Estimating the Optimum Tilt Angles for South-Facing Surfaces in Palestine
Abstract
:1. Introduction
1.1. Physical Characteristics of Palestine
1.2. The Situation of Electric Energy in Palestine and Net-Metering Regulations
2. Methodology
Solar Angles
3. Literature Review
4. Results and Discussion
4.1. Part One: Mathematical Model Results
4.1.1. Daily Optimum Tilt Angle
4.1.2. Monthly Optimum Tilt Angle
4.1.3. Seasonal Optimum Tilt Angle
4.1.4. Semi-annually Optimum Tilt Angle
4.1.5. Annually Optimum Tilt Angle
4.2. Part Two: Results Based on PVWatts and PVGIS
5. Case Studies of two Palestinian Cities
6. Comparison of the Present Work with Previously Published Papers
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
δ | Declination angle |
n | The day number |
Latitude angle | |
h | Hour angle |
α | The altitude angle |
hs | The hour angles at sunrise and sunset |
β | The tilt angle |
ASHRAE | American Society of Heating, Refrigerating and Air-Conditioning Engineers |
Id | Daily extraterrestrial radiation |
Ip | Extraterrestrial radiation for a particular period |
PV | Photovoltaic |
βopt,d | Daily optimum tilt angle |
βopt,m | Monthly optimum tilt angle |
Im | Monthly total extraterrestrial radiation |
F | The tilt factor |
βopt,s | Seasonally optimum tilt angle |
Is | Seasonal extraterrestrial radiation |
βopt,sa | Semi-annual optimum angle |
Isa | Semi-annal extraterrestrial radiation |
Iy | The yearly extra-terrestrial radiation |
βopt,y | The annual optimum tilt angle |
PEA | Palestinian Energy Authority |
PCBS | Palestinian Central Bureau of Statistics |
NREL | National Renewable Energy Laboratory -USA |
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Location | Tilt Angle (Optimum in Degree) | Latitude | Reference |
---|---|---|---|
Damascus | 30.56° | 33.5° | [26] |
Northern Jordan | 30° Average 10° Summer 50° Winter | 32.5° | [27] |
Austria | 30° | 47.5° | [28] |
Germany | 45° | 51.2° | [28] |
Tehran | 35.7° | 35.7° | [29] |
Isfahan | 32° | 36.5° | [29] |
Shiraz | 29.4° | 29.6° | [29] |
Mashhad | 36.2° | 36.3° | [29] |
Tabriz | 38° | 38.1° | [29] |
Pristina | 8.9° Summer 25.7° Spring 50.9° Autumn 62.1° Winter 34.7° Average | 42.7° | [19] |
Cyprus | 20° Summer 50° Winter | 35.1° | [23] |
Montreal | 37° | 45.5° | [30] |
Bordeaux | 33° | 44.8° | [30] |
Cologne | 32° | 50.9° | [30] |
Hong Kong | 20° | 22.4° | [30] |
Rajko | 24° | 42.1° | [30] |
Zahedan | 26.70° | 29.5° | [30] |
Birjand | 29.93° | 32.9° | [31] |
Shraz | 25.88° | 52.9° | [31] |
Tabas | 30.16° | 33.6° | [31] |
Yazd | 29.05° | 31.9° | [31] |
Kerman | 23.95° | 36.7° | [31] |
Assiut | 27° | 27.2° | [32] |
Valencia | 31° | 39° | [33] |
Darussalam | 3.3° | 4.5° | [34] |
Beijing | 39.2° | 39.9° | [35] |
Kunming | 27.9° | 24.9° | [35] |
Shanghai | 28° | 31.2° | [35] |
Guangzhou | 22° | 23.1° | [35] |
Chengdu | 23° | 30.6° | [35] |
Xi’an | 30.1° | 34.3° | [35] |
Yinchuang | 38.3° | 38.5° | [35] |
Shenyang | 40.3° | 41.8° | [35] |
Izmir | 0° June 61° December | 38.4° | [36] |
Gaza Strip | 32.1° | 31.5° | [37] |
Damascus | 33.7° | 33.5° | [37] |
Beirut | 33.8° | 33.9° | [37] |
Tunis | 35.2° | 33.9° | [37] |
Seville | 36.6° | 37.4° | [37] |
Milan | 41.8° | 45.5° | [37] |
Mu’tah | 28.5° | 31.7° | [11] |
Sanya | −18.1° June 49.9° December | −11.5° | [38] |
Shanghai | −7.6° June 61.4° December | 31.2° | [38] |
Zhengzhou | 5.5° June 64.3° December | 34.7° | [38] |
Harbin | 12.6° June 73.7° December | 45.8° | [38] |
Mohe | 16.6° June 80.0° December | 52.9° | [38] |
Lhasa | −8.9° June 59.9° December | 29.7° | [38] |
Date | Day Number (n) | Latitude (°) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | ||
17 Jan. | 17 | 30.92 | 35.39 | 39.88 | 44.37 | 48.86 | 53.34 | 57.80 | 62.23 | 66.61 | 70.94 | 75.19 | 79.34 | 83.33 |
