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Research Papers

# Solar Field Optical Characterization at Stillwater Geothermal/Solar Hybrid PlantOPEN ACCESS

[+] Author and Article Information
Guangdong Zhu

National Renewable Energy Laboratory,
15013 Denver West Parkway,
Golden, CO 80401
e-mail: Guangdong.Zhu@nrel.gov

Craig Turchi

National Renewable Energy Laboratory,
15013 Denver West Parkway,
Golden, CO 80401

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received July 26, 2016; final manuscript received December 2, 2016; published online January 27, 2017. Assoc. Editor: Wojciech Lipinski.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Sol. Energy Eng 139(3), 031002 (Jan 27, 2017) (10 pages) Paper No: SOL-16-1342; doi: 10.1115/1.4035518 History: Received July 26, 2016; Revised December 02, 2016

## Abstract

Concentrating solar power (CSP) can provide additional thermal energy to boost geothermal plant power generation. For a newly constructed solar field at a geothermal power plant site, it is critical to properly characterize its performance so that the prediction of thermal power generation can be derived to develop an optimum operating strategy for a hybrid system. In the past, laboratory characterization of a solar collector has often extended into the solar field performance model and has been used to predict the actual solar field performance, disregarding realistic impacting factors. In this work, an extensive measurement on mirror slope error and receiver position error has been performed in the field by using the optical characterization tool called distant observer (DO). Combining a solar reflectance sampling procedure, a newly developed solar characterization program called firstoptic and public software for annual performance modeling called system advisor model (SAM), a comprehensive solar field optical characterization has been conducted, thus allowing for an informed prediction of solar field annual performance. The paper illustrates this detailed solar field optical characterization procedure and demonstrates how the results help to quantify an appropriate tracking-correction strategy to improve solar field performance. In particular, it is found that an appropriate tracking-offset algorithm can improve the solar field performance by about 15%. The work here provides a valuable reference for the growing CSP industry.

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## Introduction

Concentrating solar power (CSP) uses mirrors to concentrate sunlight and convert solar power into heat, which can then be directed to a thermodynamic cycle to generate electricity [14]. As a mature CSP technology, parabolic troughs can produce heat at a temperature of 400 °C or higher [2,5] and generate electricity through a standalone power plant. In addition, the produced heat can be hybridized naturally with other types of heat sources to produce electricity, such as the integrated solar combined-cycle [6,7] and geothermal/solar hybrid systems [8]. For the latter concept, adding solar heat from CSP to a geothermal power plant can boost power generation during the daytime, when the increasing ambient temperature and/or degrading geothermal resource result in lower power production.

The Stillwater geothermal plant located in Fallon, NV is an example of a geothermal operation where Enel Green Power has recently adopted solar hybridization [9,10]. The solar field is about 17 MWth at the design point and uses SkyTrough parabolic trough collectors []. The heat-transfer fluid (HTF) in the trough receiver is pressurized water, and the design HTF inlet and outlet temperatures are about 149 °C and 199 °C, respectively. The heated HTF is used to heat the brine flow with a degraded temperature. Solar field specifications at the Stillwater plant site are summarized in Table 1.

A key task is to properly characterize the performance of the new Stillwater solar field. Optical characterization of a utility-scale solar field is a broad topic. SolarPACES has developed multiple international guidelines on solar mirror reflectance [12,13] and solar system annual modeling [1416] that provide guidance to the growing CSP industry. Solar reflectance correlates mirror reflectance with the solar spectrum [13,1722] and becomes a fairly complex topic in the CSP applications. Solar reflectance used to be measured at a single small acceptance angle (often with a narrow band of visible light wavelength) and now is more appropriately modeled in a more comprehensive way as more modern instrumentation becomes available. No guidelines exist regarding optical characterization of the solar field. One major reason is that a variety of optical tools exist and each has its limitations regarding measurement results and conditions [2328]. Most tools are designed to measure one specific type of optical error, such as mirror specular reflectance [12,19], mirror slope error [23,24,2732], or receiver temperature [3335]. Furthermore, very few tools are suitable for use in the field. Past work [12,19,2325,2731,3335] has predicted solar field performance based on laboratory measurement; such prediction inappropriately disregards the deviation of a solar collector from its design-point performance measured in the laboratory.

To fully characterize the optical performance of a solar field, one needs to obtain precise optical and geometric measurements of solar collectors in the field, including mirror specular reflectance, receiver absorptance and receiver glass-envelope transmittance, mirror slope error, receiver position error, and collector tracking error. Among these, mirror slope error has been considered the dominant error source [36,37]. Other error sources, such as mirror reflectance, receiver absorptance, and receiver position error, could also significantly impact the collector performance, depending on specific cases [38]. In this work, mirror specular reflectance, mirror slope error, and receiver position error were measured in the field to best predict the actual solar field performance. Mirror reflectance measurements use a newly developed specular reflectance model, and mirror slope error and receiver position error measurements use a newly developed optical tool called distant observer (DO) [39,40]. DO is one of the very few tools suitable for outdoor field environments, along with the airborne method proposed by Prahl and others [32,41].

The focus of this paper is to: (1) exhibit a comprehensive and accurate field optical characterization by using state-of-the-art models and tools, which will provide valuable guidance to future field optical characterization work; and (2) employ an optical model and thermal performance model to predict annual thermal energy production as a function of time. The modeling of a geothermal/solar thermal hybrid system is a separate work and can be found elsewhere [9].

