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Evaluation and comparison of an adaptive method technique for improved performance of linear Fresnel secondary designs
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Evaluation and comparison of an adaptive method technique for improved performance of linear Fresnel secondary designs ⁎
Madeline Hack, Guangdong Zhu , Tim Wendelin Thermal Systems Group, National Renewable Energy Laboratory (NREL), Golden, CO, USA
H I G H L I G H T S in-depth comparison is conducted on four linear Fresnel secondary designs. • An newly proposed adaptive method has a superior performance to all other designs. • The of optical error to secondary reflector designs is carefully examined. • Impact • Impact of absorber size to secondary reflector designs is carefully examined.
A R T I C L E I N F O
A B S T R A C T
Keywords: Concentrating solar power Linear Fresnel collector Secondary reflector Solar optics
As a line-focus concentrating solar power (CSP) technology, linear Fresnel collectors have the potential to become a low-cost solution for electricity production and a variety of thermal energy applications. However, this technology often suffers from relatively low performance. A secondary reflector is a key component used to improve optical performance of a linear Fresnel collector. The shape of a secondary reflector is particularly critical in determining solar power captured by the absorber tube(s), and thus, the collector’s optical performance. However, to the authors’ knowledge, no well-established process existed to derive the optimal secondary shape prior to the development of a new adaptive method to optimize the secondary reflector shape. The new adaptive method does not assume any pre-defined analytical form; rather, it constitutes an optimum shape through an adaptive process by maximizing the energy collection onto the absorber tube. In this paper, the adaptive method is compared with popular secondary-reflector designs with respect to a collector’s optical performance under various scenarios. For the first time, a comprehensive, in-depth comparison was conducted on all popular secondary designs for CSP applications. It is shown that the adaptive design exhibits the best optical performance.
1. Introduction Two common approaches for generating electricity from solar energy include photovoltaic (PV) and concentrating solar power (CSP) technologies [1,2]. PV directly converts solar irradiation into electricity while CSP uses large-aperture reflectors to concentrate direct normal irradiation (DNI) onto absorber tube(s) at the reflector focal line. This concentrated irradiation is absorbed by a heat-transfer media (fluid or particles) flowing through a receiver, delivering this high-temperature thermal energy to a thermodynamic power cycle where it is converted into electricity. The typical fluid outlet temperature of the absorber may range from 200 °C to 600 °C depending on the CSP technology used [3–5]. Some experimental facilities may achieve even higher temperatures [5]. Because a conventional steam-Rankine power block is an
⁎
integral component in CSP systems, a CSP plant is typically deployed at a utility-scale for electricity generation, and thus, it is more capitalintensive compared with PV which is capable of flexible-scale deployment [6]. However, unlike PV, CSP’s thermal energy storage provides low-cost dispatchability to a grid with high penetration of renewable energy [7–9]. Thus, CSP and PV can be complementary approaches in a future renewables-dominated electricity market, along with other types of renewable energy such as wind, geothermal, and biomass. In addition to electricity generation, CSP collectors can generate heat for a variety of applications such as heating, cooling, water desalination, process heat, and complementary heat addition to other energy sectors such as geothermal and fossil-fuel power plants [10–13]. With the decreasing cost of new emerging technologies in the near future, CSP could be very competitive in the energy market.
Corresponding author. E-mail address: [email protected] (G. Zhu).
http://dx.doi.org/10.1016/j.apenergy.2017.09.009 Received 21 June 2017; Received in revised form 23 August 2017; Accepted 7 September 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Hack, M., Applied Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.09.009
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with an optical component due to the existence of the aforementioned system optical errors. If one assumes that the sun shape and all the system optical errors follow a Gaussian distribution, then the root mean square (RMS) of the overall beam-spread distribution can be estimated as the following:
CSP includes a range of technologies [14–17]: parabolic trough [3], linear Fresnel [4,18], power tower (or central receiver) [5], and dish/ engine. The global CSP installed capacity has reached more than 6 GWe as of 2016 [19]. Parabolic troughs are the dominating mature technology in the market and power towers are emerging into the CSP electricity market with increasing deployment. The greater deployment of linear Fresnel technology, a line-focusing technology along with parabolic troughs, is constrained by its performance and cost [4,20]. Linear Fresnel includes a low-profile array of tracking primary mirrors and a fixed receiver assembly with an optional secondary reflector [21–23]. It has been treated as a low-cost technology, but it suffers from low performance. Apart from the relatively high cosine loss associated with the primary reflectors, another primary reason for the low performance of existing linear Fresnel technologies is due to the existence of a large number of design parameters. These include geometric and optical parameters of each collector component; thus, no robust numerical method can fully optimize a linear Fresnel collector [4,24]. The objective of the present work is to investigate secondary-reflector designs to improve the performance of linear Fresnel collectors using a single-tube receiver. This paper compares a newly proposed adaptive design by Zhu from the National Renewable Energy Laboratory (NREL) [25] to past designs, such as the