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Determination of optimum tilt angle of single and multi rows of photovoltaic arrays for selected sites in Jordan
Solar & WindTechnologyVoI. 7, No. 6, pp. 739-745, 1990
0741-983X/90 $3.00+.00 PergamonPressplc
Printed in Great Britain.
TECHNICAL NOTE Determination of optimum tilt angle of single and multi rows of photovoltaic arrays for selected sites in Jordan MARWAN MAHMOUD and
ISMAIL N A B H A N
Royal Scientific Society, Renewable Energy Research Centre, P.O. Box 925819, A m m a n , Jordan (Received 20 October 1989 ; accepted 24 November 1989)
Abstract--Solar radiation measured by the Jordanian Meteorological Department (using actinographs) at six Jordanian sites during some, or most, of the period from 1971 to 1987 has been analysed to determine the monthly, and thus the yearly, o p t i m u m tilt angles for both single row and multi-rows o f photovoltaic arrays operating in such sites. Also a comparison between the solar energy captured by a stationary mounting structure and that captured by a variable-angle mounting structure is carried out. Relative to structures of constant tilt angle the results obtained show an improvement of 5.6% by using PV-mounting structures of adjustable tilt angle.
1. I N T R O D U C T I O N
lishment: rack and direct. The rack design can be used to m o u n t modules on the ground or a fiat roof. The direct design specifically represents ways of attaching modules to a house with a south-facing sloped roof in the northern hemisphere.
The photovoltaic array can be fixed or it can be tracking the sun with or without concentrating capability. For rural/ remote applications where PV systems are expected to operate reliably with m i n i m u m maintenance, the tracking configuration is not practical because the mechanical assembly required to track the sun generally outweighs the extra energy gained through tracking. As an alternative for the tracking configuration, the variable-angle mounting structure is proposed and studied in detail in this paper.
2.1.1. Rack mount. Photovoltaic modules installed on a horizontal surface, be it the ground or a fiat roof, are mounted on a tilted support frame or rack. There is a wide variety of rack designs made of aluminium or hot galvanized steel to ensure a high corrosion protection of the PV array. Some rack m o u n t designs afford the option of tracking the sun or adjusting the tilt a n g l e b y simply loosening or moving a bolt. A rack m o u n t provides easy access to the front and rear of the module for maintenance and testing. The module operating temperature is as low as possible, since outdoor ventilation of the front and back of the modules provides quick heat transfer. Racks situated on the ground m u s t be m o u n t e d on a solid concrete foundation to prevent high winds from uprooting the array support. Poured concrete or concrete blocks with auger-type anchors screwed into the ground will serve this purpose. Large arrays that are mounted on the ground are arranged in rows that are set sufficiently far apart to prevent one row from shading another. The m i n i m u m distance, X, between rows of PV-arrays is given by the equation :
2. P H O T O V O L T A I C ARRAY I N S T A L L A T I O N A photovoltaic array consists of any number of photovoltaic modules connected together electrically to provide a single electrical output with a certain nominal voltage and power. The installation of a photovoltaic array can be divided into two separate tasks: physical and electrical. The physical installation involves m o u n t i n g the photovoltaic modules on a sturdy frame that will maintain the array's tilt and position throughout the worst weather conditions. The electrical installation entails wiring the modules together in their prescribed parallel and/or series configuration and leading the main power lines to the power-conditioning equipment and the load.
X = L[sin S tan (23.5 ° +
2.1. Physical installation
A variety of factors must be considered when physically installing a photovoltaic array. A support structure must be able to support the modules through adverse wind and weather for the expected lifetime of the array, and yet be situated in a location where sunlight all year around is not blocked. The price of a mounting structure must be kept as low as possible. Finally, since photovoltaic arrays are often installed in areas of high visibility, they need to be physically agreeable. Two basic photovoltaic-module m o u n t i n g schemes are usually used by industry and research estab-
(1)
where: L = the length of the arrays as shown in Fig. 1 ; ~b = site latitude (degree) ; S = tilt angle (degree). 2.1.2. Direct mount. The asphalt shingles of a conventional
roof can be replaced by a solar-cell shingles in a direct-mount configuration. This configuration affords no ventilation of the module's back surface, and as a result the solar-cell operating temperature in the daytime is on average about 20°C to 30°C higher than with the rack configuration. A higher operating temperature decreases the cell efficiency and sub739
740
Technical Note Table 1. Geographical positions of selected sites
Station Amman Aqaba lrbid G h o r Sail Kharana Shoubak
Table 3. Reflectivity values for 15 characteristic surfaces
Altitude (m)
Lat. 'N
Long. ~'E
766 2 616 -350 650 1365
31.98 29.52 32.55 31.03 31.70 30.52
35.98 35 35.85 35.47 36.48 35.33
stantially increases the chances of temperature-induced malfunctions, such as cell cracking or the degradation of materials. Direct-mount installation costs are fairly low, since there is a little mounting hardware involved. 2.2. Electrical installation The electrical installation of a photovoltaic array involves a variety of tasks to ensure that various components are well interconnected and protected. The right type of electrical wire for the particular application must be selected and routed in a safe way, especially for the PV arrays mounted on a variable tilt angle-support structure. Connections between the wire and various terminals on a solar-cell module or system must be made securely.
No.
Average reflectivity
Surface
l 2
Snow (freshly fallen or with ice film) Water surfaces (relatively large incidence angles) 3 Soils (clay, loam) 4 Earth roads 5 Coniferous forest (winter) 6 Forests in autumn, ripe field crops, plants 7 Weathered blacktop 8 Weathered concrete 9 Dead leaves 10 Dry grass 11 Green grass 12 Bituminous and gravel roof 13 Crushed rock surface 14 Building surfaces, dark (red brick, dark paints) 15 Building surfaces, light (light brick, light paints)
0.75 0.07 0.14 0.04 0.07 0.26 0.10 0.22 0.30 0.20 0.26 0.13 0.20 0.27 0.60
horizontal, the a m o u n t of diffuse light decreases while the proportion of light reflected off the ground increases.