16 Febr. | 47 | 19.74 | 24.51 | 29.29 | 34.06 | 38.83 | 43.59 | 48.34 | 53.08 | 57.79 | 62.46 | 67.09 | 71.66 | 76.15 |
16 Mar. | 75 | 3.64 | 8.63 | 13.62 | 18.61 | 23.60 | 28.59 | 33.58 | 38.57 | 43.56 | 48.55 | 53.53 | 58.51 | 63.48 |
15 April | 105 | −14.74 | −9.87 | −5.01 | −0.16 | 4.69 | 9.52 | 14.33 | 19.11 | 23.85 | 28.54 | 33.15 | 37.64 | 41.92 |
15 May | 135 | −28.21 | −23.67 | −19.16 | −14.68 | −10.26 | −5.90 | −1.64 | 2.49 | 6.44 | 10.12 | 13.36 | 15.87 | 16.98 |
11 June | 162 | −33.83 | −29.47 | −25.15 | −20.89 | −16.71 | −12.63 | −8.69 | −4.96 | −1.51 | 1.50 | 3.81 | 4.86 | 3.32 |
17 July | 198 | −31.27 | −26.83 | −22.43 | −18.07 | −13.77 | −9.56 | −5.47 | −1.54 | 2.15 | 5.47 | 8.23 | 10.00 | 9.80 |
16 Aug. | 228 | −20.48 | −15.73 | −10.99 | −6.27 | −1.58 | 3.09 | 7.71 | 12.27 | 16.74 | 21.10 | 25.27 | 29.15 | 32.50 |
15 Sept. | 258 | −3.32 | 1.67 | 6.66 | 11.66 | 16.65 | 21.64 | 26.63 | 31.62 | 36.61 | 41.60 | 46.58 | 51.56 | 56.54 |
15 Oct. | 288 | 15.02 | 19.88 | 24.75 | 29.61 | 34.47 | 39.33 | 44.18 | 49.01 | 53.83 | 58.63 | 63.40 | 68.13 | 72.80 |
14 Nov. | 318 | 28.37 | 32.92 | 37.48 | 42.04 | 46.60 | 51.15 | 55.68 | 60.19 | 64.65 | 69.06 | 73.41 | 77.65 | 81.76 |
10 Dec. | 344 | 33.78 | 38.17 | 42.57 | 46.98 | 51.39 | 55.78 | 60.16 | 64.50 | 68.79 | 73.03 | 77.17 | 81.20 | 85.06 |
Date | City | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Day Number (n) | Jenin | Tulkarm | Nablus | Ramallh | Jerusalem | Hebron | Jerico | Gaza | Rafah | |
17 Jan. | 17 | 59.98 | 59.85 | 59.77 | 59.49 | 59.38 | 59.46 | 59.16 | 59.16 | 58.95 |
16 Febr. | 47 | 50.68 | 50.53 | 50.45 | 50.14 | 50.03 | 50.12 | 49.79 | 49.79 | 49.57 |
16 Mar. | 75 | 36.04 | 35.89 | 35.80 | 35.48 | 35.36 | 35.45 | 35.11 | 35.11 | 34.87 |
15 April | 105 | 16.68 | 16.54 | 16.45 | 16.15 | 16.03 | 16.12 | 15.79 | 15.79 | 15.56 |
15 May | 135 | 0.41 | 0.29 | 0.21 | −0.05 | −0.15 | −0.08 | −0.36 | −0.36 | −0.56 |
11 June | 162 | −6.82 | −6.94 | −7.00 | −7.25 | −7.34 | −7.27 | −7.52 | −7.52 | −7.71 |
17 July | 198 | −3.51 | −3.63 | −3.70 | −3.95 | −4.05 | −3.98 | −4.25 | −4.25 | −4.44 |
16 Aug. | 228 | 9.96 | 9.82 | 9.74 | 9.45 | 9.34 | 9.42 | 9.11 | 9.11 | 8.89 |
15 Sept. | 258 | 29.09 | 28.94 | 28.85 | 28.53 | 28.41 | 28.50 | 28.16 | 28.16 | 27.92 |
15 Oct. | 288 | 46.56 | 46.41 | 46.33 | 46.02 | 45.90 | 45.99 | 45.66 | 45.66 | 45.43 |
14 Nov. | 318 | 57.90 | 57.77 | 57.69 | 57.40 | 57.29 | 57.37 | 57.06 | 57.06 | 56.85 |
10 Dec. | 344 | 62.30 | 62.17 | 62.09 | 61.81 | 61.71 | 61.79 | 61.49 | 61.49 | 61.28 |
Month | Latitude | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | ||
January | βopt,m | 30.83 | 35.31 | 39.79 | 44.28 | 48.77 | 53.25 | 57.70 | 62.13 | 66.51 | 70.84 | 75.08 | 79.21 | 83.17 |
Im | 363.69 | 361.52 | 359.03 | 356.17 | 352.82 | 348.86 | 344.07 | 338.15 | 330.63 | 320.73 | 307.07 | 287.01 | 254.55 | |
February | βopt,m | 20.30 | 25.05 | 29.80 | 34.55 | 39.30 | 44.04 | 48.76 | 53.47 | 58.15 | 62.79 | 67.38 | 71.90 | 76.32 |
Im | 310.38 | 309.81 | 309.11 | 308.27 | 307.24 | 305.99 | 304.45 | 302.51 | 300.01 | 296.71 | 292.17 | 285.62 | 275.49 | |
March | βopt,m | 3.62 | 8.59 | 13.57 | 18.54 | 23.51 | 28.48 | 33.44 | 38.41 | 43.36 | 48.32 | 53.26 | 58.19 | 63.10 |
Im | 326.49 | 326.48 | 326.45 | 326.40 | 326.33 | 326.25 | 326.13 | 325.98 | 325.77 | 325.48 | 325.08 | 324.50 | 323.59 | |
April | βopt,m | −14.83 | −9.98 | −5.14 | −0.30 | 4.52 | 9.33 | 14.11 | 18.87 | 23.57 | 28.22 | 32.78 | 37.19 | 41.35 |
Im | 316.49 | 316.67 | 316.79 | 316.83 | 316.79 | 316.66 | 316.41 | 316.01 | 315.38 | 314.44 | 312.99 | 310.74 | 307.03 | |
Im (negative values of βopt,m are considered zero) | 305.95 | 311.88 | 315.51 | 316.82 | 316.79 | 316.66 | 316.41 | 316.01 | 315.38 | 314.44 | 312.99 | 310.74 | 307.03 | |