In this paper, Sec. 2 gives the optical test plan. Sections 3 and 4 present and discuss in detail the solar reflectance measurements and collector optical error measurements, respectively. Sections 5 and 6 provide calculations of the overall optical performance and annual energy generation of the solar field, based on the optical measurement results. Finally, discussion and conclusions are given in Secs. 7 and 8.

## Optical Test Plan

The optical tools used in this field optical test are summarized in Table 2. By using these tools, measurements of mirror specular reflectance, mirror slope error, and receiver position error can be conducted in the field. The solar field at the Stillwater geothermal/solar plant includes 11 SkyTrough collector loops, each of which consists of four solar collector assemblies (SCAs). Each SCA includes eight solar collector elements/modules (SCEs), about 110 m long and 6 m in aperture width. The solar field layout is a standard row-to-row formation. See Table 1 for further properties of the Stillwater plant.

The objective of the optical test is to obtain the average optical performance of the solar field. In reality, it is not possible to measure every single mirror facet or receiver tube. A sampling process needs to be developed to manage measurement time and ensure sufficient accuracy at the same time. For this solar field, loop 5 is equipped with sophisticated instrumentation to measure real-time loop temperature, mass flow rate, and pressure, and it is intended to be used as a test loop for the plant acceptance test to represent the entire solar field. For this reason, a detailed optical test plan is specifically designed for the whole field and loop 5, as summarized in Table 3.

It is straightforward and efficient (about 30 readings per hour) to use reflectometers (D&S 15R and 410-Solar) to measure mirror reflectance in the field [13,42,43]. The DO implementation requires certain preparation steps and may take a half hour to 1 h to measure each module [39,40]. The measurement number for D&S was selected based on previous work [13]; because this is the first time to implement a slope error/receiver position error measurement in the field, a maximum number of sampled measurements is selected during the planned two-day test period.

## Solar Reflectance Measurement

For the SkyTrough collector as specified in Table 1, the receiver will only accept the reflected sun rays within about 1.35 deg around the specular direction, outside of which the light will not be intercepted/absorbed. It is the specular reflectance of a mirror that determines optical performance of a trough collector (and other types of CSP collectors). Many specular reflectance models have been proposed and often suffer from certain theoretical/realistic limitations [12,13], such as only being suitable to specific instrumentation or a specific type of reflector. Here, a newly proposed solar reflectance model is adopted [13] that is generic and flexible in accommodating various levels of measurements.

###### Solar Reflectance Model.

The mathematical model of solar-weighted specular reflection is defined as follows: Display Formula

(1)$ρspecSW(φ)=ρspec,totSW∫0Ω(φ)fSW(φ)⋅dΩ$

Here, $ρspecSW$ is the solar-weighted specular reflectance at the acceptance angle $φ$, and $ρspec,totSW$ is the total solar-weighted specular reflectance. A general description of mirror reflection is provided in Fig. 1.

A simple and effective form for mirror specularity profile is a Gaussian distribution Display Formula

(2)

The coefficient ensures an overall integral equal to 1 when assuming $σs≪1$. Here, $σs$ is the root mean square (RMS) of the Gaussian function, expressed in radians.

###### Solar Reflectance Measurements.

First, the D&S R15 reflectometer [13,42] is used to measure the mirror reflectance across the entire solar field. The measurements are plotted for different loops in Fig. 2. The mirror reflectance is measured at a full acceptance angle of 25 mrad and at a single wavelength of 660 nm. As seen in the figure, loops 1, 5, 7, 9, and 10 have a slightly higher reflectance than the average. Some reflectance variance across loops in the figure comes from measurement uncertainties (including instrumentation repeatability of ±0.2%), whereas other variance comes from damage to reflector panels in certain loops (e.g., loop 8) due to rainwater trapped within some mirror panel storage containers during their long-time outdoor storage prior to solar field construction.

Next, for selected mirror modules, mirror reflectance at various acceptance angles is also measured using the D&S reflectometer. The results are plotted in Fig. 3, and the measurements by the D&S reflectometer are denoted by

Display Formula

(3)$ρspc660,m(φi), i=1,2,3$

Here, m is the sample number, m = 1, 2,…, Mspc, and Display Formula

(4)$φ1=3.5 mrad; φ2=12.5 mrad; φ3=23 mrad$

In the formula, the half acceptance angle is used; the full acceptance angle is twice the half acceptance angle, which is more often referred to in practice.

Specular reflectance increases with acceptance angle. How fast the specular reflectance increases with the increasing acceptance angle defines the mirror specularity. In addition, another reflectometer, the SOC 410-Solar [43], is also used to measure solar-weighted hemispherical and specular reflectance. The two reflectometers complement one another—the D&S measures reflectance at various acceptance angles, but at a single wavelength, whereas the SOC measures solar-weighted reflectance with multiple bands of wavelength representing the solar spectrum, but at a single large acceptance angle.

###### Solar Field Average Reflectance Characterization.

Based on the data over varying acceptance angles, a single-Gaussian specularity profile can be derived. For three measurements at of each mirror panel m, Eqs. (1)(3) expand to Display Formula

(5)$ρspec,tot660,m⋅(1−e−(φi2⋅σ660nm)2)=ρspec660,m(φi), i=1,2,3$

The unknown parameters $ρspec,tot660,m$ and $σ660nm$ can be solved from the equations above by using least-squares fitting, based on the measurements at three acceptance angles. The single Gaussian fitting curves are then plotted against the raw data points in Fig. 4.