3. S U R F A C E O R I E N T A T I O N AND S O L A R INTENSITY
4. O P T I M U M S U R F A C E O R I E N T A T I O N
The orientation of a surface on earth is defined by two angles : the surface tilt or slope angle and the surface azimuth angle, as shown in Fig. 2. The tilt angle indicates how far up from the horizontal a surface is slanted, while the azimuth angle denotes how the surface is positioned relative to the true n o r t ~ s o u t h and east west coordinates (due south represents an azimuth angle of 0 ~, due east is - 9 0 °, north is 180 ° and west is + 90°). The sunlight received by a surface on earth can be divided into three different types : direct, diffuse and reflected. Diffuse sunlight approaches a surface from all unobstructed angles, while direct-beam rays strike the surface from only one angle. In addition to diffuse and direct light, an angled surface can also receive reflected light from the ground or other appropriately positioned surfaces. As a result, a horizontal surface with a zero tilt angle receives the m a x i m u m diffuse and m i n i m u m reflected light possible, and as a south-facing surface is tilted up from the
The a m o u n t of direct-beam solar energy that a surface receives is optimized by keeping the surface at right angles to the sun's direct radiation at all times of the day. In most cases, maneuvering a surface is impractical and affects the system reliability negatively. The cost of the energy and the mechanical assembly required to track the sun consistently each day generally outweighs the extra energy obtained through tracking when fiat-plate solar-cell modules without concentrators are used. The next best propositions are to fix the surface's position so that the sun's angle on the plane is closest to the perpendicular most of the time, or to make it able to be constructed for seasonal adjustment. 5. S O L A R R A D I A T I O N IN T H E S E L E C T E D SITES The sites considered in this study are located roughly between 29.52 ° and 32.55 ° N, latitude and 35 ° and 36.48 ° E, longitude. In Table 1, the geographical positions of the
Table 2. Monthly averages of daily solar radiation intensity (kWh/m 2) on a horizontal plane for the selected sites Station
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
Amman Aqaba Irbid G h o r Sail Kharana Shoubak
2.475 3.985 3.207 3.31 3.102 3.80
3.021 4.776 3.881 3.788 4.45 4.601
3.985 5.217 4.927 4.741 5.287 5.868
5.043 6.925 5.856 5.705 6.832 6.867
5.775 7.053 6.984 6.484 7.716 7.692
6.31 7.518 7.60 7.00 8.018 8.262
6.286 7.518 7.622 6.821 7.925 8.262
5.763 6.925 7.111 6.449 7.123 7.855
4.973 6.193 6.159 5.600 6.275 6.925
3.881 5.054 4.94 4.601 4.706 5.647
2.917 4.067 3.765 3.59 3.59 4.404
2.243 2.975 3.067 2.986 2.684 3.602
Technical Note
L
×
741
4 ~
Fig. 1. M i n i m u m distance between rows of PV-arrays.
West
North
sourS °
--
East
19 = S u r f a c e
tilt
~5 : S u r f a c e
angle.
azimuth
angle.
Fig. 2. Orientation angle of a given surface on earth.
70
Aqabo
60
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Technical Note
locations under study are given. These regions represent the main climatological variation in Jordan, and are the most important sites for eventual applications of solar energy. The global radiation on a horizontal surface (by actinographs) is currently measured by the Jordanian Meteorological Department. In 1986 the Royal Scientific Society installed nine stations equipped with data loggers and pyranometers in different locations of Jordan. The measured global radiation on a horizontal surface fcr such regions is shown in Table 2.
The input data to the program are: 12 monthly data of daily average of global radiation, latitude o f the site, albedo (appropriate values for such quantity can be obtained from Table 3), single array or rows (if rows selected, the minimum distance between rows is assumed according to eq. (1), in Section 2.1.I.). The subdivision of the total radiation collected by the PV array into beam, diffuse and albedo components is also done by this program. Results and discussions
6. DETERMINATION OF O P T I M U M TILT ANGLES Calculation of the optimum tilt angles for the selected sites required a computer program that was developed at the RSS.
The optimum tilt angles and the relevant beam, diffuse and albedo components for single row and multi rows of PV systems in the selected sites, which were determined by the above mentioned program, are shown in Tables 4 and 5.
