# Comparative Approach For The Optimization Of Tilt Angle To Receive Maximum Radiation

DOI : 10.17577/IJERTV1IS5008

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#### Comparative Approach For The Optimization Of Tilt Angle To Receive Maximum Radiation

1Abhishek Agarwal , 2Vineet Kumar Vashishtha, 3Dr. S.N. Mishra

1 Department of Mechanical Engineering, KNIT-Sultanpur, UP, India-228118

3Asst. Professor., Department of Mechanical Engineering, I.I.T, U.P. ,India Ghaziabad-201003

2Professor., Department of Mechanical Engineering, KNIT-Sultanpur, UP, India-228118

ABSTRACT

India is both densely populated and has high solar insolation, providing an ideal combination for solar power in India. As the angle between the sun and a fixed surface is continually changing, the power density on a fixed PV module is less than that of the incident sunlight. Since the flat plate solar collectors are placed at an angle to the horizontal, it is necessary to calculate the optimum tilt angle which maximizes the amount of collected energy. The best way to collect the maximum solar energy is by using solar tracking systems, and thus to maximize the collected beam radiation. In this paper a mathematical model was used for estimating the total (global) solar radiation on a tilted surface, and to determine the optimum tilt angle and orientation (surface azimuth angle) for the solar collector in India at four different locations on a monthly basis, as well as for a specific period. The results reveal that changing the tilt angle 12 times in a year (i.e. using the monthly-averaged optimum tilt angle) maintains approximately the total amount of solar radiation near the maximum value that is found by changing the tilt angle daily to its optimum value. This achieves a yearly gain in solar radiation of 4.56% more than the case of a solar collector fixed on a horizontal surface.

Keywords: solar collector, optimum tilt angle, clearness index, solar radiation.

1. INTRODUCTION

The natural energy flows through the Earths ecosystem are immense, and the theoretical potential of what they can produce for human needs exceeds current energy consumption by many times. For example, solar power plants on one percent of the worlds desert area would generate the worlds entire electricity demand today [1].

unprecedented manner and mankind seeks for additional energy sources.

Energy sources are vital and essential ingredients for all human transactions and without them human activity of all kinds and aspects cannot be progressive. Population growth at the present average rate of 2% also exerts extra pressure on limited energy sources Renewable energy supplies 19 percent of global final energy consumption, counting traditional biomass, large hydropower, and renewable (small hydro, modern biomass, wind, solar, geothermal, and bio fuels). Of this 19 percent, traditional biomass, used primarily for cooking and heating, accounts for approximately 13 percent and is growing slowly or even declining in some regions as biomass is used more efficiently or is replaced by more modern energy forms. Hydropower represents 3.2 percent and is growing modestly but from a large base. Other renewable account for 2.6 percent and are growing very rapidly in developed countries and in some developing countries. The amount of solar energy received by the surface of the earth per minute is greater than the energy utilization by the entire population in one year. Solar energy is referred to as renewable and/or sustainable energy because it will be available as long as the sun continues to shine. Estimates for the life of the main stage of the sun are another 4 5 billion years. The energy from the sunshine, electromagnetic radiation, is referred to as insulation.

The sun is a sphere of intensely hot gaseous matter with a diameter of . In effect the sun is a continuous fusion reactor in which hydrogen is turned into helium. The suns total energy output is

In recent centuries the types and magnitudes of the

3.8 1020 MW which is equal to

63 MW m2 of the suns

energy requirements have increased in an surface. This energy radiates outwards in all directions.

Only a tiny fraction,

1.7 1014 kwof the total radiation

calculating the hourly solar irradiation components

emitted is intercepted by the earth [1].

The performance of a solar collector 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 collector, the tilt angle, defined as the angle of collectors with respect to horizontal, is a dominant parameter affecting the collectible radiation of a fixed collector. In general, the optimal tilt angle of a fixed collector 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 collector.