May | βopt,m | −28.21 | −23.68 | −19.18 | −14.71 | −10.29 | −5.95 | −1.70 | 2.42 | 6.35 | 10.00 | 13.21 | 15.66 | 16.63 |
Im | 339.30 | 340.66 | 341.82 | 342.78 | 343.56 | 344.11 | 344.41 | 344.37 | 343.87 | 342.69 | 340.47 | 336.54 | 329.67 | |
Im (negative values of βopt,m are considered zero) | 299.00 | 311.97 | 322.85 | 331.55 | 338.03 | 342.26 | 344.26 | 344.37 | 343.87 | 342.69 | 340.47 | 336.54 | 329.67 | |
June | βopt,m | −33.80 | −29.45 | −25.13 | −20.87 | −16.69 | −12.61 | −8.67 | −4.93 | −1.48 | 1.54 | 3.84 | 4.90 | 3.36 |
Im | 335.61 | 337.94 | 340.02 | 341.89 | 343.54 | 344.98 | 346.18 | 347.08 | 347.59 | 347.56 | 346.75 | 344.86 | 341.86 | |
Im (negative values of βopt,m are considered zero) | 278.87 | 294.28 | 307.83 | 319.46 | 329.08 | 336.67 | 342.22 | 345.79 | 347.47 | 347.56 | 346.75 | 344.86 | 341.86 | |
July | βopt,m | −31.17 | −26.72 | −22.32 | −17.96 | −13.66 | −9.45 | −5.36 | −1.43 | 2.26 | 5.58 | 8.34 | 10.10 | 9.85 |
Im | 341.46 | 343.31 | 344.93 | 346.34 | 347.54 | 348.52 | 349.23 | 349.61 | 349.54 | 348.82 | 347.13 | 343.89 | 338.27 | |
Im (negative values of βopt,m are considered zero) | 292.18 | 306.63 | 319.09 | 329.47 | 337.71 | 343.79 | 347.71 | 349.50 | 349.54 | 348.82 | 347.13 | 343.89 | 338.27 | |
August | βopt,m | −20.23 | −15.49 | −10.76 | −6.05 | −1.36 | 3.29 | 7.90 | 12.45 | 16.91 | 21.24 | 25.38 | 29.21 | 32.49 |
Im | 327.47 | 327.95 | 328.31 | 328.55 | 328.67 | 328.63 | 328.41 | 327.94 | 327.13 | 325.81 | 323.70 | 320.29 | 314.53 | |
Im (negative values of βopt,m are considered zero) | 307.27 | 316.04 | 322.54 | 326.72 | 328.58 | 328.63 | 328.41 | 327.94 | 327.13 | 325.81 | 323.70 | 320.29 | 314.53 | |
September | βopt,m | −2.95 | 2.03 | 7.00 | 11.98 | 16.95 | 21.93 | 26.89 | 31.86 | 36.82 | 41.77 | 46.72 | 51.65 | 56.56 |
Im | 310.24 | 310.24 | 310.23 | 310.21 | 310.17 | 310.11 | 310.04 | 309.93 | 309.79 | 309.58 | 309.29 | 308.85 | 308.16 | |
Im (negative values of βopt,m are considered zero) | 309.83 | 310.24 | 310.23 | 310.21 | 310.17 | 310.11 | 310.04 | 309.93 | 309.79 | 309.58 | 309.29 | 308.85 | 308.16 | |
October | βopt,m | 15.41 | 20.26 | 25.10 | 29.94 | 34.78 | 39.61 | 44.43 | 49.24 | 54.03 | 58.79 | 63.52 | 68.19 | 72.79 |
Im | 333.11 | 332.82 | 332.44 | 331.96 | 331.36 | 330.62 | 329.70 | 328.52 | 326.98 | 324.94 | 322.12 | 318.04 | 311.76 | |
November | βopt,m | 28.56 | 33.10 | 37.65 | 42.20 | 46.75 | 51.29 | 55.81 | 60.30 | 64.75 | 69.14 | 73.46 | 77.68 | 81.74 |
Im | 344.87 | 343.21 | 341.30 | 339.07 | 336.46 | 333.34 | 329.56 | 324.87 | 318.91 | 311.06 | 300.26 | 284.49 | 259.38 | |
December | βopt,m | 33.83 | 38.21 | 42.61 | 47.02 | 51.43 | 55.82 | 60.19 | 64.53 | 68.83 | 73.06 | 77.20 | 81.22 | 85.08 |
370.09 | 367.20 | 363.94 | 360.22 | 355.91 | 350.83 | 344.73 | 337.21 | 327.66 | 315.07 | 297.63 | 271.71 | 228.61 | ||
Total | 4019.18 | 4017.79 | 4014.36 | 4008.69 | 4000.40 | 3988.92 | 3973.31 | 3952.18 | 3923.26 | 3882.89 | 3824.65 | 3736.52 | 3592.91 | |
Total Im (negative values of βopt,m are considered zero) | 3841.70 | 3892.07 | 3930.32 | 3956.31 | 3970.48 | 3974.02 | 3967.68 | 3950.78 | 3923.15 | 3882.89 | 3824.65 | 3736.52 | 3592.91 |
Month | City | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Jenin | Tulkarm | Nablus | Ramallah | Jerusalem | Jericho | Hebron | Ghaza | Rafah | ||
January | βopt,m | 59.89 | 59.75 | 59.67 | 59.39 | 59.28 | 59.36 | 59.06 | 59.06 | 58.85 |
Im | 341.32 | 341.50 | 341.60 | 341.97 | 342.11 | 342.01 | 342.40 | 342.40 | 342.67 | |
February | βopt,m | 51.08 | 50.94 | 50.85 | 50.55 | 50.44 | 50.52 | 50.20 | 50.20 | 49.98 |
Im | 303.55 | 303.61 | 303.65 | 303.77 | 303.81 | 303.78 | 303.90 | 303.90 | 303.99 | |
