Category Control of Solar Energy Systems

The Sun’s Position

Along with the weather conditions, another factor that determines the amount of incident radiation on a solar collector is the apparent movement of the Sun across

image4

Fig. 1.4 nt of the Earth s rotation around the Sun

the sky during the day. The Earth’s orbit around the Sun has an elliptical trajectory, with 3% eccentricity. The imaginary line that represents the orbit described by the Earth is called the ecliptic. As it orbits, the axis of terrestrial rotation always forms the same 23.45° angle between the perpendicular and the ecliptic plane. The angle formed by the ecliptic plane and the equator varies during the year as shown in Fig. 1.4. This angle, known as the declination, varies from -23.45° on the winter solstice to 23.45° on the summer solstice. The Tropic of Cancer (23...

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Measurement of Solar Irradiance

Pyranometers are the sensors used to measure global solar irradiance, that is, the Sun’s energy coming from all directions in the hemisphere above the plane of the instrument. The measurement is of the sum of the direct and the diffuse solar irradi – ance.

To measure the direct normal component of the solar irradiance only, an instru­ment called a normal incidence pyrheliometer (NIP), or simply pyrheliometer is used.

The diffuse irradiance can be measured by modifying a pyranometer using a shadowing device large enough to block the direct irradiance onto this sensor.

The description of different pyranometers and pyrheliometers can be found in [359].

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Extraterrestrial Solar Irradiance

Подпись: Eext — Ec Подпись: 1 + 0.034 cos Подпись: 360Nd 365.25 Подпись: W/m2 Подпись: (1.1)

As the Earth’s orbit is elliptical, the intensity of solar radiation received outside the Earth’s atmosphere varies as the square of the Earth-Sun distance D. The solar irradiance variation can be approximated by [359]

where Eext is the extraterrestrial solar irradiance outside the Earth’s atmosphere and Nd is the day number (starting at January 1st).

The extraterrestrial solar irradiance falling on a surface parallel to the ground (Fig. 1.3) is [359]

image009

image3

Fig. 1.3 The cosine effect as it relates to the concept of extraterrestrial horizontal irradiance, [359]

where 0z the angle between the two surfaces, which is the solar zenith angle. Reduc­tion of radiation by the cosine of the angle between the solar radiation and a surface normal is called the cosine effect.

B...

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Solar Constant

The radiation intensity on the surface of the Sun is approximately 6.33 ■ 107 W/m2. Since radiation spreads out as the distance squared, by the time it travels to the Earth (1496 ■ 1011 m or 1 AU is the average Earth-Sun distance, Do), the radiant energy falling on 1 m2 of surface area is reduced to 1367 W as depicted in Fig. 1.2 [359]. The intensity of the radiation leaving the Sun is relatively constant. Therefore, the intensity of solar radiation at a distance of 1 AU is called the solar constant Ec and has a currently accepted value of 1367 W/m2 [359].

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Solar Radiation

The Earth receives most of its energy from the Sun in the form of solar electromag­netic radiation. The Sun contains 99.9% of the total mass of the solar system. The average density of the Sun is surprisingly low (1.4 g/cm3), the reason being that it is mostly composed of the lightest elements, hydrogen (70% by mass) and helium (27% by mass). The Sun’s core is mostly composed of helium (65% by mass) while the hydrogen is reduced to 35% by mass because of being consumed in fusion re­actions. Most of the other renewable sources of energy, such as wind energy, wave energy and bio-fuels depend on the Sun’s energy. Furthermore, some of the non­renewable energy sources such as fossil fuels were originated by solar energy in the past...

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Solar Energy Fundamentals

1.1 Introduction

The use of renewable energy, such as solar energy, experienced a great impulse during the second half of the 1970s just after the first big oil crisis. At that time, economic issues were the most important factor and so interest in these types of process decreased when oil prices fell. There is renewed interest in the use of re­newable energies nowadays, driven by the need of reducing the high environmental impact produced by the use of fossil energy systems.

As pointed out in [369], renewable spending has increased 30% in 2010 to a total of $243 billion. Nine-tenth of that is in the G-20 advanced industrial countries. The European region was the leading recipient of clean energy finance...

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Variables and Parameters

Symbol

Description

Units

Chapter

a

discrete transfer function pole descriptive parameter

4,5

auxiliary transfer function (linear model of resonances)

4

A

shutter aperture

m

7

A

state matrix

2

Aac

accumulation tank area

2

m2

7

af

discrete transfer function pole descriptive parameter

2

m2

5

Af

cross-sectional area for flow inside pipe

4, 5

afv

required DSG feed valve aperture

%

4

at

midpoint of fuzzy set Ai

5

Ai

fuzzy set

5

aiv

required DSG injector valve aperture

%

4

Am

cross-sectional area of pipe wall

m2

4-6

heliostat mirror area

6

an

heliostat-normal azimuth angle

rad, °

2

apv

DSG steam pressure valve aperture

%

4

as

azimuth

ra...

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Acknowledgements

The authors would like to thank a number of people and institutions who have made this book possible. Firstly, we thank Janet Buckley, who translated part of the book from our native language to English and corrected and polished the style of the rest. Our thanks go to Javier Aracil who introduced us to the exciting world of Auto­matic Control and to many other colleagues and friends from various universities, especially M. R. Arahal, C. Bordons, F. Gordillo, M. G. Ortega, F. J. Garcfa-Martrn, P. Lara (University of Seville, Spain), F. Rodriguez, J. L. Guzman, J. C. Moreno, J. D. Alvarez, C. M. Cirre, A. Pawlowski, M. Pasamontes, D. Lacasa, J. Gonzalez, M. Peralta, C. Rodriguez, M. Perez (University of Almerfa, Spain), L. Valenzuela, E. Zarza, L. J. Yebra, M. Romero, L. Roca, J...

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