Solar Radiation

Practical Modeling for Renewable Energy Applications

Daryl Ronald Myers

• Publisher: CRC Press
• Year: 2017
• Print ISBN: 9780367840099
• eBook ISBN: 9781351832472
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Written by a leading scientist with over 35 years of experience working at the National Renewable Energy Laboratory (NREL), Solar Radiation: Practical Modeling for Renewable Energy Applications brings together the most widely used, easily implemented concepts and models for estimating broadband and spectral solar radiation data. The author addresses various technical and practical questions about the accuracy of solar radiation measurements and modeling.

While the focus is on engineering models and results, the book does review the fundamentals of solar radiation modeling and solar radiation measurements. It also examines the accuracy of solar radiation modeling and measurements. The majority of the book describes the most popular simple models for estimating broadband and spectral solar resources available to flat plate, concentrating, photovoltaic, solar thermal, and daylighting engineering designs. Sufficient detail is provided for readers to implement the models in assorted development environments.

Covering the nuts and bolts of practical solar radiation modeling applications, this book helps readers translate solar radiation data into viable, real-world renewable energy applications. It answers many how-to questions relating to solar energy conversion systems, solar daylighting, energy efficiency of buildings, and other solar radiation applications.

1	Fundamentals of Solar Radiation

The Sun remains fixed in the center of the circle of heavenly bodies, without changing its place; and the Earth, turning upon itself, moves round the Sun.

—Galileo Galilei, 1615

1.1 THE SUN AS A STAR

Earth orbits a star, the sun, which is the ultimate source of all energy driving the process of animate and inanimate life cycles on the planet. The sun’s nuclear furnace continually fills the volume of surrounding space with energetic elementary particles and photons of electromagnetic radiation. The sun’s electromagnetic spectrum spans an enormous range of wavelengths of frequencies of radiation, from gamma and x-rays, to ultraviolet (UV), visible, infrared (IR), and radio waves. For the purposes of this book, we are interested in so-called optical solar radiation, from the UV wavelengths to the near- and mid-infrared wavelengths that Earth’s atmosphere allows to reach the ground. We denote this region of interest as optical solar radiation even though only a subset of the spectrum, that within the photopic response of the human eye, is “optically visible.” The details of the distribution of optical radiation as a function of wavelength are discussed in this chapter.

1.2 THE EARTH AND THE SUN

1.2.1 THE ORBIT AND ROTATION OF THE EARTH

Earth orbits the sun in a very slightly elliptical orbit, with an eccentricity ε (ratio of major to minor axis) of 0.0167. Earth also rotates once every 23 h 56 min, with respect to the distant stars (a sidereal day), and a period of 24.0 h (the definition of the solar day) about an axis titled at an angle of 23.5° to the plane of that orbit. The average distance between the Earth and the sun is the astronomical unit (AU) of 93 million miles (or 149,597,870.7 km).

The tilted axis of rotation produces the seasonal weather changes we experience, as shown in Figure 1.1. That tilt also causes the daily changes in the points on the horizon where the sun rises and sets, the path of the sun through the sky dome, and the period of daylight to change throughout the year. The eccentricity of the orbit produces changes in the Earth–Sun distance, or “radius vector” r, with respect to the mean distance of 1 AU. The closest approach of the Earth to the sun (perihelion = 147.09 × 10⁶ km) is around the first week in January, and the greatest Earth–Sun distance (152.1 × 10⁶ km) is around the first week of July. The actual dates vary from year to year, depending on leap years, and small cumulative geophysical or gravitational influences [1].

FIGURE 1.1 Earth’s orbit and the seasons. (From Wikipedia, http://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Seasons1.svg/700px-Seasons1.svg.png.)

1.2.2 THE SUN AND INTENSITY OF EXTRATERRESTRIAL SOLAR RADIATION

Earth intercepts only a minute fraction of the energy radiated by the sun into the surrounding spherical volume of space. The “flux density” or “intensity” of the radiation, in terms of watts per square meter of area (Wm²) at distance R from the sun falls off as 1/R². Investigation of the intensity Io of the solar radiation at the average distance of the Earth’s orbit, or so-called extraterrestrial radiation (ETR), has long been a subject of scientific investigation. During the space age, satellite-based estimates of the intensity of solar radiation at 1 AU vary around Io = 1366 Wm² with an uncertainty of about ±7 Wm². For most of the period from 1970 to 2010, the accepted value of Io was 1366.1 Wm² [2,3].

In 2011, instrumentation issues with historical measurements in conjunction with new measurements from space produced a value of Io = 1361 Wm² [4]. Note that this difference amounts to ±0.5%, and the choice of Io in the model scenarios that follow change depending on which value of Io the user selects.

The eccentric Earth orbit results in a +3% increase in the solar radiation intensity at perihelion and a –3% decrease at aphelion. This variation can be accounted for by relying on detailed astronomical calculations such as appear in the annual astronomical or nautical almanacs published for astronomers and navigators relying on classical techniques [5,6]. Two popular equatio...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Series Editor
• Series Editor’s Preface
• Preface
• Acknowledgments
• About the Author
• Chapter 1 Fundamentals of Solar Radiation
• Chapter 2 Introduction to Solar Radiation Measurements
• Chapter 3 Modeling Clear Sky Solar Radiation
• Chapter 4 Modeling Global Irradiance under All Sky Conditions
• Chapter 5 Modeling Missing Components
• Chapter 6 Applications: Modeling Solar Radiation Available to Collectors
• Chapter 7 Introduction to Modeling Spectral Distributions
• Chapter 8 Introduction to Modeling Daylight
• Chapter 9 Summary and Future Prospects
• Appendix A: Bird Clear Sky Model in Excel
• Appendix B: Excel Structure for DISC Model of Direct Normal Irradiance (DNI) from Global Horizontal Irradiance (GHI)
• Appendix C: Tables for CIE D65 Reference Spectrum and Spectral Daylight Temperature Model
• Appendix D: SPCTRL2 FORTRAN Source Code
• Appendix E: Photopic Response Function V(λ) Curve
• Appendix F: Perez Anisotropic Model Coefficients for Luminous Efficacy and Zenith Luminance Model
• Index