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.

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.

Table 1

Solar field specifications at Stillwater geothermal/solar hybrid plant site

Solar field aspectsValue
LocationFallon, NV
Solar field area (acres)20
Collector aperture area (m2)25,000
Solar collector modelSkyTrough [11]
Solar collector aperture (m)6
Solar collector focal length (m)1.71
Solar absorber size (m)0.08
Solar collector module length (m)13.9
Reflector materialReflecTech PLUS [11]
Nominal power output (MWth), assuming a DNI of 900 W/m2, and an ambient temperature of 21 °C17
Solar field configurationU shape
Number of collector loops11
Number of solar collector modules per loop28
Inlet temperature (°C)149
Outlet temperature (°C)199
Heat-transfer fluid (HTF)Demineralized water
Solar field aspectsValue
LocationFallon, NV
Solar field area (acres)20
Collector aperture area (m2)25,000
Solar collector modelSkyTrough [11]
Solar collector aperture (m)6
Solar collector focal length (m)1.71
Solar absorber size (m)0.08
Solar collector module length (m)13.9
Reflector materialReflecTech PLUS [11]
Nominal power output (MWth), assuming a DNI of 900 W/m2, and an ambient temperature of 21 °C17
Solar field configurationU shape
Number of collector loops11
Number of solar collector modules per loop28
Inlet temperature (°C)149
Outlet temperature (°C)199
Heat-transfer fluid (HTF)Demineralized water

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.

Table 2

Technical specifications of optical test tools used in this study

InstrumentManufacturerMeasured parametersSpecifications
410-SolarSurface Optics CorporationaSolar-weighted hemispherical reflectance solar-weighted total specular reflectance (6 deg half aperture)Incidence 20 deg wavelengths: seven bands
D&S 15 RDevices and Services CompanybSpecular reflectance at 7, 15, 25, and 46 mrad. A D&S model can be customized with either three aperture angles. The adopted D&S model uses 7, 25, and 46 mradIncidence 15 deg wavelength: 660 nm repeatability: 0.002 reflectance unit
Distant observer (DO)NREL under DOE fundsMirror slope error: transversal direction receiver position error: two directions in transversal planeMajor components: high-precision camera photogrammetry-based program
InstrumentManufacturerMeasured parametersSpecifications
410-SolarSurface Optics CorporationaSolar-weighted hemispherical reflectance solar-weighted total specular reflectance (6 deg half aperture)Incidence 20 deg wavelengths: seven bands
D&S 15 RDevices and Services CompanybSpecular reflectance at 7, 15, 25, and 46 mrad. A D&S model can be customized with either three aperture angles. The adopted D&S model uses 7, 25, and 46 mradIncidence 15 deg wavelength: 660 nm repeatability: 0.002 reflectance unit
Distant observer (DO)NREL under DOE fundsMirror slope error: transversal direction receiver position error: two directions in transversal planeMajor components: high-precision camera photogrammetry-based program

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.

Table 3

Optical test plan summary

Measurement metrics of interestInstrumentProcedure
Specular reflectance at one acceptance angleD&S 15R• Select 44 modules across the whole solar field and select 14 modules at loop 5
• Clean the mirror patch of interest for measurements for each module
• Use D&S 15R to measure specular reflectance at 25 mrad aperture
Specularity and solar-weighted specularD&S 15R410-solar• Select four modules at loop 5
• Clean the mirror patch of interest for measurements for each module
• Use D&S reflectometer to measure specular reflectance at 7, 25, and 46 mrad
• Use 410-solar reflectometer to measure solar-weighted specular reflectance
Mirror slope error and receiver position errorDO• Select ten modules across the whole solar field and select four modules at loop 5
• Implement DO technique for measurements
Measurement metrics of interestInstrumentProcedure
Specular reflectance at one acceptance angleD&S 15R• Select 44 modules across the whole solar field and select 14 modules at loop 5
• Clean the mirror patch of interest for measurements for each module
• Use D&S 15R to measure specular reflectance at 25 mrad aperture
Specularity and solar-weighted specularD&S 15R410-solar• Select four modules at loop 5
• Clean the mirror patch of interest for measurements for each module
• Use D&S reflectometer to measure specular reflectance at 7, 25, and 46 mrad
• Use 410-solar reflectometer to measure solar-weighted specular reflectance
Mirror slope error and receiver position errorDO• Select ten modules across the whole solar field and select four modules at loop 5
• Implement DO technique for measurements

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:
ρspecSW(φ)=ρspec,totSW0Ω(φ)fSW(φ)dΩ
(1)

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.

