INFLUENCE OF MEASUREMENT EQUIPMENT ON THE UNCERTAINTY OF PERFORMANCE DATA FROM TEST LOOPS FOR CONCENTRATING SOLAR COLLECTORS Nicole Janotte*, Eckhard Lüpfert*, Robert Pitz-Paal*, Klaus Pottler**, Markus Eck***, + Eduardo Zarza , Klaus-Jürgen Riffelmann# * Researcher, Dipl.-Ing., Research Area Head, Dr.-Ing., Division Head, Prof. Dr.-Ing., German Aerospace Center (DLR), Institute of Technical Thermodynamics Solar Research, 51147 Köln, Germany, Phone: +49 2203 6012431, Fax: +49 2203 6014141, e-mail:
[email protected] ** Researcher, Dr. rer.nat. German Aerospace Center (DLR), Institute of Technical Thermodynamics Solar Research, Plataforma Solar de Almería (PSA), P.O. Box 39, 04200 Tabernas, Spain *** Researcher, Dr.-Ing., German Aerospace Center (DLR), Institute of Technical Thermodynamics Solar Research, Pfaffenwaldring 38-40, 70569 Stuttgart, Germany +
Research Area Head, Dr.-Ing., Ciemat, Plataforma Solar de Almería (PSA), P.O. Box 22, 04200 Tabernas, Spain
#
Engineering Manager, Dr.-Ing., Flagsol GmbH, Mühlengasse 7, 50667 Köln, Germany
Abstract Parabolic trough concentrating collectors play a major role in the energy efficiency and economics of concentrating solar power plants. Therefore, existing collector systems are constantly enhanced and new types developed. Thermal performance testing is one step generally required in the course of their testing and qualification. For outdoor tests of prototypes a heat transfer fluid loop (single collectors or entire loop) needs to be equipped with measurement sensors for inlet, outlet and ambient temperature as well as irradiance, wind speed and mass or volumetric flow sensors to evaluate the heat balance. Assessing the individual measurement uncertainties and their impact on the combined uncertainty of the desired measurement quantity one obtains the significance of the testing results. The method has been applied to the EuroTrough collector tests performed at PSA. Test results include the uncertainty range of the resulting modeling function and exemplify the effects of the sensors and their specifications on the parameters. Recommendations for suitable sensor types and classes as well as the required number of sensors and their location are given on the basis of experience gained during tests of concentrating collectors. Keywords: parabolic trough, extended prototype testing, efficiency, thermal measurement, measurement uncertainty, combined uncertainty, qualification 1 Introduction The present favorable market environment for concentrating solar power (CSP) in Spain and the US resulting in a growing activity on this sector has increased the demand for its key components triggering numerous new developments and enhancements. As the currently most mature technology parabolic troughs have been emphasized on lately. Once a development has been completed and prototypes have been erected in a test loop, 1 2 thermal collector testing according to EN 12975-2 or ASTM 905 is one step of a qualification routine in order to assess their potential and rate their thermal performance. Conventionally, this includes quasi steady-state testing for incidence angle modifier (IAM) as well as thermal efficiency and thermal losses at different temperature levels resulting in a characterization of the steady-state thermal behavior of the collector. These tests are time consuming, their results depend on the solar radiation and sun position during the tests and their validity is limited to time series without variations in testing conditions, a precondition hard to fulfill when necessarily testing outdoors under the influence of sun position and meteorological variations. 3 Recent investigations however, encourage the adaptation and application of existing alternative testing procedures for non-concentrating solar thermal collectors under quasi-dynamic conditions also proposed in EN
1
12975-2. They benefit from less restrictive testing requirements and yield a full thermal characterization of the collectors in its operation range. While thermal performance testing is indispensable to verify proper collector/loop functioning, there are more 4 suitable methods for assessing its optical properties. These have been described in the work by Lüpfert et al.