March | βopt,m | 35.89 | 35.74 | 35.65 | 35.33 | 35.21 | 35.30 | 34.96 | 34.96 | 34.72 |
Im | 314.66 | 314.65 | 314.66 | 314.64 | 314.63 | 314.64 | 314.62 | 314.62 | 314.60 | |
April | βopt,m | 16.46 | 16.31 | 16.23 | 15.92 | 15.81 | 15.89 | 15.57 | 15.57 | 15.34 |
Im | 316.24 | 316.25 | 316.25 | 316.28 | 316.29 | 316.28 | 316.31 | 316.31 | 316.32 | |
May | βopt,m | 0.35 | 0.23 | 0.15 | −0.11 | −0.21 | −0.14 | −0.42 | −0.42 | −0.62 |
Im | 344.44 | 344.44 | 344.44 | 344.44 | 344.44 | 344.44 | 344.44 | 344.44 | 344.44 | |
Im (negative values of βopt,m are considered zero) | 344.44 | 344.44 | 344.44 | 344.44 | 344.44 | 344.44 | 344.43 | 344.43 | 344.42 | |
June | βopt,m | −6.80 | −6.91 | −6.98 | −7.22 | −7.31 | −7.24 | −7.50 | −7.50 | −7.68 |
Im | 346.66 | 346.63 | 346.62 | 346.56 | 346.53 | 346.55 | 346.49 | 346.49 | 346.44 | |
Im (negative values of βopt,m are considered zero) | 344.22 | 344.11 | 344.05 | 343.81 | 343.72 | 343.79 | 343.52 | 343.52 | 343.33 | |
July | βopt,m | −3.40 | −3.52 | −3.59 | −3.84 | −3.94 | −3.87 | −4.14 | −4.14 | −4.33 |
Im | 349.47 | 349.45 | 349.45 | 349.42 | 349.41 | 349.42 | 349.39 | 349.39 | 349.37 | |
Im (negative values of βopt,m are considered zero) | 348.85 | 348.80 | 348.76 | 348.63 | 348.58 | 348.62 | 348.48 | 348.48 | 348.37 | |
August | βopt,m | 10.15 | 10.01 | 9.93 | 9.64 | 9.53 | 9.61 | 9.30 | 9.30 | 9.08 |
Im | 328.22 | 328.23 | 328.24 | 328.27 | 328.28 | 328.27 | 328.30 | 328.30 | 328.32 | |
September | βopt,m | 29.34 | 29.19 | 29.10 | 28.78 | 28.66 | 28.75 | 28.41 | 28.41 | 28.18 |
Im | 320.26 | 320.26 | 320.27 | 320.27 | 320.27 | 320.27 | 320.28 | 320.28 | 320.28 | |
October | βopt,m | 46.80 | 46.66 | 46.57 | 46.26 | 46.15 | 46.23 | 45.91 | 45.91 | 45.68 |
Im | 329.15 | 329.19 | 329.21 | 329.28 | 329.31 | 329.29 | 329.37 | 329.37 | 329.42 | |
November | βopt,m | 58.02 | 57.89 | 57.80 | 57.52 | 57.41 | 57.49 | 57.18 | 57.18 | 56.97 |
Im | 327.39 | 327.52 | 327.61 | 327.90 | 328.01 | 327.93 | 328.23 | 328.23 | 328.45 | |
December | βopt,m | 62.33 | 62.20 | 62.13 | 61.85 | 61.74 | 61.82 | 61.53 | 61.53 | 61.32 |
Im | 341.24 | 341.46 | 341.60 | 342.07 | 342.24 | 342.11 | 342.60 | 342.60 | 342.95 | |
Total | 3962.59 | 3963.21 | 3963.58 | 3964.86 | 3965.34 | 3964.99 | 3966.32 | 3966.32 | 3967.24 | |
Total (negative values of βopt,m are considered zero) | 3959.54 | 3960.03 | 3960.33 | 3961.33 | 3961.69 | 3961.43 | 3962.44 | 3962.44 | 3963.12 |
Latitude | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | ||
β = 0 | I | 3653.77 | 3637.62 | 3596.30 | 3530.22 | 3440.05 | 3326.73 | 3191.50 | 3035.91 | 2861.94 | 2672.05 | 2469.50 | 2258.81 | 2047.02 |
βopt,d | I | 4027.36 | 4025.97 | 4022.56 | 4016.93 | 4008.71 | 3997.32 | 3981.83 | 3960.87 | 3932.20 | 3892.18 | 3834.50 | 3747.30 | 3605.51 |
F | 1.1022 | 1.1068 | 1.1185 | 1.1379 | 1.1653 | 1.2016 | 1.2476 | 1.3047 | 1.3740 | 1.4566 | 1.5527 | 1.6590 | 1.7613 | |
βopt,m | I | 4019.18 | 4017.79 | 4014.36 | 4008.69 | 4000.40 | 3988.92 | 3973.31 | 3952.18 | 3923.26 | 3882.89 | 3824.65 | 3736.52 | 3592.91 |
F | 1.1000 | 1.1045 | 1.1162 | 1.1355 | 1.1629 | 1.1990 | 1.2450 | 1.3018 | 1.3708 | 1.4531 | 1.5488 | 1.6542 | 1.7552 | |
βopt,s | I | 3958.60 | 3957.14 | 3953.53 | 3947.57 | 3938.80 | 3926.72 | 3910.22 | 3887.86 | 3857.20 | 3814.27 | 3752.10 | 3657.37 | 3501.03 |
F | 1.0834 | 1.0878 | 1.0993 | 1.1182 | 1.1450 | 1.1804 | 1.2252 | 1.2806 | 1.3478 | 1.4275 | 1.5194 | 1.6192 | 1.7103 | |
βopt,sa | I | 3952.82 | 3951.37 | 3947.71 | 3941.62 | 3932.68 | 3920.26 | 3903.33 | 3880.34 | 3848.79 | 3804.52 | 3740.23 | 3641.86 | 3478.27 |
F | 1.0818 | 1.0863 | 1.0977 | 1.1165 | 1.1432 | 1.1784 | 1.2230 | 1.2781 | 1.3448 | 1.4238 | 1.5146 | 1.6123 | 1.6992 | |
