Calculo de trayectoria solar

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Revised January 2008



NREL/TP-560-34302

Solar Position Algorithm for
Solar Radiation Applications

Ibrahim Reda and Afshin Andreas

National Renewable Energy Laboratory
1617 Cole Boulevard Golden, Colorado 80401-3393
NREL is a U.S. Department of Energy Laboratory Operated by Midwest Research Institute • Battelle • Bechtel Contract No. DE-AC36-99-GO10337

Revised January2008



NREL/TP-560-34302

Solar Position Algorithm for
Solar Radiation Applications

Ibrahim Reda and Afshin Andreas
Prepared under Task No. WU1D5600

National Renewable Energy Laboratory
1617 Cole Boulevard Golden, Colorado 80401-3393
NREL is a U.S. Department of Energy Laboratory Operated by Midwest Research Institute • Battelle • Bechtel Contract No. DE-AC36-99-GO10337 Acknowledgment
We thank Bev Kay for all her support by manually typing all the data tables in the report into text files, which made it easy and timely to transport to the report text and all of our software code. We also thank Daryl Myers for all his technical expertise in solar radiation applications.

NOTICE This report was prepared as an account of work sponsored by an agency of the UnitedStates government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to anyspecific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.Available electronically at http://www.osti.gov/bridge Available for a processing fee to U.S. Department of Energy and its contractors, in paper, from: U.S. Department of Energy Office of Scientific and Technical Information P.O. Box 62 Oak Ridge, TN 37831-0062 phone: 865.576.8401 fax: 865.576.5728 email: reports@adonis.osti.gov Available for sale to the public, in paper, from: U.S. Department ofCommerce National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 phone: 800.553.6847 fax: 703.605.6900 email: orders@ntis.fedworld.gov online ordering: http://www.ntis.gov/ordering.htm

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Table of Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Time Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Procedure . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
SPA Evaluation and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
List of Figures Figure 1. Uncertainty of cosine the solar zenith angle resulting from 0.01/ and 0.0003/
uncertainty in the anglecalculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Figure 2. Difference between the Almanac and SPA for the ecliptic longitude & latitude, and the apparent right ascension & declination on the second day of each month at 0-TT for the years 1994, 1995, 1996, and 2004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Figure 3....
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