compound parabolic concentrator (CPC) [26–28], trapezoidal design [29], and the butterfly design [30]. To the authors’ knowledge, no similar methods to NREL’s adaptive method exist in the past. The CPC is a popular secondary reflector profile that has been widely accepted in stationary solar concentrators and can be adopted in linear Fresnel collector designs. The CPC is designed to accommodate the sun’s full-sun-cone light absorption characteristics. The trapezoidal design is commonly used as a secondary reflector due to its simplistic design and low manufacturing costs [29]. Finally, the butterfly profile is a relatively new design composed of two symmetric parabolas. In addition, a secondary additional can greatly help achieve a better uniform distribution of concentrated solar flux on the absorber tube and reduce the associated thermal stress [28]. For the first time, a comprehensive, in-depth comparison was conducted on all popular secondary designs for CSP applications. In addition, the impact of the collector optical errors and absorber size (i.e., concentration ratio) are also carefully examined through rigorous optical analysis, which authors have not found elsewhere. This paper is organized as follows: in Section 2, basic aspects of linear Fresnel collector are introduced; then various secondary-reflector designs are explained and defined in Section 3; next, Section 4 describes the baseline linear Fresnel collector used to evaluate various secondaryreflector designs, the performance metrics, and the modeling tool; Section 5 presents an overall performance comparison between all four secondary designs; a more in-depth comparison between the adaptive and CPC designs are conducted in Section 6; finally, the conclusions are given in Section 7.
2 2 2 2 σtotal = σsun + σspecularity + (2σslope )2 + (2σtrack )2 + σreceiver .
(1)
Here, σspecularity , σslope , σtrack , and σreceiver are the RMS for mirror specularity, mirror slope error, mirror tracking error, and receiver-related optical error, respectively. The factor of 2 for the slope error and the tracking error comes from the law of reflection. It is mathematically convenient to assume Gaussian distributions for all error sources in order to approximate the size of the broadened sun beam as it approaches the secondary reflector. Knowing the beam spread can help determine the secondary-reflector aperture width [25]. 3. Secondary designs Four secondary designs are considered in the performance comparison in this work, each of which is briefly described below. 3.1. Adaptive design NREL’s proposed adaptive method does not assume a predefined analytical curve for the secondary profile [25]. Instead, the adaptive method accounts for the collector optical errors and aims to maximize the amount of power to the absorber by using the law of reflection to develop the optimal profile. The adaptive profile depends on the specific linear Fresnel configuration (both geometry and optics) such as absorber size and position, and collector-field size. As an adaptive method, the starting point for the secondary-reflector surface is determined by its pre-defined aperture width. As illustrated in Fig. 2, at the starting edge of the aperture, the principal incidence is determined based on the incoming ray intensity distribution. The principal incidence is the angle at which the maximum amount of sun ray power will be reflected to the absorber. The desirable reflection direction is set as the vector from the surface point to the absorber center. As Fig. 2 illustrates, with the known incoming principal incidence and the desirable reflection direction, the surface normal and tangent vectors are then determined. The next point along the secondary-reflector surface will advance along the surface tangent with a specified step per the required surface accuracy. The principal incidence, reflection, surface normal, and surface tangent for subsequent surface points can be determined by repeating the process for starting point. This algorithm has been improved since it was developed in an earlier publication [25]. While NREL’s adaptive method is applied to linear Fresnel systems in this study, it has the flexibility to assess one or more absorber tubes and various linear Fresnel configurations. It is also applicable to secondary optics in all solar thermal collectors such as parabolic trough, central receiver, and dish/engine collectors.
2. Aspects of linear Fresnel As illustrated in Fig. 1, the geometry of a typical linear Fresnel collector includes primary reflectors, a secondary reflector, and an absorber. The primary reflector is an array of flat or quasi-flat mirrors tilted to track the sun and concentrate the sun’s rays onto the absorber. The secondary reflector captures stray light from the primary reflector and reflects it onto the absorber. Solar collector optics aim to maximize energy collection by the absorber. Various optical error sources exist in a linear Fresnel system. Such errors include imperfect mirror specularity, primary mirror slope error, primary mirror tracking error, absorber position error, and similar associated errors on secondary reflectors. Designing a collector system starts by assuming a defined sun shape and, as the light is reflected through the system, the optical errors can distort the original image. In reality, the sun shape is always broadened when interacting
3.2. Compound parabolic concentrator (CPC) design The CPC design is commonly used in low-concentration stationary collectors and is a good candidate for a linear Fresnel secondary reflector due to the optical benefit of accepting light from a wide angular range. The CPC is defined by two separate curves: an ordinary involute near the absorber and a macro-focal parabola defining the edges [26,31,32]. Using polar coordinates as shown in Fig. 3, the CPC profile can be defined by:
r (θ) =
ra , cos(θ−tan−1 (I (θ)/ ra))
(2)
where ra is the radius of the absorber tube, θ is the polar coordinate angle, and I (θ) is the tangent distance from the absorber to the CPC 2
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Fig. 1. Linear Fresnel collector characteristics: (a) geometry and (b) optics images adapted from Zhu [25].