Table 4. Monthly averages of daily beam, albedo and diffuse radiation on the calculated optimum surface angle (expressed in kWh/m ~ day) for single row PV systems in the selected sites Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
63 5.672 0.513 0.463 6.648
54 5.355 0.742 0.393 6.489
33 3.978 1.398 0.124 5.499
11 5.127 1.528 0.001 6.656
0 5.126 1.927 0 7.053
0 5.616 1.902 0 7.518
0 5.7 1.818 0 7.518
8 4.839 1.724 0 6.563
28 4.929 1.303 0.091 6.323
50 5.073 0.878 0.347 6.298
60 5.242 0.623 0.424 6.289
62 3.612 0.691 0.334 4.637
Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m 2)
60 2.515 0.753 0.258 3.526
50 2.377 1.055 0.207 3.640
31 2.454 1.569 0.079 4.102
l0 2.766 2.061 0 4.827
0 3.50 2.272 0 5.775
0 4.00 2.309 0 6.309
0 4.04 2.246 0 6.286
9 3.392 2.076 0 5.468
27 3.324 1.634 0.066 5.023
50 3.272 1.096 0.266 4.634
60 3.062 0.784 0.304 4.150
62 2.739 0.686 0.252 3.317
Ghor sail Optimum tilt angle (deg.) Beam (kWh/m 2) Beam (kWh/m:) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m z)
62 4.264 0.651 0.651 0.372 5.286
52 3.593 0.979 0.979 0.285 4.857
34 3.403 1.461 1.461 0.122 4.986
11 3.520 1.948 1.948 0 5.469
0 4.363 2.121 2.121 0 6.484
0 4.89 2.115 2.115 0 7.007
0 4.723 2.098 2.098 0 6.821
9 4.226 1.894 1.894 0 6.12
28 4.143 1.482 1.482 0.082 5.708
50 4.441 0.964 0.964 0.316 5.721
61 4.410 0.685 0.685 0.389 5.484
65 3.973 0.607 0.607 0.371 4.952
Irbid Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m 2)
64 4.355 0.595 0.386 5.336
54 4.015 0.882 0.319 5.217
36 3.814 1.349 0.148 5.311
13 3.766 1.871 0.003 5.639
0 5.046 1.938 0 6.984
0 5.712 1.887 0 7.599
0 5.848 1.775 0 7.623
l0 5.182 1.599 0 6.781
31 5.154 1.184 0.122 6.46
53 5.395 0.75 0.389 6.534
63 5.244 0.547 0.438 6.229
66 4.605 0.517 0.394 5.517
Shoubak Optimum tilt angle (deg.) Beam (kWh/m z) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m 2)
63 5.421 0.504 0.488 6.413
54 5.173 0.747 0.395 6.315
37 5.142 1.083 0.189 6.414
13 5.085 1.53 0.002 6.617
0 6.05 1.646 0 7.692
0 6.71 1.552 0 8.26
0 6.82 1.444 0 8.26
9 6.254 1.22 0 7.474
31 6.270 0.870 0.125 7.26
48 6.578 0.568 0.352 7.498
62 6.452 0.42 0.494 7.37
66 5.598 0.454 0.463 6.515
Kharana Optimum tilt angle (deg.) Beam (kWh/m z) Diffuse (kWh/m 2) Albedo (kWh/m z) Total (kWh/m 2)
62 3.886 0.669 0.348 4.904
55 5.085 0.743 0.382 6.210
37 4.297 1.261 0.171 5.729
15 5.094 1.504 0.009 6.607
0 6.07 1.64 0 7.716
0 6.32 1.70 0 8.018
0 6.29 1.640 0 7.925
9 5.171 1.607 0 6.778
31 5.260 1.163 0.125 6.548
51 4.756 0.893 0.339 5.987
62 4.562 0.648 0.403 5.613
64 3.347 0.642 0.323 4.313
Aqaba Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m 2) Amman
Technical Note
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744
Technical Note
Figure 3 shows the yearly behavior of the monthly averages of the calculated optimum tilt angles, while Fig. 4 shows the distribution of the monthly average of solar radiation intensity received on the surfaces at these angles. As can be observed, the annual optimum tilt angle for multi rows PV system, is always less than that of single row system due to the fact that multiple rows of modules do not collect the radiation reflected by the ground (except, of course, for the first row). Moreover they collect a reduced a m o u n t of diffuse radiation, due to the presence of the other rows as shown in Fig. 5. Since the optimum tilt angle over a full year must balance the summer m a x i m u m and winter m i n i m u m declination angle, and to maximize the solar energy received during the winter and summer months, the PV mounting structure has to be constructed for seasonal mounting at three tilt angles (latitude, latitude - 1 0 , latitude +20). A comparison between the monthly average of the daily solar radiation received at three different tilt angle surfaces and that of a surface fixed at the optimum tilt angle is shown in Table 6.
According to this table the variable angle mounting structure shows an annual average of 5.6% improvement in radiation received over the structure with fixed optimum tilt angle. This means that for a photovoltaic pumping system which is designed for pumping 40 m3/day, the increment in the daily pumped water, using variable-angle mounting structure, is equal to 2.24 m 3. The above mentioned percentage increases to achieve the double value during the main winter months. It is worth mentioning, that this improvement is achieved without considerable additional cost.
