Nonlinear characteristics of observed solar radiation data

Abstract The solar radiation data is one of the most important indicators for photovoltaic (PV) power generation application. It is utilized frequently for system capacity plan, operation and dispatch, reliability evaluation, system modeling and simulation of photovoltaic power station. Faced with the nonlinear, non-stationary characteristics of the observed solar radiation data, a detailed study is achieved in this investigation. Some observed data from North American solar radiation stations is implemented to analyze their box dimensions and Hurst exponent indexes firstly, which are the single scale fractal characteristics. Then, the Multi-fractal Detrended Fluctuation Analysis (MDFA) method is employed to study its multi-fractal characteristics. In addition, the power-law distribution is found in statistics and power spectrum scales, which can describe its heavy tail, nonlinear, non-stationary characteristics. Results show that the box dimensions and Hurst exponent indexes in daily or yearly scale are close to constants and vary in the location of stations; the MDFA results show its obvious multi-fractal characteristics, which are affected by time and location factors; the power-law distribution of solar radiation data in statistics and spectrum scales reveals its non-stationary characteristic, and the power-law index is in a narrow range. These results have significant value and reference for the PV power plant location selection, capacity determination, solar radiation prediction, and operation schedule. It has explored a new way for solar radiation data research as well.

[1]  E. Dutton,et al.  Do Satellites Detect Trends in Surface Solar Radiation? , 2004, Science.

[2]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[3]  F. Auerbach.  Das Gesetz der Bevölkerungskonzentration. , 1913 .

[4]  T. Soubdhan,et al.  Classification of daily solar radiation distributions using a mixture of Dirichlet distributions , 2009 .

[5]  D. Robinson,et al.  Solar radiation modelling in the urban context , 2004 .

[6]  F. Hocaoglu,et al.  Hourly solar radiation forecasting using optimal coefficient 2-D linear filters and feed-forward neural networks , 2008 .

[7]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[8]  Tom Markvart,et al.  PV system sizing using observed time series of solar radiation , 2006 .

[9]  Zekai Şen,et al.  Fuzzy algorithm for estimation of solar irradiation from sunshine duration , 1998 .

[10]  R. Richter,et al.  Estimation of incident solar radiation on the ground from multispectral satellite sensor imagery , 2006 .

[11]  W. Beckman,et al.  Solar Engineering of Thermal Processes , 1985 .

[12]  Toshitsugu HARA,et al.  Chaotic fluctuation in natural wind and its application to thermal amenity , 1997 .

[13]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[14]  Adel Mellit,et al.  A simplified model for generating sequences of global solar radiation data for isolated sites: Using artificial neural network and a library of Markov transition matrices approach , 2005 .

[15]  R. Voss,et al.  ‘1/fnoise’ in music and speech , 1975, Nature.

[16]  W. Reed,et al.  From gene families and genera to incomes and internet file sizes: why power laws are so common in nature. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  R. Moharil,et al.  Reliability analysis of solar photovoltaic system using hourly mean solar radiation data , 2010 .

[18]  C. Richter.  An instrumental earthquake magnitude scale , 1935 .

[19]  Richard Perez,et al.  Maximizing the value of customer-sited PV systems using storage and controls , 2007 .

[20]  M. E. J. Newman,et al.  Power laws, Pareto distributions and Zipf's law , 2005 .

[21]  A. Lo.  Long-Term Memory in Stock Market Prices , 1989 .

[22]  Viorel Badescu,et al.  Modeling Solar Radiation at the Earth's Surface: Recent Advances , 2014 .

[23]  Hamdy K. Elminir,et al.  Estimation of solar radiation components incident on Helwan site using neural networks , 2005 .

[24]  F. Hooge.  1/f noise sources , 1994 .

[25]  D. Schertzer,et al.  Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes , 1987 .

[26]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[27]  M. Iqbal.  An introduction to solar radiation , 1983 .

[28]  Seul-Ki Kim,et al.  MODELING AND SIMULATION OF A GRID-CONNECTED PV GENERATION SYSTEM FOR ELECTROMAGNETIC TRANSIENT ANALYSIS , 2009 .

[29]  Xianzhong Duan,et al.  Self-organized criticality of power system faults and its application in adaptation to extreme climate , 2009 .

[30]  T. Newell,et al.  Fundamentals of Solar Energy Conversion , 1983 .

[31]  A. Ghanbarzadeh,et al.  The potential of different artificial neural network (ANN) techniques in daily global solar radiation modeling based on meteorological data , 2010 .

[32]  J. Mubiru,et al.  Estimation of monthly average daily global solar irradiation using artificial neural networks , 2008 .

[33]  F. S. Tymvios,et al.  Comparative study of Ångström's and artificial neural networks' methodologies in estimating global solar radiation , 2005 .