3.3. Trapezoidal design
shape. The CPC acceptance angle (θa ) influences the range of accepted angles for the CPC design by defining the secondary’s aperture width (rw ) and distance from the absorber to the secondary’s edge (Δh ). The ideal involute would touch the absorber tube, but a gap typically exists between the absorber and the CPC cusp due to the glass envelope that often encompasses the absorber for high-temperature applications. The involute and parabolic shapes must be adjusted by a factor of θ0 ; if there were no gap, the value of θ0 would equal zero. The involute is defined π by the bounds ⎡0,θa + 2 ⎤ and is illustrated by the line segment AB in ⎣ ⎦ π 3π Fig. 3. The macro-focal parabola is bounded by ⎡θa + 2 , 2 −θa⎤ and is ⎣ ⎦ illustrated by the line segment BC in Fig. 3. The equation for I (θ) is detailed as follows:
ra (θ + θ0), 0 ⩽ θ ⩽ θa + ⎧ ⎪ I (θ) = ra θ + θa + π + 2θ0 − cos(θ − θa) ), θ + π < θ ⩽ ⎨ ( 2 ⎪ a 1 + sin(θ − θa) 2 ⎩
r θa = tan−1 ⎛ w ⎞ Δ ⎝ h⎠ ⎜
θ0 =
rg 2 ra
The trapezoidal design is well known for its simplistic design and ease of construction. The design may be used with a number of absorber tubes [29]; however, for this design validation, only one absorber tube will be used for comparison. Trapezoidal design may reach higher performance in multi-tube receivers. As shown in Fig. 4, the design is defined by the following equation: h
− rw ⩽ x ⩽ − tanθa ⎧ x ∗tan(θTC ), TC ⎪ h h − θ a < x < tanθa y = ha, TC TC ⎨ ⎪ (r −x ) ∗tan(θ ), ha ⩽ x ⩽ r w TC w tanθTC ⎩
π 2 3π −θa 2
Here, rw is the secondary-aperture width, ha is the secondary-reflector height, and θTC is the inclination of the side section of the secondary shape. When designing the trapezoidal geometry, the height must be selected to minimize the number of rays reflected and not captured by the absorber. The top-right corner of the trapezoid should be 45° from the origin to minimize missed rays.
(3)
⎟
−1 −cos−1
(4)
ra rg
(6)
3.4. Butterfly design
(5)
The butterfly design has two parabolic wings that are used to focus light on the absorber [33]. The wings are fashioned by rotating a parabola by an angle of (θB ). The parabola’s vertex is defined by focal length and the angle of rotation. In this case, the focal length is the
From these equations, the polar coordinates can be converted into Cartesian coordinates along the x and y axis to create the final shape file. Some variations of the CPC design exist to accommodate practical issues, but the one described here has the highest performance [32].
Fig. 2. Adaptive design methodology to optimize secondary reflector profile: (a) creation of the first two surface points and (b) the complete optimal surface. Adapted from Zhu [25].
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Fig. 3. Compound parabolic concentrator (CPC) design.
radius of the absorber outer layer. The parabola’s focal point is at the center of the absorber (0,0) and the vertex of the parabola is defined by ( x v ,yv ), as seen in Fig. 5. The one-side symmetric parabola is defined as below:
x = x ′cos(θB ) + y′sin(θB ); y = −x ′sin(θB ) + y′cos(θB )
(x ′−x v )2 y′ = yv + 4ra
θB =
tan−1
wfield h
(9)
2
x v = (−racos(θB )); yv = rasin(θB )
(10)
(7)
x max =
cos(θB ) ∗ 2ra 1−
(8)
Here, θB is defined by the primary field width and the height of the absorber tube above the primary mirrors. Other constants in Eqs. (7) and (8) are defined as follows:
1 1 + w 2field + h2
(11)
Here, wfield is the width of the primary mirror field and h is the height of the absorber above the primary mirrors.
Fig. 4. Trapezoid concentrator design.
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Fig. 5. Butterfly secondary design.
