There have been many published articles describing solar position algorithms for solar radiation applications. The best uncertainty achieved in most of these articles is greater than ±0.01/ in calculating the solar zenith and azimuth angles. For some, the algorithm is valid for a limited number of years varying from 15 years to a hundred years. This report is a step by step procedure for implementing an algorithm to calculate the solar zenith and azimuth angles in the period from the year-2000 to 6000, with uncertainties of ±0.0003/. The algorithm is described by Jean Meeus [3]. This report is written in a step by step format to simplify the complicated steps described in the book, with a focus on the sun instead of the planets and stars in general. It also introduces some changes to accommodate for solar radiation applications. The changes include changing the direction of measuring azimuth angles to be measured from north and eastward instead of being measured from south and eastward, and the direction of measuring the observer's geographical longitude to be measured as positive eastward from Greenwich meridian instead of negative. This report also includes the calculation of incidence angle for a surface that is tilted to any horizontal and vertical angle, as described by Iqbal [4]. v Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to
There have been many published articles describing solar position algorithms for solar radiation applications. The best uncertainty achieved in most of these articles is greater than ±0.01/ in calculating the solar zenith and azimuth angles. For some, the algorithm is valid for a limited number of years varying from 15 years to a hundred years. This report is a step by step procedure for implementing an algorithm to calculate the solar zenith and azimuth angles in the period from the year -2000 to 6000, with uncertainties of ±0.0003/. The algorithm is described by Jean Meeus [3]. This report is written in a step by step format to simplify the complicated steps described in the book, with a focus on the sun instead of the planets and stars in general. It also introduces some changes to accommodate for solar radiation applications. The changes include changing the direction of measuring azimuth angles to be measured from north and eastward instead of being measured from south and eastward, and the direction of measuring the observer's geographical longitude to be measured as positive eastward from Greenwich meridian instead of negative. This report also includes the calculation of incidence angle for a surface that is tilted to any horizontal and vertical angle, as described by Iqbal [4]. v
In the most comprehensive pyrheliometer comparison known to date, 33 instruments were deployed to measure direct normal solar radiation over a 10-month period in Golden, Colorado. The goal was to determine their performance relative to four electrical-substitution cavity radiometers that were calibrated against the World Radiometric Reference (WRR) that is maintained at the World Radiation Center in Davos, Switzerland. Because of intermittent cabling problems with one of the cavity radiometers, the average of three windowed, electrical-substitution cavity radiometers served as the reference irradiance for 29 test instruments during the 10-month study. To keep the size of this work manageable, comparisons are limited to stable sunny conditions, passing clouds, calm and windy conditions, and hot and cold temperatures. Other variables could have been analyzed, or the conditions analyzed could have employed higher resolution. A more complete study should be possible now that the instruments are identified; note that this analysis was performed without any knowledge on the part of the analyst of the instruments' manufacturers or models. Apart from the windowed cavities that provided the best measurements, two categories of performance emerged during the comparison. All instruments exceeded expectations in that they measured with lower uncertainties than the manufacturers' own specifications. Operational 95% uncertainties for the three classes of instruments, which include the uncertainties of the open cavities used for calibration, were about 0.5%, 0.8%, and 1.4%. The open cavities that were used for calibration of all pyrheliometers have an estimated 95% uncertainty of 0.4%-0.45%, which includes the conservative estimate of 0.3% uncertainty for the WRR.
Accurate solar radiation measurements require properly installed and maintained radiometers with calibrations 8 traceable to the World Radiometric Reference (WRR). This study analyzes the performance of 51 commercially 9 available and prototype radiometers used for measuring global horizontal irradiances (GHI) or direct normal 10 irradiances (DNI). These include pyranometers, pyrheliometers, rotating shadowband radiometers (RSR) 2 , and a 11 pyranometer with an internal shading mask deployed at the National Renewable Energy Laboratory's (NREL) Solar 12 Radiation Research Laboratory (SRRL). The radiometers in this study were deployed for one year (from April 1, 13 2011, through March 31, 2012) and their measurements were compared under clear sky, partly cloudy, and mostly 14 cloudy conditions to reference values of low estimated measurement uncertainties. Mean Bias Difference (MBD) 15 and Root Mean Square Difference (RMSD) statistics were used as metrics to compare the GHI and DNI values 16 from individual instruments with concurrent measurements using the reference instruments over time intervals of 17 one-minute, 10-minute, and hourly averages. Deviations from the reference irradiance measurements were 18 calculated as a percent and W/m 2 of the reference value for solar zenith angles ranging from 17.5 degrees to 85 19 degrees (the range of available solar zenith angles throughout the year at SRRL, excluding data near sunrise and 20 sunset). Under clear-sky conditions when the solar zenith angle was less than 60 degrees, differences of less than 21 +5% were observed among all GHI and DNI measurements when compared to the reference radiometers. For GHI 22 these normalized differences increased up to +17% under mostly-cloudy and clear-sky conditions when the solar 23 zenith angle was greater than 60 degrees. The normalized differences were greater yet under mostly-cloudy 24 conditions (approaching +40%) for few DNI data sets at higher solar zenith angles. The intent of this paper is to 25 present a general overview of each radiometer's performance based on the instrumentation and environmental 26 conditions available at NREL.
The Measurements and Instrumentation Team within the Distributed Energy Resources Center at the National Renewable Energy Laboratory, NREL, calibrates pyranometers for outdoor testing solar energy conversion systems. The team also supports climate change research programs. These activities led NREL to improve pyranometer calibrations. Low thermal-offset radiometers measuring the sky diffuse component of the reference solar irradiance removes bias errors on the order of 20 Watts per square meter (W/m2) in the calibration reference irradiance. Zenith angle dependent corrections to responsivities of pyranometers removes 15 to 30 W/m2 bias errors from field measurements. Detailed uncertainty analysis of our outdoor calibration process shows a 20% reduction in the uncertainty in the responsivity of pyranometers. These improvements affect photovoltaic module and array performance characterization, assessment of solar resources for design, sizing, and deployment of solar renewable energy systems, and ground-based validation of satellite-derived solar radiation fluxes.
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