We shall begin the discussion by limiting ourselves to using one predictor variable only, the clearness index. It is the most significant predictor, and as such is the basis for the earlier models. In Section 8, we discuss the use of additional explanatory variables.
There are two data sets for consideration in the development of the model and its subsequent use. The first, Adelaide, is a good quality data set recorded by the Australian Bureau of Meteorology (BOM). The second, Geelong, is a set of data collected at a private weather station at Deakin University, near Melbourne. The reading apparatus is known to fail from time to time and will give infeasible values for diffuse radiation. We deal specifically with an hourly time scale in this investigation. Many of the simulations used to model the performance of systems under the influence of solar inputs for which this estimation technique is required, such as house energy ratings scheme software, are hourly based. The first step in analysing the data is to construct two new variables. The variables are
where Ig, Id, H0 are the global, diffuse and extraterrestrial radiation integrated over the hour in question. Figures 8.1 and 8.2 display hourly values of diffuse fraction against the clearness index.
In Fig. 8.2, the points in the top right hand corner may be considered suspect due to the high clearness index combined with a high diffuse fraction. These values may be spurious and are best removed from the data set before continuing with model fitting. So we thus define the basis for our initial investigation. We examine a model relating diffuse fraction, and thus diffuse radiation, to clearness index. Subsequently, we develop a methodology for rejecting data values with low probability of being feasible.
O1——————- 1——————- T————————————— T——————- T————————————— T——————- T—————————————
0 0.1 0.2 0.3 0.4 0.5 0,6 0,/ 0.0 0.4 І
Fig. 8.2 Geelong – raw data
We begin with examining qualitatively the rationale for using a logistic function to model the diffuse fraction as a function of clearness index. We then derive the mathematical framework supporting the suitability of this form of relationship.