7. C O N C L U S I O N S The following conclusions are drawn from this study : (a) From a technical and economical viewpoint, utilizing the variable angle mounting structure is better than incurring an additional investment in increasing the capacity of the PV plant. (b) The cost of the photovoltaic-array structure must be as low as possible without affecting durability. The struc-
Table 5. Monthly averages of daily beam and diffuse radiation on the calculated optimum tilt angles (expressed in k W h / m 2 day) for multi row PV systems in the selected sites Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
Aqaba O p t i m u m tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Total (kWh/m 2)
53 5.676 0.47 6.146
42 5.343 0.718 6.061
24 3.932 1.373 5.305
l0 5.122 1.495 6.618
0 5.126 1.927 7.053
0 5.616 1.902 7.518
0 5.7 1.818 7.518
8 4.838 1.685 6.523
20 4.901 1.284 6.185
38 5.054 0.858 5.912
50 5.234 0.577 5.811
51 3.569 0.646 4.215
Amman O p t i m u m tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Total (kWh/m 2)
47 2.462 0.728 3.19
35 2.284 1.076 3.36
19 2.362 1.591 3.953
10 2.766 2.013 4.779
0 3.153 2.222 5.375
0 3.62 2.258 5.879
0 3.662 2.196 5.859
9 3.392 2.03 5.422
17 3.255 1.641 4.896
35 3.199 1.117 4.317
47 3.014 0.768 3.782
50 2.328 0.66 2.988
G h o r sail Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m z) Total (kWh/m 2)
52 4.236 0.604 4.84
39 3.528 0.97 4.498
23 3.336 1.462 4.798
l0 3.515 1.908 5.423
0 4.363 2.121 6.484
0 4.89 2.115 7.007
0 4.723 2.098 6.821
9 4.226 1.852 6.078
19 4.094 1.474 5.567
39 4.410 0.936 5.346
50 4.39 0.648 5.038
53 3.939 0.577 4.516
lrbid Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Total (kWh/m 2)
54 4.335 0.555 4.890
43 3.975 0.854 4.829
26 3.757 1.336 5.094
10 3.747 1.845 5.592
0 5.046 1.938 6.984
0 5.712 1.887 7.599
0 5.848 1.775 7.623
9 5.18 1.565 6.745
23 5.124 1.163 6.287
43 5.394 0.718 6.112
53 5.24 0.511 5.752
57 5.589 0.472 5.061
Shoubak Optimum tilt angle (deg.) Beam ( k W h / m 2) Diffuse (kWh/m 2) Total (kWh/m:)
54 5.447 0.476 5.923
44 5.162 0.725 5.887
28 5.125 1.057 6.182
l0 5.073 1.503 6.576
0 6.083 1.609 7.692
0 6.743 1.517 8.26
0 6.85 1.412 8.26
9 6.254 1.193 7.447
24 6.259 0.847 7.106
43 6.565 0.52 7.085
53 6.477 0.377 6.854
51 5.607 0.408 6.015
Kharana O p t i m u m tilt angle (deg.) Beam (kWh/m z) Diffuse (kWh/m-') Total (kWh/m 2)
51 3.844 0.634 4.478
45 5.074 0.706 5.780
26 4.248 1.257 5.504
10 5.066 1.494 6.561
0 6.07 1.64 7.716
0 6.32 1.70 8.018
0 6.29 1.64 7.925
9 5.173 1.571 6.745
23 5.241 1.141 6.382
39 4.717 0.877 5.594
50 4.538 0.622 5.16
53 3.317 0.595 3.913
Technical Note
745
Table 6. Comparison between energy (expressed in k W h / m 2) received at a fixed angle surface and that received at a surface tilted at three different tilt angles Total radiation received at given surface angle Aqaba O p t i m u m tilt 20 ° tilt 30" tilt 50 '~ tilt
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
5.809 6.065 5.493 6,454 5,932 6.041 6,173 6.189 6.32 6.612 6.28 6.494 6.59 6.426 5.493 6.32 6.511 6.478
Oct.
Nov.
Dec.
6,042 5,637 4.112
5.86 "} j~ 6.2
6,298 6.209 4.554
Amman O p t i m u m tilt 20' tilt 30 ° tilt 50°tilt
3.105 3.429 4.089 4.739 5.078 5.377 5.44 5.293 5.022 4,394 3.667 2.870 4.38 4,785 5.195 5,535 5.583 5.371 } 4.102 5.02 ~ 4.56 3.49 3.641 4,636 4,114 3,266
G h o r sail 20 ° tilt 20 ° tilt 30 ° tilt 50 ° tilt
4.663 4.602 4,979 5.302 5.515 5.713 5.681 5.807 5.705 4.481 4.92 4,302 5.14 5.428 5.811 6.106 6.029 6.009 "1 4.979 5,705 ~ 5,505 5.186 4.854 5,721 5,411 4.83
Irbid O p t i m u m tilt 20 ° tilt 30 ° tilt 50 ° tilt
4.752 4.953 5.304 5.454 5.877 6.083 6,249 6,413 6,459 6,237 5.58 4,798 5.68 5.615 6.292 6.643 6.763 6.693 "1 5.288 6.458 ~ 6.01 5.209 5.204 6.524 6.101 5,334
Shoubak O p t i m u m tilt 2O° tilt 30 ° tilt 50 ° tilt
5,715 5.981 6.404 6.379 6.365 6,468 6.639 7,002 7.262 7.188 6.608 5,681 6.47 6.586 6.871 7.138 7.254 7.352 ") 6.383 7.265 ~ 6.87 6.271 6.3 7,511 7,226 6.313
Kharana O p t i m u m tilt 20 ° tilt 30 ° tilt 50 ° tilt
4.30
5,711 5.695 6.481 6.607 6.558 6.632 6.493 6,546 5.671 4.958 3.746 5.78 6,588 6.927 6.972 7.001 6.679 ] 5,703 6.547 ~ 6.1 4.812 6.188 5.985 5.525 4.215
ture must be able to withstand the worst wind loading conditions expected at the site. (c) Multi rows of photovoltaic arrays collect the m a x i m u m annual energy at a tilt angle lower than that of a single row photovoltaic arrays, which is due to the fact that
" RefLected diffuse
r=,,oo/ /
~
~
•
CoLLecteddiffuse ~ ~'~
radiation
/
~
j
Fig. 5. Portion of diffuse radiation shadowed by the PV array/string placed in front.
multi rows of modules do not collect the radiation reflected by the ground as well as they collect less diffuse radiation. So it is always advisable to arrange the modules into single rows wherever there is enough area. (d) The variable-angle m o u n t i n g structure shows an annual average of 5.6% improvement in radiation received over the structure with fixed o p t i m u m tilt angle. Fortunately this percentage increases to reach twice its value during the winter season. REFERENCES I. Matthew Buresch, PhotovoltaicEnergy Systems. McGrawHill, New York (1983). 2. P. Spirito and G. F. Vital, Electrical energy production from renewable energy sources. Photovoltaic systems and use of local resources. Sogesta, Italy (1988).
