Chapter 12; Solar Radiation.

PART III: SOLAR PHOTOVOLTAIC APPLICATIONS

12. SOLAR RADIATION

  • The performance of solar technology (solar collectors, photovoltaics, thermal devices) relies on solar radiation.

  • This chapter examines the Earth-Sun geometry, angles affecting radiation on collector surfaces, and measurement methods for solar radiation.

12.1 The Sun and the Earth

12.1.1 Extra-terrestrial Solar Radiation

  • The Sun, about 1.30 x 10⁹ m in diameter, is primarily hydrogen (~73%) and helium (~25%).

  • Nuclear fusion in the Sun produces energy, with a surface temperature around 5760 K.

  • Earth receives energy through electromagnetic radiation ranging from 0.15 μm to 120 μm, including ultraviolet, visible, and infrared spectra.

12.1.2 Solar Spectrum at the Earth's Surface

  • 174 × 10¹⁵ W is received as solar irradiation at the upper atmosphere but undergoes interactions in the atmosphere:

    • 6% is reflected, 16% absorbed, resulting in three types of solar radiation: direct (beam), diffuse, and reflected (albedo).

  • Total radiation reaching Earth is the sum of direct, diffuse, and reflected radiation, termed global radiation.

  • Solar radiation spectrum shifts significantly from extra-terrestrial levels due to atmospheric absorption.

  • Approximate distribution:

    • Ultraviolet: 7.6%

    • Visible: 48.4%

    • Infrared: 43%

    • Other: 1%

12.2 The Sun-Earth Movement

  • Earth’s motion includes revolution around the Sun and daily rotation on its axis.

  • The tilt of Earth's axis (23.45°) influences seasons, not the revolution itself.

12.2.1 Declination Angle

  • Declination angle varies between -23.45° and +23.45° due to the Earth's axial tilt.

  • Can be calculated as:

    [\delta = 23.34 \sin \left(\frac{360}{365} (284 + n)\right)]

12.2.2 Apparent Motion of the Sun and Solar Altitude

  • The apparent motion results from Earth’s rotation, with the Sun rising in the east and setting in the west.

  • Solar altitude angle: [\alpha = 90 - \phi + \delta] (where ( \phi ) is latitude).

12.3 Angle of Sunrays on Solar Collector

  • The angle of incidence is critical for optimal solar radiation absorption by collectors.

  • Defined as the angle between incoming sunrays and the collector's normal surface.

  • Key parameters affecting the angle: Latitude, Day of the Year, Time of Day, Collector Inclination, Surface Azimuth.

12.3.1 Local Apparent Time (LAT)

  • LAT adjusts for differences in longitude and equation of time to determine solar noon based on geographic location.

12.3.2 Sunrise, Sunset and Day Length

  • Relationships governing day length and sunrise/sunset times can be determined using solar angles.(e.g. [\cos \theta = -\tan \delta \tan \phi])

12.3.3 Path of Sun's Motion

  • The path varies by season, influencing sunlight capture times.

12.3.4 Optimal Angle for Fixed Collector Surface

  • Fixed collectors should ideally face true south and be tilted at latitude angles.

12.3.5 Optimal Inclination of Collector in Summer and Winter

  • Seasonal adjustments can lead to improved solar collection performance. Suggested angles: -15° in summer and +15° in winter.

12.4 Sun Tracking

  • Tracking maximizes solar collection efficiency.Types:

    • Two-axis Tracking: Moves in both azimuth and altitude.

    • One-axis Tracking: Moves along a single axis, either east-west or north-south.

12.5 Estimating Solar Radiation Empirically

  • Empirical methods estimate solar radiation based on local meteorological data.

12.5.1 Monthly Average Daily Global Radiation

  • Calculation formula includes sunshine hours and extra-terrestrial radiation estimates.

12.5.2 Monthly Average Daily Diffuse Radiation

  • Estimation based on monthly global radiation and clearness index.

12.5.3 Monthly Average Hourly Global and Diffuse Radiation

  • Derived from daily data; specific formulas provided.

12.5.4 Solar Radiation on Tilted Surface

  • Total radiation includes contributions from direct, diffuse, and reflected components.

12.6 Measurement of Solar Radiation

  • Instruments include pyranometers for global and diffuse radiation and pyrheliometers for direct radiation, often tracked through the two-axis tracking system.

Review Questions

  • Questions such as defining air mass, calculating angles of incidence, and understanding differences in solar radiation types are essential for a comprehensive understanding of solar radiation dynamics.