4. Approach
Fresnel reflector that uses waterborne hollow plastic tubes to carry mini-size mirrors [36], as shown in Fig. 6. A basin holds 50 four-inchwide flat reflectors supported by these plastic tubes. One basin on each side of the receiver assembly forms a collector module. The geometrical and optical attributes of the current generation of Hyperlight reflectors are summarized in Tables 1 and 2. For the Hyperlight Energy linear Fresnel design, the secondary-reflector aperture is required to intercept 95% of reflected power for the outermost mirror and it is determined to be 0.35 m [25]. The inner primary mirrors are closer to the receiver assembly and will reflect higher percentage of light to the secondary aperture. The aperture of the secondary reflector is held constant for various secondary designs throughout the paper for a consistent performance comparison. The sun shape is assumed to have
A baseline linear Fresnel collector configuration is defined to compare the performance between different secondary designs described in Section 3. A performance metric, defined as the secondary intercept factor, is adopted to evaluate the optical performance of a secondary design. SolTrace, a ray-trace software package developed by NREL, is then used to calculate the secondary intercept factor for secondary reflectors and other relevant collector performance metrics [34,35]. 4.1. Baseline hyperlight energy linear Fresnel system Hyperlight Energy (Hyperlight) is developing a new type of linear
Fig. 6. Illustration of Hyperlight Energy Linear Fresnel reflectors [36].
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Table 1 Geometric specifications of Hyperlight collector. Total collector width (m) Total collector effective width (wfield , m)
12.8 12.5
Net reflector aperture width (wn , m) Number of basins along width Basin width (m) Basin length (m) Basin spacing along width (m) Basin spacing along length (m) Number of reflectors per basin Reflector width (m) Reflector spacing (m) Position of inner reflector relative to inner edge (m) Position of outer reflector relative to inner edge (m) Receiver assembly Absorber tube height (m) Absorber tube diameter (m) *(varied in 6.3)
10.5 2 6.1 15.7 1 0.67 50 0.105 0.115 0.15 5.9 7 0.09
Table 2 Optical properties of Hyperlight collector based on measurements or vendor’s specifications. Primary reflector Reflectance of primary reflector RMS of specularity (Gaussian, mrad) RMS of slope error and tracking error (Gaussian, mrad) Absorber tube Transmittance of glass envelope Absorptance of surface coating Position error (vertical, mm) Secondary reflector Reflectance of secondary reflector Specularity (Gaussian, mrad) *(varied in 6.2) Slope error (Gaussian, mrad) *(varied in 6.2)
0.94 1.5 3 0.97 0.96 [0, 30] Fig. 7. Transversal and longitudinal incidences angle for a linear Fresnel collector [38]. 0.94 1.5 2
reflectance, transmittance and the absorptance. 4.3. SolTrace
an annual average of circumsolar ratio of 10% and is represented by a Gaussian distribution with an RMS of 2.8 mrad [37].
The collector optical performance can be calculated using SolTrace [3] or other analytical methods [38]. SolTrace is a ray-tracing software tool developed by NREL to specifically model and analyze the optical performance of concentrating solar power systems. It uses a MonteCarlo algorithm to simulate sun shape and efficiently account for effects of various system optical errors. The software uses geometric optics to calculate ray intersections with various surfaces. At the same time, the model is statistically influenced to capture the probabilistic nature of sun angular intensity distributions and system optical errors. A series of SolTrace models was developed to recreate the Hyperlight Energy collector configuration and then simulate the optical performance of the different secondary-reflector profiles. Throughout the paper, the Hyperlight linear Fresnel collector is used as the baseline to compare performance of different secondaryreflector designs. Fig. 8 illustrates SolTrace model of a linear Fresnel collector with a secondary reflector at normal incidence. In all SolTrace models, one million rays were used for computing optical efficiency and secondary intercept factor, based on a preliminary convergence analysis. In the convergence analysis, a series of SolTrace simulations were performed with a wide range of number of rays. It is shown that the absorbed power changes less than 0.5% when the number of ray is more than 0.2 million. When 1 million rays are used, the convergence error is less than 0.1%. To be conservative, 1 million rays were used for all SolTrace models in the work presented.
4.2. Performance metrics The optical performance of a linear Fresnel collector can be characterized by optical efficiency with various forms:
η (θ⊥,θ∥) = ρ ·τ ·α·γ1st (θ⊥,θ∥)·γ2nd (θ⊥,θ∥) = ηo ·IAM (θ⊥,θ∥) ≅ ηo ·IAM t (θ⊥)·IAM l (θ∥)
(12)
Here, ρ is the primary mirror reflectance, τ is the absorber glass-envelope transmittance, and α is the average absorber coating absorptance. ηo is the nominal optical efficiency when the sun is at normal incidence and IAM is the incidence angle modifier, which can be approximated by decomposing IAM into two incidence angle modifiers (IAM t and IAM l ) along transversal and longitudinal directions [38]. IAM is equal to 1 at normal incidence. θ⊥ and θ∥ are the transversal and longitudinal incidence angle, respectively, as illustrated in Fig. 7. γ1st is the primary intercept factor accounting for the cosine loss, shading and blocking effect, and intercept accuracy of the primary reflector array with respect to the secondary-reflector aperture. It does not account for the primary reflector reflectance, the receiver glass envelope transmittance and the receiver absorptance. γ2nd is the secondary reflector factor and will be used to characterize the performance of different secondary-reflector designs. Because some rays reach the receiver without secondary reflection and some rays reach the receiver through secondary or multiple reflections, it is mathematically convenient to account for the secondary reflector reflectance in the secondary reflector. Thus, the secondary reflector reflectance does not appear in Eq. (12). The collector intercept factor is then the multiplication of the primary and secondary intercept factor without accounting for the
5. Comparison of four secondary designs at normal incidence The different secondary designs (Adaptive, CPC, Trapezoidal, and Butterfly) were first evaluated at normal incidence when the sun is directly above the collector. The secondary intercept factor and the overall collector optical efficiency are calculated for each of the designs. As shown in Fig. 9, the adaptive design outperformed the selected 6
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Fig. 8. Snapshots of SolTrace models to illustrate (a) entire linear Fresnel collector and (b) NREL’s adaptive secondary reflector with 100 rays plotted for visualization.
