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Fig. 4.24 Seasonal and bi-seasonal data scatter for Istanbul
Fig. 4.25 Seasonal and bi-seasonal data scatter for Ankara

References

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Chapter 5

Non-Linear Solar Energy Models

5.1 General

As already explained in the previous chapter different versions of linear AMs are in use extensively in solar energy studies for estimation of the global terrestrial solar radiation amounts from the sunshine duration data. However, atmospheric turbidity and transmissivity, planetary boundary layer turbulence, cloud thickness, and temporal and spatial variations cause embedding of non-linear elements in the solar radiation phenomena. Hence, the use of simple linear models cannot be justified physically except statistically without thinking about obtaining the model parameter estimations. In the literature, most often the linear models are either modified with the addition of extra terms in the hope of explaining the non-linear features or adjustment of the linear model parameters by relating them to geographical, meteorological, and other variables. Non-linearity in solar radiation and sunshine duration relationships is represented initially through classic statistical techniques by the addition of non-linear terms to the basic AM of Chap. 4. Some other researchers have incorporated the non-linear behavior in the models by expressing the linear model parameters in terms of each other or in terms of sunshine and solar radiation variables. Such models reduce to the classic linear solar radiation models under a set of specific assumptions.

In this chapter after the general review of available classic non-linear models, additional innovative non-linear models are presented with fundamental differences and distinctions. Fuzzy logic and genetic algorithm approaches are presented for the non-linear modeling of solar radiation from sunshine duration data.

5.2 Classic Non-Linear Models

Most of the sunshine duration based solar radiation estimation models are modifications of the AM (Chap. 4, Eq. 4.30). Some authors have suggested changing the

Zekai Sen, Solar Energy Fundamentals and Modeling Techniques DOI: 10.1007/978-1-84800-134-3, ©Springer 2008

Fig. 5.1 Benson et al. (1984) seasonal model

model parameters a and b seasonally thus arriving at better estimations (Abdalla and Baghdady 1985; Benson et al., 1984; Rietveld 1978). Barbara et al. (1978), Sen and Oztopal (2003), and Suleiman (1985) have expressed the global irradiation in terms of the sunshine duration and the geographic location. Hay (1984) related clouds and the atmospheric conditions to the solar radiation estimation. He proposed the use of the AM with a modified day-length instead of S and solar radiation that first hits the ground instead of H (Chap. 4). In the search for the non-linearity effects, Benson et al. (1984) have suggested modification of the AM with two six-month seasons, similar to the linear cluster model (LCM) as proposed by Sen and Oztopal (2003), namely, October-March and April-September periods leading to two different linear models as follows:

H0 S0

respectively. It is to be noticed that although the summations of a + b in these two models are the same, a and b have different values in the two periods. These linear models represent the scatter region by two non-parallel AMs as in Fig. 5.1.

Gopinathan (1988) has related the AM parameters to geographic elevation, h, and the ratio of sunshine duration as follows:

Fig. 5.2 Gopinathan (1988) model

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Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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