Modeling Solar Radiation at the Earth’s Surface

Fractal Classification of Typical Meteorological Days from Global Solar Irradiance: Application to Five Sites of Different Climates

Samia Harrouni

1 Introduction

To electrify remote areas, the use of solar energy is the best economical and techno­logical solution. The choice of the sites for the installation of photovoltaic systems and the analysis of their performances require the knowledge of the solar irradiation data. To meet these requirements, we have to classify the days into typical cases for a given site.

Many studies have investigated the problem of typical day’s classification. These studies differ by the parameters used as criterion for the classification. This chapter presents a classification method of daily solar irradiances which is mainly based on fractals.

Fractals are objects presenting high degree of geometrical complexity, their description and modeling is carried out using a powerful index called fractal di­mension. This later contains information about geometrical irregularities of fractal objects over multiple scales. The fractal dimension of a curve, for instance, will lie between 1 and 2, depending on how much area it fills. The fractal dimension can then be used to compare the complexity of two curves (Dubuc et al. 1989). In solar field, the fractal dimension is directly related to the temporal fluctuation of the irradiance signals. We can then quantify the solar irradiance fluctuations in order to establish a classification according to the atmospheric state (Maafi and Harrouni 2000, 2003; Harrouni and Guessoum 2003; Harrouni and Maafi 2002).

Our classification method defines two thresholds of the fractal dimensions using first a heuristic method then a statistical one. This allows determining three classes of days: clear sky day, partially clouded sky day and clouded sky day.

Samia Harrouni

Solar Instrumentation & Modeling Group/LIWS - Faculty of Electronics and Computer, University of Science and Technology H. Boumediene, Algiers, Algeria, e-mail: sharrouni@yahoo. fr

This chapter is devoted to the fractal classification of typical meteorological days from global solar irradiances. We start in Section 2 with generalities on the solar radiation especially the most commonly used models to estimate the amount of ra­diation falling on a tilted plane. Then, we deal in the Section 3 with the problem of the fractal dimension estimation giving a short survey of existing methods. In Section 4, we present a new method to evaluate the fractal dimension of discrete temporal signals or curves with an optimization technique: the “Rectangular cov­ering method”. To evaluate its accuracy, the proposed method is applied to fractal signals whose theoretical fractal dimensions are known: Weierstrass function (WF) and fractional Brownian motion (FBM). Section 5 focuses on the classification of irradiances into typical days. This section begins with a survey of existing methods, and then the “Rectangular covering methods” is presented. Thereafter, we will be interested in the application of this method to five sites of different climates. Finally, in Section 6, we give a conclusion and discuss experimental results.