Informes Técnicos Ciemat 904 octubre, 1999 SRADLIB:ACLibraryfor Solar Radiation Modelling J.L.Balenzategui Departamento de Energías Renovables Toda correspondenica en relación con este trabajo debe dirigirse al Servicio de Información y Documentación, Centro de investigaciones Energéticas, Medioambientales y Tecnológicas, Ciudad Universitaria, 28040-MADRID, ESPAÑA. Las solicitudes de ejemplares deben dirigirse a este mismo Servicio. Los descriptores se han seleccionado del Thesauro del DOE para describir las materias que contiene este informe con vistas a su recuperación. La catalogación se ha hecho utilizando el documento DOE/TiC-4602 (Rev. 1) Descriptive Cataloguing On-Line, y la clasificación de acuerdo con el documento DOE/TIC.4584-R7 Subject Categories and Scope publicados por el Office of Scientific and Technicai Information del Departamento de Energia de los Estdos Unidos. Se autoriza la reproducción de los resúmenes analíticos que aparecen en esta publicación. Depósito Legal: M -14226-1995 ISSN: 1135-9420 ÑIPO: 238-99-003-5 Editorial CIEMAT CLASIFICACIÓN DOE Y DESCRIPTORES 140100; 990200 SOLAR RADIATION; DIFFUSE SOLAR RADIATION; DIRECT SOLAR RADIATION; SOLAR ENERGY; RENEWABLE ENERGY RESOURCES; COMPUTER CALCULATIONS; DATA ANALYSIS COMPUTER CODES: PROGRAMMING "SRADLIB: A C Library for Solar Radiation Modelling" Balenzategui, J. L 118 pp. 18 figs. 24refs. Abstract: This document shows the result of an exhaustive study about the theoretical and numerical models available in the literature about solar radiation modelling. The purpose of this study is to develop or adapt mathematical models describing the solar radiation specifically for Spain locations as well as to créate computer tools able to support the labour of reasearchers or engineers needing solar radiation data to solve or improve the technical or energetic performance of solar systems. As result of this study and revisión, a C library (SRADLIB) is presented as a key tool for the compilation of the mathematical models from different authors, for the comparison among the different approaches and for its application in computer programs. Different topics related to solar radiation and its modelling are first discussed, including the assumptions and conventions adopted and describing the most accepted and used current state-of-the-art models. Some typical problems in the numerical calculation of radiation valúes are also posed with the proposed solution. The document includes next a complete reference of the developed functions, with many examples of application and calculus. "SRADLIB: Una Librería en C para el Modelado de la Radiación Solar" Balenzategui, J. L. 118 pp. 18 figs. 24refs. Resumen: Este documento muestra el resultado de un exhaustivo estudio sobre los modelos teóricos y matemáticos para el modelado de la radiación solar disponibles en la literatura. El propósito de este estudio es desarrollar o adaptar modelos matemáticos que describan la radiación solar específicamente para localidades españolas así como crear herramientas informáticas que apoyen la labor de investigadores o ingenieros que precisan datos de radiación solar para solucionar o mejorar el rendimiento técnico o energético de sistemas solares. Como resultado de este estudio y revisión, se presenta una librería en lenguaje C (SRADLIB) como herra- mienta