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Fusing photovoltaic data for improved confidence intervals

Institute of Statistics, RWTH Aachen University, W¨ullnerstr. 3, D-52056 Aachen, Germany

Special Issues: Solar PV Energy

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.
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Keywords Bayes; credible interval; decorrelation; jackknife; nonparametric estimation; power output; resampling; round robin; variance estimation

Citation: Ansgar Steland. Fusing photovoltaic data for improved confidence intervals. AIMS Energy, 2017, 5(1): 125-148. doi: 10.3934/energy.2017.1.125

References

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This article has been cited by

  • 1. Moustapha Ba, Harry Ramenah, Camel Tanougast, Forseeing energy photovoltaic output determination by a statistical model using real module temperature in the north east of France, Renewable Energy, 2017, 10.1016/j.renene.2017.10.051
  • 2. Harry Ramenah, Philippe Casin, Moustapha Ba, Michel Benne, Camel Tanougast, Accurate determination of parameters relationship for photovoltaic power output by augmented dickey fuller test and engle granger method, AIMS Energy, 2018, 6, 1, 19, 10.3934/energy.2018.1.19
  • 3. Ansgar Steland, Yuan-Tsung Chang, Jackknife variance estimation for general two-sample statistics and applications to common mean estimators under ordered variances, Japanese Journal of Statistics and Data Science, 2019, 10.1007/s42081-019-00034-2

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Copyright Info: 2017, Ansgar Steland, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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