0741-983X/90 $3.00+.00 PergamonPressplc
Printed in Great Britain.
TECHNICAL NOTE Determination of optimum tilt angle of single and multi rows of photovoltaic arrays for selected sites in Jordan MARWAN MAHMOUD and
ISMAIL N A B H A N
Royal Scientific Society, Renewable Energy Research Centre, P.O. Box 925819, A m m a n , Jordan (Received 20 October 1989 ; accepted 24 November 1989)
Abstract--Solar radiation measured by the Jordanian Meteorological Department (using actinographs) at six Jordanian sites during some, or most, of the period from 1971 to 1987 has been analysed to determine the monthly, and thus the yearly, o p t i m u m tilt angles for both single row and multi-rows o f photovoltaic arrays operating in such sites. Also a comparison between the solar energy captured by a stationary mounting structure and that captured by a variable-angle mounting structure is carried out. Relative to structures of constant tilt angle the results obtained show an improvement of 5.6% by using PV-mounting structures of adjustable tilt angle.
1. I N T R O D U C T I O N
lishment: rack and direct. The rack design can be used to m o u n t modules on the ground or a fiat roof. The direct design specifically represents ways of attaching modules to a house with a south-facing sloped roof in the northern hemisphere.
The photovoltaic array can be fixed or it can be tracking the sun with or without concentrating capability. For rural/ remote applications where PV systems are expected to operate reliably with m i n i m u m maintenance, the tracking configuration is not practical because the mechanical assembly required to track the sun generally outweighs the extra energy gained through tracking. As an alternative for the tracking configuration, the variable-angle mounting structure is proposed and studied in detail in this paper.
2.1.1. Rack mount. Photovoltaic modules installed on a horizontal surface, be it the ground or a fiat roof, are mounted on a tilted support frame or rack. There is a wide variety of rack designs made of aluminium or hot galvanized steel to ensure a high corrosion protection of the PV array. Some rack m o u n t designs afford the option of tracking the sun or adjusting the tilt a n g l e b y simply loosening or moving a bolt. A rack m o u n t provides easy access to the front and rear of the module for maintenance and testing. The module operating temperature is as low as possible, since outdoor ventilation of the front and back of the modules provides quick heat transfer. Racks situated on the ground m u s t be m o u n t e d on a solid concrete foundation to prevent high winds from uprooting the array support. Poured concrete or concrete blocks with auger-type anchors screwed into the ground will serve this purpose. Large arrays that are mounted on the ground are arranged in rows that are set sufficiently far apart to prevent one row from shading another. The m i n i m u m distance, X, between rows of PV-arrays is given by the equation :
2. P H O T O V O L T A I C ARRAY I N S T A L L A T I O N A photovoltaic array consists of any number of photovoltaic modules connected together electrically to provide a single electrical output with a certain nominal voltage and power. The installation of a photovoltaic array can be divided into two separate tasks: physical and electrical. The physical installation involves m o u n t i n g the photovoltaic modules on a sturdy frame that will maintain the array's tilt and position throughout the worst weather conditions. The electrical installation entails wiring the modules together in their prescribed parallel and/or series configuration and leading the main power lines to the power-conditioning equipment and the load.
X = L[sin S tan (23.5 ° +
2.1. Physical installation
A variety of factors must be considered when physically installing a photovoltaic array. A support structure must be able to support the modules through adverse wind and weather for the expected lifetime of the array, and yet be situated in a location where sunlight all year around is not blocked. The price of a mounting structure must be kept as low as possible. Finally, since photovoltaic arrays are often installed in areas of high visibility, they need to be physically agreeable. Two basic photovoltaic-module m o u n t i n g schemes are usually used by industry and research estab-
(1)
where: L = the length of the arrays as shown in Fig. 1 ; ~b = site latitude (degree) ; S = tilt angle (degree). 2.1.2. Direct mount. The asphalt shingles of a conventional
roof can be replaced by a solar-cell shingles in a direct-mount configuration. This configuration affords no ventilation of the module's back surface, and as a result the solar-cell operating temperature in the daytime is on average about 20°C to 30°C higher than with the rack configuration. A higher operating temperature decreases the cell efficiency and sub739
740
Technical Note Table 1. Geographical positions of selected sites
Station Amman Aqaba lrbid G h o r Sail Kharana Shoubak
Table 3. Reflectivity values for 15 characteristic surfaces
Altitude (m)
Lat. 'N
Long. ~'E
766 2 616 -350 650 1365
31.98 29.52 32.55 31.03 31.70 30.52
35.98 35 35.85 35.47 36.48 35.33
stantially increases the chances of temperature-induced malfunctions, such as cell cracking or the degradation of materials. Direct-mount installation costs are fairly low, since there is a little mounting hardware involved. 2.2. Electrical installation The electrical installation of a photovoltaic array involves a variety of tasks to ensure that various components are well interconnected and protected. The right type of electrical wire for the particular application must be selected and routed in a safe way, especially for the PV arrays mounted on a variable tilt angle-support structure. Connections between the wire and various terminals on a solar-cell module or system must be made securely.
No.
Average reflectivity
Surface
l 2
Snow (freshly fallen or with ice film) Water surfaces (relatively large incidence angles) 3 Soils (clay, loam) 4 Earth roads 5 Coniferous forest (winter) 6 Forests in autumn, ripe field crops, plants 7 Weathered blacktop 8 Weathered concrete 9 Dead leaves 10 Dry grass 11 Green grass 12 Bituminous and gravel roof 13 Crushed rock surface 14 Building surfaces, dark (red brick, dark paints) 15 Building surfaces, light (light brick, light paints)
0.75 0.07 0.14 0.04 0.07 0.26 0.10 0.22 0.30 0.20 0.26 0.13 0.20 0.27 0.60
horizontal, the a m o u n t of diffuse light decreases while the proportion of light reflected off the ground increases.