Combined with the average solar field reflectance and the solar-weighted reflectance, the average solar-weighted reflectance is calculated for the whole solar field and loop 5 in Table 4. The average solar-weighted reflectance is derived using the solar reflectance model in Sec. 3.1. More specifically

Display Formula

(6)$ρspec,totSW¯⋅(1−e−(φ2⋅σSW¯)2)=ρspecSW¯(φ)$

Here, the calculation of solar-weighted values is simplified with available measurement capabilities by assuming Display Formula

(7)$ρspec,totSW¯=ρspec,tot660¯⋅(ρspec,SOCSWρspec,SOC660)¯$
Display Formula
(8)$σSW¯=σ660nm$

Here, $ρspec,totSW¯$ is the average solar-weighted specular reflectance derived from the D&S measurements. $ρspec,SOCSW$ and $ρspec,SOC660nm$ are the solar-weighted value and the 660-nm-wavelength value measured by the SOC reflectometer, respectively; and $(ρspec,SOCSW/ρspec,SOC660nm)¯$ is the average of the ratio of two reflectance measurements by the SOC reflectometer. $σSW¯$ is the solar-weighted specularity RMS value. The solar reflectance measurements using the SOC reflectometer comply with solar reflectance test standard ASTM E903 and solar spectrum standard ASTM G173. Equations (7) and (8) are used to approximate solar-weighted specular reflectance due to the availability of in-field instrumentation according to the SolarPACES solar mirror reflectance measurement guideline [12].

The measurement uncertainty at a 95% confidence level is also given for the average values and is calculated by using a simple student t method based on the number of measurements.

## Measurement of Mirror Slope Error and Receiver Position Error

DO is an optical tool developed by NREL to characterize solar collector optical errors, including mirror slope error and receiver alignment/position error [39,40]. It uses photogrammetry to capture the collector error through the reflection images of the receiver on the reflector. An example reflection image is given in Fig. 5. The distortion of the receiver reflection indicates the inaccurate mirror shape and/or misplaced receiver locations. Four targets (black dot centered on a white background) are attached on the collector module corners and provide the position reference for the photogrammetry analysis, as shown in Fig. 6. The original image can then be rescaled to a regular square image (right image in Fig. 5). By combining with the camera optical specifications, the mirror slope error can be derived for one horizontal segment of the mirror module by using a sophisticated software package. The characterization of the full collector module requires a series of photos to be taken, while the receiver reflection sweeps from one module edge to the other with the collector's rotation. During this measurement, the collector tracking angles stay between 10 deg and 20 deg above the horizon. It should be noted that the typical operating range is 10–170 deg. Thus, one underlying assumption is that the slope error measurement does not vary at a significant degree with varying collector orientation.

The receiver position error along x and z directions are plotted for one 13.9-m-long module at the Stillwater plant in Fig. 7. Note that the receiver position error indicates the receivers' distortion due to gravity. The average position error is about 26.4 mm along x and 11.0 mm along z. The SkyTrough collector is designed with some receivers mounted below focus and some above, so that when they expand at operating temperature, all of the receivers move closer into focus. The receiver offset along z will be reduced under normal operational conditions.

The mirror slope error on the entire sample mirror module is also calculated and plotted in Fig. 8. The average and RMS values of the mirror slope error are −3.8 mrad and 3.1 mrad, respectively. Note that the receiver misalignment is included as part of the mirror slope error.

A number of collector modules were measured using DO. A total of 12 data sets were identified to provide valid measurements. The mean value and RMS of the mirror slope error for the valid data sets are plotted in Fig. 9. The average mean value is about deg 4.0 mrad. This nonzero mean value of slope error is due to gravity-induced displacement of the receiver and frame, which is greatest at low tracking angles. The average RMS value is about 3.0 mrad.

## Optical Characterization of Solar Collector

###### Intercept Factor.

The optical performance of a solar collector largely depends on two aspects: optical properties and geometric accuracy. Optical properties include mirror reflectance, absorber-tube absorptivity, and receiver-envelope transmissivity; geometric accuracy refers to mirror slope error, receiver position error, and tracking error. The solar collector optical specifications and optical error measurements are summarized for the Stillwater solar field in Table 5.

Once the collector optical characterization parameters are obtained, an optical performance calculation program called firstoptic can be used to derive the collector optical performance. firstoptic employs the most accurate optical treatment of collector optical error measurements, and it derives analytical mathematical formulae to calculate the intercept factor of a trough collector [37,38,44]. It can provide fast, accurate calculation of intercept factor and incidence-angle modifier (IAM) [44]. The intercept factor for each collector module is plotted in Fig. 10. The intercept factor varies from 0.65 to 0.95, closely correlated to the slope error measurements in Fig. 9 because the collector slope error typically dominates the collector performance.

###### Tracking Offset.

The predicted intercept factor values above are substantially lower than the anticipated target performance. It can be seen that the slope error magnitude strongly impacts the collector performance. From Fig. 9, the mean value of each data set is negative between −2.9 mrad and −5.0 mrad. Theoretically, the slope error with a mean of −1 mrad can be compensated by +2 mrad tracking error, which results in an effective slope error with a mean of 0 mrad. Thus, this tracking-offset strategy can be applied to each collector sample with exactly twice the mean value of the measured slope error. The intercept factor with appropriate tracking offset for each measured collector module is recalculated against the one without the tracking correction in Fig. 11. Here, it is assumed that the tracking-offset algorithm is able to reduce the mean value of slope error for any collector to be 1 mrad. As seen in the figure, the collector performance is improved substantially. With the tracking offset, the intercept factor becomes close to the unity for all cases. The average intercept factor increases from 0.827 without tracking offset to 0.991 with tracking offset. According to the vendor, field calibration of the tracking-offset algorithm is an anticipated step of the field commissioning, and it clearly improves solar field performance to a significant degree.

