar PV array will generate as much energy as it
took to manufacture, construct and install the solar PV array in the first place) are located
and what the optimal angles of inclination and orientation are to achieve this. The research
showed that a solar PV array located in the South/South East of the U.K orientated due
South with an inclination of around 30° would give the highest energy yield ratios, and thus
generate the most energy. Figure 14 displays the results of research by Pavlovic et al (2010),
which compared the various angles of inclination and orientation of a solar PV panel in
Serbia in an attempt to optimize solar irradiation collection. As can be seen, a Southerly
orientated solar PV panel generates over 30 Wh more than a solar PV panel which is
oriented Easterly and 40 Wh more than one oriented Westerly for this location.
Figure 14. Solar PV array outputs for Serbia based on different angles of inclination and
orientation. Pavlovic et al (2010). (It should be noted that 0° is used as a referent position
and therefore should not be considered the optimal inclination.)
Rowlands, Kemery and Beausoleil-Morrison (2011) suggest that for maximum generation of
revenue, the optimal orientation may be a few degrees either side of South depending on
the tariff and at what times it is most beneficial to generate energy, as the price per kWh is
38
likely to be more at certain times of the day depending on the demand from the property.
The maximum deviation from due South as suggested by the study is 6°, which for reference
terms is less than both South South West and South South East which are 22.5° either side
of due South and as such does not represent a significant divergence. In the case of the
Abbot’s Mill Project, where the majority of the electricity demand will be met by the
hydroelectric waterwheel and thus mostly negating the demand on the solar PV array, the
desire to generate at certain times of the day will be removed, therefore eliminating the
need to adjust the angle of orientation.
An in-depth study by Lave and Kleissl (2011) suggests that for certain locations an optimal
orientation for a solar PV array can be as much as 10° off the suggested due south
orientation as a result of daily typical weather patterns, such as morning cloud that is
dispersed as the day warms up. This would mean that more or less solar irradiation is being
collected by the solar PV array either before or after solar noon and as East represents the
solar irradiation received before solar noon and West the solar irradiation received after
solar noon, the solar PV array would need to be adjusted to make better use of the
irradiation when there is no cloud cover i.e. orientated West or East accordingly. As there
is no obvious daily weather pattern that exists for Kent or more specifically Canterbury,
where the Abbot’s Mill Project is located, then no additional adjustment to the orientation
of the solar PV array is needed.
6.7.3 PVGIS suggested optimal inclination and orientation
The PVGIS solar photovoltaic energy calculator has a feature where the slope (inclination)
and azimuth (orientation) of the solar photovoltaic array can be optimised for the
designated location. As can be seen from Figure 15, PVGIS has determined that the optimal
inclination for the Abbot’s Mill Project solar photovoltaic array is 38° and the optimal
orientation for the array is -1°, which equates to 1° east from due south. Figure 16 shows
that whilst the optimised inclination and orientation of the solar photovoltaic array
produces an extra 10 kWh/m²/year, the electrical energy generated by the array remains the
same, suggesting that precise optimisation of the array is unnecessary for the gains achieved
and that there is some degree of flexibility concerning how far the array can be orientated
39
away from the optimal angles of orientation and inclination before significant power loss is
noted.
Figure 15. Stage 1 of the PVGIS solar PV energy calculator with suggested optimally
inclined and orientated solar array. PVGIS (2012b).
Figure 16. Stage 2 of the PVGIS solar PV energy calculator showing 10 kWh/m²/year extra
irradiation due to being optimally angled. PVGIS (2012b).
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6.8 Shortcomings of and Improvements to the Laboratory based
Experiment
Whilst the laboratory experiment was conducted as thoroughly and meticulously as possible
given the equipment and facilities available, the validity of the results can unfortunately be
called into question due to errors which could have arisen from not adhering to STC and
fluctuations in the ambient conditions between measurement readings. Ideally the
experiment would have been conducted in a specialist chamber where the temperature,
irradiance, air mass and wind speed can all be kept constant and therefore any changes in
the readings are the result of altering the angle of the solar PV panel. Without the ability to
control the test conditions and therefore ensure that the test conditions are the same for
every measurement, it cannot be guaranteed that the changes in power output are solely
from altering the angles of inclination and orientation. The overriding fault with the
experiment was the inability to control the heat generated by the 500W lamp and the affect
this had on the solar PV panel. As previously discussed, an increase in temperature has an
adverse effect on efficiency and the heat produced by the 500W lamp was sufficient to raise
the ambient temperature of the room from 16.5°C to 18°C in the short space of time the
experiment took place and although the necessary equipment to accurately measure the
temperature of the solar PV panel was unavailable, it felt hotter at the end of the of the
experiment than it did at the beginning.