2. LITERATURE REVIEW

There are various devices for absorbing the solar radiation. The Sun rays are to be always focused onto the absorber plate. The collector has to be rotated by tracking system, but the tracking system is very costly so we cannot use this for every system economically. Due to this reason the solar collector is fixed either monthly, seasonally or yearly pattern, based on our requirements. Ahmad M. Jamil and Tiwari

G.N. [2] analyzed the theoretical aspects of choosing a tilt angle for the solar flat-plate collectors used at ten different stations in the world and makes recommendations on how the collected energy can be increased by varying the tilt angle. For Indian stations, the calculations are based upon the measured values of monthly mean daily global and diffuse solar radiation on a horizontal surface. As explained in Bekker et al [3]. The orientation and tilt of the panels directly relates to the annual energy yield of the panels Mehleri E.D. et. al. [4] determined optimum tilt angle and orientation for solar photovoltaic arrays in order to maximize incident solar irradiance exposed on the array, for a specific period of time. The ratio of monthly average hourly diffuse radiation to monthly average hourly global radiation was correlated by Ulgen Koray and Hepbasli Arif [5] with the monthly average hourly clearness index in the form of the polynomial relationships for the city of Izmir in the western part of Turkey.

The values of the monthly average daily clearness index ranged from 0.41 to 0.66, averaged for the same period.

KorayUlgen [5] found that the optimum tilt angle changes between 0 (June) and 61 (December) throughout the year. In winter (December, January, and February) the tilt should be 55.7, in spring (March, April, and May) 18.3, in summer (June, July, and August) 4.3, and in autumn (September, October, and November) 43. Sakonidou E.P. et. al. [6] developed a mathematical model. The model starts by

(direct, diffuse, ground-reflected) absorbed by the solar chimney of varying tilt and height for a given time (day of the year, hour) and place (latitude). Moghadam Hamid et. al. [7] estimated solar global radiation on a horizontal surface using a mathematical model and the results were compared.

Ibrahim D. [8] examined for selection of optimum tilt angle of Cyprus. For maximum radiation the results were calculated by varying tilt angle form 0Â° to 90Â° with the increment of 10Â°.

Tang R. and Tong W. [9] presented a mathematical procedure to compare the optimum tilt angles of collectors through monthly diffused radiation and actual monthly diffused radiations. The best orientation for solar collectors in Izmir was south facing.

1. PROBLEM IDENTIFICATION

Based on the literature survey it is sen that the incident solar radiations on a collector surface are greatest for an optimal tilt angle of the collector at a particular region which is also not constant throughout the year. To obtain maximum power output from the solar collector system it is desirable to tilt the collector to that tilt angle at which the incident solar radiations are maximum. If not monthly, the tilt angles of the collector surfaces can be changed four times in a year to their seasonal optimum tilt angles at which slightly less power is obtained than monthly optimal angles but large compared to yearly optimal tilt angle.

2. OBJECTIVE OF THE STUDY

The following objectives are covered under this study:

1. Daily and monthly Optimum slope angles.

2. Seasonal Optimum tilt angles.

3. Yearly optimum tilt angle.

4. To compare the different model.

5. To compare with the solar panel setup installed at Village Nandha, Bhiwani, Haryana

Joakim WidÃ©n [10] mentioned the models of solar radiation, daylight and solar cells as a chapter in his thesis. M.S.Alam [11] et.al. developed a mathematical model for simulation of solar radiation system by using dynamics methodology in their paper.

Angstroms equation[20] is used to express the average radiation on a horizontal surface in terms of

constants 1,2 and the observed values of average length of solar days.

Fig.1- Solar Panel installed at MGICC-Delhi Govt., Alipur-Bakauli, New Delhi

The constants 1,2 will be determined for this model based on actual old measurements and equating the data in the Angstroms equation given as follows:

Manes A, and Ianetz A. [1] presented energy radiates outwards in all directions. Only a tiny fraction, of the total radiation emitted is intercepted by the earth. The variation of the earth-sun distance due to earths orbit causes variable extraterrestrial radiation. The dependence of extraterrestrial radiation on time of year is indicated by Duffie J.A. and Beckman W. A. [13]:

G=

The sunset hour angle for any day (n) of the year can be obtained as follows. 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.