For a linear Fresnel collector, both transversal and longitudinal incidence angles are adopted to characterize its relative position of the sun. The secondary intercept factor for both adaptive and CPC designs is plotted as a function of transversal and longitudinal incidence angles in Fig. 10. It can be seen that the adaptive design continues to outperform the CPC secondary design through the entire range of incidence angles. The adaptive design’s secondary intercept factor average of 94.9% is 2.9% higher than the CPC’s average. An interesting phenomenon is the drop of the CPC performance at a transversal angle of 30°. The reason is as follows: because the involute shape does not intersect the absorber radius, the gap between the glass envelope and the secondary reflector allows for some rays to reflect past the absorber tube, instead of hitting the absorber tube [39]. Overall, both secondary-reflector designs exhibit high performance over a majority of incidence angles.
designs with a secondary intercept factor of 95%. The CPC performed 3% less than the adaptive-derived secondary, but outperformed both the Trapezoidal and Butterfly profiles. Moving forward, only the adaptive and CPC designs were used for more detailed comparison. 6. Comparisons of the adaptive and CPC designs In this section, a more in-depth comparison is conducted between the adaptive design and the CPC design, with respect to varying incidence angles, system optical error, and absorber size. 6.1. Impact of varying incidence angle During the actual operation of a CSP plant, a collector experiences a wide range of varying incidence angle while the sun moves in the sky. 7
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generate 3.1% more power than the CPC design. For the Hyperlight Energy baseline collector, an average 3.1% increase in the collector optical efficiency for the adaptive method will result into a 3.1% increase in energy production and then a 3.1% gain in annual revenue as well. If the target profit ratio is 8–10%, a 3.1% increase in the collector optical efficiency would indicate a 30–37.5% increase in the profit. 6.2. Impact of optical error The system optical error has a substantial impact on the collector performance. In general, the increasing optical error leads to decreasing collector performance. Here, the impact of increasing system error to the secondary-reflector performance is examined. The overall RMS of system optical error excluding the sun shape ranges from 0 to 20 mrad, as defined in Eq. (1). The secondary intercept factor and the collector optical efficiency at normal incidence are plotted as a function of the system error RMS for both adaptive and CPC designs in Fig. 13. It can be seen that the secondary intercept factor for both designs decreases with the increasing optical error RMS. It is noted that the adaptive design is consistently better than the CPC design through the whole range of optical error RMS, and the relative difference between two designs increases with the increasing optical error RMS.
Fig. 9. Comparison of the secondary intercept factor and the collector optical efficiency for four different secondary-reflector designs. Secondary intercept factors are 94.8% for the adaptive, 92.1% for the CPC, 81.4% for the trapezoidal, and 48.5% for the butterfly.
6.3. Impact of absorber size
In Fig. 11, the collector optical efficiency is also plotted as a function of transversal and longitudinal incidence angles for both secondary designs. In addition to the performance of the secondary reflector, the collector optical efficiency takes into account the cosine loss, primary reflector performance (such as shading and blocking), and optical loss due to the components’ optical properties (such as primary reflector reflectance, absorber surface absorptance, and absorber glass envelope transmittance). Thus, it is more sensitive to the sun incidence than that of the secondary reflector. At the high incidence angles, the primary intercept loss such as the shading and blocking loss and the cosine loss starts to dominate [25] so that the difference of the collector optical efficiency between two methods becomes minimal. A performance comparison is also conducted for a representative day of May at Imperial, CA. The weather data comes from the TMY3 data from NREL’s System Advisor Model (SAM) program [40]. As shown in Fig. 12, the transversal and longitudinal incidence angles are plotted as a function of time of day and both incidence angles change during the day. The DNI, the absorbed power by receiver per unit area of primary reflector for two secondary designs are also plotted as a function of time of day. The adaptive design performs consistently better than the CPC design. For the whole day, the adaptive design can
With a fixed reflector array, a decreasing absorber diameter corresponds to an increasing concentration ratio and leads to a decreasing absorber surface—thus resulting in a decreasing thermal loss. At the same time, a smaller absorber may accept less solar power due to the narrowed acceptance angle of the absorber, as illustrated in Fig. 1(b). The absorber diameter will also affect secondary-reflector design. When an absorber diameter changes, both adaptive and CPC designs need to be re-optimized. For a selected absorber diameter, the secondary-reflector aperture is re-calculated based on the criterion of 95% intercept power [25]. Once the secondary aperture is determined, the secondaryreflector shape can be derived based on either the adaptive method or the CPC method. Here, the optical performance of secondary-reflector designs is plotted as a function of the absorber diameter in Fig. 14. With the decreasing absorber diameter, the secondary intercept factor decreases for both secondary designs. Once again, the adaptive design has a better performance than the CPC design for the entire range of absorber diameters. The relative performance difference increases with decreasing absorber diameter and varies between 2.7% and 6.5%. Please note that the optimization of absorber size is out of scope here because the
Fig. 10. Comparison of the secondary intercept factor for both adaptive and CPC designs as a function of (a) transversal incidence angle (setting longitudinal angle to be zero) and (b) longitudinal incidence angle (setting transversal angle to be zero).