Fig. 1
Schematic of mirror reflectance [13]
Fig. 1
Schematic of mirror reflectance [13]
Close modal
A simple and effective form for mirror specularity profile is a Gaussian distribution
f(φ)=12πσs2 e(φ2σs)2
(2)

The coefficient 1/2πσs2  ensures an overall integral equal to 1 when assuming σs1. 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.

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. 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.
Close modal

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

Fig. 3
Specular reflectance (at a wavelength of 660 nm) as a function of acceptance aperture size for four mirror panel samples
Fig. 3
Specular reflectance (at a wavelength of 660 nm) as a function of acceptance aperture size for four mirror panel samples
Close modal
ρspc660,m(φi),i=1,2,3
(3)
Here, m is the sample number, m = 1, 2,…, Mspc, and
φ1=3.5mrad;φ2=12.5mrad;φ3=23mrad
(4)

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 φi, i=1,2,3 of each mirror panel m, Eqs. (1)(3) expand to
ρspec,tot660,m(1e(φi2σ660nm)2)=ρspec660,m(φi),i=1,2,3
(5)

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.

Fig. 4
Fitted mirror specularity profile using a single-Gaussian approximation
Fig. 4
Fitted mirror specularity profile using a single-Gaussian approximation
Close modal

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

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.

Solar fieldLoop 5
Average solar-weighted specular reflectance ρspec,totSW¯0.9043 ± 0.00330.9124 ± 0.0052
Average specularity RMS value σSW¯1.92 ± 0.261.92 ± 0.26
Solar fieldLoop 5
Average solar-weighted specular reflectance ρspec,totSW¯0.9043 ± 0.00330.9124 ± 0.0052
Average specularity RMS value σSW¯1.92 ± 0.261.92 ± 0.26
ρspec,totSW¯(1e(φ2σSW¯)2)=ρspecSW¯(φ)
(6)
Here, the calculation of solar-weighted values is simplified with available measurement capabilities by assuming
ρspec,totSW¯=ρspec,tot660¯(ρspec,SOCSWρspec,SOC660)¯
(7)
σSW¯=σ660nm
(8)

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.

Fig. 5
A snapshot of distant observer (DO) optical characterization: raw photo (left) and scaled photo (right)
Fig. 5
A snapshot of distant observer (DO) optical characterization: raw photo (left) and scaled photo (right)
Close modal
Fig. 6
Rescaling of the raw image based on the target locations [40]
Fig. 6
Rescaling of the raw image based on the target locations [40]
Close modal

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.

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. 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.
Close modal

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.

Fig. 8
Slope error distribution over one collector module of a SkyTrough collector module (indexed by L5R2M10)
Fig. 8
Slope error distribution over one collector module of a SkyTrough collector module (indexed by L5R2M10)
Close modal

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.

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. 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.
Close modal

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.

Table 5

Solar collector optical specifications and optical error measurements

ParametersValueSource
ReceiverAbsorptance0.96Manufacturer
Glass-envelope transmittance0.97Manufacturer
MirrorSolar-weighted specular reflectance0.904Measured
Specularity—RMS1.92 mradMeasured
Slope error—mean value−4.0 mradMeasured, including the receiver position error
Slope error—mean value with tracking offset1.0 mrad
Slope error—RMS3.0 mrad
CollectorTracking error1 mradDesign parameter
ParametersValueSource
ReceiverAbsorptance0.96Manufacturer
Glass-envelope transmittance0.97Manufacturer
MirrorSolar-weighted specular reflectance0.904Measured
Specularity—RMS1.92 mradMeasured
Slope error—mean value−4.0 mradMeasured, including the receiver position error
Slope error—mean value with tracking offset1.0 mrad
Slope error—RMS3.0 mrad
CollectorTracking error1 mradDesign parameter

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.

Fig. 10
Intercept factor calculation for all sampled collector modules
Fig. 10
Intercept factor calculation for all sampled collector modules
Close modal

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.

Fig. 11
Intercept factor calculation for all sampled collector modules with and without tracking-offset algorithm
Fig. 11
Intercept factor calculation for all sampled collector modules with and without tracking-offset algorithm
Close modal

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
IAM(θ)=kIAM,0+kIAM,1θcos(θ)+kIAM,2θ2cos(θ)+kIAM,3θ3cos(θ)
(9)
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
η(θ)=ηoIAM(θ)=ρταγIAM(θ)
(10)

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.

Fig. 12
Incidence-angle modifier (IAM) curve: circles mark the predicted data points, and the line indicates the fitting function
Fig. 12
Incidence-angle modifier (IAM) curve: circles mark the predicted data points, and the line indicates the fitting function
Close modal
Table 6

Stillwater solar field optical performance

No tracking offsetWith tracking offset
Nominal optical efficiency0.6960.840
Nominal intercept factor0.8270.991
kIAM,011
kIAM,10.0138−0.0140
kIAM,2−0.22340.0622
kIAM,30.1225−0.0909
No tracking offsetWith tracking offset
Nominal optical efficiency0.6960.840
Nominal intercept factor0.8270.991
kIAM,011
kIAM,10.0138−0.0140
kIAM,2−0.22340.0622
kIAM,30.1225−0.0909

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%).