Fig.2- Earth Sun Geometry 6- EARTH-SUN GEOMETRY

The term Earth rotation refers to the spinning of our planet on its axis. At any one moment in time, one half of the Earth is in sunlight, while the other half is in darkness. The edge dividing the daylight from night is called the circle of illumination. The Earths rotation also creates the apparent movement of the Sun across the horizon.

Fig.-3-Sun Path for Village Nandha, Haryana along the year

The annual change in the relative position of the Earth's axis in relationship to the Sun causes the height of the Sun or solar altitude to vary in our skies. Solar altitude is normally measured from either the southern or northern point along the horizon and begins at zero degrees. Maximum solar altitude occurs when the Sun is directly overhead and has a value of 90Â°.

7- MODELS FOR CALCULATION OF CLEARNESS INDEX

The monthly-average clearness index is the ratio of the monthly average daily radiation on a horizontal surface (H) to the monthly average daily extraterrestrial radiation ( )

Chandel S.S. [12] gave a relation between mean daily sunshine duration n and the mean daily global solar radiation h as a function of latitude, altitude, maximum and minimum temp of a site.

Where, is the difference in maximum and minimum temperature, Ã˜ is the latitude of the site (Nandha is 28.8482), h is the latitude from the mean sea height. The altitude of Haryana varies between 700 to 3600 ft (200 meters to 1200 meters) above sea level, the monthly mean maximum and minimum temperature is taken from the Indian Meteorological Department

An empirical method for the estimation of the monthly average daily total radiation incident on a tilted surface was developed by Liu B.Y.H. and Jordan R.C. [15]. In their correlation, the diffuse to total radiation ratio for a horizontal Surface is expressed in terms of the monthly clearness index Kt with the following equation:

Collares P. and M. Rabl A. [14] expressed the same parameter by also considering the sunset hour angle:

Knowing the value of the clearness index; one can calculate the diffuse component, Hdiff as follows (Erbs D.G. et al.) [16].

For 81.4

Where as > 81.4Â°

Then, the direct daily component can be computed.

The total solar radiation on a tilted surface is made up of the direct or beam solar , diffuse

radiation , and ground reflected on a tilted surface

Liu, B.Y.H. and Jordan R. C. [15] and anisotropic Hay,

J.E. [17] ones. The daily beam radiation received on an inclined surface can be expressed as

where H and are the monthly mean daily global and diffuse radiation on a horizontal surface, and Rb is the ratio of the average daily beam radiation on a tilted surface to that on a horizontal surface. The daily ground reflected radiation can be written as

= H (1-cos)/2

Liu, B.Y.H. and Jordan R. C. [15] have suggested that can be estimated by assuming that it has the value which would be obtained if there were no atmosphere. For surfaces in the northern hemisphere, sloped towards the equator, the equation for Rb is given as below Miguel A. et. al. [18] and is used in the present study.

Where

' is the sunset hour angle for the tilted surface for the mean day of the month. min means the smaller of the two terms in the bracket.

For surfaces in the southern hemisphere, sloped towards the equator, the equation for Rb is given as below Liu, B.Y.H. and Jordan R. C. [15].

Where

Optimum tilt angle curve along the year, in winter, the tilt angle approaches to 55Â°, while in summer it approaches to 8Â°. Assuming all previous angles are random variables, so the expected values for those variables as follows:

[ ] = [ ] [ ]

Fig.4- Optimum Tilt angle Vs Days

The methods for approximation the ratio of diffuse solar radiation on a tilted surface to that of a horizontal are classified as isotropic and anisotropic models. The isotropic models assume that the intensity of diffuse sky radiation is uniform over the sky dome. Hence, the diffuse radiation incident on a tilted surface depends on the fraction of the sky dome seen by it. The anisotropic models assume the anisotropy of the diffuse sky radiation in the circumsolar region (sky near the solar disc) plus and isotropically distributed diffuse component from the rest of the sky dome. The sky- diffuse radiation can be expressed as-

Where Rd is the ratio of the average daily diffuse radiation on a tilted surface to that on a horizontal surface.

