The aleatory stratified amostral plan was used in the statistic evaluation. Basically, in this method, a subdivision of samples into sub-populations or groups is done, leading to smaller

errors. This is a consequence of a variation reduction between sample units of a same group, related to variation between sample units of different ones.

Sample size was determined in two stages. In the first one, a “pilot” sample was created to raise previous information about the population, considering a maximum error of 5%. This value was also adopted to test’s significance level. The second stage is the sample calculation, in which pilot sample results were used. Statistic classic equations, detailed by LEITE [2] were used for calculations of stratified sampling with piece’s casual distribution.

Since the number of analyzed factors is small and it was necessary to identify possible grouping and number of groups, the neural networks technique was used. This method is very efficient for problems of multivariate analysis, grouping and prediction, besides hierarchic agglomerative techniques: centroide and Ward [3].

Euclidian distance, which is a multivariate measure [3], was used in pieces selection into the groups. In agreement to data complexity a technique was selected to get to results. Also, it was developed in Matlab a special software to perform the statistic data treatment.

After data treatment and conglomerates detachment, preliminary percentages of the analysis’ factors were calculated (Table 1).

During the data processing, it was identified that the problems found in systems were repetitive. This fact allowed a reduction in the number of samples to be visited.

3. Sizing estimation and energy savings software (Long term performance)

As a part of this project, softwares were developed as assistant tools that help to identify the main characteristics of the studied system. One of them, developed in Matlab, estimates the necessary collector area and the storage tank volume, through radiation calculations [4] in tilt and arbitrary oriented planes for any location and economy level required, based on the modified model of F-Chart [4]. Shading incidence in solar collectors arrays is introduced in these calculations to achieve its influence value over monthly and annual energy economy generated by the solar system. To validate obtained data, this software also simulates the value of monthly electric energy bill for studied residences, through daily bath habits and other family use of electric household appliances.

Shading incidence values and consequent solar radiation reduction over the solar collectors’ plane were calculated using Ecotect 5.20 (Figure 3), which is an environment analysis tool, and a scripting, developed by the project’s team. Thus, it was possible to estimate the reduction, due to these shading data, of annual F-chart value for each studied system.

WINTER SUMMER

Figure 3 — Shading calculation for a studied solar system

Moreover, studies indicate that hourly data is the most adjusted for shading analysis, because, similar shading values can promote different reductions in the incident radiation depending on the hour observed.