βopt,y | I | 3653.99 | 3652.54 | 3648.73 | 3642.33 | 3632.91 | 3619.77 | 3601.84 | 3577.44 | 3543.91 | 3496.82 | 3428.34 | 3323.42 | 3148.68 |
F | 1.0001 | 1.0041 | 1.0146 | 1.0318 | 1.0561 | 1.0881 | 1.1286 | 1.1784 | 1.2383 | 1.3087 | 1.3883 | 1.4713 | 1.5382 |
City | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Jenin | Tulkarm | Nablus | Ramallah | Jerusalem | Jericho | Hebron | Gaza | Rafah | ||
β = 0 | I | 3117.38 | 3122.04 | 3124.83 | 3134.68 | 3138.35 | 3135.60 | 3145.97 | 3145.97 | 3153.24 |
βopt,d | I | 3972.32 | 3972.94 | 3973.31 | 3974.61 | 3975.09 | 3974.73 | 3976.08 | 3976.08 | 3977.02 |
F | 1.2742 | 1.2725 | 1.2715 | 1.2679 | 1.2666 | 1.2676 | 1.2639 | 1.2639 | 1.2613 | |
βopt,m | I | 3962.59 | 3963.21 | 3963.58 | 3964.86 | 3965.34 | 3964.99 | 3966.32 | 3966.32 | 3967.24 |
F | 1.2711 | 1.2694 | 1.2684 | 1.2648 | 1.2635 | 1.2645 | 1.2608 | 1.2608 | 1.2581 | |
βopt,s | I | 3900.08 | 3900.74 | 3901.14 | 3902.22 | 3903.04 | 3902.66 | 3904.09 | 3904.09 | 3905.09 |
F | 1.2511 | 1.2494 | 1.2484 | 1.2449 | 1.2437 | 1.2446 | 1.2410 | 1.2410 | 1.2384 | |
βopt,sa | I | 3892.90 | 3893.59 | 3893.99 | 3895.42 | 3895.95 | 3895.55 | 3897.04 | 3897.04 | 3898.06 |
F | 1.2488 | 1.2471 | 1.2461 | 1.2427 | 1.2414 | 1.2424 | 1.2387 | 1.2387 | 1.2362 | |
βopt,y | I | 3590.777454 | 3591.50 | 3591.93 | 3593.44 | 3594.00 | 3593.58 | 3595.16 | 3595.16 | 3596.25 |
F | 1.1519 | 1.1504 | 1.1495 | 1.1464 | 1.1452 | 1.1461 | 1.1428 | 1.1428 | 1.1405 |
Season | Latitude | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | ||
Autumn | βopt,s | 14.27 | 19.02 | 23.78 | 28.53 | 33.27 | 38.00 | 42.72 | 47.40 | 52.05 | 56.65 | 61.17 | 65.56 | 69.76 |
Is | 963.57 | 962.33 | 960.72 | 958.67 | 956.11 | 952.89 | 948.83 | 943.63 | 936.81 | 927.61 | 914.72 | 895.64 | 865.08 | |
Winter | βopt,s | 28.77 | 33.28 | 37.80 | 42.32 | 46.84 | 51.35 | 55.83 | 60.28 | 64.69 | 69.03 | 73.28 | 77.39 | 81.26 |
Is | 1039.09 | 1033.75 | 1027.58 | 1020.41 | 1011.95 | 1001.94 | 989.75 | 974.63 | 955.33 | 929.81 | 894.47 | 842.27 | 756.98 | |
Spring | βopt,s | −13.34 | −8.59 | −3.84 | 0.90 | 5.62 | 10.31 | 14.96 | 19.56 | 24.09 | 28.50 | 32.76 | 36.74 | 40.22 |
Is | 956.61 | 957.39 | 957.84 | 957.95 | 957.68 | 956.95 | 955.64 | 953.56 | 950.40 | 945.63 | 938.33 | 926.76 | 907.23 | |
Is (negative values of βopt,s are considered zero) | 930.78 | 946.66 | 955.70 | 957.95 | 957.68 | 956.95 | 955.64 | 953.56 | 950.40 | 945.63 | 938.33 | 926.76 | 907.23 | |
Summer | βopt,s | −28.49 | −23.99 | −19.52 | −15.10 | −10.73 | −6.43 | −2.24 | 1.81 | 5.65 | 9.18 | 12.20 | 14.35 | 14.72 |
Is | 999.32 | 1003.66 | 1007.39 | 1010.53 | 1013.06 | 1014.93 | 1016.00 | 1016.04 | 1014.66 | 1011.22 | 1004.58 | 992.69 | 971.75 | |
Is (negative values of βopt,s are considered zero) | 878.32 | 916.95 | 949.46 | 975.65 | 995.37 | 1008.55 | 1015.22 | 1016.04 | 1014.66 | 1011.22 | 1004.58 | 992.69 | 971.75 | |
Total | 3958.60 | 3957.14 | 3953.53 | 3947.57 | 3938.80 | 3926.72 | 3910.22 | 3887.86 | 3857.20 | 3814.27 | 3752.10 | 3657.37 | 3501.03 | |
Total (negative values of βopt,s are considered zero) | 3811.76 | 3859.69 | 3893.46 | 3912.69 | 3921.11 | 3920.33 | 3909.45 | 3887.86 | 3857.20 | 3814.27 | 3752.10 | 3657.37 | 3501.03 |
Season | City | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Jenin | Tulkarm | Nablus | Ramallah | Jerusalem | Jericho | Hebron | Gaza | Rafah | ||
Autumn | βopt,s | 45.03 | 44.88 | 44.80 | 44.50 | 44.39 | 44.47 | 44.15 | 44.15 | 43.93 |
Is | 946.44 | 946.59 | 946.68 | 947.01 | 947.13 | 947.04 | 947.38 | 947.38 | 947.61 | |
Winter | βopt,s | 58.03 | 57.89 | 57.81 | 57.53 | 57.42 | 57.50 | 57.20 | 57.20 | 56.98 |
Is | 982.74 | 983.19 | 983.46 | 984.10 | 984.76 | 984.50 | 985.48 | 985.48 | 986.17 | |