It is suggested that for future experiments the Standard Test Conditions are adhered to and
a specialist chamber used so that the ambient conditions can be controlled. It is also
recommended that the same solar PV panels that are to be used on the Abbot’s Mill Project
are also used in the experiments to replicate, as closely as possible, the conditions and
components that will be at the site.
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7.0 Conclusion
Without taking actual measurements of the direct beam, diffuse and reflected irradiation,
clearness index, sunset hour angle and the declination angle over a sustained period of time
at the Abbot’s Mill Project, it is almost impossible to calculate the precise optimal angle of
inclination for the solar array. However, as has been previously demonstrated, an exact
optimal angle of inclination is not necessarily needed to achieve performance efficiencies
which are within 10% of the total possible maximum, insomuch that a leeway of 20° either
side of the optimum angle of inclination should not produce a noticeable difference in the
annual power output. Based on the research conducted within the report and that of
others, an angle of inclination which is as close to being optimised or as such as is close
enough to not reduce performance by a significant margin, can therefore be deduced. The
features of Abbot’s Mill Project’s location are that most of the solar irradiation will be
collected by the solar PV array during the summer months when the days are at their
longest and the solar altitude angle is at its greatest. Furthermore, cloud cover is prevalent
and thus a significant proportion of the total global irradiation that the solar PV array will
receive will be diffuse radiation. While the use of the latitude angle for the optimal
inclination angle is sufficient for locations closer to the equator, which have less cloud cover
and more sunlight hours, the use of the latitude angle of 51° at the Abbot’s Mill Project
would not be suitable to collect the diffuse irradiation and peak summer irradiation. As has
been suggested by Thomas and Fordham (2003), a reduction of the latitude angle by 20°
would produce an optimal inclination angle of 31°. This is within 5° of the generally accepted
optimal inclination quoted for the U.K of 36°, however both the Luque and Hegedus (2011)
and PVGIS (2012b) calculations suggest an optimal inclination of 38° for the Abbot’s Mill
Project. As such if the Abbot’s Mill Project solar PV array is inclined anywhere between the
angles of 31° and 39° then this shall be deemed optimal in the respect that no significant loss
in performance can be detected, however 35° shall be used if a single figure is to be chosen.
The optimal angle of orientation for the Abbot’s Mill Project solar PV array was calculated
to be Due South. Due South was shown to be the optimal orientation for the vast majority
of solar PV arrays in the Northern Hemisphere and therefore it can be concluded that the
Longitude can be used to calculate the optimum angle of orientation to within a high level of
certainty.
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It was calculated that the power output would not drop below 95% until the angle of
orientation had been aligned past 27.5° and 13° for the angle of inclination.
The experiment showed that altering the angle of inclination had a greater effect on power
output than altering the angle of orientation, which is what was predicted at the beginning of
the report.
It was calculated that the 4kWp solar PV array would generate 3572.7 kWh/year. When the
calculations were validated against the PVGIS solar energy calculator the figure that was
calculated was 4140 kWh/year, however the Energy Saving Trust solar energy calculator
produced a figure that was closer to the figure generated by the methodology used in at the
report of 3446 kWh/year. There is a degree of uncertainty with all the calculations due to
assumptions made, and therefore there is likely to be some discrepancy between what is
calculated and what is actually produced. The PVGIS solar energy calculator has the most
scientific basing and therefore is the most likely to be correct. An average of all three
calculations gives 3719 kWh/year, which considering the variability in estimations, is a
plausible figure.
43
8.0 Appendix
8.1 Calculations
Calculation for Air Mass at certain times of year
1 / (sin θ)
θ = solar altitude
θ for Abbot’s Mill Project at midday June 21st 2013 = 60.45°
θ for Abbot’s Mill Project at midday December 21st 2013 = 15.54°
44
8.2 Experiment Results
Table 3. Averaged power output readings against varying angles of orientation and
inclination, with calculated maximum angle away from 0° before power output drops below
95%.
45
8.3 Risk Assessment
46
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