# Category Solar Energy Fundamentals and Modeling Techniques

## A Simple Power Model

The non-linear least squares technique depends on the minimization of the predic­tion error square summation from a non-linear equation. The non-linearity exists in the power term of the solar radiation model as presented in the text by Eq. 5.12. In order to predict the solar radiation amount (H/H0) at any time instant, say i, from the fractal exponent model there is an error, є;, involved as follows:

(H)-ap+41)’+й (B1)

or the error term is calculated as

S p

H0] ; S0, ;

and the sum of error squares for n predictions becomes notationally as

2

The partial derivatives of this expression with respect to model parameters a, b, and c leads to

In order to find the optimum solution of parameter estimates these three differentials must be set equal to zero:

and

Hence, there are three unknowns an...

## A Simple Explanation of Beta Distribution

If a random variable x is equally likely to take any value in the interval 0 to 1, then its probability distribution function (PDF) is constant over this range. The beta PDF is a very flexible function for use in describing empirical data such as a’ and b’ as in Chap. 4. The general form of this distribution is given by Benjamin and Cornell (1970) as

f (x) = 1 xr 1(1 – x )r – 1 (0 <y< 1),

P

where в is the normalizing constant as

(r – 1)!(t – r – 1)!

ЇЇ-Т)

for integer r and t – r values, otherwise

Г(г)T(t – r)
r(t)

in which Г (.) is the incomplete gamma function of the argument. Herein, r and t are the PDF parameters related to the mean x and variance a2 parameters as follows:

_ r

x =

t

and

2 r (t – r ) ax — .

x t2(t + r)

## Future Expectations

In general, there are two main reasons for future energy research. First, as a re­sult of global warming, atmospheric and environmental pollution due to energy consumption, present day energy patterns, using predominantly fossil fuels, must be either improved in their quality or more significantly, they must be substituted with more environmentally reliable clean and renewable energy sources. The sec­ond reason for future research is the appreciation that the fossil fuel reserves are limited and bound to be exhausted sooner or later. If the necessary precautions are not taken from now on by radical innovations in energy systems and their tech­nologies, then future human generations on the earth will face an extremely pre­carious position...

## Solar Energy and Desalination Plants

Water is an extremely important commodity for the improvement of arid (desert) and semi-arid environments. As for the water production technology, desalination plants widely use fossil fuels. Hence, for the improvement of these regions it is necessary to shift from fossil fuel usage to some environmentally friendly energy source, such as solar energy as it is available abundantly in such environments. It is necessary to develop a sustainable water production system using the renewable energy that is presented by solar energy instead of fossil fuels in these regions. Specifically, the Arabian Gulf countries have the latest water production technology and the use of the solar energy alternative for this purpose must be investigated in spite of fossil fuel availability...

## Solar Energy Home

Careful building design makes the best use of natural daylight. In order to make the best use of solar energy, it is necessary to understand the climate of the re­gion. Buildings that are inappropriate for the local climate cause energy wastage (Howell 1986). In order to gather radiation directly by devices, house roofs are con­structed as discrete solar collectors.

It is possible to consider a south-facing window as a kind of passive solar heat­ing element. Solar radiation will enter during daylight hours, and if the building’s internal temperature is higher than that outside then heat will be conducted and con – vected back out. Here, the main question is whether more heat flows in than out, so that the window provides a net energy benefit...

## Hydrogen Storage and Transport

It is an unfortunate characteristic of solar energy that it arrives in a quite random manner depending on the meteorological conditions and it does not arrive at all time to suit our needs. Since the time of usage does not always match with the time of availability, it is necessary to store the solar energy at times of availability so as to use it at times of need.

The need for new and renewable energy alternatives due to the depletion of con­servative energy sources also brought about studies on the efficient usage and trans­mission of available energies. As is well known, the major criticism against these energy alternatives is the problem of energy storage (Tsur and Zemel 1992)...

## Fuel Cells

A fuel cell is an electrochemical energy converter. It converts the chemical energy of fuel (H2) directly into electricity. A fuel cell is like a battery but with constant fuel and oxidant supply (Fig. 7.12).

Fuel cells are preferred for the following reasons (Barbir 2005):

1. Promise of high efficiency

2. Promise of low or zero emissions

3. Run on hydrogen/fuel may be produced from indigenous sources/issue of na­tional security

4. Simple/promise of low cost

5. No moving parts/promise of long life

6. Modular

7. Quiet