Spring | βopt,s | 17.23 | 17.09 | 17.01 | 16.71 | 16.60 | 16.69 | 16.37 | 16.37 | 16.15 |
Is | 954.73 | 954.79 | 954.83 | 954.96 | 955.00 | 954.97 | 955.10 | 955.10 | 955.19 | |
summer | βopt,s | −0.22 | −0.34 | −0.42 | −0.68 | −0.78 | −0.70 | −0.98 | −0.98 | −1.18 |
Is | 1016.17 | 1016.16 | 1016.16 | 1016.15 | 1016.15 | 1016.15 | 1016.13 | 1016.13 | 1016.12 | |
Is (negative values of βopt,s are considered zero) | 1016.16 | 1016.15 | 1016.13 | 1016.08 | 1016.05 | 1016.07 | 1015.99 | 1015.99 | 1015.91 | |
Total | 3900.08 | 3900.74 | 3901.14 | 3902.22 | 3903.04 | 3902.66 | 3904.09 | 3904.09 | 3905.09 | |
Total (negative values of βopt,s are considered zero) | 3900.07 | 3900.72 | 3901.11 | 3902.15 | 3902.95 | 3902.58 | 3903.94 | 3903.94 | 3904.88 |
Period | Latitude | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | ||
Warm period (April to September) | βopt,sa | −22.26 | −17.65 | −13.05 | −8.48 | −3.95 | 0.52 | 4.93 | 9.23 | 13.40 | 17.34 | 20.95 | 23.97 | 25.82 |
Isa | 1937.51 | 1942.25 | 1946.01 | 1948.80 | 1950.53 | 1951.05 | 1950.06 | 1947.10 | 1941.36 | 1931.50 | 1915.14 | 1887.75 | 1839.69 | |
Isa (negative values of βopt,sa are considered zero) | 1793.09 | 1850.84 | 1895.74 | 1927.47 | 1945.89 | 1951.05 | 1950.06 | 1947.10 | 1941.36 | 1931.50 | 1915.14 | 1887.75 | 1839.69 | |
Cold period (October to March) | βopt,sa | 22.59 | 27.21 | 31.84 | 36.46 | 41.08 | 45.68 | 50.26 | 54.81 | 59.31 | 63.75 | 68.09 | 72.28 | 76.20 |
Isa | 2015.31 | 2009.12 | 2001.70 | 1992.82 | 1982.15 | 1969.21 | 1953.27 | 1933.24 | 1907.43 | 1873.02 | 1825.09 | 1754.11 | 1638.58 | |
Total | 3952.82 | 3951.37 | 3947.71 | 3941.62 | 3932.68 | 3920.26 | 3903.33 | 3880.34 | 3848.79 | 3804.52 | 3740.23 | 3641.86 | 3478.27 | |
Total (negative values of βopt,sa are considered zero) | 3808.40 | 3859.96 | 3897.44 | 3920.29 | 3928.04 | 3920.26 | 3903.33 | 3880.34 | 3848.79 | 3804.52 | 3740.23 | 3641.86 | 3478.27 |
Period | City | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Jenin | Tulkarm | Nablus | Ramallah | Jerusalem | Jericho | Hebron | Gaza | Rafah | ||
Warm period (April to September) | βopt,sa | 7.06 | 6.93 | 6.86 | 6.58 | 6.48 | 6.55 | 6.26 | 6.26 | 6.05 |
Isa | 1948.89 | 1948.98 | 1949.03 | 1949.20 | 1949.27 | 1949.22 | 1949.40 | 1949.40 | 1949.51 | |
Cold period (October to March) | βopt,sa | 52.51 | 52.37 | 52.29 | 52.00 | 51.89 | 51.97 | 51.66 | 51.66 | 51.44 |
Isa | 1944.01 | 1944.61 | 1944.96 | 1946.22 | 1946.68 | 1946.33 | 1947.64 | 1947.64 | 1948.55 | |
Total | 3892.90 | 3893.59 | 3893.99 | 3895.42 | 3895.95 | 3895.55 | 3897.04 | 3897.04 | 3898.06 |
Latitude | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | |
βopt,y | 0.63 | 5.18 | 9.73 | 14.25 | 18.75 | 23.21 | 27.62 | 31.94 | 36.14 | 40.17 | 43.92 | 47.18 | 49.45 |
Iy | 3653.99 | 3652.54 | 3648.73 | 3642.33 | 3632.91 | 3619.77 | 3601.84 | 3577.44 | 3543.91 | 3496.82 | 3428.34 | 3323.42 | 3148.68 |
City | |||||||||
---|---|---|---|---|---|---|---|---|---|
Jenin | Tulkarm | Nablus | Ramallah | Jerusalem | Jericho | Hebron | Gaza | Rafah | |
βopt,y | 29.75 | 29.62 | 29.55 | 29.27 | 29.17 | 29.24 | 28.95 | 28.95 | 28.74 |
Iy | 3590.78 | 3591.50 | 3591.93 | 3593.44 | 3594.00 | 3593.58 | 3595.16 | 3595.16 | 3596.25 |
Jerusalem | Gaza City | |||||
---|---|---|---|---|---|---|
Period | Yearly Optimum Tilt Angle | |||||
Mathematical Model | PVGIS | PVWatts | Mathematical Model | PVGIS | PVWatts | |
29 | 28 | 26 | 29 | 28 | 29 | |
Semi-annual optimum tilt angle | ||||||
Warm period (April to September) | 6 | 9 | 11 | 6 | 9 | 12 |
Cold period (October to March) | 52 | 51 | 46 | 52 | 50 | 50 |
Seasonal optimum tilt angle | ||||||
Autumn | 44 | 43 | 41 | 44 | 43 | 43 |
Winter | 57 | 56 | 51 | 57 | 55 | 56 |
Spring | 17 | 20 | 17 | 16 | 19 | 19 |
Summer | −1 | 3 | 7 | −1 | 0 | 5 |