The large slope error is induced by the effect of gravity on the collector. The gravity-induced deflection is greatest at low tracking angles and is less when the collector is oriented straight up. When the impact of gravity-induced deflection varies with tracking angle, the tracking-offset value is a function of collector position. In reality, a tracking-offset algorithm can be directly incorporated into the tracking control program of the drive so that the collector performance can be improved.

###### Incidence-Angle Modifier (IAM).

An IAM is typically used to describe the solar collector performance under nonzero incidence angles, that is, for different sun positions throughout the year. A common form for the IAM is Display Formula

(9)$IAM(θ)=kIAM,0+kIAM,1⋅θ cos(θ)+kIAM,2⋅θ2 cos(θ)+kIAM,3⋅θ3 cos(θ)$

The fitting function is typically of second or third order. In the work described here, it is found that a better fit is provided with the third-order function because of its higher accuracy. In either form, the optical efficiency at a nonzero incidence angle is given by Display Formula

(10)$η(θ)=ηo⋅IAM(θ)=ρταγ⋅IAM(θ)$

Here, θ is the solar incidence angle in radians (always positive in Eq. (9)), ρ is the parabolic mirror reflectivity, τ is the receiver glass-envelope transmissivity, α is the average receiver coating absorptivity, and γ is the collector intercept factor. The nominal optical performance and the IAM coefficients are provided in Table 6. The IAM is also plotted as a function of incidence angle in Fig. 12.

## Annual Thermal Generation From Solar Field

After detailed solar field optical characterization, system advisor model (SAM) software can be used to calculate annual energy generation performance of a solar field [45]. SAM was developed by NREL to evaluate technical and economic performance of renewable energy systems and is available to the public. SAM allows users to configure a renewable energy system with specific technology and evaluate its performance at certain locations under specific financial conditions. With a temporal weather resource file at a location, SAM can calculate annual performance of a solar field, such as hourly based thermal energy, electricity, and cash flow. Combined with system cost models, SAM can calculate financial matrices of a solar energy system, such as levelized cost of energy (LCOE) and internal rate of return (IRR).

Models for different renewable energy systems are regularly added and updated by NREL researchers. Currently, however, a solar/geothermal performance model is not available in SAM. The strategy to estimate the hybrid plant performance is to combine SMA's solar field performance module and a separate geothermal power-cycle model developed by Idaho National Laboratory (INL). The SAM solar field performance module uses the dimensions of the Stillwater solar field and the collector/receiver parameters from the solar collector manufacturers (Huiyin [46]). Using a local weather file at the hybrid plant location and optical characterization results from Tables 5 and 6, the SAM solar field module can calculate the thermal power generation as a function of time. The design outlet temperature of the solar field is about 200 °C, but varies during real-world operation because the HTF mass flow cannot be readily controlled at the actual plant.

Thermal energy generation results from SAM can be input to the INL geothermal power-cycle model. The INL model combines these results with the solar heat input and geothermal heat to then calculate real-time power generation. The detailed modeling process and results can be found in Ref. [9].

Three SAM cases are summarized in Table 7, and the hourly output for a typical year in Stillwater, NV, is given in Fig. 13. Case 1 provides a reference annual performance for the Stillwater solar field by using the default performance metrics provided by the vendors; case 2 and case 3 are the performance modeling based on the field test results given earlier in this paper. Case 2 does not apply the tracking-offset algorithm, whereas case 3 does include the algorithm. The comparison shows that the actual solar field performance will be about 9% lower than that expected from the reference case (case 1). The vendor indicated that it was a reasonable value considering the storage history and fabrication details of the Stillwater equipment. The greatest deviations are in the mirror reflectance (−3%) and geometric accuracy of the collector (−7%).

It is also shown that a significant boost in performance can be obtained if an appropriate tracking-offset algorithm is implemented. In the perfect case, this tracking offset could boost the as-measured performance by almost 15%, as shown by case 3 in Table 7.

## Discussion

Optical characterization is always a great challenge in the field, especially at a utility scale. Practically speaking, it is impossible to measure every solar collector module in the field; therefore, a statistical sampling procedure is implemented to ensure a certain level of measurement uncertainties. In reality, numerous factors affect the prediction of solar field performance. So the overall uncertainty of the nominal optical/thermal efficiency may be at a level of 3–5% [15]. By taking this as a reference, an appropriate number of sampling measurements can be determined. In the real world, the measurement accuracy is often constrained by certain time demands, and the maximum number of measurements is typically taken within the allowable test period. If the measurement uncertainty is not acceptable, additional measurements will be needed.

It is more complex to calculate the uncertainty of the average solar field optical efficiency. As shown in Fig. 11, with tracking offset, the collector intercept factor values are all above 0.99, and their variation is not obviously correlated with the slope error variation. This is because the relatively large receiver (80-mm diameter) can tolerate a larger optical error. Thus, the uncertainty of solar field average intercept factor is very small compared with the uncertainty of the solar field average slope error. The dominant source of solar field uncertainty is therefore the uncertainty of the solar-weighted total specular reflectance. According to Eq. (10), the uncertainty of solar-weighted total reflectance results in the same amount of uncertainty on the performance prediction, assuming that the uncertainty from other parameters (all manufacturer's values) can be reasonably neglected.

