Solar Panel Angle

Special Issue of International Journal of Sustainable Development and Green Economics (IJSDGE), ISSN No.: 2315-4721, V-2, I-1, 2, 2013

85

OPTIMAL SLOPE ANGLES FOR SOLAR PHOTOVOLTAIC PANELS FOR MAXIMUM SOLAR ENERGY GAIN

PRIYA YADAV1 & S. S. CHANDEL2

1,2Centre for Energy and Environment, National Institute of Technology, Hamirpur, Himachal Pradesh-177005, India

Abstract- In this study, a mathematical model is used to determine the solar radiation incident on a inclined surface and the optimum slope angles for each month, season and year are calculated for solar photovoltaic panels at NIT Hamirpur, Himachal Pradesh, India. It is found that the optimum slope angles are found to be between 00 (June) and 560 (December) throughout the year. In winter the optimum slope angle is 530, in spring 30.60, in summer 00, and in autumn 24.60. The yearly average tilt angle is found to be 27.10 for the location. The maximum solar energy gain is 11% found at monthly optimum tilt angles in comparison to horizontal surface and 5% in comparison to yearly optimum tilt. Keywords- Optimum tilt angle, Solar photovoltaic, Solar Radiation, Extraterrestrial Radiation, Clearness index,.

I. INTRODUCTION

Solar energy is a vast inexhaustible source of energy. And can meet all the energy requirements on earth, if utilised efficiently. As the earth keeps revolving around the sun as well as on its own axis, the intensity of solar radiation varies throughout the day and year. So in order to collect maximum solar energy, it is important to determine the correct orientation and slope of the solar photovoltaic (PV) panels. This problem can be solved by tracking the sun daily throughout the year. But tracking devices are not economically viable for small scale power systems. The output of PV systems can be increased by using monthly and seasonal tracking manually. For this purpose the optimum tilt angle for each month of the year has to be determined. The orientation of the collectors has to be towards equator for maximum solar radiation gain i.e. in the northern hemisphere the PV panels are to be installed facing true south and in southern hemisphere these should be facing true north. Solar radiation data is generally measured by the horizontal pyranometer in the form of global radiation. Solar collectors are adjusted at an optimum tilt angle so that they capture maximum sunlight. The tilt angle is defined as the angle which the solar collectors make with horizontal surface to maximize the collected energy and the collector output. Tilt angle greatly influences the performance of solar PV panels. Maximum output can be obtained by solar collectors if they are installed at an optimum tilt. Tilt angle of a collector depends on geographical conditions, day of the year and latitude of a place. Therefore different places will have different tilt angles for different seasons. A lot of research work has been done in this area. Various researchers have presented different models for calculation of optimum tilt angle. The main difference lies in the calculation

of diffused radiation which depends on the clearness index. It was concluded that opt= -, where is latitude angle of a particular location and is the declination angle of that place at a particular time of the year. Different recommendations have been made by a number of researchers for choosing the optimum tilt angle depending on latitude of a place [1], [2]. Heywood, Lunde and Garge concluded that opt= 150 [2], [3], [4]. Duffie & Beckman suggested that opt= (+150) 150 [5]. For simplification, the optimum tilt angle is generally taken equal to the latitude of the location at which the collectors are to be installed [6] ,[7] ,[8]. Palvic concluded that to obtain maximum solar radiation, the solar panels should be installed facing true south [9]. In this paper the monthly, seasonally and yearly optimum tilt angles for solar PV systems installed at Centre for Energy & Environment, National Institute of Technology [NIT] Hamirpur, Himachal Pradesh, India, are determined. A computer program in MATLAB software is developed for this purpose. The collected energy is simulated as the tilt angle is varied. The hourly global radiation data recorded at the automatic data acquisition system installed at the Centre for Energy & Environment at NIT is obtained. This data is then averaged to get the monthly average daily global radiation on horizontal surface. The monthly average daily global radiation on tilted surface is estimated using mathematical calculations. The optimum tilt angle for each month is determined by looking for the values on which the global radiation is maximum for a particular day of the month. II. SOLAR RADIATION BASICS Extraterrestrial radiation is the solar radiation outside earths surface. Its intensity varies throughout the year so an average constant value of S0= 1367 W/m2

Optimal Slope Angles for Solar Photovoltaic Panels for Maximum Solar Energy Gain


86

is taken. Variation in solar constant over the time of the year is given by the equation:

Where is the sunshine hour angle of the month in consideration.

The polar axis of earth is inclined by an angle of 66.550 to the elliptical plane and by 23.450 from perpendicular to elliptical plane. The rotation of earth on its inclined polar axis with respect to elliptic plane is responsible for different seasons on earth. It causes lengthy days in summer and shorter days in winter. The angle made by the lines joining the centre of the earth to centre of the sun with its projection on the equatorial plane of the earth is called declination angle. It varies due to the inclination of earths polar axis and its revolution around the sun. it varies between -23.450 to 23.450. The formula for declination angle is given by:

Where n is the nth day of the year.