2 Measurement Needs Regardless of the actual testing procedure (quasi steady-state or quasi dynamic) the key to the analysis of thermal collector tests lies in balancing the energy of the system, hence quantities to be measured are essentially the same. The heat gain over the collector describing the useful heat output of the system under investigation is of particular interest. In accordance with EN 12975-2 rather than measuring the inlet and outlet enthalpies themselves, the respective temperatures of the heat transfer fluid (HTF) are measured. In combination with the measured mass flow rate and manufacturers’ information on the specific heat capacity of the fluid as function of temperature of the HTF these are subsequently used to calculate the heat gain Q gain m c p (Tout Tin ) , with the value of c p corresponding to the mean fluid temperature. Alternatively, measurements of the volumetric flow rate of the HTF in combination with density as a function of temperature and the temperature at the point of flow measurement can be used for determining the mass flow rate of the HTF. Measuring ambient conditions is essential in order to correlate measured collector/loop performance to ambient influences as well as monitoring their variations. The solar energy available to the system is quantified as the 5 product of the net collector aperture area and the beam irradiance Gb (incident perpendicular to the collector aperture Gb = Eb cos(φ)) Q solar Anet Gb . Usually, the final test result considered is either the specific heat gain per collector aperture or the thermal efficiency ηth Q m c p (Tout Tin ) Q gain m c p (Tout Tin ) or th gain . Anet Gb Anet Anet Qsolar The ambient temperature Tamb is necessary for quantifying the temperature difference between the system and surroundings. Furthermore, the wind velocity and actual tracking position should be used for monitoring purposes and indicating measurement periods during which valid data is collected. As a function of the most influential quantities, beam irradiance, mean fluid and ambient temperature, steadystate collector behavior can be modeled as th a0 a1
T T (Tm Ta ) a 2Gb m a Gb Gb
2
according to EN 12975-2. Since the system under investigation is a high concentration parabolic trough, the contribution of diffuse radiation Gd is not taken into account. However, this approach is to be reconsidered for every system and testing conditions. Diffuse radiation would be of particular importance as a heat source for example, if the heat losses of a non-focused system were to be measured during the day. The standard also includes a more general, quasi dynamic collector performance model for the specific collector heat gain given by Q gain dT F Kb ( ) Gb F Kd Gd c6 uG c1 (Tm Ta ) c2 (Tm Ta ) 2 c3 u (Tm Ta ) c4 ( EL Ta4 ) c5 m . A dt This modeling approach considers IAM influences, diffuse irradiance, wind dependent heat losses, longwave irradiance and heat capacitance of the system for varying operating temperature. Although not directly measured data of the performance tests themselves, the above mentioned manufacturers’ information on properties of the HTF (specific heat capacity, density, etc.) is a vital input to the test analysis and therefore ought to be checked. 3 Uncertainty in Measurement As described in the previous section the heat gain and thermal efficiency are typical examples of measurands that cannot be measured directly but only as function of other measured quantities, namely inlet and outlet
2
temperature, mass/volumetric flow rate, ambient temperature and irradiance. Therefore, evaluating the impact of the uncertainty of the measured quantities on the uncertainty of the resulting value is of importance. 3.1
Basics 6
According to the Guide to the Expression of Uncertainty in Measurement (GUM) two types of uncertainty are generally distinguished: Type A for experimental data that is characterized by repeated measurements of a quantity and Type B for non-experimental data obtained from other sources such as experience or knowledge of the system or previously evaluated measurement data. The two types of uncertainty are evaluated separately in terms of best estimate xi and standard uncertainty ui that fully describe the data: Type A For n repeated measurements under the same conditions the best estimate for the expected value of the quantity is their arithmetic mean xi
xi xi
1 n xi , k n k 1
and the best estimate for its probability distribution is the experimental variance of the observations 1 n s2 ( X i ) ( xi ,k xi ) 2 n 1 k 1 with experimental variance of the mean being the best estimate of its variance s 2 ( xi ) , s 2 ( xi ) n resulting in an uncertainty of
u ( x i ) s ( xi ) s 2 ( xi ) . Type B Evaluating standard uncertainty from an a-priory distribution given in handbooks, calibration certificates or by manufacturers’ guarantees is particularly relevant when modelling measurement equipment uncertainty. In this case the uncertainty of the measurement is usually stated to lie within specific bounds [a -, a+] without any further information about its distribution. Therefore, the most suitable way of including all available information is by describing it with a rectangular distribution as illustrated in Figure 1.