3. S U R F A C E O R I E N T A T I O N AND S O L A R INTENSITY
4. O P T I M U M S U R F A C E O R I E N T A T I O N
The orientation of a surface on earth is defined by two angles : the surface tilt or slope angle and the surface azimuth angle, as shown in Fig. 2. The tilt angle indicates how far up from the horizontal a surface is slanted, while the azimuth angle denotes how the surface is positioned relative to the true n o r t ~ s o u t h and east west coordinates (due south represents an azimuth angle of 0 ~, due east is - 9 0 °, north is 180 ° and west is + 90°). The sunlight received by a surface on earth can be divided into three different types : direct, diffuse and reflected. Diffuse sunlight approaches a surface from all unobstructed angles, while direct-beam rays strike the surface from only one angle. In addition to diffuse and direct light, an angled surface can also receive reflected light from the ground or other appropriately positioned surfaces. As a result, a horizontal surface with a zero tilt angle receives the m a x i m u m diffuse and m i n i m u m reflected light possible, and as a south-facing surface is tilted up from the
The a m o u n t of direct-beam solar energy that a surface receives is optimized by keeping the surface at right angles to the sun's direct radiation at all times of the day. In most cases, maneuvering a surface is impractical and affects the system reliability negatively. The cost of the energy and the mechanical assembly required to track the sun consistently each day generally outweighs the extra energy obtained through tracking when fiat-plate solar-cell modules without concentrators are used. The next best propositions are to fix the surface's position so that the sun's angle on the plane is closest to the perpendicular most of the time, or to make it able to be constructed for seasonal adjustment. 5. S O L A R R A D I A T I O N IN T H E S E L E C T E D SITES The sites considered in this study are located roughly between 29.52 ° and 32.55 ° N, latitude and 35 ° and 36.48 ° E, longitude. In Table 1, the geographical positions of the
Table 2. Monthly averages of daily solar radiation intensity (kWh/m 2) on a horizontal plane for the selected sites Station
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
Amman Aqaba Irbid G h o r Sail Kharana Shoubak
2.475 3.985 3.207 3.31 3.102 3.80
3.021 4.776 3.881 3.788 4.45 4.601
3.985 5.217 4.927 4.741 5.287 5.868
5.043 6.925 5.856 5.705 6.832 6.867
5.775 7.053 6.984 6.484 7.716 7.692
6.31 7.518 7.60 7.00 8.018 8.262
6.286 7.518 7.622 6.821 7.925 8.262
5.763 6.925 7.111 6.449 7.123 7.855
4.973 6.193 6.159 5.600 6.275 6.925
3.881 5.054 4.94 4.601 4.706 5.647
2.917 4.067 3.765 3.59 3.59 4.404
2.243 2.975 3.067 2.986 2.684 3.602
Technical Note
L
×
741
4 ~
Fig. 1. M i n i m u m distance between rows of PV-arrays.
West
North
sourS °
--
East
19 = S u r f a c e
tilt
~5 : S u r f a c e
angle.
azimuth
angle.
Fig. 2. Orientation angle of a given surface on earth.
70
Aqabo
60
Single
row
---
Multi
rows
---.
40 3O
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.
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742
Technical Note
locations under study are given. These regions represent the main climatological variation in Jordan, and are the most important sites for eventual applications of solar energy. The global radiation on a horizontal surface (by actinographs) is currently measured by the Jordanian Meteorological Department. In 1986 the Royal Scientific Society installed nine stations equipped with data loggers and pyranometers in different locations of Jordan. The measured global radiation on a horizontal surface fcr such regions is shown in Table 2.
The input data to the program are: 12 monthly data of daily average of global radiation, latitude o f the site, albedo (appropriate values for such quantity can be obtained from Table 3), single array or rows (if rows selected, the minimum distance between rows is assumed according to eq. (1), in Section 2.1.I.). The subdivision of the total radiation collected by the PV array into beam, diffuse and albedo components is also done by this program. Results and discussions
6. DETERMINATION OF O P T I M U M TILT ANGLES Calculation of the optimum tilt angles for the selected sites required a computer program that was developed at the RSS.
The optimum tilt angles and the relevant beam, diffuse and albedo components for single row and multi rows of PV systems in the selected sites, which were determined by the above mentioned program, are shown in Tables 4 and 5.
