تست بهره وری گردآورنده خورشیدی: عدم قطعیت در برآورد پارامترهای رگرسیون و تجزیه و تحلیل حساسیت

The results obtained from efficiency tests conducted on a flat plate solar collector, according to the ISO 9806/1 test procedure, have been used to determine the uncertainty in the curve fitting parameters. The said standard, though requiring certain levels of accuracy in the measuring process, doesnot provide any method to determine the uncertainty of the efficiency curve parameters. The methodology used in the present paper (not provided by the ISO standard) allows solving the above mentioned problem and evaluating not only the parameters and their uncertainties but also the reliability of the test procedure and its goodness toward fitness. In order to evaluate the effects of measurement errors on the values of the uncertainty in estimated parameters, a sensitivity analysis has also been conducted. Strong dependence of some uncertainties, involving a larger accuracy level in the estimation of the measured parameters, is a clear indication of the present investigations.

ISO standards are mainly used for determination of the collector efficiency by means of a least squares fit performed on the measured data. It is, however, to be noted that to use such standard, it is essential to have a certain level of accuracy, especially for the sensors and instrumentation, but the fact remains that no prescribed methodology is available to determine the uncertainty of the efficiency curve parameters. In order to solve the above mentioned problem, an attempt has been made to deal with the problem using both the results available in the literature [1] and [2] and experimental data collected in our laboratory. A detailed sensitivity analysis has been conducted to determine the influence of the uncertainties in the measured parameters on the uncertainty level that can be assigned to coefficients of the efficiency curve. The present work has been done by a group of researchers from the Solar Collector and Overall System Test Laboratory at the ENEA (Agency for New Technology, Energy and Environment) Research Centre, Trisaia, in Southern Italy. The laboratory performs efficiency tests both on glazed and unglazed solar collectors, according to ISO standards 9806/1 and 3. Systems performance tests are conducted using ISO standard 9459/2 [3], [4] and [5]. The experimental data collected over a period of nearly two years has been used. Over this period, about 30 collectors, made in Italy and/or abroad, have been tested. The sensors, instrumentation and control system used permits an accuracy level much higher than the one requested by the ISO standards. At present, though the test facilities are available to work with collectors in a fixed position (facing the equator) in a semi-automatic way, steps have already been taken to make the system fully automatic while working with sun following solar collectors. The sensors and instrumentation employed, along with their accuracy, a brief resume of uncertainty theory and curve fitting and, finally, a sensitivity analysis performed and the results obtained, are discussed in the present paper.

The results of a flat plate solar collector efficiency test have been examined. An estimation of the parameters with their uncertainties has been developed according to a methodology, based on well known statistical tools, which takes into account the global uncertainties of the measurement process (not only the uncertainties in efficiency measurement, different from measure to measure, but also the errors affecting T* and GT*2 in the 3-parameters model). The sensitivity analysis performed has also emphasized a strong dependence of the values of the uncertainty in the estimated parameters from some measurement errors. The following conclusions can be drawn, starting from these evaluations: • The ISO standard requires the use of the least squares method in order to estimate the efficiency curve parameters without suggesting any methodology to evaluate the uncertainties in the estimated parameters. In this manner, not only no information about the reliability of curve fitting can be retrieved, but also it is difficult to make a comparison of the results obtained from different laboratories. • The use of χ2 fitting not only helps to solve this problem but also allows a check of the test procedure and the goodness-of-fit. • The experimental results have emphasized that the uncertainties in the estimated regression parameters are mainly due to errors associated with the measurements of solar irradiance and temperature difference. More accurate measurement of such parameters would certainly be helpful to improve the whole uncertainty picture.