clave para la recopilación de los modelos matemáticos de diferentes autores, para la comparación entre las differentes aproximaciones propuestas y su aplicación en programas de ordenador. Se discuten, en primer lugar, diferentes temas relacionados con la radiación solar y su modelado, incluyendo las convencio- nes y asumpciones adoptadas y describiendo los modelos más aceptados y usados en el presente estado del arte. Se plantean asimismo algunos problemas típicos en el cálculo numérico de los valores de radiación junto con la solución propuesta. El documento incluye a continuación una referencia completa de las funciones desarrolladas, con numerosos ejemplos de aplicación y cálculo. Contents List of symbols ¡v List of figures vi List oftables vi l.INTRODUCTION 1 2.SRADLIB TOPICS 3 2.1. BASIC SUN-EARTH RELATIONSHIPS AND SIGN CONVENTION 3 2.1.1. Radiation on tilted surfaces 5 2.1.2. Solar Declination 6 2.1.3. Other basic magnitudes 7 2.2. TIME CONVENTION 8 2.3. YEARDURATION 10 2.4. SUNRISE, SUNSET AND DAY LENGTH 11 2.5. SUNRISE AND SUNSET PROBLEMS CALCULATING HOURLY RADIATION 12 2.6. CALCULATION OF RADIATION OVER CERTAIN PERIOD BY DIRECT RNTEGRATION 13 2.7. TMY FILES 15 2.8. INTERPOLATION OF RADIATION VALÚES 16 2.9. RATIO FUNCTIONS 17 2.10. HORIZONTAL HOURLY DIFFUSE RADIATION 18 2.10.1. Erbs' correlation 19 2.10.2. Boes' correlation 19 2.10.3. Orgill & Holland's correlation 20 2.10.4. Reindl2 correlation 20 2.10.5. Reindl3 correlation 20 2.10.6. Madrid 1 correlation 21 2.10.7. Madrid2 correlation 21 2.1 1. TlLTED SURFACE HOURLY DIFFUSE RADIATION 22 2.11.1. Goitnd Radiation 23 2.11.2. Isotropic model 23 2.11.3. Temps & Coulson's model 23 2.11.4. Klucher's model 24 2.11.5. Hay & Davies' model 24 2.11.6. Reindl's model 24 2.11.7. Perezl model 25 2.11.8. Perezl model 26 2.12. CONSTANTS AND STRUCTURES 27 2.13. FUTURE IMPROVEMENTS 29 2.14. ACKNOWLEDGEMENT 30 3.LIBRARY REFERENCE 31 3.1. GENER.AL OVERVIEW ABOUT THE SRADLIB FUNCTIONS 31 3.2. FUNCTION REFERENCE 35 3.2.1. AngToHour 55 3.2.2. AngToNoon 36 3.2.3. CoslncidAng 37 3.2.4. CosSolZenilh 39 3.2.5. DataSmooth 40 3.2.6. DayAngle 42 3.2.7. DayNiimber 43 3.2.8. DeclinCoop, DeclinPerr, DeclinSpen 44 3.2.9. EccenCorrDuff, EccenCorrSpen 45 3.2.10. ExtDayRad, ExtDayRadlnt 46 3.2.11. ExtHonrRad, ExtHourRadCor, ExtHourRadlnt 48 3.2.12. Extlrrad 51 3.2.13. ExtMADayRad, ExtMADayRadlnt 52 3.2.14. ExtMAHourRad. 54 3.2.15. HDayLength 56 3.2.16. HorHDC_Boes, HorHDCJErbs, HorHDCJladridl, HorHDCJladrid2, HorHDCjDrgill, HorHDC_Reindl2, HorHDCJLeindB 57 3.2.17. HorSimrise, HorSunset 59 3.2.18. HourAngle 61 3.2.19. Hourlnteg 62 3.2.20. IncidAng 64 3.2.21. inRanBt, InRange, InRanTp, inRanWt 65 3.2.22. InterpRad 67 3.2.23. LatTime 70 3.2.24. LstTime 72 3.2.25. OfJTime 73 3.2.26. PstTime 74 3.2.27. radien, radlwar 75 3.2.28. RbDayRad 76 3.2.29. RbHourRad 78 3.2.30. Rblrrad 79 3.2.31. RbMADayRad 50 3.2.32. RbMAHourRad. 