Analysis and synthesis of the variability of irradiance and PV power time series with the wavelet transform

Solar Energy

Volumn 85, Issue 1, 2011, Pages 188-197

  Perpinan O ^a   Lorenzo, E ^b  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b INSTITUTO DE ENERGÍA SOLAR   (Spain)

Author keywords

Irradiance fluctuations; Long memory process; Nonstationary; Power fluctuations; Wavelet analysis; Wavestrapping

Indexed keywords

INCIDENT SOLAR RADIATION; LOW PASS FILTERS; STOCHASTIC SYSTEMS; TIME SERIES; WAVELET ANALYSIS; WAVELET TRANSFORMS;

IRRADIANCE FLUCTUATIONS; LONG MEMORY PROCESS; NONSTATIONARY; POWER FLUCTUATIONS; WAVESTRAPPING;

TIME SERIES ANALYSIS;

IRRADIANCE; TIME SERIES; VARIANCE ANALYSIS; WAVELET ANALYSIS;

EID: 78650303509     PISSN: 0038092X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.solener.2010.08.013     Document Type: Article

References (30)

1. Aguiar R.J., Collares-Pereira M. Statistical properties of hourly global radiation. Solar Energy 1992, 48(3):157-167.
2. Aguiar R.J., Collares-Pereira M., Conde J.P. Simple procedure for generating sequences of daily radiation values using a library of markov transition matrices. Solar Energy 1998, 40(3):269-279.
3. Caamaño E., Laukamp H., Jantsch M., Erge T., Thornycroft J., de Moor H., Cobben S., Suna D., Gaiddon B. Interaction between photovoltaic distributed generation and electricity networks. Progress in Photovoltaics: Research and Applications 2008, 10.1002/pip.845.
4. Cleveland W.S. Visualizing Data 1993, Hobart Press, Summit, New Jersey, USA.
5. Constantine, W., Percival, D., 2010. wmtsa: Insightful Wavelet Methods for Time Series Analysis, r package version 1.0-5. URL <>http://CRAN.R-project.org/package=wmtsa.
6. Cornish C.R., Bretherton C.S., Percival D.B. Ma ximal overlap wavelet statistical analysis with application to atmospheric turbulence. Boundary-layer Meteorology 2006, 119(2):339-374. URL 10.1007/s10546-005-9011-y.
7. Domingues M.O., Mendes O., da Costa A.M. On wavelet techniques in atmospheric sciences. Fundamentals of Space Environment Science 2005, 35(5):831-842. 10.1016/j.asr.2005.02.097.
8. Few, S., 2008. Time on the horizon. Tech. rep. Perceptual Edge. URL <>http://www.perceptualedge.com/articles/visualbusinessintelligence/timeonthehorizon.pdf.
9. Heer, J., Kong, N., Agrawala, M., 2009. Sizing the horizon: the effects of chart size and layering on the graphical perception of time series visualizations. In: ACM Human Factors in Computing Systems (CHI). pp. 1303-1312. URL <>http://vis.berkeley.edu/papers/horizon/2009-TimeSeries-CHI.pdf.
10. Kawasaki N., Oozeki T., Kurokawa K., Otani K. An evaluation method of the fluctuation characteristics of photovoltaic systems by using frequency analysis. Solar Energy Materials and Solar Cells 2006, 90. 10.1016/j.solmat.2006.02.034.
11. Labat D. Recent advances in wavelet analyses: part 1. A review of concepts. Journal of Hydrology 2005, 314(1-4):275-288. 10.1016/j.jhydrol.2005.04.003.
12. Lau K.-M., Weng H. Climate signal detection using wavelet transform: how to make a time series sing. Bulletin of the American Meteorological Society 1995, 76(12):2391-2402.
13. Marcos J., Marroyo L., Lorenzo E., Alvira D., Izco E. Power output fluctuations in large scale PV plants: One year observations with 1s resolution and a derived analytic model. Progress in Photovoltaics 2010.
14. Mellit A., Benghanem M., Kalogirou S.A. An adaptive wavelet-network model for forecasting daily total solar-radiation. Applied Energy 2006, 83.
15. Oh H.S., Ammann C.M., Naveau P., Nychka D., Otto-Bliesner B.L. Multi-resolution time series analysis applied to solar irradiance and climate reconstructions. Journal of Atmospheric and Solar-Terrestrial Physics 2003, 65(2):191-201.
16. Percival D.P. On estimation of the wavelet variance. Biometrika 1995, 82(3):619-631. URL .
17. Percival D., Walden A.T. Wavelet Methods for Time Series Analysis 2006, Cambridge University Press.
18. Percival D., Sardy S., Davison A. Nonlinear and nonstationary signal processing. Wavestrapping Time Series: Adaptive Wavelet-Based Bootstrapping 2000, Cambridge University Press, pp. 442-471, URL .
19. Perpiñán, O., 2010. solar: Solar photovoltaic systems. R package version 0.14. URL <>http://CRAN.R-project.org/package=solaR.
20. Priestley M.B. Evolutionary spectra and non-stationary processes. Journal of the Royal Statistical Society. Series B (Methodological) 1965, 27:204-237.
21. Ramachandran, J., Pearsall, N.M., Putrus, G.A., 2004. Reduction in solar radiation fluctuation by spatial smoothing effect. In: 19th European Photovoltaic Solar Energy Conference. pp. 2900-2903.
22. R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0 (2010). URL <>http://www.R-project.org.
23. Sarkar, D., Andrews, F., 2010. latticeExtra: Extra Graphical Utilities Based on Lattice. r package version 0.6-12/r148. URL <>http://R-Forge.R-project.org/projects/latticeextra/.
24. Sarkar, D., 2010. lattice: Lattice graphics, R package version 0. 18-3. URL <>http://CRAN.R-project.org/package=lattice.
25. Tomson T., Tamm G. Short-term variability of solar radiation. Solar Energy 2006, 80:600-606. 10.1016/j.solener.2005.03.2009.
26. Torrence C., Compo G.P. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 1998, 79(1):61-78.
27. Tufte E.R. The Visual Display of Quantitative Information 2001, Graphic Press.
28. Whitcher B., Byers S.D., Guttorp P., Percival D.B. Testing for homogeneity of variance in time series: long memory, wavelets, and the nile river. Water Resources Research 2002, 38(5). http://staff.washington.edu/dbp/PDFFILES/wrr.pdf. 10.1029/2001WR000509.
29. Woyte A., Belmans R., Nijs J. Fluctuations in instantaneous clearness index: analysis and statistics. Solar Energy 2007, 81:195-206.
30. Zeileis A., Grothendieck G. zoo: S3 infrastructure for regular and irregular time series. Journal of Statistical Software 2005, 14(6):1-27. URL .