optimization of tilt angle for photovoltaic array

Ashok Kumar et al. / International Journal of Engineering Science and Technology (IJEST)

OPTIMIZATION OF TILT ANGLE FOR PHOTOVOLTAIC ARRAY Ashok Kumar Department of Mechanical Engineering, National Institute of Technology, Hamirpur, Himachal Pradesh-177055.India

N.S.Thakur Centre For Excellence in Energy & Environment National Institute of Technology, Hamirpur, Himachal Pradesh-177055.India Rahul Makade Department of Mechanical Engineering, National Institute of Technology, Hamirpur, Himachal Pradesh-177055.India

Maneesh Kumar Shivhare Department of Mechanical Engineering, National Institute of Technology, Hamirpur, Himachal Pradesh-177055.India Abstract The performance of a solar radiation conversion system is affected by its tilt angle with the horizontal plane, thus photovoltaic array need to be tilted at the correct angle to maximize the performance of the System, This paper deals with the determination of optimum tilt angle for solar PV array in order to maximize incident solar irradiance. The model starts by calculating the monthly averaged daily solar irradiation components (direct, diffuse, ground-reflected) absorbed by the solar PV array of varying tilt, for this purpose Khatkar Kalan (Punjab ) is selected (latitude=31.06) where the photovoltaic arrays are installed. It is found that the optimum tilt angle changes between 60.5◦ (January) and 62.5◦ (December) throughout the year. In winter (December, January, and February) the tilt should be 57.48◦, in spring (March, April, and May) 18.16◦, in summer (June, July, and August) 2.83◦, and in autumn (September, October, and November) 43.67◦. The yearly average of this value was found to be 30.61◦ which is nearly equal to the angle selected at Khatkar Kalan. Keywords: solar PV array, optimum tilt angle, clearness index, solar radiation. Introduction The sun is a sphere of intensely hot gaseous matter with a diameter of 1.39 × 10 m.In effect the sun is a continuous fusion reactor in which hydrogen is turned into helium. The sun’s total energy output is 3.8 ×1020 MW which is equal to 63MW m2 of the sun’s surface. This energy radiates outwards in all directions. Only a tiny fraction, 1.7 ×1014 kw of the total radiation emitted is intercepted by the earth [1]. However, even with this small fraction it is estimated that 30 min of solar radiation falling on earth is equal to the world energy demand for one year. The performance of a solar PV array is highly influenced by its angle of tilt with the horizontal. This is due to the facts that tilt angle change the solar radiation reaching the surface of the PV array, the tilt angle, defined as

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the angle of PV arrays with respect to horizontal, is a dominant parameter affecting the collectible radiation of a fixed PV array. In general, the optimal tilt angle of a fixed PV array is related to the local climatic condition, geographic latitude and the period of its use. Hence, different places will have different optimal tilt angles for a yearly-used solar PV array. To date, a number of studies on the optimal tilt angle of PV arrays have been conducted [1–8], and a lot of empirical correlations for estimating the optimal tilt-angle are available in the literature [2, 5–8]. It is reported in the literature that the optimum orientation of the PV array should be directly towards the equator, facing south in the northern hemisphere and the optimum tilt angle depends only on the latitude. For example, Lunde [8] and Garge [9] β opt

= ±15° , Duffie and Beckman [10] suggested

β opt = (φ + 15° ) ± 15° , and Heywood [11] concluded that β opt = (φ + 15° ) , where φ

latitude of the location

and where plus, and minus signs is used in winter and summer respectively. This paper examines the theoretical aspects of choosing a tilt angle for the solar flat-plate PV arrays used at Kharkar Kalan (Punjab) and makes recommendations on how the collected energy can be increased by varying the tilt angle seasonally four times a year. A computer program is developed to simulate the collected energy as the tilt angle is varied.

Fig. 1: Solar panels installed at Khatkar Kalan, Punjab at 30° tilt angle

Models for calculation of solar radiation on a horizontal surface The total daily irradiation on a horizontal plane, H, is the combination of two components: the direct (beam) irradiation and the diffuse irradiation from the sky. The Solar radiation data are commonly available in two forms, the monthly average daily global solar radiation on a horizontal surface (H) and the hourly total radiation on a horizontal surface (I ), in this case all the calculations are related to the monthly average daily global solar radiation.

