Nonlinear Modeling of Solar Radiation and Wind Speed Time Series PDF
Preview Nonlinear Modeling of Solar Radiation and Wind Speed Time Series
SPRINGER BRIEFS IN ENERGY Luigi Fortuna Giuseppe Nunnari Silvia Nunnari Nonlinear Modeling of Solar Radiation and Wind Speed Time Series 123 SpringerBriefs in Energy More information about this series at http://www.springer.com/series/8903 Luigi Fortuna Giuseppe Nunnari (cid:129) Silvia Nunnari Nonlinear Modeling of Solar Radiation and Wind Speed Time Series 123 Luigi Fortuna Silvia Nunnari Dipartimento di IngegneriaElettrica Dipartimento di IngegneriaElettrica Elettronica eInformatica Elettronica eInformatica Universitàdegli Studi diCatania Universitàdegli Studi diCatania Catania Catania Italy Italy Giuseppe Nunnari Dipartimento di IngegneriaElettrica Elettronica eInformatica Universitàdegli Studi diCatania Catania Italy MATLAB®isaregisteredtrademark of TheMathWorks,Inc.,3 AppleHillDrive, Natick, MA01760-2098,USA, http://www.mathworks.com. ISSN 2191-5520 ISSN 2191-5539 (electronic) SpringerBriefs inEnergy ISBN978-3-319-38763-5 ISBN978-3-319-38764-2 (eBook) DOI 10.1007/978-3-319-38764-2 LibraryofCongressControlNumber:2016938671 ©TheAuthor(s)2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland This book is dedicated to our readers Preface Low carbon has become a global issue, as testified at the recent World Climate Summit2015,heldinParis.Nowadays,theonlyviablealternativetothiscrisisisto develop as much as possible the use of the so-called renewable energy, as the possibility of obtaining clean energy through fusion processes being remote. Several forms of alternative sources of energy are present in nature almost in unlimited quantities, referred to as renewable, because they are continuously regenerated. The main source for renewable energies is the Sun. From the Sun are naturallyderived accumulations ofwater toproduce hydroelectric power, windfor aeolicturbinegenerators,andphotovoltaicsplantstogenerateelectricenergy.Also, from the photosynthesis process it is possible to derive energy from biomass. A challenging problem with integrating renewable energy based plants, such as solar and wind speed ones, into electric grid is that these plants are intermittent. Thus,predictingtheweathervariablesisofgreatinterestforapplications.Thereare essentially two ways to address this issue. One is by using Numerical Weather Forecasting (NWF) models, which are reliable but quite complex and require real-time information, which is usually available from Meteorological Agencies only. Furthermore, it has been pointed out that NWF models have high errors in forecasting meteo variables at local-scale areas and without appropriate postpro- cessing are often inferior to machine learning approaches. The other kinds of methodsarerepresentedbytheso-calledstatisticalmodelingapproaches,whichare based on the use of past data recorded at the site of interest. The latter kinds of methods, compared to the former ones, require less computational efforts, but are appropriate for short-time horizons only. This book is devoted to study statistical prediction models for solar radiation and wind speed time series and asses their performance in the range (1, 24) hours. Furthermore, the problem of classifying daily patterns of both solar radiation and wind speed will be addressed as a useful strategy to obtain statistical properties for longer prediction range. The book con- cisely describes the main techniques of time series analysis, with an emphasis on solarradiationandwindspeed,sincetheyarethemainkindsofrenewableenergies involved in the production of electrical energy. The forecasting problem is vii viii Preface addressedbyusingtheembeddingphasespaceapproach,whichisoneofthemost powerful methods proposed in the literature for modeling complex systems. Further, the book will guide the reader in applying some machine learning tech- niques to classify the daily patterns; thus allowing to perform statistical analyses that are notpossibleby using traditional techniques.The concepts will be exposed as much as possible avoiding unnecessary mathematical details, focusing on very concrete examples in order to ensure a better understanding of the proposed techniques.Developingvarioustopics,thereaderswillbeguidedonhowtofindthe most appropriate software and data resources with which they could perform their own experiments. The structure of the book is as follows. Methods for analysis of timeseriesareconciselyreportedinChap.1.Applicationofthesemethodstosolar radiationandwindspeed time series aredescribed inChaps.2and3,respectively. Modeling approaches for solar radiation and wind speed time series, focusing essentially on nonlinear autoregressive (NAR) and Embedded Phase Space (EPS)models,aregiveninChap.4.Identificationofsolarradiationandwindspeed hourly average prediction models is reported in Chaps. 5 and 6, respectively. Classification of daily patterns of solar radiation and wind speed time series are describedinChaps.7and8,respectively.ConcludingremarksaregiveninChap.9 and finally, a list of software functions and dataset mentioned in the book is included in Appendix A. Catania Luigi Fortuna April 2016 Giuseppe Nunnari Silvia Nunnari Acknowledgments The authors wish to thank Prof. Giorgio Guariso of the Politecnico di Milano for helpful discussions about the topics addressed in this book. The authors also thank the University of Catania for the funding support under the grant FIR 2014. ix Contents 1 Time Series Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Stationarity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Recurrence Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Linear Detrending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Noise Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.5 Power Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.6 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.7 Mutual Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.8 Noise 1/f and Random Walks . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.9 Fractal Dimension and Hurst Exponent. . . . . . . . . . . . . . . . . . . 5 1.9.1 The Box-Dimension. . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.9.2 The Hurst Exponent. . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.10 Multifractals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.11 False Nearest Neighbors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.12 Lyapunov Spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.13 Daily Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.14 Time Series Clustering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.14.1 The Exclusive Clustering . . . . . . . . . . . . . . . . . . . . . . 11 1.14.2 The Overlapping Clustering . . . . . . . . . . . . . . . . . . . . 11 1.14.3 The Hierarchical Clustering. . . . . . . . . . . . . . . . . . . . . 12 1.14.4 The Probabilistic Clustering . . . . . . . . . . . . . . . . . . . . 12 1.14.5 Feature Based Clustering . . . . . . . . . . . . . . . . . . . . . . 13 1.14.6 Choosing the Number of Clusters . . . . . . . . . . . . . . . . 13 1.15 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Analysis of Solar Radiation Time Series. . . . . . . . . . . . . . . . . . . . . 17 2.1 Energy from the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 The Solar Radiation Data Set . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.1 Stationarity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 Autocorrelation and Mutual Information. . . . . . . . . . . . 20 xi
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