It is also noted that not every optical error source is measured in the field. Measuring certain optical metrics, such as receiver absorptance and receiver-glass transmittance, are not feasible in the field due to unavailability of required instruments. The sun shape is always varying under instantaneous weather conditions. In addition, the work in this paper measured mirror reflectance, mirror specularity, mirror slope error, and receiver position error, and it provides the most comprehensive optical characterization of a large-scale solar field. The metrics missed by the analysis are mirror slope error along the longitudinal direction and collector error as a function of tracking position. The former was shown to have a minimal impact on collector optical performance compared with the measured mirror slope error along transversal direction [44,47]. The impact of the latter is still unknown.

## Conclusions

To conclude, a comprehensive optical test has been performed at the Stillwater plant solar field. First, the calculation of solar field average solar-weighted reflectance and specularity is allowed by measurements of mirror specular reflectance at various acceptance sizes and solar-weighted reflectance. The mirror slope error and receiver position error are measured by DO, one of very few tools suitable for both types of collector errors in the field condition. During the optical test, sufficient measurement data were taken to obtain the solar field average values. To the authors' knowledge, this represents the most comprehensive optical characterization in a utility-scale field.

By employing the firstoptic software, the measurement results are readily interpreted to derive the solar field average optical performance under normal incidence and non-normal incidence angle. Then, all measured and derived optical performance metrics are input to SAM for the thermal energy annual performance at an hourly basis by using local satellite weather data. This analysis indicates that annual delivered energy from the solar field would be about 9% lower than the collector manufacturer's prediction if an appropriate tracking-offset algorithm is not implemented. The analysis also shows that further calibration incorporating an SCA tracking-offset algorithm can potentially improve performance by as much as 15%.

The detailed performance predictions from SAM will serve as an input to INL's plant model of the Stillwater power block, thus allowing engineers to model plant performance and explore optimal integration strategies of solar thermal power into a geothermal binary power-cycle.

The work in this paper illustrates a detailed process on how to collect and interpret various types of measurement data by using state-of-the-art optical tools and models, and it will serve as a valuable guideline in the area of solar field optical characterization.

## Acknowledgements

The work at NREL was supported by the U.S. Department of Energy under Contract No. DE-AC36-08-GO28308. Funding was supplied by the DOE's Geothermal Technologies Office (GTO). The authors wish to thank Tim Wendelin, Dale Jenne (from NREL), and Daniel Wendt (from INL) for their assistance in taking measurements in the field. Special thanks go to Sander Cohan, Lorenzo Angelini, Alessio De Marzo, and Fabrizio Bizzarri from Enel Green Power for their kind and most considerable support for our test measurements on site.