H = H dir + H diff

(1)

The daily extraterrestrial solar irradiation

Ho =

24 × 3600

π

H o on a horizontal plane is given as,

360n   πω   Gsc 1 + 0.033cos sin φ sin δ   ×  cos φ cos δ sin ω + 365   180  

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(2)

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Gsc is the solar constant (1367W m 2 ) , n is the number of the day of year starting from the first of January (n=1 on January 1st and n=365 on December 31st, February 29th is ignored), φ is the latitude of the site, δ is the declination and ω is the sunset hour angle given as, Where

ω = arccos ( − tan φ tan δ ) The declination angle

(3)

ω for any day (n) of the year can be obtained as follows,

 360 ( 284 + n ) 365  

δ = 23.45sin 

(4)

Models for calculation of clearness index The monthly-average clearness index

Kt

is the ratio of the monthly average daily radiation on a horizontal

surface (H) to the monthly average daily extraterrestrial radiation ( H o ) that is (Duffie and Beckman, 1991):

Kt =

H Ho

(5)

The clearness index,

Kt

gives a measure of the atmospheric effects at a place on the insolation. However, the

clearness index is a stochastic parameter, which is a function of time of year, season, climatic condition and geographic location [12].kimbal [13] was the first to suggest that solar radiation is closely related to sunshine hour duration and averaged monthly values of cloudiness. Angstrom[14] gave a relation between mean daily sunshine duration ‘n’ and the mean daily global solar radiation ‘h’ angstrom’s formula is quite convenient to use but it does not consider the effect of latitude and altitude of the station. Chandel [15] gave a relation to find the clearness index as a function of latitude, altitude, maximum and minimum temp of a site. 0.5

  p  H = K t =  ΔT sin φ    × 7.9 × φ −1 Ho  po    Where, ΔT is the difference in maximum and minimum temperature, latitude from the mean sea and

(6)

φ is the latitude of the site, h is the

p −0.0001184× h ) , the monthly mean maximum and minimum temperature is = e( po

take from the ‘Indian meteorological department’ based upon 1901-2000 data which was available.

Knowing the value of the clearness index; one can calculate the diffuse component, H diff as follows (Erbs et al.1982). For

ω ≤ 81.4

2 3 4 1 − 0.2727 K t + 2.4495 K t − 11.9514 K t + 9.3879 K t , K t < 0.715 = H 0.143, K t ≥ 0.715

H diff

Where as

(7)

ω > 81.4

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2 3 1 + 0.2832 K t − 2.5557 K t + 0.8448K t , K t < 0.722 = H 0.143, K t ≥ 0.722

H diff

(8)

Models for calculation of solar radiation on a tilted surface The total solar radiation on a tilted surface

(

)

( H t ) is made up of the direct or beam solar radiation ( H dir ) ,

(

)

diffuse radiation H diff , and ground reflected radiation H ref , assuming isotropic reflection. As a consequence, the monthly-average daily solar radiation on a tilted surface

( Ht )

may be expressed as follows

(Liu and Jordan, 1960):

H t = H dir Rb +

H diff 2

(1 + cos β ) +

Hρ (1 − cos β ) 2

(9)

Where is the ratio of the average beam radiation on the tilted surface to that on a horizontal surface, is a function of the transmittance of the atmosphere, which depend upon the atmosphere cloudiness, water vapour, particulate concentration. However, liu and jordan (1960), have suggested that can be estimated to be the ratio of extraterrestrial radiation on the tilted surface to that on a horizontal surface for each month. For a surface facing directly towards the equator.

