Calibration and Measurement Uncertainty Estimation of Radiometric Data Preprint A. Habte, M. Sengupta, I. Reda, and A. Andreas National Renewable Energy Laboratory J. Konings Hukseflux Thermal Sensors Presented at Solar 2014 San Francisco, California July 6–10, 2014 NREL is a national laboratory of the U.S. Department of Energy Office of Energy Efficiency & Renewable Energy Operated by the Alliance for Sustainable Energy, LLC This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. Conference Paper NREL/CP-5D00-62214 November 2014 Contract No. DE-AC36-08GO28308 NOTICE The submitted manuscript has been offered by an employee of the Alliance for Sustainable Energy, LLC (Alliance), a contractor of the US Government under Contract No. DE-AC36-08GO28308. 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Box 62 Oak Ridge, TN 37831-0062 phone: 865.576.8401 fax: 865.576.5728 email: mailto:[email protected] Available for sale to the public, in paper, from: U.S. Department of Commerce National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 phone: 800.553.6847 fax: 703.605.6900 email: [email protected] online ordering: http://www.ntis.gov/help/ordermethods.aspx Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 16560, photo by Dennis Schroeder, NREL 17613, photo by Dean Armstrong, NREL 17436, photo by Pat Corkery, NREL 17721. Calibration and Measurement Uncertainty Estimation of Radiometric Data Aron Habte Jörgen Konings Manajit Sengupta Hukseflux Thermal Sensors Ibrahim Reda Delft The Netherlands Afshin Andreas [email protected] National Renewable Energy Laboratory 1617 Cole Blvd. Golden, CO 80401, USA [email protected] [email protected] [email protected] [email protected] ABSTRACT 1. INTRODUCTION Evaluating the performance of photovoltaic cells, modules, and Accuracy of radiometric data is essential for understanding and arrays that form large solar deployments relies on accurate assessing investment risks of the system performance of measurements of the available solar resource. Therefore, renewable energy. Most applications of uncertainty calculations determining the accuracy of these solar radiation measurements use factory radiometric specifications as final uncertainty provides a better understanding of investment risks. This values for calibration and field measurements or other methods becomes especially important as deployment size and of calculating uncertainties. Accuracy and uncertainty investment costs grow to hundreds of millions of dollars. The specifications for radiometers are based on a wide range of accuracy of measurements is also important for acceptance approaches and data analysis techniques. This paper addresses a testing and operations. detailed application to calculate calibration and field measurement uncertainties. This method provides guidelines Radiometers such as pyranometers are used to measure global and recommended procedures for estimating uncertainties in horizontal irradiance or plane of array irradiance, whereas the calibrations and measurements by solar pyranometers and pyrheliometers are used to measure direct normal irradiance. pyrheliometers using a Guide to the Expression of Uncertainty Currently, most radiometric data users rely on manufacturers’ (GUM) method. Standardized analysis based on these specifications of calibration uncertainty to quantify the procedures will ensure that the uncertainty quoted for data uncertainty of measurements. However, the accuracy of solar collected by these radiometers can be compared based on radiation measured by radiometers depends not only on the documented methods of derivation. One important note: the specifications of the instrument but also on the (a) calibration calibration uncertainty example provided here is based on the procedure, (b) measurement conditions and maintenance, and Broadband Outdoor Radiometer CALibration method, which is (c) environmental conditions. Therefore, statements about the employed at the National Renewable Energy Laboratory. overall measurement uncertainty can be made only on an However, the methodology described below is applicable to all individual basis, taking all relevant factors into account. This radiometer calibration systems. The principles and essential paper provides guidelines and recommended procedures for steps, including the estimation of magnitudes and types of estimating the uncertainty in calibrations and measurements by uncertainties (Type A and/or Type B), are similar. radiometers using methods that follow the Guide to the Expression of Uncertainty (GUM). Standardized analysis based on these procedures ensures that the uncertainty quoted is well documented. Keywords: Global Horizontal Irradiance; Direct Normal Irradiance; Type A; Type B; Uncertainty 1 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 2. METHOD AND RESULT The calibration of broadband radiometers involves the direct measurement of a standard source (solar irradiance or artificial The purpose of estimating uncertainties is to maintain light). However, in this paper the calibration method is based measurement traceability by establishing an unbroken chain of on outdoor calibration using the solar irradiance as the source. comparisons that a measurement is in agreement within The accuracy of the calibration is dependent on the sky acceptable limits of uncertainty with respect to the International condition, maintenance of the test, and reference instruments, System of Units. Meanwhile, the uncertainty estimates in the including the leveling of the instruments. All of these factors radiometric data have a significant effect on the uncertainty of are included when estimating calibration uncertainties. Five the expected electrical output of solar energy systems. The steps are carried out in the estimation of calibration uncertainty uncertainty estimate of broadband radiometric data is (Fig. 1). These steps are adopted from (1), which includes a performed on two specific components: (a) the uncertainty in summarized version of the BIPM GUM. The GUM method the calibration of the measurement system and (b) the employs two types of uncertainty estimates: Type A and Type uncertainty in the routine or field measurement system. This B. Type A uncertainty uses a statistical method of valuation, guide provides steps for evaluating the uncertainty in each of such as standard deviation. Type B is based on any non- the calibration and measurement stages. The guide is based on statistical evaluation, such as manufacturers’ specifications, the International Bureau of Weights and Measures (BIPM, from literature, or professional judgment. One assumption the French name) Guide to the Uncertainty in Measurements, or considered in this paper is that the sources of uncertainty GUM. variables are uncorrelated because each of them are measured or estimated using independent methods. Sources of Standard Sensitivity Combined Expanded Uncertainties Uncertainty Coefficient Uncertainty Uncertainty (u) (c) (uc) (U95=k*uc) Calculated Calculated using Obtained from Calculated using the Calculated using partial the root sum of manufacturers’ combined using expanded derivative the squares of specifications, uncertainty times the uncertainty and from the the standard previous coverage factor statistical measurement uncertainty experience, and/or (k =1.96 for a 95% distribution equation for times the literature confidence interval) each variable sensitivity coefficient Fig.1 Calibration and measurement uncertainty estimation flow chart 2.1 Measurand and Measurement Equation uncertainty associated with these terms must be stated. G is the calculated irradiance. The first step in the uncertainty calculation is to determine the measurement equation. This is a mathematical description of = ( ) + the relation of the measurand (solar irradiance) as a function of where N is the beam irradiance,퐺 푁 ∗ in퐶퐶퐶 Wm푍-2; Z 퐷is the solar zenith the input variables (such as