We calculate the collector coefficients and their uncertainties with the least square and the weighed least square methods for a quasi-dynamic test [ 1 ].

The 95% confidence limits for each collector coefficient are calculated as well as the respective limits for the collector efficiencies resulting from the identified model. Using the test data, the confidence limits for the efficiencies can be validated, which proves that the uncertainties of the “collector coefficients» as well as the “efficiency curve" of the collector can be determined in a reliable way. However, a review of these uncertainty statements still requires a more comprehensive analysis of several complete tests.

The weighted least square method (WLS) gets slightly different coefficients with the same collector as the least square method (LS). It should be the more accurate one, as mentioned earlier. This statement has yet to be supported by the use of a more extended database.

Like both the quasi-dynamic and the steady-state tests are performed under outdoor conditions, from the measurement conditions Point of view it is impossible to repeat them, because weather conditions (combination of solar radiation and ambient temperature) always vary. Thus, to get a quantitative statement on the test reproducibility, the need for an extended database is again underlined. It should be remarked that this reproducibility is strictly related to the defined standard test conditions (or data selection conditions) as given by EN 12975 [ 1 ].

The easy implementation in EXCEL™ spreadsheet makes it possible to apply the WLS method regularly for collector test evaluations.

Acknowledgements: The test data was gained using the equipment of ITW at the University of Stuttgart, for which we express our gratitude.

4. REFERENCES

[ 1 ] CEN (2000) Standart 12975-2: Solar thermal systems and components — Solar collectors — Part 2: Test methods, European Committee for Standardisation.

[ 2 ] ISO (1994) Standard 9806-1: Test Methods for Solar Collectors. Part 1: Thermal Performance of Liquid Heating Collectors Including Pressure Drop. ISO, Switzerland.

[ 3 ] Press W., Teukolsky S. A., Vetterling W. T., Flannery B. P. (1996). Numerical Recipes, 2nd ed. Cambridge University Press, Oxford.

[ 4 ] NBR 10184 (1988) Coletores solares planos para liquida — Determinagao do rendimento termico, ABNT, Brazil.

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[ 6 ] Muller-Scholl Ch., Frei U. (2000) Uncertainty analyses in solar collector measurements, Proc. of the Eurosun 2000.

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Proc. ISES Solar World Congress.

[ 8 ] Sabatelli V., Marano D., Braccio G., Sharma V. K. (2002) Efficiency test of solar collectors: uncertainty in the estimation of regression parameters and sensitivity analyses, Energy Conversion & Management, Vol. 42.

[ 9 ] Kratzenberg M., Beyer H. G., Colle S. (2002) Setup of a test facility for the characterization of thermal collectors according to the Euronorm at the “Universidade Federal de Santa Catarina”, Proc. “Sun at the end of the world” International solar energy congress and exhibition, Universidad Tecnica Federico Santa Marfa.

[ 10 ] Kratzenberg M., Beyer H. G., Colle S., Albertazzi Gongalves A. (2003) Test facility for quasi­dynamic collector tests for the characterization of thermal solar collectors in accordance with the international norms, metrologia-2003 — Metrologia para a Vida, Sociedade Brasileira de Metrologia (SBM).

[ 11 ] Kratzenberg M., Beyer H. G., Colle S., Petzoldt D. (2004) Bestimmung der Kollektorparameter und ihrer Unsicherheiten uber die Methode der gewichteten Fehlerquadrate fur den statischen und den quasi-dynamischen Kollektortest, Proc. Otti-Kolleg Thermische Solarenergie.