Figure 1. Rectangular distribution (Type B) A (rectangular) distribution in turn is described by its expected value
xi X i E ( X i )
x f ( x) dx
1 a a
a
x dx
a
a a 2
and the associated variance, hence standard uncertainty
u 2 ( xi ) 2 ( x) E (( x E ( X )) 2 ) E ( x 2 ) E ( X ) 2
(a a ) 2 . 12
The best estimate of the resulting value for the target quantity is obtained by processing the best estimates of the N measured quantities according to the underlying functional relationship. The uncertainty of this target quantity,
3
the so called combined uncertainty, is calculated from the individual uncertainties of the N contributing quantities according to
f u ( y ) i 1 xi N
2 c
2
N u 2 ( xi ) i 1
1 2 f j 1 2 x i x j N
2 3 f f u 2 ( xi ) u 2 ( x j ) , xi xi x 2j
valid for independent input quantities only. The second term allows for significant non-linearities in the functional relationship. The relative contribution of N individual measured quantities is expressed by their uncertainty contribution UC 2 . f or uncertainty index UC i u i UI i 100 N i xi UCi2 i 1
The expanded uncertainty U defines an interval about the measurement value expected to encompass a large fraction of the distribution of values that could be reasonably attributed to the measurand: U k uc ( y) . The difficulty of the above approach lies in determining the coverage factor k, that itself depends on the yet unknown distribution of the measurand y. On the assumption of sufficiently large numbers of normally distributed results a coverage of 2σ (covered fraction of 0.95) is obtained for k=2. Therefore k is set to the value of 2 for this investigation. Further specifications for the choice of k are given in GUM6.
3.2 Application The exemplary performance measurement data for the present investigation stems from quasi steady-state testing of the EuroTrough test collector at the Plataforma Solar de Almería (PSA). Measurements have been grouped into operation points of reasonably similar operation conditions and consecutively been evaluated for Type A uncertainty. In terms of measurement equipment of Type B the relevant equipment specification and its translation into standard uncertainty ui is summarized in Table 1. Specified Uncertainty Uncertainty Model Sensors value reference ui² PT-100 Tamb
± 0.5°C
absolute
0.08
PT-100, 1/5 class B Tin, Tout (triple measurement)
±1/3000 Tave +0.02 K
average of three temperature meas.
1 1 Tave 0.04 12 1500
Thermocouple Type J, THTF
0.75%
measured value
1 2 0.015 THTF 12
V
± 0.75%
measured value
1 0.015 V 12
Cleanliness χ (estimate)
± 0.005
absolute
0.0005 2 3
non-linearity
0.5%
measured value
temp. dependence
2.0%
measured value
spectral selectivity non-stability
neglected neglected
measured value measured value
-
measured value
1 0.005 0.02 DNI 2 3
1st class pyrheliometer
Vortex Shedding device
pyrheliometer combined
2
2
(0.005 DNI ) 2 3 (0.02 DNI ) 2 3
Table 1. Test Loop Measurement Equipment Uncertainty The measurement uncertainty of the direct normal irradiance can be attributed to different effects that have been evaluated in a first analysis step in order to describe its total measurement uncertainty (s. Table 1). Furthermore,
4
triple measurements of the HTF temperature at collector in- and outlet have been summarized to yield one effective uncertainty for these temperature measurements. Resulting from two reflectivity measurements (one of the clean reflector and on the test day) the uncertainty of cleanliness measurements stated above is estimated. 4 Fitting The actual collector parameters result from fitting a selected model equation to the measurement data as shown in Figure 2.
Figure 2. Schematic representation of a recommended fitting procedure7 The previously evaluated combined uncertainty of the operation points serves as a weighting factor in the χ²fitting (Weighted Least Squares). The advantage of this approach is that points with relatively high levels of uncertainty have less impact on the resulting fit than those with low levels. For N operation points to be fitted with a function containing M parameter this reads8 N y y ( xi ; a1 a M ) . 2 i ui i 1 As the data is fraught with uncertainty in x and in y this weighting uncertainty is calculated as9
y u u xi 2 i
2 y
2
u x2i .