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Fig. 11. Comparison of the collector optical efficiency for both adaptive and CPC designs as a function of (a) transversal incidence angle (setting longitudinal angle to be zero) and (b) longitudinal incidence angle (setting transversal angle to be zero).
Fig. 12. Performance comparison in a day of May at Imperial, CO: (a) transversal and longitudinal incidence angles as a function of time of day; (b) DNI, absorbed power by receiver for two secondary designs as a function of time of day. 1
Secondary Intercept Factor (-)
0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 Adaptive
0.55 0.5
CPC
3
4
5
6
7
8
9
10
Optical Error RMS (mrad)
(b)
(a)
Fig. 13. (a) The secondary intercept factor of the adaptive and CPC designs and (b) their relative performance difference as a function of the collector optical error RMS.
7. Conclusions
increasing absorber size leads to a decrease in the concentration ratio and the change in the overall heat transfer coefficient between the absorber and the ambient.
In this work, four different secondary-reflector designs are summarized, and their performance is carefully compared under various conditions by assuming a commercial linear Fresnel collector as the 9
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Fig. 14. (a) The secondary intercept factor of the adaptive and CPC designs and (b) their relative performance difference as plotted as a function of absorber diameter.
that the receiver assembly cost is not a dominating cost item, and thus the design with highest optical performance – the adaptive design – is selected as the optimal solution. Its performance will be further validated through the next phase of the project.
baseline. It is shown that NREL’s newly developed adaptive design presents the best performance among all four designs. At normal incidence, the secondary intercept factor for the adaptive is 2.7%, 13.4% and 46.3% (in the absolute value) higher than that of the CPC, the trapezoid and the butterfly, respectively. The butterfly design has the worst optical performance because it does not take into account the sun shape in the derivation process. The trapezoid concentrator design has poor performance as well because its simple geometry was intended for thermal insulation of the linear Fresnel receiver assembly. The CPC design was determined to be efficient, along with NREL’s adaptive design. The comparison is conducted for receiver assembly designs using one single receiver tube and it should be noted that the comparison results may vary for different concentration ratios or multi-tube receiver design. The adaptive and CPC designs are shown to be much superior to the other designs, so they were further compared with respect to various system aspects such as varying incidence angles, system optical error, and absorber diameter. The results indicate that NREL’s adaptive design has consistently better performance than the CPC design under all scenarios. For the baseline collector configuration, the adaptive is about 2.9% higher for varying transversal and longitudinal incidence angles. For a given day in May at Imperial, CA, the adaptive design can generate 3.1% more power than the CPC design. With the increasing optical error and decreasing absorber size, the relative advantage of the adaptive increases from 2.9% to about 7%. The key reason is that NREL’s adaptive method takes into account the fact that not all reflected light will reach the absorber, whereas the CPC design inherently assumes the completeness of the broadened sun cone through each stage of a linear Fresnel collector. An increasing optical error or a decreasing absorber tube would lead to an increasing departure from the assumption that the complete broadened sun cone will be absorbed by the receiver tube, so that the advantage of the adaptive method becomes more pronounced. With respect to the manufacturability, although the trapezoid design stands for the easiest solution, one identified manufacture entity has stated that new irregular shape of a secondary reflector will not incur a substantial cost increase. A demonstration Hyperlight Energy linear Fresnel loop adopting the new adaptive design is planned to be completed in a near future and a collector performance campaign will be conducted. System cost and economics may also play a role in determining the optimal solution. If the receiver assembly cost is relatively high compared with the overall system cost, a life economic analysis would be essential to determine the final optimal solution. Otherwise, the receiver design with highest performance most likely becomes the optimal solution. For the Hyperlight collector development, it is found