## Nomenclature

• $f$ =

mirror specularity profile distribution function

• $α$ =

• $γ$ =

collector intercept factor

• $η$ =

optical efficiency at normal incidence for NSO solar field

• $θ$ =

incidence angle with respect to mirror surface normal, rad or deg

• $λ$ =

light wavelength, nm

• $ρ$ =

reflectance

• $ρspecSW$ =

solar-weighted specular reflectance

• $ρspec,totSW$ =

solar-weighted total specular reflectance

• $ρspec,tot660$ =

total specular reflectance at 660-nm wavelength

• $ρspec,tot660¯$ =

solar field average of total specular reflectance at 660-nm wavelength

• $σs$ =

overall RMS value of a specularity profile distribution function, mrad

• $σsSW$ =

solar-weighted mirror specularity RMS of NSO, mrad

• $τ$ =

• $φ$ =

acceptance (zenith) angle with respect to the specular direction, mrad

• $Ω$ =

solid angle, sr

Acronyms
• CSP =

concentrating solar power

• D&S =

Devices and Services

• IAM =

incidence-angle modifier

• MW =

megawatts

• NREL =

National Renewable Energy Laboratory

• RMS =

root mean square

• SCA =

solar collector assembly

• SCE =

solar collector element

• SOC =

Surface Optics Corporation

• SW =

solar-weighted

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Arvesen, J. C. , Greffin, R. N. , and Pearson, B. D. , 1969, “ Determination of Extraterrestrial Solar Spectral Irradiance From a Research Aircraft,” Appl. Opt., 8(11), pp. 2215–2232. [PubMed]
Heimsath, A. , Kutscheidt, G. , and Nitz, P. , 2010, “ Detailed Optical Characterization of Reflector Materials for CSP Applications,” SolarPACES 2010, Perpignan, France, Sept. 21–24.
Nicodemus, F. E. , Richmond, J. C. , Hsia, J. J. , Ginsberg, I. W. , and Limperis, T. , 1977, “ Geometrical Considerations and Nomenclature for Reflectance,” National Bureau of Standards, Department of Commerce, Washington, DC.
Andraka, C. , Sadlon, S. , Myer, B. , Trapeznikov, K. , and Liebner, C. , 2009, “ SOFAST: Sandia Optical Fringe Analysis Slope Tool for Mirror Characterization,” SolarPACES 2009, Berlin, Germany, Sept. 15–18.
Wendelin, T. , May, K. , and Gee, R. , 2006, “ Video Scanning Hartmann Optical Testing of State-of-the-Art Parabolic Trough Concentrators,” ASME Paper No. ISEC2006-99172.
Pottler, K. , Lupfert, E. , Johnston, G. , and Shortis, M. , 2005, “ Photogrammetry: A Powerful Tool for Geometric Analysis of Solar Concentrators and Their Components,” ASME J. Sol. Energy Eng., 127(1), pp. 94–101.
Roger, M. , Prahl, C. , and Ulmer, S. , 2008, “ Fast Determination of Heliostat Shape and Orientation by Edge Detection and Photogrammetry,” 14th CSP SolarPACES Symposium, Las Vegas, NV, Mar. 4–7.
Pottler, K. , Lupfert, E. , Ulmer, S. , Landmann, M. , and Mutzel, M. , 2011, “ Geometric Evaluation of Parabolic Trough Collector Module Ultimate Trough,” CSP Services GmbH, Cologne, Germany.
Ulmer, S. , Heinz, B. , Pottler, K. , and Lupfert, E. , 2009, “ Slope Error Measurements of Parabolic Troughs Using the Reflected Image of the Absorber Tube,” ASME J. Sol. Energy Eng., 131(1), p. 011014.
Knauer, M. C. , Kaminski, J. , and Hausler, G. , 2004, “ Phase Measuring Deflectometry: A New Approach to Measure Specular Free-Form Surfaces,” Proc. SPIE 5457, p. 366.
Burke, J. , Li, W. , Heimsath, A. , von Kopylow, C. , and Bergmann, R. B. , 2013, “ Qualifying Parabolic Mirrors With Deflectometry,” J. Eur. Opt. Soc., 8, p. 13014.
Heimsath, A. , Platzer, W. , Bothe, T. , and Wansong, L. , 2008, “ Characterisation of Optical Components for Linear Fresnel Collectors by Fringe Reflection Method,” SolarPACES Conference, Las Vegas, NV, Mar. 4–7.
Diver, R. B. , and Moss, T. A. , 2007, “ Practical Field Alignment of Parabolic Trough Solar Concentrators,” ASME J. Sol. Energy Eng., 129(2), pp. 153–159.
Burkholder, F. , and Kutscher, C. , 2009, “ Heat Loss Testing of Schott's 2008 PTR70 Parabolic Trough Receiver,” National Renewable Energy Laboratory, Golden, CO, NREL Report No. NREL/TP-5500-45633.
Kutscher, C. , Burkholder, F. , and Stynes, K. , 2012, “ Generation of a Parabolic Trough Collector Efficiency Curve From Separate Measurements of Outdoor Optical Efficiency and Indoor Receiver Heat Loss,” ASME J. Sol. Energy Eng., 134(1), p. 011012.
NREL, “ Heat Collection Element (HCE) Temperature Survey,” National Renewable Energy Laboratory, Golden, CO, accessed in 2015,
Gee, R. , Brost, R. , Zhu, G. , and Jorgensen, G. , 2010, “ An Improved Method for Characterizing Reflector Specularity for Parabolic Concentrators,” 16th SolarPACES, Perpignan, France, Sept. 21–24.
Zhu, G. , and Lewandowski, A. , 2012, “ A New Optical Evaluation Approach for Parabolic Trough Collectors: First-Principle OPTical Intercept Calculation (FirstOPTIC),” ASME J. Sol. Energy Eng., 134(4), p. 041005.
Zhu, G. , 2013, “ Study on the Optical Impact of Receiver Position Error on Parabolic Trough Collectors,” ASME J. Sol. Energy Eng., 135(3), p. 031021.
Stynes, K. , and Ihas, B. , 2012, “ Slope Error Measurement Tool for Solar Parabolic Through Collectors,” World Renewable Energy Forum, Denver, CO, May 13–17.
Stynes, K. , and Ihas, B. , 2012, “ Absorber Alignment Measurement Tool for Solar Parabolic Trough Collectors,” ASME Paper No. ES2012-91283.
Prahl, C. , Stanicki, B. , Hilgert, C. , Ulmer, S. , and Roger, M. , 2011, “ Airborne Shape Measurement of Parabolic Trough Collector Fields,” 17th SolarPACES Conference, Granada, Spain, Sept. 20–23.
Devices and Services, 2014, “ Portable Specular Reflectometer 15R-USB,” Devices and Services, Co., Dallas, TX, accessed in 2015,
SOC, 2009, “ SOC-100 User's Manual—Hemispherical Directional Reflectometer (HDR),” Surface Optics Corporations, San Diego, CA.
Binotti, M. , Zhu, G. , Gray, A. , Manzolini, G. , and Silva, P. , 2013, “ Geometric Analysis of Three-Dimensional Effects of Parabolic Trough Collectors,” Sol. Energy, 88, pp. 88–96.
NREL, 2015, “ System Advisor Model 2015.1.30,” National Renewable Energy Laboratory, Golden, CO, accessed in 2015,
Sun 2 Market Solutions, 2012, “ Performance Comparison of Huiyin's Vacuum Receiver Tubes,” Huiyin-Group, Sun to Market Solutions S.L., Madrid, Spain, accessed in 2015,
Bendt, P. , Rabl, A. , Gaul, H. W. , and Reed, K. A. , 1979, “ Optical Analysis and Optimization of Line Focus Solar Collectors,” Solar Energy Research Institute, Golden, CO.
View article in PDF format.