The diffuse radiation models chosen for study were as follows Kamali G.H. [19].

9- ISOTROPIC MODELS

• Liu and Jordan model (1962) Rd= [3 + cos (2)] / 4

• Tian et al. model (2001) Rd= 1- /4

• Koronakis model (1986) Rd= 1/3 [2+ cos ]

• Badescu model (2002) Rd= [3+ cos 2] /4

1. ANISOTROPIC MODELS

• Hay model (1979)

• Skartveit and Olseth model (1986)

Where

• Reindl et al. model (1990)

• Steven and Unsworth model (1980)

1. TOTAL RADIATION ON A TILTED

SURFACE, can thus be expressed as

2. SITE ANALYSIS

Historical data for the specific site at Stellenbosch suggests that the total energy received on a horizontal surface differs from January to June.

 Jan Feb Mar Apr May Jun July kWh/m2/d 3.41 4.31 5.45 6.68 7.43 7.17 5.68 Aug Sep Oct Nov Dec Annual 5.29 5.55 5.30 4.23 3.36 5.32

Table 1- Horizontal Irradiation data for Nandha, Haryana

Fig.5 – Daily solar radiation for Village Nandha, Haryana horizontal

Fig.6.-Daily Averaged Insolation Incident On A Horizontal Surface-Nandha, Haryana

Table.2- Horizontal Irradiation data for New Delhi

 Month Jan Feb Mar Apr May Jun July kWh/m2/d 3.8 4.68 5.8 6.30 6.42 6.07 5.22 Aug Sep Oct Nov Dec Annual 4.81 5.06 4.83 4.18 3.52 5.06

Fig.7 – Daily solar radiation for New Delhi – horizontal

#### Fig.8-Daily Averaged Insolation Incident On A Horizontal Surface-New Delhi, India.

3. RESULT AND DISCUSSION

The average winter value of H is 1.4858

W/m2day and its average summer value is 2.6843Ã— W/m2day

Fig.9- Monthly Average daily Extraterrestrial, Global, Direct and Diffuse solar radiation on horizontal surfaces at Village Nandha, Haryana

Fig.10-Monthly-average daily solar radiation availability of tilted surface at Village Nandha, Haryana

Fig shows the beam radiation dominates throughout the year where the maximum beam radiation reaches in the month of May (2.3066 X 107 W/m2 day) whereas the least amount of beam radiation occurs in the month of December (1.1026 X 107 W/m2 day). The remaining city consider in the study is Delhi. Delhi shows somewhat similar trend as that of Village Nandha, Haryana. Fig. shows the average daily total solar radiation at Village Nandha, Haryana on a south

facing surface as the angle of tilt is varied from 0 to 90 in steps of 0.5Â°. It is clear from these graphs that a unique 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 flat-plate collector in January is 60 and the total monthly solar radiation falling on the surface at this tilt is 2.4438Ã—107 W/m2day.The optimum tilt angle in June goes to a minimum of zero degree and the total monthly solar radiation at this angle is 2.6841Ã—107 W/m2 day. The optimum tilt angle then increases during the winter months and reaches a maximum of 62Â° in December which collects 2.5717Ã—107 W/m2day of solar energy monthly. The optimum angle of tilt of a flat-plate collector in January is 44.5Â° and the total monthly solar radiation falling on the surface at this tilt is 3.3610Ã—107 W/m2day. The optimum tilt angle in May goes to a minimum of zero degree and the total monthly solar radiation at this angle is W/m2day.