Thus, finding the minimum of χ² requires an iterative method, such as the Levenberg-Marquard algorithm. This not only yields the parameters of the best fit but also their standard uncertainties obtained form the main diagonal of the Covariance matrix. Off-diagonal elements describe the correlation between the different parameters of the fit and are required for determining the standard combined uncertainty of the predicted values using the fit according to N f u c2 ( y ) i 1 xi
N N 2 f f u ( xi ) 2 u ( xi , x j ) . x x i 1 j i 1 i j
The second term quantifies the impact of the correlation between fitting parameters. For visualisation purposes however, it is advantageous to determine the range of values about the fit that can reasonably be attributed to it. For enveloping 95% of all values this range is delimited by the highest and the lowest possible fits with respect to the expanded uncertainty of the parameters (example see Figure 4 (right)). 5
Results
5.1 Test result uncertainty In the case of the PSA test loop set-up the uncertainty analysis results in averaged uncertainty contributions for one operational point as illustrated in Figure 3. The given values represent the combination of Type A and Type B uncertainties. Breaking them further down however, shows that Type B uncertainty largely outweighs Type A uncertainty for every measurement quantity, meaning that the precision of the measurements is quite high but their accuracy is in the given range. In the case of this particular combination of measurement equipment the largest contribution to the standard uncertainty of the thermal efficiency originates from irradiance measurement equipment uncertainty followed by uncertainty in the HTF temperature measurement - hence the determined density-, the uncertainty of measuring the volumetric flow rate and mirror cleanliness. As a result of triple temperature measurement and the use of PT-100, sensor uncertainties of inlet and outlet temperature measurements turn out to be negligible for the given set-up. Compared to the uncertainty of the thermal efficiency (y-axis), the uncertainty of the reduced temperature difference (x-axis) is small and its uncertainty bar barely visible in Figure 4.
5
.
VHTF
Toutlet 5.95%0.81% THTF & HTF 27.3%
Gb 61.7%
0.59% Tinlet 3.59%
Figure 3. Average Uncertainty Contributions of Measured Quantities to the Thermal Efficiency 5.2 Fitting parameter uncertainty Using the previously stated function for steady-state thermal collector efficiency the described method yields the fitting parameters given in Table 2. The associated graphs (Figure 4) illustrate that the resulting Fit I has a maximum at elevated temperature difference, which is unsuitable to model the thermal losses increasing with temperature. This maximum of Fit I is a consequence of its non-restricted fitting parameters and the uneven spacing of measurement points, a typical situation for collector performance testing because measuring at very low temperature difference would require cooling of the fluid below ambient temperature. A way of overcoming this fitting difficulty is to restrict the linear term, in this case setting a1=0, which leads to Fit II. Furthermore, different types of fitting parameter restrictions have shown that the linear term and the uncertainty of the independent variable can be neglected without compromising the fitting result and its uncertainty for the given constellation. This facilitates the fitting procedure.
Figure 4. Fitting Results of the Efficiency Test Data (left) and the 95% Probability Range for Thermal Efficiency Predictions using the Best Fit (right), DNI=1000 W/m², from EuroTrough collector tests at PSA
6
Fit I Fit II
Parameters a1 a2 in Km²/W in (Km²/W)² -0.1388 8.44E-4 0.563E-4
a0 0.737 0.751
uc(a0) 0.0249 0.0085
Uncertainties uc(a1) in Km²/W 0.2387 -
uc(a2) in (Km²/W)² 5.22E-4 9.83E-5
evaluation unsuitable result
Table 2. Resulting Fitting Parameters and Their Uncertainty In turn, predictions using the above fit are fraught with uncertainty depending on the uncertainty of the fitting parameters. 95% of the range of values that can be reasonably attributed to a predicted value are covered by expanded parameter uncertainty on the basis of k=2. For the given fit this results in a probability area about the fit as shown in Figure 4 (right). Hence, the optical collector efficiency (for a reduced temperature difference of 0 Km2/W) can be predicted up to an uncertainty of ±1.7%-points and its thermal efficiency up to an uncertainty between ±1.7%- and ±10%-points depending on the reduced temperature difference of the operation point. This is on the assumption that the operation point itself is not fraught with uncertainty.