Rb =

cos (φ − β ) cos δ sin ω ' + (π 180 ) ω ' sin (φ − β ) sin δ cos φ cos δ sin ω + (π 180 ) ω sin φ sin δ

(10)

where is the sunset hour angle for the tilted surface given by

ω = arccos ( − tan φ tan δ )  ω ' = min   arccos ( − tan (φ − β ) tan δ ) 

(11)

Where “min” means the smaller of the two items in the bracket. 5. Result and discussion Fig. (2) Shows the monthly average daily global solar radiation H and the monthly average extraterrestrial daily radiation H0 on a horizontal surface in the city of Khatkar kalan (Punjab) in India. The average 7

2

7

2

winter value of H is 1.4858×10 W m day and its average summer value is 2.6843×10 W m day . In winter months, the beam components are much higher than the diffuse component. In summer months, the beam component is more than diffuse component and thus the main contribution comes from the beam component. In monsoon season, the diffuse component is nearly equal to the beam component.

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Solar Radiation107 (W/m2)

Ashok Kumar et al. / International Journal of Engineering Science and Technology (IJEST)

5 4 3 2 1 0

Months Extraterrestial solar radiation

Global

Diffuse

Direct

Fig.2: Monthly-average daily extraterrestrial, global, direct and diffuse solar radiation on horizontal surfaces at khatkar kalan (Punjab).

Figs. (3(a) and 3(b)) show the average daily total solar radiation at Khatkar Kalan on a south facing surface as the angle of tilt is varied from 0o to 90o in steps of 0.5. It is clear from these graphs that a unique β opt exists for each month of the year for which the solar radiation is at a peak for the given month. The optimum angle of tilt of a photovoltaic array PV array in January is 60.50 and the total monthly solar radiation falling on the surface at 7

2

this tilt is 2.4438×10 W m day . The optimum tilt angle in June goes to a minimum of zero degree and 7

2

the total monthly solar radiation at this angle is 2.6841×10 W m day . The optimum tilt angle then increases during the winter months and reaches a maximum of 62.5o in December which collects

2.5717×107 W m 2 day of solar energy monthly. Table1. Optimum Tilt Angle

Months

βopt

for Each Month of the Year for a South Facing Solar PV array at Khatakar Kalan (Punjab).

β opt

Monthly Radiation

107 W m 2 January February March April May June July August September October November December

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60.5 50.5 36.5 18.0 0 0 0 8.5 26 46.5 58.5 62.5

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2.4438 2.5391 2.5746 2.6801 2.7839 2.6841 2.2952 2.0969 2.1374 2.4989 2.7239 2.5717

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7

2.8

JAN TO JUNE

x 10

2.6

2

SOLAR RADIATION (W/m)

2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8

0

10

JAN

20

30

40

50

ANGLE MARCH

FEB

60

70

APRIL

80

MAY

90

JUNE

Figure 3a Monthly-average daily solar radiation availability of tilted surfaces at khatkar kalan(Punjab)

JULY TO DEC

7

2.8

x 10

2.6

2

SOLAR RADIATION (W/m)

2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8

JULY 0

10

AUG 20

30

SEP 40

OCT 50

60

NOV 70

DEC 80

90

ANGLE Figure 3b Monthly-average daily solar radiation availability of tilted surfaces at khatkar kalan(Punjab)

Table 2 shows the monthly, seasonal, and the yearly average tilt angles as well as the corresponding radiations at Khatkar kalan India. The seasonal average was calculated by finding the average value of the tilt angle for each season and the implementation of this requires the PV array tilt to be changed four times a year. The yearly average tilt was calculated by finding the average value of the tilt angles for all months of the year. The yearly average tilt was found to be 30.16o for khatar kalan and these results in a fixed tilt throughout the year. When the monthly optimum tilt angle was used, the yearly collected solar energy was 2.500775×107 W m 2 day . With the seasonally adjusted tilt angles, the yearly collected solar energy was 2.3669×107 W m 2 day . Finally, with the yearly average tilt angle, the yearly collected solar energy was 2.227168×10 7 W m 2 day .when the