## References

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Zhu, G. , Kearney, D. , and Mehos, M. , 2014, “ On Characterization and Measurement of Average Solar Field Mirror Reflectance in Utility-Scale Concentrating Solar Power Plants,” Sol. Energy, 99, pp. 185–202.
Eck, M. , Barroso, H. , Blanco, M. , Burgaleta, J.-I. , Dersch, J. , Feldhoff, J. F. , Garcia-Barberena, J. , Gonzalez, L. , Hirsch, T. , Ho, C. , Kolb, G. , Neises, T. , Serrano, J. A. , Tenz, D. , Wagner, M. , and Zhu, G. , 2011, “ guiSmo: Guidelines for CSP Performance Modeling—Present Status of the SolarPACES Task-1 Project,” 17th SolarPACES Conference, Granada, Spain, Sept. 20–23.
Kearney, D ., 2011, “ Utility-Scale Parabolic Trough Solar Systems: Performance Acceptance Test Guidelines,” National Renewable Energy Laboratory, Golden, CO, Report No. NREL/SR-5500-48895.
Kearney, D. , 2013, “ Utility-Scale Power Tower Solar Systems: Performance Acceptance Test Guidelines,” National Renewable Energy Laboratory, Golden, CO, Report No. NREL/SR-5500-57272.
Pettit, R. B. , 1977, “ Characterization of the Reflected Beam Profile of Solar Mirror Materials,” Sol. Energy, 19(6), pp. 733–741.
Montecchi, M. , 2013, “ Approximated Method for Modelling Hemispherical Reflectance and Evaluating Near-Specular Reflectance of CSP Mirrors,” Sol. Energy, 92, pp. 280–287.
Meyen, S. , Lupfert, E. , Pernpeintner, J. , and Fend, T. , 2009, “ Optical Characterization of Reflector Material for Concentrating Solar Power Technology,” SolarPACES 2009, Berlin, Germany, Sept. 15–18.
Arvesen, J. C. , Greffin, R. N. , and Pearson, B. D. , 1969, “ Determination of Extraterrestrial Solar Spectral Irradiance From a Research Aircraft,” Appl. Opt., 8(11), pp. 2215–2232. [PubMed]
Heimsath, A. , Kutscheidt, G. , and Nitz, P. , 2010, “ Detailed Optical Characterization of Reflector Materials for CSP Applications,” SolarPACES 2010, Perpignan, France, Sept. 21–24.
Nicodemus, F. E. , Richmond, J. C. , Hsia, J. J. , Ginsberg, I. W. , and Limperis, T. , 1977, “ Geometrical Considerations and Nomenclature for Reflectance,” National Bureau of Standards, Department of Commerce, Washington, DC.
Andraka, C. , Sadlon, S. , Myer, B. , Trapeznikov, K. , and Liebner, C. , 2009, “ SOFAST: Sandia Optical Fringe Analysis Slope Tool for Mirror Characterization,” SolarPACES 2009, Berlin, Germany, Sept. 15–18.
Wendelin, T. , May, K. , and Gee, R. , 2006, “ Video Scanning Hartmann Optical Testing of State-of-the-Art Parabolic Trough Concentrators,” ASME Paper No. ISEC2006-99172.
Pottler, K. , Lupfert, E. , Johnston, G. , and Shortis, M. , 2005, “ Photogrammetry: A Powerful Tool for Geometric Analysis of Solar Concentrators and Their Components,” ASME J. Sol. Energy Eng., 127(1), pp. 94–101.
Roger, M. , Prahl, C. , and Ulmer, S. , 2008, “ Fast Determination of Heliostat Shape and Orientation by Edge Detection and Photogrammetry,” 14th CSP SolarPACES Symposium, Las Vegas, NV, Mar. 4–7.
Pottler, K. , Lupfert, E. , Ulmer, S. , Landmann, M. , and Mutzel, M. , 2011, “ Geometric Evaluation of Parabolic Trough Collector Module Ultimate Trough,” CSP Services GmbH, Cologne, Germany.
Ulmer, S. , Heinz, B. , Pottler, K. , and Lupfert, E. , 2009, “ Slope Error Measurements of Parabolic Troughs Using the Reflected Image of the Absorber Tube,” ASME J. Sol. Energy Eng., 131(1), p. 011014.
Knauer, M. C. , Kaminski, J. , and Hausler, G. , 2004, “ Phase Measuring Deflectometry: A New Approach to Measure Specular Free-Form Surfaces,” Proc. SPIE 5457, p. 366.
Burke, J. , Li, W. , Heimsath, A. , von Kopylow, C. , and Bergmann, R. B. , 2013, “ Qualifying Parabolic Mirrors With Deflectometry,” J. Eur. Opt. Soc., 8, p. 13014.
Heimsath, A. , Platzer, W. , Bothe, T. , and Wansong, L. , 2008, “ Characterisation of Optical Components for Linear Fresnel Collectors by Fringe Reflection Method,” SolarPACES Conference, Las Vegas, NV, Mar. 4–7.
Diver, R. B. , and Moss, T. A. , 2007, “ Practical Field Alignment of Parabolic Trough Solar Concentrators,” ASME J. Sol. Energy Eng., 129(2), pp. 153–159.
Burkholder, F. , and Kutscher, C. , 2009, “ Heat Loss Testing of Schott's 2008 PTR70 Parabolic Trough Receiver,” National Renewable Energy Laboratory, Golden, CO, NREL Report No. NREL/TP-5500-45633.
Kutscher, C. , Burkholder, F. , and Stynes, K. , 2012, “ Generation of a Parabolic Trough Collector Efficiency Curve From Separate Measurements of Outdoor Optical Efficiency and Indoor Receiver Heat Loss,” ASME J. Sol. Energy Eng., 134(1), p. 011012.
NREL, “ Heat Collection Element (HCE) Temperature Survey,” National Renewable Energy Laboratory, Golden, CO, accessed in 2015,
Gee, R. , Brost, R. , Zhu, G. , and Jorgensen, G. , 2010, “ An Improved Method for Characterizing Reflector Specularity for Parabolic Concentrators,” 16th SolarPACES, Perpignan, France, Sept. 21–24.
Zhu, G. , and Lewandowski, A. , 2012, “ A New Optical Evaluation Approach for Parabolic Trough Collectors: First-Principle OPTical Intercept Calculation (FirstOPTIC),” ASME J. Sol. Energy Eng., 134(4), p. 041005.
Zhu, G. , 2013, “ Study on the Optical Impact of Receiver Position Error on Parabolic Trough Collectors,” ASME J. Sol. Energy Eng., 135(3), p. 031021.
Stynes, K. , and Ihas, B. , 2012, “ Slope Error Measurement Tool for Solar Parabolic Through Collectors,” World Renewable Energy Forum, Denver, CO, May 13–17.
Stynes, K. , and Ihas, B. , 2012, “ Absorber Alignment Measurement Tool for Solar Parabolic Trough Collectors,” ASME Paper No. ES2012-91283.
Prahl, C. , Stanicki, B. , Hilgert, C. , Ulmer, S. , and Roger, M. , 2011, “ Airborne Shape Measurement of Parabolic Trough Collector Fields,” 17th SolarPACES Conference, Granada, Spain, Sept. 20–23.
Devices and Services, 2014, “ Portable Specular Reflectometer 15R-USB,” Devices and Services, Co., Dallas, TX, accessed in 2015,
SOC, 2009, “ SOC-100 User's Manual—Hemispherical Directional Reflectometer (HDR),” Surface Optics Corporations, San Diego, CA.
Binotti, M. , Zhu, G. , Gray, A. , Manzolini, G. , and Silva, P. , 2013, “ Geometric Analysis of Three-Dimensional Effects of Parabolic Trough Collectors,” Sol. Energy, 88, pp. 88–96.
NREL, 2015, “ System Advisor Model 2015.1.30,” National Renewable Energy Laboratory, Golden, CO, accessed in 2015,
Sun 2 Market Solutions, 2012, “ Performance Comparison of Huiyin's Vacuum Receiver Tubes,” Huiyin-Group, Sun to Market Solutions S.L., Madrid, Spain, accessed in 2015,
Bendt, P. , Rabl, A. , Gaul, H. W. , and Reed, K. A. , 1979, “ Optical Analysis and Optimization of Line Focus Solar Collectors,” Solar Energy Research Institute, Golden, CO.

