Abstract

A solar photovoltaic module or solar collector collects the maximum solar radiation when the sun’s rays strike it at right angles. Sun tracking mechanism is not cost-effective but an adjustable (tilt angle) solar photovoltaic modules mount (south facing in northern hemisphere & north facing in southern hemisphere) with an appropriate tilt angle measuring scale, will be cost-effective. In this paper, design of the tilt angle scale for a given site is described. For example, the tilt angle scales for sites 23.5°N, 26°N & 30°N are shown.

Key Words

Solar Photovoltaic Module, Sunlight power, Optimal tilt angle, Site latitude, Earth’s trajectory, Equinoxes, Winter & Summer solstice.

Introduction

A solar photovoltaic module generates more electrical power when more sunlight power incidents on it. The sunlight power incident on a module depends not only on the power contained in the sunlight but also on the angle between the module and the sun’s rays. When the sun’s rays fall normally on the module’s surface, the incident sunlight power is maximum. The amount of sunlight power incident on the module’s surface is the component of the incoming sunlight power perpendicular to the module’s surface^[1]. The following fig.1 shows ways to calculate the sunlight power incident on a module’s surface.

S_module = S_incoming Sin(α+β) —————————– (1)

Where

S_incoming is the incoming sunlight power, S_module is the incident sunlight power on the module’s surface, α is the sun’s elevation angle and β is the tilt angle of the SPV module.

Fig.1 Measurement of Sunlight Power incident on SPV Module’s surface

The sun’s position in the sky is defined by two angles: Altitude & Azimuth. Because of the earth’s tilt, the path that the sun travels changes throughout the year. It follows its lowest path at the winter solstice (December 21 in northern hemisphere & June 21 in southern hemisphere). Following the winter solstice, the sun traces a progressively higher path in the sky until it reaches its highest path on summer solstice (June 21 in northern hemisphere & December 21 in southern hemisphere). Following the summer solstice, the sun’s path become lower every day until it again reaches its lowest path on winter solstice ^[2].

Significance of the Tilt Angle Scale

A solar photovoltaic module collects the maximum solar radiation when the sun’s rays strike it at right angles. As the SPV module is tilted away from perpendicular alignment to the sun’s rays, less solar energy is received. However, a small deviation (± 5°) away from the ideal tilt will not affect energy output much. The optimal orientation for a solar energy system depends on the site latitude, date & time of the year. Sun tracking mechanism ^[3] is not cost-effective but an adjustable (tilt angle) solar photovoltaic modules mount (south facing in northern hemisphere & north facing in southern hemisphere) will be cost-effective. The SPV modules that are used to produce electricity over the year are usually tilted at an angle equal to the latitude of the site. With this tilt angle the modules produce optimum energy output only at equinoxes (on March 21 & September 22). On other dates the modules do not collect sunlight as efficiently.

To maximize annual electricity of the SPV modules an adjustable (tilt angle) SPV modules mount with an appropriate tilt angle scale as shown in below photograph, can be used.

Design of the Tilt Angle Scale

Deep analysis of geography of earth’s trajectory around the sun ^[4-11] and the data is available on websites: www.timeanddate.com , www.ngdc.noaa.gov &  www.rredc.nrel.gov concludes that the optimal tilt angles for the SPV modules at a site in northern hemisphere with latitude L are as follow.

From Vernal Equinox to Autumnal Equinox

• L on 21^st March & on 22^nd September (Equinoxes)
• (L-5°) on 3^rd April & on 9^th September (2 weeks difference)
• (L-10°) on 17^th April & on 26^th August  (next 2 weeks difference)
• (L-15°) on 1^st May & on 12^th August  (next 2 weeks difference)
• (L-20°) on 22^nd May & on 22^nd July  (next 3 weeks difference)
• (L-23.5°) on 21^st June (Summer solstice)

From Autumnal Equinox to Vernal Equinox

• L  on 22^nd September & on 21^st March (Equinoxes)
• (L+5°) on 6^th October & on 7^th March (2 weeks difference)
• (L+10°) on 19^th October & on 22^nd February  (next 2 weeks difference)
• (L+15°) on 3^rd November & on 8^th February  (next 2 weeks difference)
• (L+20°) on 23^rd November & 23^rd January  (next 3 weeks difference)
• (L+23.5°) on 22^nd December (Winter solstice)

For example, the Tilt Angle Scale for sites 23.5°N, 26°N & 30°N are shown in figures 2,3 & 4 respectively. Some of the Earth’s big cities & important solar hubs are at these sites ^[12-15]. For example, these lines pass through USA, Egypt, and India, portions of Central America, Northern Africa, Sahara Desert, Thar Desert and Saudi Arabia Desert. Mean annual surface albedo value of these sites is about 18% ^[16].

Fig.2: – SPV Module Tilt Angle Scale at the Site L= 23.5°N

Fig.3: – SPV Module Tilt Angle Scale at the Site L= 26°N

Fig.4: – SPV Module Tilt Angle Scale at the Site L= 30°N

Acknowledgement

This research paper is sponsored by University Grant Commission, New Delhi under the Major Research Project, Department of Physics, SGN Khalsa PG College, Sri Ganganagar (Rajasthan), India. The 1^st author is P.I. of the project.

MRP Title: – Water Voltammeters Panel for Hydrogen Production from Solar Energy

References

[1] Solar Radiation on a Tilted Surface. – www.pvcdrom.pveducation.org

[2] Siting of Active Solar Collectors and Photovoltaic Modules – www.ngdc.noaa.gov

[3] Changing System Parameters – www.rredc.nrel.gov

[4] Solar elevation angle – www.wikipedia.com

[5] The March Equinox Explained – www.timeanddate.com

[6] The September Equinox Explained – www.timeanddate.com

[7] The June Solstice Explained – www.timeanddate.com

[8] The December Solstice Explained – www.timeanddate.com

[9] An Explanation of Equinoxes – www.timeanddate.com

[10] Seasons Calculator – www.timeanddate.com

[11] Sun Calculator – www.timeanddate.com

[12] Thar Desert – www.wikipedia.com

[13] World Map with Latitude and Longitude – www.mapsofworld.com

[14] World Map Political – www.mapsofworld.com

[15] The Tropic of Cancer – www.geography.about.com

[16] Mean Annual Adbedo – www.eoearth.org