Spline adjustment for modelling solar intermittences
AbstractOne of the reasons why photovoltaic technology is not massively installed is its variation in production. This variation is due to intermittences in the solar resource. Based on real data from the microgrid of the Renewable Energy Development Center (CEDER, Spain) and another scenario in Xalapa (México), the study determines the solar intermittences produced and grouped monthly. The period of data acquisition, in the first study, was from May 30th, 2012 to March 3rd, 2015 with the help of a Baseline Surface Radiation Network (BSNR) team; in the second, 2014 measurements were obtained from a meteorological station certified by the National Meteorological System (SMN). The analysis is based on the determination of monthly frames of reference for radiation by third-degree spline adjustments with smoothing, using the JUMP statistical application software (JMP © 2009, SAS Institute, version 8.0.2). The results of the analyses have provided important information to understand the unstable appearance of solar radiation and, in turn, will be the basis of a control system to optimize photovoltaic production.
M. Abdollahi and G. B. Gharehpetian, “Dynamic performance enhancement of microgrids by advanced sliding mode controller,” Electrical Power and Energy Systems, vol. 33, no. 1, January 2011. [Online]. Available: https://doi.org/10.1016/j.ijepes.2010.08.011
J. M. Guerrero and et al., “Distributed generation: Toward a new energy paradigm,” IEEE Industrial Electronics Magazine, vol. 4, no. 1, March 2010. [Online]. Available: https://doi.org/10.1109/MIE.2010. 935862
B. V. Mathiesen, H. Lund, and K. Karlsson, “100% renewable energy systems, climate mitigation and economic growth,” Applied Energy, vol. 88, no. 2, February 2011. [Online]. Available: https: //doi.org/10.1016/j.apenergy.2010.03.001
S. Chowdhury, S. P. Chowdhury, and P. Crossley, Microgrids and Active Distribution Networks, 1st ed. London, UK: The Institution of Engineering and Technology, 2009.
E. Lorenz, D. Heinemann, H. Wickramarathne, H. G. Beyer, and S. Bofinger. (2007) Forecast of ensemble power production by grid-connected pv systems. [Online]. Available: https://bit.ly/ 2Xzu0bM
R. Perez and et al., “Validation of short and medium term operational solar radiation forecasts in the US,” Solar Energy, vol. 84, no. 12, December 2010. [Online]. Available: https: //doi.org/10.1016/j.solener.2010.08.014
R. A. López, L. Hernández, J. A. D. Ángel, and Q. Hernández, “Relationship between environmental variables and the performance of solar radiation using the spline fit,” Dyna Energía y Sostenibilidad, vol. 5, January 2016. [Online]. Available: http://dx.doi.org/10.6036/ES8138
A. F. Barrientos, J. Olaya, and V. M. González, “Un modelo spline para el pronóstico de la demanda de energía eléctrica,” Revista Colombiana de Estadística, vol. 30, no. 2, pp. 187–202, Dec. 2007.
J. Bedolla and et al., “Aproximación de perfiles discretos en elementos de contacto de ensambles mecánicos,” Ing. invest. y tecnol., vol. 14, no. 1, pp. 99–111, Jan. 2013.
A. Toriz and A. Sánchez, “Exploración integrada probabilista para robots móviles en ambientes complejos,” Computación y Sistemas, vol. 18, no. 1, January 2014. [Online]. Available: http: //dx.doi.org/10.13053/CyS-18-1-2014-028
R. A. Lopez, L. Hernández, L. O. Jamed, and V. A. Gomez, “Solar intermittency with spline fit modeling. microgrid case CEDER, soria, spain,” in I Ibero-American Congress of Smart Cities (ICSC-CITIES 2018), Soria Spain, 2018, pp. 592–601.
