Abstract
Characterizing and testing photovoltaic modules requires carefully made measurements on important variables such as the power output under standard conditions. When additional data is available, which has been collected using a different measurement system and therefore may be of different accuracy, the question arises how one can combine the information present in both data sets. In some cases one even has prior knowledge about the ordering of the variances of the measurement errors, which is not fully taken into account by commonly known estimators. We discuss several statistical estimators to combine the sample means of independent series of measurements, both under the assumption of heterogeneous variances and ordered variances. The critical issue is then to assess the estimator’s variance and to construct confidence intervals. We propose and discuss the application of a new jackknife variance estimator devised by [1] to such photovoltaic data, in order to assess the variability of common mean estimation under heterogeneous and ordered variances in a reliable and nonparametric way. When serial correlations are present, which usually a ect the marginal variances, it is proposed to construct a thinned data set by downsampling the series in such a way that autocorrelations are removed or dampened. We propose a data adaptive procedure which downsamples a series at irregularly spaced time points in such a way that the autocorrelations are minimized. The procedures are illustrated by applying them to real photovoltaic power output measurements from two different sun light flashers. In addition, focusing on simulations governed by real photovoltaic data, we investigate the accuracy of the jackknife approach and compare it with other approaches. Among those is a variance estimator based on Nair’s formula for Gaussian data and, as a parametric alternative, two Bayesian models. We investigate the statistical accuracy of the resulting confidence resp. credible intervals used in practice to assess the uncertainty present in the data.
Highlights
The characterization and testing of photovoltaic (PV) modules in terms of their electrical properties and, especially, their energy yield as measured by the power output is an important but expensive task
The jackknife variance estimator was applied to the Nair estimator for ordered variance, but we AIMS Energy do not report the results, since they were quite similar to the results for the Graybill-Deal estimator
As both the measurement uncertainty in terms of the standard deviation of measurement errors and the distributional shape of the measurement error may differ substantially, the question arises how one can assess the standard error of such a common mean estimator
Summary
The characterization and testing of photovoltaic (PV) modules in terms of their electrical properties and, especially, their energy yield as measured by the power output is an important but expensive task. There are various factors which influence those electric properties such as the irradiance and its spectrum, the module temperature and, for some module technologies, to which extent the module has been recently exposed to light For tasks such as certification and testing, power output measurements are taken in a flasher under standard conditions (STC), in order to evaluate the nominal specifications. More accurate variance estimators will lead to more accurate confidence intervals, which are highly recommended to quantify the uncertainty present in the data Known results such as those in [2], where an exact formula for the variance and bounds for the distribution of a widely used common mean estimator are established, are restricted to the case of normally distributed measurements.
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