Dynamic behavior of solar radiation

Abstract

This chapter is addressed mainly to engineers working on utilization of solar energy converted from the global radiation. Authors expect that the reader is acquainted with fundamentals and terminology of solar engineering (explained for instance in Duffie and Beckman 1991). Global (or: total) solar radiation is the sole energy carrier for the whole nature. Fossil fuels are in fact chemically stored primeval solar radiation. Yet more - thermal stresses and fatigue due to changing insolation involve the destruction of the lithosphere and they also participate in the development of (desert) landscape. Variability of the insolation has to be considered in the solar engineering too and it is analyzed in this chapter with different approaches. Utilization of the solar energy is mostly supported and limited with its storing, which has to be based on the consideration of the dynamical behavior of solar radiation. Fatigue effects mentioned above assess the life-time of materials used and should be considered in solar engineering (Koehl 2001; Carlson et al. 2004). Solar radiation on the infinitely (in practice - sufficiently) long time axis is a stationary ergodic process that includes both periodical and stochastic components. It remains always in the interval between zero and some upper value not exceeding the solar constant. Still, solar radiation could be a non-stationary process during some shorter time interval, intended for practical problem-solving. Periodical component has the astronomical and stochastic component has the meteorological origin. Figure 10.1 shows the yearly diagram of the (relative) normal extraterrestrial irradiance (Kondratyev 1969), which is a result of the elliptic trajectory of the Earth around the Sun. Other small variations of the solar constant have second order meaning (e.g. Duffie and Beckman 1991). Declination caused by the slope of the Earths axis with regard to the elliptic path about the Sun and rotation of the Earth involves additional periodical changes of solar radiation. These processes assess the yearly periodical component. Diurnal periodical component is assessed by rotation of the Earth. The state of the atmosphere involves both stochastic and periodical changes. The turbidity of the atmosphere and cloud cover has mainly stochastic origin, but not only. Periodical monsoon seasons in tropical areas are well known. Less attention has been paid to the trajectories of Atlantic (Prilipko 1982) and Arctic (Brümer et al. 2000) cyclones (Fig. 10.2) over Northern Europe (Scotland, Scandinavia, the Baltic states and North-West Russia), which have also seasonally periodical behavior. Numerous varying cyclones involve fast and frequent changes in solar radiation. Therefore, this area requires attention from the point-of-view of transient effects of solar radiation. Frequent and crucial changes in the radiation level will lead to problems concerning the power network, if numerous grid-connected photovoltaic (PV) plants will realized (Jenkins 2004). Cyclones emphasize the share of diffuse radiation. The annual ratio of diffuse Gd fraction to the global G radiation (irradiance) is well correlated with the cyclonic activity. In Estonia Gd/G=0.5 (Russak and Kallis 2003), but in Israel it is significantly lower Gd/G≤0.4 (Lyubansky et al. 1999). The character of clouds has indirect impact on the variability of solar radiation. High clouds Ci, Cc, Cs reduce the value of direct radiation and its increments too. High variability of solar radiation and high values of its fluctuations are most probable in the occurrence of convective clouds Cu and Cb (Mullamaa 1972). Commonly, the instant values of diffuse radiation and the mentioned ratio are determined by the simultaneous existence of several cloud layers. To solve practical problems of solar engineering, the infinite long-time axis has to be divided into finite intervals. In some cases, during the mentioned interval, solar radiation could be considered a constant. Figure 10.3 shows the behavior of direct beam irradiance Gb in the clear-sky conditions (Riihimaki and Vignola 2005), which can be well approximated with a constant value in the significant share of a day. On the other hand, the same variable has infinitely high changes around sunrise and sunset moments, although these time intervals are out of scope for engineering purposes. As energy supply is based on global radiation G, below we will consider it as the basic variable. While some technological solutions perform differently from direct and diffuse components, these have to be also mentioned. Depending on the averaging interval, the solar radiation data sets are mostly compound processes that contain both periodical and random components. A trend of an unknown data set may be a fragment of a periodical component with the period longer than the used set. © 2008 Springer-Verlag Berlin Heidelberg. All rights are reserved.