Fig. 1 Definition of solar angles [10]

A. Global, beam and diffused irradiance: The incident radiation which reaches the earths surface without being absorbed or scattered is called beam radiation. Some of the radiation from the sun is scattered back to the atmosphere and some of it is scattered to earth, this scattered radiation reaching the earths surface is called diffused radiation. When the solar radiation reaches the earths surface, some of it is reflected by the ground and other objects on ground. This radiation is called reflected radiation. The global

radiation is the sum of beam, diffused and reflected radiations. B. Calculation of clearness index: The monthly-average clearness index KT is the ratio of the monthly average daily radiation on a horizontal surface (Hg) to the monthly average daily extraterrestrial radiation (Ho) that is [5]:

The clearness index, KT gives a measure of the atmospheric effects at a place on the solar insolation. However, the clearness index is a stochastic parameter, which is a function of time of year, season, climatic condition and geographic location [11]. Knowing the value of the clearness index; we can calculate the diffuse component, Hd as follows [12]:

III. MODELING As the data available is in the form of global radiation on horizontal surface, we need to determine the solar radiation at tilted surface. For this correlation procedures are required. The solar radiation on tilted plane is taken as the combination of direct beam, diffused and reflected components of global radiation [13]:

Where Rb is the ratio of the average beam radiation on the tilted surface to that on a horizontal surface. It is a function of the transmittance of the atmosphere, which depends upon the atmosphere cloudiness, water vapour, particulate concentration [13].



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is the reflectivity of ground surface. HB, HD & HR are beam, diffused and reflected radiations respectively on tilted surface. The value of is generally taken as 0.2.

IV. RESULTS AND DISCUSSION The monthly average daily extraterrestrial radiation is calculated using eq. (2) and the beam and diffused components of global radiation are calculated from equations (8) and (9). It is found that the diffused component is greater than beam component in winter months whereas beam component is higher in summer months as shown in fig.3.

Fig. 2 Monthly average daily global radiation (Hg) and monthly

average daily extra-terrestrial radiation (Ho) on a horizontal surface

To maximize the solar radiation on a collector, the collector needs to be mounted at an optimum tilt angle. This tilt angle is calculated using equations given in modelling section. The tilt angle is varied in steps of 10 and the angle for which monthly average daily solar radiation is maximum, is taken to be the optimum tilt angle for that month. The variation of solar radiation with tilt angle from 00 to 900 for twelve months of the year is shown in Fig. 4 and Fig. 5. The peaks of these curves correspond to maximum solar radiation at optimum tilt angle for each month of the year.

Fig. 3 Monthly average daily global radiation (Hg), beam radiation (Hb) and diffuse radiation (Hd) on a horizontal

surface at Hamirpur (H.P.), India

The optimum tilt angle for each month is calculated. Then average optimum tilt angles are calculated for four seasons of the year. Yearly optimum tilt angle is calculated by averaging the monthly optimum tilt angles over the year.

Fig. 4 Monthly average daily total solar radiation (in

kWh/m2/day) on a south facing panel in Hamirpur (HP), India for the months of January-June

The seasonal average is calculated by finding the average value of the tilt angle for each season, and for its implementation, the panel tilt be has to be changed four times a year. It is found that in winter (November, December & January) the tilt is 530, in spring (February, March & April) 30.60, in summer (May, June & July) 00, and in autumn (August, September & October) 24.60. The yearly average tilt is calculated by finding the average value of the tilt angle for all months of the year

Fig. 5 Monthly average daily total solar radiation (in

kWh/m2/day) on a south facing panel in Hamirpur for the months of July-December

Monthly, seasonal and yearly optimum tilt angles are plotted against the months of a year in Fig. 6.

0

2

4

6

8

10

kWh/

m2 /

day

Hg

Ho

01234567

Jan Mar May Jul Sep Nov

kWh/

m2 /

day

Hg

Hd

Hb



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Fig. 6 Optimum monthly average, seasonal average, and yearly

average tilt angles for each month of the year .

The yearly average of these values is found to be 27.10 and this indicates an optimum fixed tilt throughout a year. Fig. 7 shows the monthly average solar energy collected throughout the year when the angle of tilt is optimum for each month, and when the seasonal and yearly average slope angles are used. Table I and Table II show the monthly average daily global solar radiation on monthly, seasonal and yearly optimum tilt angles. The yearly collected solar energy when solar radiation fall on horizontal surface is measured to be 1572 kWh/m2. The yearly collected solar energy is found to be 1766 kWh/m2 for collectors mounted at monthly optimum tilt, 1753 kWh/m2 for seasonal optimum tilt and 1678 kWh/m2 for yearly average tilt angles.