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Photovoltaic array is set at the seasonal tilt angle there is a reduction of 5.33% as compared to monthly, similarly there is a reduction of 9.16% the photovoltaic array is set at yearly tilt angle. The yearly optimum tilt ° angle is a fixed value for any solar PV array throughout the course of a year. It is 30.61 for Khatkar kalan and oriented towards the south. The amount of solar radiation received by the solar PV array tilted at yearly optimum angle facing south was computed. Fig 4 shows the Optimum, seasonal average, and yearly average tilt angles for each month of the year. The Validation of the data is done from the solar plant which is install at khatkar kalan (Punjab). The model calculate the yearly optimum tilt angle of 30.61o where as the solar plant at khatkar kalam is install at 30o. Table 2 monthly, seasonal, and the yearly average tilt angles as well as the corresponding radiations at Khatkar kalan India

Months

Global radiation at monthly tilt angle in 107 W m 2 60.5 2.4438 50.5 2.5391 36.5 2.5746 18 2.6801 0 2.7839 0 2.6841 0 2.2952 8.5 2.0969 26 2.1371 26.5 2.4789 58.5 2.7239 62.5 2.5717 2.500775

Jan Feb March April May June July Aug Sep Oct Nov Dec Total

Global radiation Seasonal tilt angle in 107 W m 2 57.8 2.4262 57.8 2.4251 18.16 2.3641 18.16 2.5799 18.16 2.5871 2.83 2.5009 2.83 2.2895 2.83 2.0916 43.67 2.0631 43.67 2.3965 43.67 2.3428 57.8 2.3360 2.3669

at

Global radiation at Yearly tilt angle 107 W m 2 30.61 2.1513 30.61 2.3888 30.61 2.3590 30.61 2.4333 30.61 2.5313 30.61 2.3419 30.61 2.0690 30.61 2.0008 30.61 2.1333 30.61 2.3124 30.61 2.3311 30.61 2.2080 2.27168

70 60 50 40

Angle 30 20 10 0

MONTHLY AVERAGE

SEASONAL AVERAGE

YEARLY AVERAGE

Figure 4. Optimum, seasonal average, and yearly average tilt angles for each month of the year.

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Experimental setup install at Khatkar kalan Simulated result at khatkar kalan

31.5

31

Tilt angle

30.5

30

29.5

29

28.5

28

2

4

6

8

10

12

Months Fig.5: Validation of the Experimental and Simulated result Conclusion

In the light of the preceding results, the following conclusions can be drawn: °



The optimum tilt angle in may ,June, july goes to a minimum of 0 .The optimum tilt angle then



increases during the winter months and reaches a maximum of 62.5 in December. The results show that the average optimum tilt angle for the summer months

°

°

°

Is 2.83 and for the winter months 57.48 .  

°

Finally, the yearly-average optimum tilt angle found to be 30.61 for a south facing solar PV array which can be used for building applications. When the Photovoltaic array is set at the seasonal tilt angle there is a reduction of 5.33% as compared to monthly, similarly there is a reduction of 9.16% the photovoltaic array is set at yearly tilt angle.

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[19] S. Armstrong*, W.G. Hurley. A new methodology to optimise solar energy extraction under cloudy conditions. Renewable Energy 35 (2010) 780–787. [20] Runsheng Tang , Tong Wu. Optimal tilt-angles for solar PV arrays used in China. Applied Energy 79 (2004) 239–248. [21] Huseyin Gunerhan, Arif Hepbasli. Determination of the optimum tilt angle of solar PV arrays for building applications. Building and Environment 42 (2007) 779–783. [22] Murat Kacira, Mehmet Simsek , Yunus Babur , Sedat Demirkol . Determining optimum tilt angles and orientations of photovoltaic panels in Sanliurfa, Turkey. Renewable Energy 29 (2004) 1265–1275. [23] H.R. Ghosh, N.C. Bhowmik, M. Hussain. Determining seasonal optimum tilt angles, solar radiations on variously oriented, single and double axis tracking surfaces at Dhaka. Renewable Energy 35 (2010) 1292–1297. [24] E.P. Sakonidou, T.D. Karapantsios , A.I. Balouktsis, D. Chassapis. Modeling of the optimum tilt of a solar chimney for maximum air flow. Solar Energy 82 (2008) 80–94.

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