Acknowledgement The work was supported by the United States Department of Energy under Contract No. DE-AC36-08GO28308 to the National Renewable Energy Laboratory, Southern California Gas Company through CEC/ EPIC Subtier Funds-In Agreement FIA-15-1809 and Combined Power LLC (Hyperlight Energy) through the Cooperative Research and Development Agreement CRD-16-625. References [1] Desideri U, Campana PE. Analysis and comparison between a concentrating solar and a photovoltaic power plant. Appl Energy 2013;113:422–33. [2] NREL. Available from:. [3] Price H, et al. Advances in parabolic trough solar power technology. J SolEnergy Eng 2002;124(2):109–25. [4] Zhu G, et al. History, current-state and future of linear fresnel concentrating solar collectors. Sol Energy 2014;103:639–52. [5] Ho C, Iverson B. Review of high-temperature central receiver designs for concentrating solar power. Renew Sustain Energy Rev 2014;29:835–46. [6] Turchi C et al. Current and future costs for parabolic trough and power tower systems in the US market. In: 16th SolarPACES international symposium. Perpignan, France; 2010. [7] Kousksou T, et al. Energy storage: applications and challenges. Sol Energy Mater Sol Cells 2014;120:59–80. [8] Mehos M, et al. An assessment of the net value of CSP systems integrated with thermal energy storage. Energy Proc 2014;69:2060–71. [9] Xu B, Li P, Chan C. Application of phase change materials for thermal energy storage in concentrated solar thermal power plants: a review to recent developments. Appl Energy 2015;160:286–307. [10] Kurup P, Turchi C. Initial investigation into the potential of CSP industrial process heat for the Southwest United States. National Renewable Energy Laboratory; 2015. [11] Zhu G, et al. Thermodynamic evaluation of solar integration into a natural gas combined cycle power plant. Renewable Energy 2015;74:815–24. [12] Li C, Goswami YD, Stefanakos E. Solar assisted sea water desalination: a review. Renew Sustain Energy Rev 2013;19:136–63. [13] Rovira A, et al. Analysis and comparison of integrated solar combined cycles using parabolic troughs and linear fresnel reflectors as concentrating systems. Appl Energy 2016;162:990–1220. [14] Kearney D, Morse F. Bold, decisive times for concentrating solar power. Solar Today 2010;24(4):32–5. [15] Tian Y, Zhao CY. A review of solar collectors and thermal energy storage in solar thermal applications. Appl Energy 2013;104:538–53. [16] Mills D. Adances in solar thermal electricity technology. Sol Energy 2004;76:19–31. [17] Sait H, et al. Fresnel-based modular solar fields for performance/cost optimization in solar thermal power plants: a comparison with parabolic trough collectors. Appl Energy 2015;141:175–89. [18] Qiu Y, et al. Study on optical and thermal performance of a linear fresnel solar reflector using molten salt as HTF with MCRT and FVM methods. Appl Energy 2015;146:162–73.
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2010;87:541–50. [30] Grena R, Tarquini P. Solar linear Fresnel collector using molten nitrates as heat transfer fluid. Energy 2011;36:1048–56. [31] Reddy KS, Prasad GSC, Sundararajan T. Optimization of solar linear fresnel reflectors system with secondary concentrator for uniform flux distribution over absorber tube. Indian Institute of Technology Madras: Solar Energy; 2016. [32] Rabl A. Active solar collectors and their applications. New York: Oxford University Press; 1985. [33] Mathur SS, Kandpal TC, Negi BS. Optical design and concentration characteristics of linear Fresnel reflector solar concentrators – I mirror elements of varying width. Energy Convers Manage 1991;31(3):205–19. [34] Wendelin T. SolTrace: a new optical modeling tool for concentrating solar optics. In: 2003 International solar energy conference, Hawaii, USA; 2003. [35] SolTrace. Available from:. [36] Hyperlight Energy. 2015. Available from:
[19] NREL. The NREL concentrating solar power program; 2015. Available from:
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Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Evaluation and comparison of an adaptive method technique for improved performance of linear Fresnel secondary designs ⁎
Madeline Hack, Guangdong Zhu , Tim Wendelin Thermal Systems Group, National Renewable Energy Laboratory (NREL), Golden, CO, USA
H I G H L I G H T S in-depth comparison is conducted on four linear Fresnel secondary designs. • An newly proposed adaptive method has a superior performance to all other designs. • The of optical error to secondary reflector designs is carefully examined. • Impact • Impact of absorber size to secondary reflector designs is carefully examined.
A R T I C L E I N F O
A B S T R A C T
Keywords: Concentrating solar power Linear Fresnel collector Secondary reflector Solar optics
As a line-focus concentrating solar power (CSP) technology, linear Fresnel collectors have the potential to become a low-cost solution for electricity production and a variety of thermal energy applications. However, this technology often suffers from relatively low performance. A secondary reflector is a key component used to improve optical performance of a linear Fresnel collector. The shape of a secondary reflector is particularly critical in determining solar power captured by the absorber tube(s), and thus, the collector’s optical performance. However, to the authors’ knowledge, no well-established process existed to derive the optimal secondary shape prior to the development of a new adaptive method to optimize the secondary reflector shape. The new adaptive method does not assume any pre-defined analytical form; rather, it constitutes an optimum shape through an adaptive process by maximizing the energy collection onto the absorber tube. In this paper, the adaptive method is compared with popular secondary-reflector designs with respect to a collector’s optical performance under various scenarios. For the first time, a comprehensive, in-depth comparison was conducted on all popular secondary designs for CSP applications. It is shown that the adaptive design exhibits the best optical performance.