Fig. 13
Hourly SAM-predicted solar field thermal energy output for Stillwater based on measured parameters listed in Table 7
Fig. 13
Hourly SAM-predicted solar field thermal energy output for Stillwater based on measured parameters listed in Table 7
Close modal
Table 7

Revised input parameters and annual energy output based on measured values at Stillwater

Case 2: revised value based on measurement at StillwaterCase 3: revised value based on measurement at Stillwater
SAM input parameterCase 1: original value from SAM default or vendor literatureWithout tracking-offset algorithm, assuming maximum observed error at low tracking anglesWith tracking-offset algorithm
Absorber absorptance (receiver)0.9630.960.96
Envelope transmittance (receiver)0.9640.970.97
Mirror reflectance0.930.904a0.904a
Geometry effects0.9520.8830.991
Tracking error0.9881b1b
IAM coefficient F0111
IAM coefficient F10.03270.0138−0.0140
IAM coefficient F2−0.1351−0.22340.0622
IAM coefficient F300.1225−0.0909
SAM annual performance prediction for 11-loop, 24,778-m2 solar field
Field thermal power produced (MWh/yr)38,90035,50040,700
Case 2: revised value based on measurement at StillwaterCase 3: revised value based on measurement at Stillwater
SAM input parameterCase 1: original value from SAM default or vendor literatureWithout tracking-offset algorithm, assuming maximum observed error at low tracking anglesWith tracking-offset algorithm
Absorber absorptance (receiver)0.9630.960.96
Envelope transmittance (receiver)0.9640.970.97
Mirror reflectance0.930.904a0.904a
Geometry effects0.9520.8830.991
Tracking error0.9881b1b
IAM coefficient F0111
IAM coefficient F10.03270.0138−0.0140
IAM coefficient F2−0.1351−0.22340.0622
IAM coefficient F300.1225−0.0909
SAM annual performance prediction for 11-loop, 24,778-m2 solar field
Field thermal power produced (MWh/yr)38,90035,50040,700
a

The measurement value accounts for damage to some panels prior to construction.

b

Included in geometry effects.

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.