The average daily total solar radiation at Delhi on a south facing surface as the angle of tilt is varied from 0Â° to 90Â° in steps of 0.5Â°. It is clear from these graphs that a unique opt exists for each month of the year for which the solar radiation is at a peak for the given month. The optimum tilt angle then increases during the winter months and reaches a maximum of 60Â° in December which collects 2.6844Ã—107 W/m2day of solar energy monthly. Table gives a list of opt for each month of the year at Village Nandha, Haryana using 2 isotropic models (Badescu model , Liu and Jordan model) and 2 anisotropic models (Reindl et al. model, Hay model) as mentioned previous. The optimum angle of tilt of a flat-plate collector in January is 60Â° by Liu & Jordan model whereas Reindl model, Hay model, Badescu model indicate the optimum tilt angle as 61.5Â°, 61Â°, 60.5Â° resp. and the total monthly solar radiation falling on the surface at this tilt is 2.4438Ã—107 W/m2day by Liu & Jordan model whereas Reindl model, Hay model, Badescu model indicate the total monthly solar radiation falling on the surface at this tilt angle is 2.6367Ã—107 W/m2day, 2.6253Ã—107 W/m2day 2.4088Ã—107 W/m2day resp. The optimum tilt angle in June goes to a minimum of zero degree as indicated by all the models and the total monthly solar radiation at this angle is 2.6841Ã—107 W/m2day. 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 30.61Â° for Village Nandha, Haryana. when the seasonal average angles are used, and when the yearly average angle is used throughout the year. When the monthly optimum tilt angle was used, the yearly collected solar energy was 2.500775 X

#### 107 W/m2 day with the seasonally adjusted tilt angles, the yearly collected solar energy was 2.3669 X 107 W/m2 day. Finally, with the yearly average tilt angle, the yearly

Table:3- Optimum Tilt Angle opt for Each Month of the Year at Nandha, (Haryana)

 Months Liu & Jordan Model Reindl Model Hay Model Badescu Model opt Ht(opt) 107 W/m2day 107W/m2day 107W/m2day 107W/m2day Dec 62 2.5717 63.5 2.7521 63 2.7437 62.5 2.5449 Jan 60 2.4438 61.5 2.6367 61 2.6253 60.5 2.4088 Feb 50 2.5391 53 2.6799 52 2.6710 50.5 2.5023 Mar 36 2.5746 38.5 2.6482 38 2.6438 35 2.5465 Apr 17.5 2.6801 18.5 2.6960 18 2.6954 16 2.6720 May 0 2.7839 0 2.7839 0 2.7839 0 2.7839 Jun 0 2.6841 0 2.6841 0 2.6841 0 2.6841 Jul 0 2.2942 0 2.2952 0 2.2941 0 2.2952 Aug 8 2.0969 9 2.1023 8.5 2.1021 6 2.0938 Sep 27.5 2.1374 28.5 2.1920 27.5 2.1874 22 2.1112 Oct 48.5 2.4989 48 2.6167 47.5 2.6095 44.5 2.4639 Nov 58 2.7239 59.5 2.8826 59 2.8755 58 2.6958 Average 30.61 2.5024 31.66 2.5808 31.20 2.5764 29.58 2.4835

Table 4- Optimum Tilt Angle opt for Each Month of the Year at Delhi

 Months Liu & Jordan Model Reindl Model Hay Model Badescu Model opt Ht(opt) 107 W/m2day 107W/m2day 107W/m2day 107W/m2day Dec 60 2.6844 61 2.8476 59.5 2.8401 60 2.6575 Jan 57.5 2.5059 59.5 2.6870 59 2.6760 57.5 2.4692 Feb 48.5 2.5727 50.5 2.7011 50 2.6930 47.5 2.5362 Mar 34 2.6558 35.5 2.7145 35 2.7114 32.5 2.6327 Apr 14.5 2.7274 15 2.7380 15 2.7377 14 2.7220 May 0 2.7804 0 2.7804 0 2.7804 0 2.7804 Jun 0 2.5742 0 2.5742 0 2.5742 0 2.5742 Jul 0 2.1796 0 2.1796 0 2.1796 0 2.1796 Aug 5 1.9561 5.5 1.9582 6 1.9582 4 1.9548 Sep 21.5 2.0467 24.5 2.0890 24 2.0853 18 2.0253 Oct 43 2.5412 45 2.6456 44.5 2.6392 42 2.5081 Nov 55.5 2.7641 56.5 2.9143 56 2.9074 55.5 2.7344 Average 28.29 2.4990 29.41 2.5691 29.08 2.5652 27.58 2.4812

collected solar energy was 2.27168 X 107 W/m2 day. The seasonal optimum tilt angle for Delhi using different models out of which the Badescu model is very close to the data available in [14].