Table 4. Monthly averages of daily beam, albedo and diffuse radiation on the calculated optimum surface angle (expressed in kWh/m ~ day) for single row PV systems in the selected sites Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
63 5.672 0.513 0.463 6.648
54 5.355 0.742 0.393 6.489
33 3.978 1.398 0.124 5.499
11 5.127 1.528 0.001 6.656
0 5.126 1.927 0 7.053
0 5.616 1.902 0 7.518
0 5.7 1.818 0 7.518
8 4.839 1.724 0 6.563
28 4.929 1.303 0.091 6.323
50 5.073 0.878 0.347 6.298
60 5.242 0.623 0.424 6.289
62 3.612 0.691 0.334 4.637
Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m 2)
60 2.515 0.753 0.258 3.526
50 2.377 1.055 0.207 3.640
31 2.454 1.569 0.079 4.102
l0 2.766 2.061 0 4.827
0 3.50 2.272 0 5.775
0 4.00 2.309 0 6.309
0 4.04 2.246 0 6.286
9 3.392 2.076 0 5.468
27 3.324 1.634 0.066 5.023
50 3.272 1.096 0.266 4.634
60 3.062 0.784 0.304 4.150
62 2.739 0.686 0.252 3.317
Ghor sail Optimum tilt angle (deg.) Beam (kWh/m 2) Beam (kWh/m:) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m z)
62 4.264 0.651 0.651 0.372 5.286
52 3.593 0.979 0.979 0.285 4.857
34 3.403 1.461 1.461 0.122 4.986
11 3.520 1.948 1.948 0 5.469
0 4.363 2.121 2.121 0 6.484
0 4.89 2.115 2.115 0 7.007
0 4.723 2.098 2.098 0 6.821
9 4.226 1.894 1.894 0 6.12
28 4.143 1.482 1.482 0.082 5.708
50 4.441 0.964 0.964 0.316 5.721
61 4.410 0.685 0.685 0.389 5.484
65 3.973 0.607 0.607 0.371 4.952
Irbid Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m 2)
64 4.355 0.595 0.386 5.336
54 4.015 0.882 0.319 5.217
36 3.814 1.349 0.148 5.311
13 3.766 1.871 0.003 5.639
0 5.046 1.938 0 6.984
0 5.712 1.887 0 7.599
0 5.848 1.775 0 7.623
l0 5.182 1.599 0 6.781
31 5.154 1.184 0.122 6.46
53 5.395 0.75 0.389 6.534
63 5.244 0.547 0.438 6.229
66 4.605 0.517 0.394 5.517
Shoubak Optimum tilt angle (deg.) Beam (kWh/m z) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m 2)
63 5.421 0.504 0.488 6.413
54 5.173 0.747 0.395 6.315
37 5.142 1.083 0.189 6.414
13 5.085 1.53 0.002 6.617
0 6.05 1.646 0 7.692
0 6.71 1.552 0 8.26
0 6.82 1.444 0 8.26
9 6.254 1.22 0 7.474
31 6.270 0.870 0.125 7.26
48 6.578 0.568 0.352 7.498
62 6.452 0.42 0.494 7.37
66 5.598 0.454 0.463 6.515
Kharana Optimum tilt angle (deg.) Beam (kWh/m z) Diffuse (kWh/m 2) Albedo (kWh/m z) Total (kWh/m 2)
62 3.886 0.669 0.348 4.904
55 5.085 0.743 0.382 6.210
37 4.297 1.261 0.171 5.729
15 5.094 1.504 0.009 6.607
0 6.07 1.64 0 7.716
0 6.32 1.70 0 8.018
0 6.29 1.640 0 7.925
9 5.171 1.607 0 6.778
31 5.260 1.163 0.125 6.548
51 4.756 0.893 0.339 5.987
62 4.562 0.648 0.403 5.613
64 3.347 0.642 0.323 4.313
Aqaba Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Albedo (kWh/m 2) Total (kWh/m 2) Amman
Technical Note
/ -E
----
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743
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Fig. 4.
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i
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744
Technical Note
Figure 3 shows the yearly behavior of the monthly averages of the calculated optimum tilt angles, while Fig. 4 shows the distribution of the monthly average of solar radiation intensity received on the surfaces at these angles. As can be observed, the annual optimum tilt angle for multi rows PV system, is always less than that of single row system due to the fact that multiple rows of modules do not collect the radiation reflected by the ground (except, of course, for the first row). Moreover they collect a reduced a m o u n t of diffuse radiation, due to the presence of the other rows as shown in Fig. 5. Since the optimum tilt angle over a full year must balance the summer m a x i m u m and winter m i n i m u m declination angle, and to maximize the solar energy received during the winter and summer months, the PV mounting structure has to be constructed for seasonal mounting at three tilt angles (latitude, latitude - 1 0 , latitude +20). A comparison between the monthly average of the daily solar radiation received at three different tilt angle surfaces and that of a surface fixed at the optimum tilt angle is shown in Table 6.
According to this table the variable angle mounting structure shows an annual average of 5.6% improvement in radiation received over the structure with fixed optimum tilt angle. This means that for a photovoltaic pumping system which is designed for pumping 40 m3/day, the increment in the daily pumped water, using variable-angle mounting structure, is equal to 2.24 m 3. The above mentioned percentage increases to achieve the double value during the main winter months. It is worth mentioning, that this improvement is achieved without considerable additional cost.