81 3.2.33. ReadGeoData 52 3.2.34. ReadTmyData 84 3.2.35. SaveAsciiFile 57 3.2.36. SinSolAlt 88 3.2.37. SolarAltitude 59 3.2.38. SolarAzimuth 90 3.2.39. SolTime 91 3.2.40. SolarZenith 92 3.2.41. TilBeamDay 93 3.2.42. TilBeamHour 94 3.2.43. TilBeamlrrad 95 3.2.44. TilBeamMADay 96 3.2.45. TilBeamMAHour 97 3.2.46. TilDayLength 98 3.2.47. TilGroundRad 99 3.2.48. TilHDifHay, TilHDiflsotrop, TilHDifKlucher, TilHDifPerezlPnt, TilHDifPerez2Pnt, TilHDifReindl, TilHDiJTemps 100 3.2.49. TilSunrise, TilSunset 103 11 — 3.2.50. TimeEqiiat 104 3.2.51. Traplnteg 105 4.THE 'SRADLIB.H' HEADER FILE 106 5.HOW TO GET SRADLIB 109 6.REFERENCES 111 • m — List of symbols a Solar altitude. fí Slope of the surface, measured from the horizontal towards the equator. § Solar declination. g Sky clearness, defined in the Pérez model. Á Geographical latitude. y Surface azimuth. Surface orientation, measured from the south (east positive) Q Angle of incidence of sunbeam radiation on an arbitrarily oriented/tilted surface. Q, Solar zenith angle. p Ground albedo. ¿y Hour angle. (¡X Mid-point hour. ¿ys Sunrise hour angle for horizontal surfaces. ¿QSS Sunset hour angle for arbitrarily oriented surfaces. (¿)sr Sunrise hour angle for arbitrarily oriented surfaces. u/ Solar azimuth. ¿j Sky brightness, defined in the Pérez model p Day angle. A¡ Anisotropy Índex, defined in the Hay & Davies model. ¿g Day length for a horizontal surface. dgs, Day length for an arbitrarily oriented surface. fío Eccentricity correction factor. ]£t Equation of time. j Modulating function, defined in the Reindl's model. p Modulating function, defined in the Ivlucher's model. F\,Fi Reduced brightness coefficients, defined in the Pérez model. 2?¡j Pérez model coefficients. fj Horizontal daily radiation on the earth's surface. JJor Daily radiation on arbitrarily tilted/oriented surfaces on the earth's surface. JJQ Extraterrestrial horizontal daily radiation. }Jonv Extraterrestrial daily radiation on arbitrarily tilted/oriented surfaces. • iv • Hgn- Daily ground radiation on arbitrarily tüted/oriented surfaces. I Horizontal global irradiance on the earth's surface. I „ Global irradiance on arbitrarüy tüted/oriented planes on the earth's surface. lo Extraterrestrial horizontal irradiance. lo* Extraterrestrial irradiance on arbitrarily tüted/oriented surfaces. ib Horizontal beam irradiance on the earth's surface. ibpY Beam irradiance on arbitrarily tüted/oriented surfaces on the earth's surface. id Horizontal diffuse irradiance on the earth's surface. i¿nv Diffuse irradiance on arbitrarily tüted/oriented surfaces on the earth's surface. J Horizontal hourly global radiation on the earth's surface. /„ Hourly global radiation on arbitrarily tüted/oriented surfaces. Jo Extraterrestrial horizontal hourly radiation. JOg. Extraterrestrial hourly radiation on arbitrarily tüted/oriented surfaces. J¿, Horizontal hourly beam radiation. lbn Horizontal hourly beam radiation projected on the normal to the surface. /(,„. Hourly beam radiation on arbitrarüy tüted/oriented surfaces. J¿ Horizontal hourly diffuse radiation. l¿n Horizontal hourly diffuse radiation projected on the normal to the surface. J¿0_ Hourly diffuse radiation on arbitrarily tüted/oriented surfaces. /_„ Hourly gound radiation on arbitrarily tüted/oriented surfaces. Jsc Solar constant. j Day number of the year. ¡lt Clearness index, ratio between horizontal hourly global radiation I on the earth's surface and the extraterrestrial horizontal hourly radiation lo. £,c Geographical local longitude. JjS Standard meridian longitude. LAT Local apparent time, also called true solar time. JjQ Longitude correction. LOT Local official time. LST Local standard time. üb Geometric factor, ratio between the cosine of the angle of incidence and the cosine of solar zenith angle.