Monthly optimum tilt angle | ||||||
January | 59 | 58 | 55 | 59 | 59 | 59 |
February | 50 | 50 | 49 | 50 | 50 | 50 |
March | 35 | 35 | 32 | 35 | 35 | 35 |
April | 16 | 16 | 17 | 16 | 17 | 16 |
May | 0 | 1 | 4 | 0 | 2 | 6 |
June | −7 | 0 | 0 | −8 | 0 | 0 |
July | −4 | 0 | 2 | −4 | 0 | 0 |
August | 10 | 11 | 14 | 9 | 10 | 12 |
September | 29 | 29 | 29 | 28 | 29 | 29 |
October | 46 | 46 | 46 | 46 | 46 | 46 |
November | 57 | 57 | 56 | 57 | 57 | 57 |
December | 62 | 61 | 56 | 62 | 61 | 61 |
Months | Monthly Average Radiation (kWh/m2/day) for Jerusalem | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
PVGIS | PVWatts | |||||||||||
β (0°) | β (28°) | β (29°) | β (30°) | β (60°) | β (90°) | β (0°) | β (26°) | β (29°) | β (30°) | β (60°) | β (90°) | |
January | 3.07 | 4.35 | 4.39 | 4.42 | 4.84 | 4.16 | 2.68 | 3.57 | 3.64 | 3.66 | 3.88 | 3.27 |
February | 3.86 | 4.96 | 4.96 | 5.00 | 5.11 | 4.11 | 3.57 | 4.49 | 4.56 | 4.57 | 4.61 | 3.66 |
March | 5.19 | 6.00 | 6.00 | 6.00 | 5.58 | 3.97 | 4.81 | 5.43 | 5.45 | 5.45 | 4.95 | 3.44 |
April | 6.40 | 6.60 | 6.57 | 6.57 | 5.43 | 3.20 | 6.13 | 6.37 | 6.33 | 6.32 | 5.16 | 2.98 |
May | 7.19 | 6.81 | 6.77 | 6.74 | 4.97 | 2.36 | 7.17 | 6.93 | 6.83 | 6.79 | 5.01 | 2.43 |
June | 8.17 | 7.40 | 7.33 | 7.27 | 5.00 | 1.91 | 8.07 | 7.53 | 7.38 | 7.33 | 5.03 | 2.08 |
July | 8.06 | 7.42 | 7.39 | 7.32 | 5.16 | 2.12 | 8.01 | 7.61 | 7.47 | 7.43 | 5.22 | 2.23 |
August | 7.39 | 7.39 | 7.35 | 7.35 | 5.74 | 2.98 | 7.28 | 7.45 | 7.39 | 7.36 | 5.79 | 3.04 |
September | 6.20 | 6.97 | 6.97 | 6.97 | 6.20 | 4.07 | 6.26 | 7.08 | 7.1 | 7.1 | 6.32 | 4.13 |
October | 4.65 | 5.84 | 5.87 | 5.90 | 5.87 | 4.52 | 4.69 | 5.86 | 5.94 | 5.96 | 5.88 | 4.49 |
November | 3.53 | 4.97 | 5.00 | 5.03 | 5.47 | 4.63 | 3.34 | 4.54 | 4.63 | 4.66 | 4.94 | 4.12 |
December | 2.86 | 4.26 | 4.29 | 4.32 | 4.87 | 4.29 | 2.45 | 3.38 | 3.46 | 3.48 | 3.77 | 3.24 |
Annual Average | 5.55 | 6.08 | 6.07 | 6.07 | 5.35 | 3.53 | 5.37 | 5.85 | 5.85 | 5.84 | 5.05 | 3.26 |
Months | Monthly Average Radiation (kWh/m2/day) for Gaza city | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
PVGIS | PVWatts | ||||||||||
β (0°) | β (28°) | β (29°) | β (30°) | β (60°) | β (90°) | β (0°) | β (29°) | β (30°) | β (60°) | β (90°) | |
January | 3.02 | 4.29 | 4.32 | 4.35 | 4.77 | 4.10 | 3.05 | 4.53 | 4.57 | 5.04 | 4.34 |
February | 3.96 | 5.11 | 5.14 | 5.18 | 5.29 | 4.25 | 3.72 | 4.93 | 4.96 | 5.07 | 4.04 |
March | 5.32 | 6.19 | 6.19 | 6.19 | 5.77 | 4.06 | 4.97 | 5.8 | 5.81 | 5.37 | 3.76 |
April | 6.53 | 6.77 | 6.73 | 6.73 | 5.53 | 3.22 | 6.19 | 6.4 | 6.39 | 5.21 | 3.01 |
May | 7.29 | 6.90 | 6.87 | 6.84 | 5.03 | 2.33 | 7.08 | 6.74 | 6.7 | 4.93 | 2.39 |
June | 8.07 | 7.30 | 7.23 | 7.20 | 4.90 | 1.86 | 7.84 | 7.11 | 7.06 | 4.85 | 2.04 |
July | 7.94 | 7.32 | 7.26 | 7.23 | 5.06 | 2.07 | 7.55 | 7.00 | 6.95 | 4.93 | 2.2 |
August | 7.32 | 7.32 | 7.29 | 7.26 | 5.68 | 2.92 | 7.03 | 7.06 | 7.03 | 5.51 | 2.92 |
September | 6.17 | 6.90 | 6.93 | 6.93 | 6.17 | 4.03 | 5.84 | 6.58 | 6.58 | 5.84 | 3.82 |
October | 4.81 | 6.10 | 6.13 | 6.13 | 6.13 | 4.71 | 4.56 | 5.89 | 5.91 | 5.91 | 4.54 |
November | 3.50 | 4.97 | 5.00 | 5.03 | 5.47 | 4.63 | 3.63 | 5.08 | 5.11 | 5.44 | 4.54 |
December | 2.89 | 4.32 | 4.39 | 4.42 | 4.97 | 4.35 | 2.84 | 4.43 | 4.47 | 5.05 | 4.44 |
Annual Average | 5.57 | 6.12 | 6.12 | 6.12 | 5.40 | 3.55 | 5.36 | 5.96 | 5.96 | 5.26 | 3.50 |
Months | Monthly Energy Generated (kWh) For Jerusalem | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
PVGIS | PVWatts | |||||||||
β = 0 | βopt,y | βopt, sa | βopt, s | βopt, m | β = 0 | βopt,y | βopt, sa | βopt, s | βopt, m | |
January | 382 | 553 | 612 | 614 | 617 | 339 | 457 | 496 | 498 | 498 |
February | 431 | 556 | 584 | 580 | 584 | 410 | 517 | 540 | 539 | 540 |