7. C O N C L U S I O N S The following conclusions are drawn from this study : (a) From a technical and economical viewpoint, utilizing the variable angle mounting structure is better than incurring an additional investment in increasing the capacity of the PV plant. (b) The cost of the photovoltaic-array structure must be as low as possible without affecting durability. The struc-
Table 5. Monthly averages of daily beam and diffuse radiation on the calculated optimum tilt angles (expressed in k W h / m 2 day) for multi row PV systems in the selected sites Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
Aqaba O p t i m u m tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Total (kWh/m 2)
53 5.676 0.47 6.146
42 5.343 0.718 6.061
24 3.932 1.373 5.305
l0 5.122 1.495 6.618
0 5.126 1.927 7.053
0 5.616 1.902 7.518
0 5.7 1.818 7.518
8 4.838 1.685 6.523
20 4.901 1.284 6.185
38 5.054 0.858 5.912
50 5.234 0.577 5.811
51 3.569 0.646 4.215
Amman O p t i m u m tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Total (kWh/m 2)
47 2.462 0.728 3.19
35 2.284 1.076 3.36
19 2.362 1.591 3.953
10 2.766 2.013 4.779
0 3.153 2.222 5.375
0 3.62 2.258 5.879
0 3.662 2.196 5.859
9 3.392 2.03 5.422
17 3.255 1.641 4.896
35 3.199 1.117 4.317
47 3.014 0.768 3.782
50 2.328 0.66 2.988
G h o r sail Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m z) Total (kWh/m 2)
52 4.236 0.604 4.84
39 3.528 0.97 4.498
23 3.336 1.462 4.798
l0 3.515 1.908 5.423
0 4.363 2.121 6.484
0 4.89 2.115 7.007
0 4.723 2.098 6.821
9 4.226 1.852 6.078
19 4.094 1.474 5.567
39 4.410 0.936 5.346
50 4.39 0.648 5.038
53 3.939 0.577 4.516
lrbid Optimum tilt angle (deg.) Beam (kWh/m 2) Diffuse (kWh/m 2) Total (kWh/m 2)
54 4.335 0.555 4.890
43 3.975 0.854 4.829
26 3.757 1.336 5.094
10 3.747 1.845 5.592
0 5.046 1.938 6.984
0 5.712 1.887 7.599
0 5.848 1.775 7.623
9 5.18 1.565 6.745
23 5.124 1.163 6.287
43 5.394 0.718 6.112
53 5.24 0.511 5.752
57 5.589 0.472 5.061
Shoubak Optimum tilt angle (deg.) Beam ( k W h / m 2) Diffuse (kWh/m 2) Total (kWh/m:)
54 5.447 0.476 5.923
44 5.162 0.725 5.887
28 5.125 1.057 6.182
l0 5.073 1.503 6.576
0 6.083 1.609 7.692
0 6.743 1.517 8.26
0 6.85 1.412 8.26
9 6.254 1.193 7.447
24 6.259 0.847 7.106
43 6.565 0.52 7.085
53 6.477 0.377 6.854
51 5.607 0.408 6.015
Kharana O p t i m u m tilt angle (deg.) Beam (kWh/m z) Diffuse (kWh/m-') Total (kWh/m 2)
51 3.844 0.634 4.478
45 5.074 0.706 5.780
26 4.248 1.257 5.504
10 5.066 1.494 6.561
0 6.07 1.64 7.716
0 6.32 1.70 8.018
0 6.29 1.64 7.925
9 5.173 1.571 6.745
23 5.241 1.141 6.382
39 4.717 0.877 5.594
50 4.538 0.622 5.16
53 3.317 0.595 3.913
Technical Note
745
Table 6. Comparison between energy (expressed in k W h / m 2) received at a fixed angle surface and that received at a surface tilted at three different tilt angles Total radiation received at given surface angle Aqaba O p t i m u m tilt 20 ° tilt 30" tilt 50 '~ tilt
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
5.809 6.065 5.493 6,454 5,932 6.041 6,173 6.189 6.32 6.612 6.28 6.494 6.59 6.426 5.493 6.32 6.511 6.478
Oct.
Nov.
Dec.
6,042 5,637 4.112
5.86 "} j~ 6.2
6,298 6.209 4.554
Amman O p t i m u m tilt 20' tilt 30 ° tilt 50°tilt
3.105 3.429 4.089 4.739 5.078 5.377 5.44 5.293 5.022 4,394 3.667 2.870 4.38 4,785 5.195 5,535 5.583 5.371 } 4.102 5.02 ~ 4.56 3.49 3.641 4,636 4,114 3,266
G h o r sail 20 ° tilt 20 ° tilt 30 ° tilt 50 ° tilt
4.663 4.602 4,979 5.302 5.515 5.713 5.681 5.807 5.705 4.481 4.92 4,302 5.14 5.428 5.811 6.106 6.029 6.009 "1 4.979 5,705 ~ 5,505 5.186 4.854 5,721 5,411 4.83
Irbid O p t i m u m tilt 20 ° tilt 30 ° tilt 50 ° tilt
4.752 4.953 5.304 5.454 5.877 6.083 6,249 6,413 6,459 6,237 5.58 4,798 5.68 5.615 6.292 6.643 6.763 6.693 "1 5.288 6.458 ~ 6.01 5.209 5.204 6.524 6.101 5,334
Shoubak O p t i m u m tilt 2O° tilt 30 ° tilt 50 ° tilt
5,715 5.981 6.404 6.379 6.365 6,468 6.639 7,002 7.262 7.188 6.608 5,681 6.47 6.586 6.871 7.138 7.254 7.352 ") 6.383 7.265 ~ 6.87 6.271 6.3 7,511 7,226 6.313
Kharana O p t i m u m tilt 20 ° tilt 30 ° tilt 50 ° tilt
4.30
5,711 5.695 6.481 6.607 6.558 6.632 6.493 6,546 5.671 4.958 3.746 5.78 6,588 6.927 6.972 7.001 6.679 ] 5,703 6.547 ~ 6.1 4.812 6.188 5.985 5.525 4.215
ture must be able to withstand the worst wind loading conditions expected at the site. (c) Multi rows of photovoltaic arrays collect the m a x i m u m annual energy at a tilt angle lower than that of a single row photovoltaic arrays, which is due to the fact that
" RefLected diffuse
r=,,oo/ /
~
~
•
CoLLecteddiffuse ~ ~'~
radiation
/
~
j
Fig. 5. Portion of diffuse radiation shadowed by the PV array/string placed in front.
multi rows of modules do not collect the radiation reflected by the ground as well as they collect less diffuse radiation. So it is always advisable to arrange the modules into single rows wherever there is enough area. (d) The variable-angle m o u n t i n g structure shows an annual average of 5.6% improvement in radiation received over the structure with fixed o p t i m u m tilt angle. Fortunately this percentage increases to reach twice its value during the winter season. REFERENCES I. Matthew Buresch, PhotovoltaicEnergy Systems. McGrawHill, New York (1983). 2. P. Spirito and G. F. Vital, Electrical energy production from renewable energy sources. Photovoltaic systems and use of local resources. Sogesta, Italy (1988).