Acknowledgment

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 =

absorptance of receiver surface

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 =

transmittance of receiver-glass envelope

φ =

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

Ω =

solid angle, sr

Acronyms

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

References

1.
Mills
,
D.
,
2004
, “
Advances in Solar Thermal Electricity Technology
,”
Sol. Energy
,
76
(
1–3
), pp.
19
31
.
2.
Price
,
H.
,
Lupfert
,
E.
,
Kearney
,
D.
,
Zarza
,
E.
,
Cohen
,
G.
,
Gee
,
R.
, and
Mahoney
,
R.
,
2002
, “
Advances in Parabolic Trough Solar Power Technology
,”
ASME J. Sol. Energy Eng.
,
124
(
2
), pp.
109
125
.
3.
Zhu
,
G.
,
Wendelin
,
T.
,
Wagner
,
M.
, and
Kutscher
,
C.
,
2014
, “
History, Current-State and Future of Linear Fresnel Concentrating Solar Collectors
,”
Sol. Energy
,
103
, pp.
639
652
.
4.
Andraka
,
C. E.
, and
Powell
,
M. P.
,
2008
, “
Dish Stirling Development for Utility-Scale Commercialization
,” 14th Biennial CSP SolarPACES Symposium, Las Vegas, NV, Mar. 4–7.
5.
Price
,
H.
, and
Kearney
,
D.
,
2005
, “
Recent Advances in Parabolic Trough Solar Power Plant Technology
,” NREL Report No. CH-550-36422.
6.
Zhu
,
G.
,
Neises
,
T.
,
Turchi
,
C.
, and
Bedilion
,
R.
,
2015
, “
Thermodynamic Evaluation of Solar Integration Into a Natural Gas Combined Cycle Power Plant
,”
Renewable Energy
,
74
, pp.
815
824
.
7.
Dersch
,
J.
,
Geyer
,
M.
,
Herrmann
,
U.
,
Jones
,
S. A.
,
Bruce
,
K.
,
Kistner
,
R.
,
Ortmanns
,
W.
,
Pitz-Paal
,
R.
, and
Price
,
H.
,
2004
, “
Trough Integration Into Power Plants—A Study on the Performance and Economy of Integrated Solar Combined Cycle Systems
,”
Energy
,
29
(
5–6
), pp.
947
959
.
8.
Turchi
,
C.
,
Zhu
,
G.
,
Wagner
,
M.
,
Williams
,
T.
, and
Wendt
,
D.
,
2014
, “
Geothermal/Solar Hybrid Designs: Use of Geothermal Energy for CSP Feedwater Heating
,”
Geothermal Resources Council 38th Annual Meeting
, Portland, OR, Sept. 28-Oct. 1,
OSTI
No. 1170300.
9.
Wendt
,
D.
,
Mines
,
G.
,
Turchi
,
C.
,
Zhu
,
G.
,
Cohan
,
S.
,
Angelini
,
L.
,
Bizzarri
,
F.
,
Consoli
,
D.
, and
A.
De Marzo
,
2015
, “
Stillwater Hybrid Geo-Solar Power Plant Optimization Analyses
,”
Geothermal Resources Council Annual Meeting
, Reno, NV, Sept. 20-23,
OSTI
No. 1253710.
10.
DiMarzio
,
G.
,
Angelini
,
L.
,
Price
,
W.
,
Chin
,
C.
, and
Harris
,
S.
,
2015
, “
The Stillwater Triple Hybrid Power Plant: Integrating Geothermal, Solar Photovoltaic and Solar Thermal Power Generation
,”
World Geothermal Congress
, Melbourne, Australia, Apr. 19–25, Paper No. 38001.
11.
Far
,
A.
, and
Gee
,
R.
,
2009
, “
The Skytrough Parabolic Trough Solar Collector
,”
ASME
Paper No. ES2009-90160.
12.
Meyen
,
S.
,
Montecchi
,
M.
,
Kennedy
,
C.
,
Zhu
,
G.
,
Gray
,
M.
,
Crawford
,
J.
,
Hiemer
,
S.
,
Platzer
,
W.
,
Heimsath
,
A.
,
O'Neill
,
M.
,
Ziegler
,
S.
,
Brandle
,
S.
, and
Fernandez
,
A.
,
2013
, “
Parameters and Method to Evaluate the Solar Reflectance Properties of Reflector Materials for Concentrating Solar Power Technology
,”
SolarPACES
, DLR Deutsches Zentrum für Luft und Raumfahrt, Köln, Germany.
13.
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
.
14.
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.
15.
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.
16.
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.
17.
Pettit
,
R. B.
,
1977
, “
Characterization of the Reflected Beam Profile of Solar Mirror Materials
,”
Sol. Energy
,
19
(
6
), pp.
733
741
.
18.
Montecchi
,
M.
,
2013
, “
Approximated Method for Modelling Hemispherical Reflectance and Evaluating Near-Specular Reflectance of CSP Mirrors
,”
Sol. Energy
,
92
, pp.
280
287
.
19.
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.
20.
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
.
21.
Heimsath
,
A.
,
Kutscheidt
,
G.
, and
Nitz
,
P.
,
2010
, “
Detailed Optical Characterization of Reflector Materials for CSP Applications
,” SolarPACES 2010, Perpignan, France, Sept. 21–24.
22.
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.
23.
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.
24.
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.
25.
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
.
26.
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.
27.
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.
28.
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
.
29.
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
.
30.
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
.
31.
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.
32.
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
.
33.
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.
34.
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
.
35.
NREL
, “
Heat Collection Element (HCE) Temperature Survey
,” National Renewable Energy Laboratory, Golden, CO, accessed in 2015, http://www.nrel.gov/csp/lab_capabilities.html#heatcollection
36.
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.
37.
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
.
38.
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
.
39.
Stynes
,
K.
, and
Ihas
,
B.
,
2012
, “
Slope Error Measurement Tool for Solar Parabolic Through Collectors
,”
World Renewable Energy Forum
, Denver, CO, May 13–17.
40.
Stynes
,
K.
, and
Ihas
,
B.
,
2012
, “
Absorber Alignment Measurement Tool for Solar Parabolic Trough Collectors
,”
ASME
Paper No. ES2012-91283.
41.
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.
42.
Devices and Services
,
2014
, “
Portable Specular Reflectometer 15R-USB
,” Devices and Services, Co., Dallas, TX, accessed in 2015, http://www.devicesandservices.com/prod02.htm
43.
SOC
,
2009
, “
SOC-100 User's Manual—Hemispherical Directional Reflectometer (HDR)
,” Surface Optics Corporations, San Diego, CA.
44.
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
.
45.
NREL
,
2015
, “
System Advisor Model 2015.1.30
,” National Renewable Energy Laboratory, Golden, CO, accessed in 2015, https://sam.nrel.gov/
46.
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, http://www.s2msolutions.com/
47.
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.