TABLE I

Monthly Optimum Tilt Angle opt and collected energy for a South facing Solar PV array at Hamirpur

(HP), India Month opt

(0) HT (kWh/m2/day)

January 51 3.50

February 42 3.95

March 33 5.55

April 17 5.70

May 0 6.32

June 0 5.93

July 0 4.29

August 8 3.75

September 25 4.57

October 41 5.28

November 52 4.80

December 56 4.45

TABLE III Seasonal and yearly average tilt angles and monthly

daily solar radiation on south-facing sloped surface at Hamirpur,H. P., India

Month

Seasons

Seasonal Average

Yearly Average

(0)

HT (kWh/m2

/day)

(0)

HT (kWh/m2

/day) Nov

Winter 53

0 3.49

27.10

3.30 Dec 3.90 3.87 Jan 5.55 5.53 Feb Sprin

g 30.60

5.56 5.62 Mar 6.32 5.83 Apr 5.93 5.22 May Sum

mer 00

4.29 3.93 Jun 3.65 3.62 Jul 4.57 4.57 Aug Autu

mn 24.60

5.13 5.17 Sep 4.79 4.48 Oct 4.45 4.06

It is deduced from Table 2 that the loss in the amount of collected energy is less than 1% (0.78 %) if the angle of tilt is adjusted seasonally instead of using opt for each month of the year at Hamirpur. The loss of energy when using the yearly average fixed tilt angle is around 5% compared with the monthly optimum tilt. The loss in energy was found to be 11% when no tilt was used compared with optimum tilt.

Fig. 7 Global radiation on tilted plane for monthly, seasonal

and yearly average tilt angle

0

10

20

30

40

50

60

Jan

Apr

Jul

Oct

tilt

ang

le (i

n de

gree

s)opt tilt (monthly)

opt tilt (seasonal)

opt tilt (yearly)

Jan

Feb

Mar

Apr

May

Jun

JulAug

Sep

Oct

Nov

Dec

Ht (monthly) 3 4 6 6 6 6 4 4 5 5 5 4

Ht (yearly) 3 4 6 6 6 5 4 4 5 5 4 4

Ht (seasonal) 3 4 6 6 6 6 4 4 5 5 5 4

0

1

2

3

4

5

6

7

Glo

bal R

adia

tion

(kW

h/m

2 /da

y)



89

V. CONCLUSION

The methodology to determine slope angles for solar photovoltaic panels has been described with case study of Hamirpur, HP , India location , however it can be used for any location world wide . The main conclusions are as follows : 1. The optimum tilt angle for this location is found to be 560 in December and 00 in May, June & July i.e. minimum in summers and maximum in winters. The yearly average optimum tilt angle is 27.10 and for different seasons i.e. for summer 00, autumn 24.60, winter 530 and for spring 30.60 . 2. The gain in energy is found to be 11% when monthly optimum tilt is used as compared to a horizontal surface and 5% when compared to yearly average tilt. The yearly collected solar energy with yearly average tilt is 1678 kWh/m2. It is 1753 kWh/m2 with seasonally adjusted tilt angle and 1766 kWh/m2 for monthly optimum tilt 3. For maximum solar energy gain ,the solar photovoltaic panels are to be inclined at optimal tilt angles for each location. The monthly, seasonal adjustment of Solar panel leads to considerable gain in Solar energy which will also lead to reduction in Solar Power Plant cost. REFERENCES

[1] D. Ibrahim, Optimum tilt angle for solar collector used in

Cyprus. Renewable Energy, Vol. 6, No. 7, pp. 813819, 1995.

[2] HP Garg, Treative on Solar Energy Vol. 1: Fundamentals of Solar Energy. Wiley, New York, 1982.

[3] PJ. Lunde, Solar Thermal Engineering, Wiley, New York, 1980.

[4] H. Heywood, Operational experience with solar water heating, J Inst Heat Vent Energy, Vol. 39, pp. 639, 1971

[5] J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes, Wiley, New York, 1991.

[6] Ashok Kumar et al., Optimization of tilt angle for photovoltaic array, International Journal of Engineering Science and Technology (IJEST), Vol. 3 No. 4, pp. 3153-3161, 2011.

[7] Koray Ulgen, Optimum tilt angle for solar collectors, Energy Sources, Part A, Vol. 28, pp. 11711180, 2006.

[8] M. Jamil Ahmad* and G.N. Tiwari, Optimization of tilt angle for solar collector to receive maximum radiation, The Open Renewable Energy Journal, Vol. 2, pp. 19-24, 2009.

[9] T. Pavlovi, et al., Determining optimum tilt angles and orientations of photovoltaic, Contemporary Materials I, Vol. 2, pp. 151-156, 2010.

[10] M. Benghanem, Optimization of tilt angle for solar panel: Case study for Madinah, Saudi Arabia, Applied Energy, Vol. 88 pp. 14271433, 2011.

[11] S.A. Klein, Calculation of monthly average insolation on tilted surfaces, Solar Energy, Vol. 19, pp. 325-9, 1977.

[12] A. Miguel et al., Diffuse solar radiation model evaluation in the north Mediterranean belt area, Solar Energy, Vol. 70, pp. 143-53, 2001.

[13] B.Y.H. Liu and R.C. Jordan, Daily insolation on surfaces tilted towards the equator, Trans. ASHRAE, Vol. 53, pp. 526-41, 1962.

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Solar Panel Angle