The optimum seasonally tilt angle is maximum in winter ie.57.33Â° and minimum i.e. 2.67Â° in summer by Liu and Jordan model. Optimum seasonally tilt angle is maximum in winter ie.57.83Â° and minimum i.e. approximately zero in summer by Badescu model. The optimum seasonally tilt angle is maximum in winter

ie.51.33Â° and minimum i.e. approximately zero in summer by Liu and Jordan model. Optimum seasonally tilt angle is maximum in winter ie.48.66Â° and minimum i.e. approximately zero in summer by Badescu model.

The optimum seasonally tilt angle is maximum in winter and minimum ie.0.33Â° in summer by Liu and Jordan model. Optimum seasonally tilt angle is maximum in winter and minimum ie.1.66Â° in summer by Badescu model. The daily variation of optimum slope has been extended to evaluate the yearly optimum tilt angle, (opt(y)) the yearly optimum tilt angle is a fixed value for any

Fig.11

-Comparison of Monthly optimum tilt angle for Delhi

solar collector throughout the course of a year. It is for Nandha, Haryana and oriented towards the south. The amount of solar radiation received by the solar collector tilted at yearly optimum angle facing south was computed. Comparison of yearly optimum tilt angle for Village Nandha, Haryana using different models which is further compared from the working setup install at Nandha, Haryana shows that P.V panel at Village Nandha, Haryana is installing at the entire model shows that the yearly optimum tilt angle is close to but Badescu model shows very closeness to the setup install at Village Nandha, Haryana it underestimate the angle just by 0.43%.

4. CONCLUSIONS

In this study the solar radiation output of solar collector is investigated at various tilt between angles 0Â° to 90Â° for south facing to calculate daily and monthly optimum tilt angles, seasonal optimum tilt angles and yearly optimum tilt angle for different locations in India.

The beam radiation dominates throughout the year where the maximum beam radiation reaches in the month of May whereas the least amount of beam radiation occurs in the month of December at Village Nandha, Haryana. The optimum tilt angle in June goes to a minimum zero degree as indicated by all the models.

1. The optimum tilt angles increases during the winter months and reaches a maximum of 62Â° in December by Liu & Jordan model whereas Reindl model, Hay model, Badescu model indicate the optimum tilt angle as 63.5Â°, 63Â°, 62.5Â° resp.

2. When the monthly optimum tilt angles were used, the yearly collected solar radiation was W/m2day When the seasonal optimum tilt angles were used the yearly collected solar radiation was W/m2day Finally, when the yearly optimum tilt angle was used, the yearly collected solar radiation was W/m2day.

3. In winter, a panel fixed at the winter angle will be

relatively efficient, capturing 81 to 88 percent of the energy compared to optimum tracking. In the spring, summer, and autumn, the efficiency is lower (74- 75% in spring/autumn, and 68-74% in summer), because in these seasons the sun travels a larger area of the sky, and a fixed panel cant capture as much of it.

4. The proper tilt and azimuth angle choice is by far more important for photovoltaic systems design than solar thermal system design.

15- SCOPE FOR FUTURE WORK

1. The optimization tilt angle for other cities can be carried out for India and other location exterior of India.

2. For optimization of tilt angle, we can use isotropic models.

3. If your solar panels will have a fixed tilt angle, and you want to get the most energy over the whole year,

Fig.12- Solar panels installed at Village Nandha, Haryana at 30Â° tilt angle

A fixed angle is convenient, but notes that there are some disadvantages. As mentioned above, youll get less power than if you adjusted the angle.

16- REFERENCES

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Author1- He is B.Tech. (Hons.) in Mechanical Engineering and pursuing M.Tech. in Thermal Engineering from KNIT, Sultanpur.

Author2- He is M.Tech. From NIT, Hamirpur and presently is Assistant Professor at Ideal Institute of Technology, Ghaziabad.

Author3- He is Professor and Head of Dept. of ME at KNIT, Sultanpur, having large research experience.