6 Conclusion For the given test set-up the optical efficiency of the parabolic trough collector can be determined up to an expanded uncertainty of ±1.7%-points and the thermal efficiency to an uncertainty between ±1.7%- and ±10%points depending on the reduced temperature difference. As these relatively large uncertainties are due to the uncertainty of the measurements, their budgets indicate room for improvement especially in terms of irradiance and HTF temperature measurements. For one operation point the actual measurements show good reproducibility but their accuracy is only in the given range. This further underlines the need for improving the measurement accuracy. Using three sensors for each, the concept of multiple sensors was successfully deployed for inlet and outlet temperature measurement. Likewise, three temperature sensors are recommended for measuring other temperatures, namely the heat transfer fluid temperature. This will reduce the uncertainty in determining the mass flow rate, hence heat gain accordingly. In the same way, it is recommended to reduce the uncertainty in measuring the direct normal irradiation by multiple sensors measuring simultaneously. Using higher class measuring equipment instead (secondary standard) would be an alternative but bring along increased equipment cost and calibration expenditure. Symbols a0, a1, a2 -, Km²/W, (Km²/W)² Anet m² c1, c2, c3, c4, c5, c6 cp J/(kgK) Eb W/m² EL W/m² f F’ G, Gd, Gb W/m²
n N
kg/s -
optical efficiency, thermal loss parameters net aperture area empirical collector parameters 1 specific heat capacity solar irradiance (beam direct on horizontal area) longwave irradiance functional relationship collector efficiency factor global irradiance, direct irradiance, beam irradiance (normal to collector aperture) coverage factor incidence angle modifier for direct radiation incidence angle modifier for diffuse radiation mass flow rate number of measurements number of fitting parameters
Q gain , Q solar
W/m²
heat gain, solar heat rate
t Tin, Tout, Ta, Tm u u(xi) uc
s °C m/s * *
time fluid inlet, outlet, ambient, mean temperature wind velocity standard uncertainty of xi combined uncertainty
k Kθb Kθd
m
7
U UC UI xi Xi E(x), σ(x), s(x)
* * * * * *
expanded uncertainty uncertainty contribution uncertainty index measurement quantity, best estimate expected value xi expected value, standard deviation, experimental standard deviation
*= units according to measurement quantity under consideration References and Notes 1
EN 12975-2:2006, Thermal solar systems and components - Solar collectors – Part 2: Test method ASTM 905: Standard Test Method for Determining Thermal Performance of Tracking Concentrating Solar Collectors, 2001. 3 H. Müller-Steinhagen, S. Fischer and E. Lüpfert: Efficiency Testing of Parabolic Trough Collectors Using the Quasi-Dynamic Test Procedure According to the European Standard EN 12975, SolarPACES Symposium 2006, Seville, Spain. 4 E. Lüpfert, K. Pottler, S. Ulmer, K.-J. Riffelmann, A. Neumann, B. Schiricke: Parabolic Trough Optical Performance Analysis Techniques; J. of Solar Energy Engineering, Vol. 129, p.147-152, May 2007. 5 E. Lüpfert U. Herrmann, H. Price, E. Zarza and R. Kistner : Towards Standard Performance Analysis for Parabolic Trough Collector Fields, Proc. 12th SolarPACES Int. Symposium, 2004, Oxaca, Mexico. 6 Guide to the Expression of Uncertainty in Measurement, International Organization for Standardization, 1995 Switzerland. 7 E. Mathioulakis, K. Voropoulos and V. Belessiotis: Assessment of Uncertainty in Solar Collector Modeling and Testing, Solar Energy, Vol.66, p.337-347, 1999. 8 W. Press, S. Teukolsky, W. Vetterling, and B. Flannery: Numerical Recipes – The Art of Scientific Computing, Cambridge University Press, second edition, 1992, Cambridge, England. 9 N. Bogdanova, L. Todorova: Algorithm for Fitting Experimental Data with Errors in Both Variables, Proc. Relativistic Nuclear Physics from 100 MeV to TeV, 2001, Varna, Bulgaria. 2
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