## Figures

Fig. 1

Schematic of mirror reflectance [13]

Fig. 2

Distribution of solar specular reflectance (at 25 mrad and at a wavelength of 660 nm) among loops. Variability comes from measurement uncertainties and damage to some panels prior to construction.

Fig. 3

Specular reflectance (at a wavelength of 660 nm) as a function of acceptance aperture size for four mirror panel samples

Fig. 4

Fitted mirror specularity profile using a single-Gaussian approximation

Fig. 5

A snapshot of distant observer (DO) optical characterization: raw photo (left) and scaled photo (right)

Fig. 6

Rescaling of the raw image based on the target locations [40]

Fig. 7

Receiver position error along x and z directions. Because these measurements were taken near the horizon, they represent a worst-case scenario that occurs during operation. Receiver position error during normal operating angles may be substantially less.

Fig. 8

Slope error distribution over one collector module of a SkyTrough collector module (indexed by L5R2M10)

Fig. 9

Slope error distribution attributes (mean value and RMS) for all sampled collector modules. Note that the mean value is dominated by the receiver's gravity-induced displacement, which is greatest at the low tracking angle while the DO measurements were conducted. Its impact on the collector performance is compensated by including a tracking-offset algorithm, to be discussed later.

Fig. 10

Intercept factor calculation for all sampled collector modules

Fig. 11

Intercept factor calculation for all sampled collector modules with and without tracking-offset algorithm

Fig. 12

Incidence-angle modifier (IAM) curve: circles mark the predicted data points, and the line indicates the fitting function

Fig. 13

Hourly SAM-predicted solar field thermal energy output for Stillwater based on measured parameters listed in Table 7

## Tables

Table 1 Solar field specifications at Stillwater geothermal/solar hybrid plant site
Table 2 Technical specifications of optical test tools used in this study
Table 3 Optical test plan summary
Table 4 Average solar reflectance measurement and the uncertainties at a 95% confidence level for the solar field and loop 5. The average solar field value is affected by measurement uncertainties and damage to some panels prior to construction. Loop 5 will be used in the future performance acceptance test at the plant.
Table 5 Solar collector optical specifications and optical error measurements
Table 6 Stillwater solar field optical performance
Table 7 Revised input parameters and annual energy output based on measured values at Stillwater
aThe measurement value accounts for damage to some panels prior to construction.
bIncluded in geometry effects.

## Errata

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