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Research Papers

Multifractal Analysis of Daily Global Horizontal Radiation in Complex Topography Island: La Reunion as a Case Study

[+] Author and Article Information
Miloud Bessafi

Laboratoire d'Energétique,
d'Electronique et Procédés (LEEP),
Université de la Réunion,
15 Avenue René Cassin,
Sainte-Clotilde 97715, La Réunion
e-mail: miloud.bessafi@univ-reunion.fr

Vishwamitra Oree

Electrical and Electronic Engineering Department,
Faculty of Engineering,
University of Mauritius,
Reduit 80837, Mauritius
e-mail: v.oree@uom.ac.mu

Abdel Anwar Hossen Khoodaruth

Mechanical and Production Engineering Department,
Faculty of Engineering,
University of Mauritius,
Reduit 80837, Mauritius
e-mail:a.khoodaruth@uom.ac.mu

Guillaume Jumaux

Direction Interrégionale,
50 Boulevard Chaudron,
Sainte-Clotilde 97490, La Réunion
e-mail: guillaume.jumaux@meteo.fr

François Bonnardot

Direction Interrégionale,
50 Boulevard Chaudron,
Sainte-Clotilde 97490, La Réunion
e-mail: francois.bonnardot@meteo.fr

Patrick Jeanty

Laboratoire d'Energétique,
d'Electronique et Procédés (LEEP),
Université de la Réunion,
15 Avenue René Cassin,
Sainte-Clotilde 97715, La Réunion
e-mail: patrick.jeanty@univ-reunion.fr

Mathieu Delsaut

Laboratoire d'Energétique,
d'Electronique et Procédés (LEEP),
Université de la Réunion,
15 Avenue René Cassin,
Sainte-Clotilde 97715, La Réunion
e-mail: mathieu.delsaut@univ-reunion.fr

Jean-Pierre Chabriat

Laboratoire d'Energétique,
d'Electronique et Procédés (LEEP),
Université de la Réunion,
15 Avenue René Cassin,
Sainte-Clotilde 97715, La Réunion
e-mail: jean-pierre.chabriat@univ-reunion.fr

Muhammad Zaid Dauhoo

Department of Mathematics,
Faculty of Science,
University of Mauritius,
Reduit 80837, Mauritius
e-mail: m.dauhoo@uom.ac.mu

Li Peng

Laboratoire d'Energétique,
d'Electronique et Procédés (LEEP),
Université de la Réunion,
15 Avenue René Cassin,
Sainte-Clotilde 97715, La Réunion
e-mail: peng.li@univ-reunion.fr

1Corresponding author.

Manuscript received June 5, 2018; final manuscript received August 28, 2018; published online October 1, 2018. Assoc. Editor: Jorge Gonzalez.

J. Sol. Energy Eng 141(3), 031005 (Oct 01, 2018) (13 pages) Paper No: SOL-18-1253; doi: 10.1115/1.4041404 History: Received June 05, 2018; Revised August 28, 2018

An accurate assessment of the amount solar radiation incident at specific locations is highly complex due to the dependence of available solar radiation on many meteorological and topographic parameters. Reunion Island, a small tropical French territory, intends to deploy solar energy technologies rapidly. In this context, the variability and intermittency of solar irradiance in different regions of the island is of immediate interest if the generated energy will be integrated in the existing energy network. This paper identifies different features of spatial and temporal variability of daily global horizontal irradiance (GHI) observed on Reunion Island. For this purpose, trends in the mean daily as well as seasonal variability of GHI were investigated. Furthermore, the intermittency and multifractal behaviors of the spatial daily GHI change were examined. Analyzing this daily variability is crucial to day-ahead forecasting of solar resource for better managing solar integration in the power grid, particularly in small island states with isolated power systems. Results revealed that the difference in cumulative GHI for two successive days ranges between −10 and 10 kW/m2/day while the highest and lowest variability of daily change occurs during summer and winter, respectively. The decorrelation distance, which gives a measure of the distance over which the variability at distinct geographic locations become independent of one another at a given timescale, was also calculated. It was found that the average decorrelation distance for day-to-day GHI change is about 22 km, a smaller value than that calculated by the previous studies using much sparser radiometric networks. The Hurst exponent, fractal co-dimension, and Lévy parameter, which describe solar radiation intermittency, were also evaluated for Reunion Island.

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Figures

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Fig. 1

Physical map of Reunion Island showing key locations

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Fig. 2

Sentinel-2A satellite images of cloud cover of Reunion Island on (a) July 16, 2016, (b) Aug. 15, 2016, (c) Sept. 24, 2016, (d) Oct. 4, 2016, (e) Nov. 23, 2016, (f) Dec. 13, 2017 (g) Jan. 2, 2017, (h) Feb. 12, 2017, (i) Mar. 3, 2017, (j) Apr. 2, 2017, (k) May 12, 2017, and (l) June 1, 20172

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Fig. 3

Map of Reunion Island showing (a) topographic features and (b) the ratio of the altitude to distance from nearest coast at the 32 measurement sites

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Fig. 4

Monthly variation of cumulative daily GHI measured at all 32 stations

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Fig. 5

Percentage of net positive/negative GHI departure from overall spatial average

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Fig. 6

Seasonal average of daily cumulative GHI at the 32 stations. Unit is kW/m²/day.

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Fig. 7

Frequency of change in cumulative daily GHI from one day to the next

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Fig. 8

Correlation coefficient between daily and its lag-one GHI time series

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Fig. 9

Measured spatial correlation of GHI for day-to-day GHI change. Red points are indicative of the decorrelation distances for DJF, MAM, JJA, and SON, and the yearly averages are shown by red arrows.

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Fig. 10

Shape of normalized experimental PDFs of the increment at different distances

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Fig. 11

Deviation of daily GHI change distribution with respect to the Gaussian distribution at different distances

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Fig. 12

Experimental high-order structure functions Sq(d) with varying moments following Eq. (3) for q = 1, 2, 3, and 4

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Fig. 13

Generalized Hurst exponent for DJF, MAM, JJA, and SON

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Fig. 14

Evolution of universal multifractal parameters of log-stable model for DJF, MAM, JJA, and SON periods, as defined by Eq. (5): (a) Hurst parameter H, (b) fractal co-dimension C1, and (c) Lévy parameter α

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Fig. 15

The multifractal spectrum f(α) for summer, winter, and two interseasons. This spectrum is constructed using Eq. (6).

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