March | 632 | 726 | 708 | 712 | 730 | 602 | 676 | 663 | 663 | 679 |
April | 732 | 751 | 752 | 758 | 758 | 721 | 746 | 746 | 751 | 751 |
May | 832 | 782 | 830 | 810 | 833 | 844 | 813 | 847 | 838 | 848 |
June | 896 | 804 | 881 | 893 | 896 | 918 | 853 | 909 | 915 | 918 |
July | 908 | 832 | 899 | 907 | 908 | 933 | 883 | 931 | 935 | 935 |
August | 841 | 837 | 856 | 848 | 857 | 845 | 861 | 869 | 864 | 872 |
September | 697 | 776 | 738 | 761 | 776 | 706 | 793 | 759 | 784 | 795 |
October | 548 | 689 | 709 | 713 | 713 | 557 | 692 | 718 | 718 | 718 |
November | 413 | 592 | 651 | 640 | 653 | 393 | 534 | 580 | 573 | 582 |
December | 352 | 539 | 611 | 616 | 617 | 306 | 426 | 469 | 473 | 474 |
Annual Sum | 7664 | 8437 | 8831 | 8852 | 8942 | 7574 | 8251 | 8527 | 8551 | 8610 |
Percentage gain with respect to a horizontal plane (%) | 10.1 | 15.2 | 15.5 | 16.7 | 8.9 | 12.6 | 12.9 | 13.7 |
Months | Monthly Energy Generated (kWh) for Gaza City | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
PVGIS | PVWatts | |||||||||
β = 0 | β opt,y | βopt, sa | βopt, s | βopt, m | β = 0 | βopt,y | βopt, sa | βopt, s | βopt, m | |
January | 369 | 535 | 592 | 594 | 594 | 371 | 557 | 614 | 618 | 618 |
February | 438 | 571 | 601 | 598 | 601 | 408 | 540 | 565 | 561 | 565 |
March | 656 | 758 | 743 | 740 | 763 | 610 | 709 | 692 | 691 | 712 |
April | 771 | 794 | 793 | 801 | 801 | 703 | 723 | 729 | 732 | 732 |
May | 879 | 827 | 878 | 859 | 880 | 820 | 776 | 821 | 809 | 824 |
June | 926 | 833 | 912 | 926 | 926 | 867 | 784 | 852 | 864 | 867 |
July | 935 | 857 | 926 | 935 | 935 | 861 | 795 | 853 | 861 | 861 |
August | 857 | 851 | 871 | 857 | 872 | 796 | 796 | 816 | 808 | 816 |
September | 704 | 785 | 745 | 769 | 785 | 648 | 726 | 698 | 710 | 726 |
October | 568 | 722 | 747 | 749 | 749 | 527 | 679 | 699 | 701 | 701 |
November | 406 | 583 | 641 | 631 | 644 | 418 | 586 | 629 | 622 | 629 |
December | 347 | 536 | 608 | 614 | 615 | 342 | 543 | 610 | 617 | 618 |
Annual Sum | 7856 | 8652 | 9057 | 9073 | 9165 | 7371 | 8214 | 8578 | 8594 | 8669 |
Percentage gain with respect to a horizontal plane (%) | 10.1 | 15.3 | 15.5 | 16.7 | 11.4 | 16.4 | 16.6 | 17.6 |
Month | Present Mathematical Model | Nijegorodor et al. [39] | P. Talebizadeh et al. [31] | |
---|---|---|---|---|
January | βopt,m | 59.28 | 57.28 | 56.10 |
February | βopt,m | 50.44 | 47.83 | 47.30 |
March | βopt,m | 35.21 | 35.78 | 31.59 |
April | βopt,m | 15.81 | 21.78 | 16.40 |
May | βopt,m | −0.21 | 5.56 | 2.74 |
June | βopt,m | −7.31 | −6.35 | −2.17 |
July | βopt,m | −3.94 | −1.72 | 0.16 |
August | βopt,m | 9.53 | 13.83 | 12.09 |
September | βopt,m | 28.66 | 29.78 | 28.70 |
October | βopt,m | 46.15 | 43.78 | 44.03 |
November | βopt,m | 57.41 | 54.56 | 54.89 |
December | βopt,m | 61.74 | 61.65 | 58.54 |
year | βopt,m | 29.17 | 30.31 | 28.83 |
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Abdallah, R.; Juaidi, A.; Abdel-Fattah, S.; Manzano-Agugliaro, F. Estimating the Optimum Tilt Angles for South-Facing Surfaces in Palestine. Energies 2020, 13, 623. https://doi.org/10.3390/en13030623
Abdallah R, Juaidi A, Abdel-Fattah S, Manzano-Agugliaro F. Estimating the Optimum Tilt Angles for South-Facing Surfaces in Palestine. Energies. 2020; 13(3):623. https://doi.org/10.3390/en13030623
Chicago/Turabian StyleAbdallah, Ramez, Adel Juaidi, Salameh Abdel-Fattah, and Francisco Manzano-Agugliaro. 2020. "Estimating the Optimum Tilt Angles for South-Facing Surfaces in Palestine" Energies 13, no. 3: 623. https://doi.org/10.3390/en13030623
APA StyleAbdallah, R., Juaidi, A., Abdel-Fattah, S., & Manzano-Agugliaro, F. (2020). Estimating the Optimum Tilt Angles for South-Facing Surfaces in Palestine. Energies, 13(3), 623. https://doi.org/10.3390/en13030623