R. H. Inman, H. T. C. Pedro, and C. F. M. Coimbra, “Solar forecasting methods for renewable energy integration,” Progress in Energy and Combustion Science, vol. 39, no. 6, December 2013. [Online]. Available: https://doi.org/10.1016/j.pecs.2013.06.002
E. Wiemken, H. G. Beyer, W. Heydenreich, and K. Kiefer, “Power characteristics of pv ensembles: experiences from the combined power production of 100 grid connected pv systems distributed over the area of germany,” Solar Energy, vol. 70, no. 6, 2001. [Online]. Available: https://doi.org/10.1016/S0038-092X(00)00146-8
K. Otani, J. Minowa, and K. Kurokawa, “Study on areal solar irradiance for analyzing areally-totalized pv systems,” Solar Energy Materials and Solar Cells, vol. 47, no. 1-4, October 1997. [Online]. Available: https://doi.org/10.1016/S0927-0248(97)00050-0
C. Wan, “Photovoltaic and solar power forecasting for smart grid energy management,” CSEE Journal of Power and Energy Systems, vol. 1, no. 14, December 2015. [Online]. Available: https://doi.org/10.17775/CSEEJPES.2015.00046
A. Genç and et al., “Statistical analysis of solar radiation data using cubic spline functions,” Energy Sources, vol. 24, no. 12, November 10 2002. [Online]. Available: https://doi.org/10.1080/ 00908310290087058
R. E. Childs, D. G. S. Chuah, S. L. Lee, and K. C. Tan, “Analysis of solar radiation data using cubic splines,” Solar Energy, vol. 32, no. 5, 1984. [Online]. Available: https://doi.org/10.1016/0038-092X(84)90141-5
H. Diagne, P. Lauret, M. David, and J. W. Boland, “Solar irradiation forecasting: state-of-the-art and proposition for future developments for small-scale insular grids,” World Renewable Energy Forum, May 2012.
A. Pankratz, Forecasting with Univariate Box-Jenkins Models: Concepts and Cases. United States: John Wiley & Sons, 1983.
R. Hyndman and et al., forecast: Forecasting functions for time series and linear models, 2019, R package version 8.7. [Online]. Available: http://pkg.robjhyndman.com/forecast
A. W. Bowman and A. Azzalini, Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations, ser. Oxford Statistical Science Series. OUP Oxford, 1997.
D. Petrinovic, “Causal cubic splines: Formulations, interpolation properties and implementations,” IEEE Transactions on Signal Processing, vol. 56, no. 11, November 2008. [Online]. Available: https://doi.org/10.1109/TSP.2008.929133
S. Couture, J. C. Beal, and Y. M. M. Antar, “The cubic spline interpolation of a standing wave envelope,” IEEE Antennas and Propagation Society International Symposium 1992 Digest, Chicago, USA, 1992.
G. Wolberg and I. Alfy, “Monotonic cubic spline interpolation,” in 1999 Proceedings Computer Graphics International, June 1999, pp. 188–195.
J. Mathews and F. Fink, Numerical Methods Using MATLAB, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1999.
M. Grasselli and D. Pelinovsky, Numerical Mathematics. Jones & Bartlett Publishers, 2008.
C. Reinsh, “Smoothing by spline functions„” Numerische Mathematik, vol. 10, pp. 177–183, 1967.
B. W. Silverman, “Some aspects of the spline smoothing approach to non-parametric regression curve fitting,” Journal of the Royal Statistical Society, Series B (Methodological), vol. 47, no. 1, September 1985. [Online]. Available: https://doi.org/10.1111/j.2517-6161.1985. tb01327.x
W. Härdle, Applied Nonparametric Regression (Econometric Society Monographs). Cambridge, UK: Cambridge University Press, 1992.
SAS Institute Inc. (2009) JMP 8.0.2 Release Notes. SAS Institute Inc. DescripciónCary, NC. [Online]. Available: http://www.jmp.com/ support/notes/41/addl/fusion_41004_6_releasenotes8_0_2.pdf
V. T. Jayadevan, J. Rodriguez, V. P. A. Lonij, and A. Cronin, “Forecasting solar power intermittency using ground-based cloud imaging,” in World Renewable Energy Forum, WREF 2012, Including World Renewable Energy Congress XII and Colorado Renewable Energy Society (CRES) Annual Conference, Denver, USA, 2012, pp. 2100–2106.
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