1. Introduction Two common approaches for generating electricity from solar energy include photovoltaic (PV) and concentrating solar power (CSP) technologies [1,2]. PV directly converts solar irradiation into electricity while CSP uses large-aperture reflectors to concentrate direct normal irradiation (DNI) onto absorber tube(s) at the reflector focal line. This concentrated irradiation is absorbed by a heat-transfer media (fluid or particles) flowing through a receiver, delivering this high-temperature thermal energy to a thermodynamic power cycle where it is converted into electricity. The typical fluid outlet temperature of the absorber may range from 200 °C to 600 °C depending on the CSP technology used [3–5]. Some experimental facilities may achieve even higher temperatures [5]. Because a conventional steam-Rankine power block is an
⁎
integral component in CSP systems, a CSP plant is typically deployed at a utility-scale for electricity generation, and thus, it is more capitalintensive compared with PV which is capable of flexible-scale deployment [6]. However, unlike PV, CSP’s thermal energy storage provides low-cost dispatchability to a grid with high penetration of renewable energy [7–9]. Thus, CSP and PV can be complementary approaches in a future renewables-dominated electricity market, along with other types of renewable energy such as wind, geothermal, and biomass. In addition to electricity generation, CSP collectors can generate heat for a variety of applications such as heating, cooling, water desalination, process heat, and complementary heat addition to other energy sectors such as geothermal and fossil-fuel power plants [10–13]. With the decreasing cost of new emerging technologies in the near future, CSP could be very competitive in the energy market.
Corresponding author. E-mail address: [email protected] (G. Zhu).
http://dx.doi.org/10.1016/j.apenergy.2017.09.009 Received 21 June 2017; Received in revised form 23 August 2017; Accepted 7 September 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Hack, M., Applied Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.09.009
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with an optical component due to the existence of the aforementioned system optical errors. If one assumes that the sun shape and all the system optical errors follow a Gaussian distribution, then the root mean square (RMS) of the overall beam-spread distribution can be estimated as the following:
CSP includes a range of technologies [14–17]: parabolic trough [3], linear Fresnel [4,18], power tower (or central receiver) [5], and dish/ engine. The global CSP installed capacity has reached more than 6 GWe as of 2016 [19]. Parabolic troughs are the dominating mature technology in the market and power towers are emerging into the CSP electricity market with increasing deployment. The greater deployment of linear Fresnel technology, a line-focusing technology along with parabolic troughs, is constrained by its performance and cost [4,20]. Linear Fresnel includes a low-profile array of tracking primary mirrors and a fixed receiver assembly with an optional secondary reflector [21–23]. It has been treated as a low-cost technology, but it suffers from low performance. Apart from the relatively high cosine loss associated with the primary reflectors, another primary reason for the low performance of existing linear Fresnel technologies is due to the existence of a large number of design parameters. These include geometric and optical parameters of each collector component; thus, no robust numerical method can fully optimize a linear Fresnel collector [4,24]. The objective of the present work is to investigate secondary-reflector designs to improve the performance of linear Fresnel collectors using a single-tube receiver. This paper compares a newly proposed adaptive design by Zhu from the National Renewable Energy Laboratory (NREL) [25] to past designs, such as the compound parabolic concentrator (CPC) [26–28], trapezoidal design [29], and the butterfly design [30]. To the authors’ knowledge, no similar methods to NREL’s adaptive method exist in the past. The CPC is a popular secondary reflector profile that has been widely accepted in stationary solar concentrators and can be adopted in linear Fresnel collector designs. The CPC is designed to accommodate the sun’s full-sun-cone light absorption characteristics. The trapezoidal design is commonly used as a secondary reflector due to its simplistic design and low manufacturing costs [29]. Finally, the butterfly profile is a relatively new design composed of two symmetric parabolas. In addition, a secondary additional can greatly help achieve a better uniform distribution of concentrated solar flux on the absorber tube and reduce the associated thermal stress [28]. For the first time, a comprehensive, in-depth comparison was conducted on all popular secondary designs for CSP applications. In addition, the impact of the collector optical errors and absorber size (i.e., concentration ratio) are also carefully examined through rigorous optical analysis, which authors have not found elsewhere. This paper is organized as follows: in Section 2, basic aspects of linear Fresnel collector are introduced; then various secondary-reflector designs are explained and defined in Section 3; next, Section 4 describes the baseline linear Fresnel collector used to evaluate various secondaryreflector designs, the performance metrics, and the modeling tool; Section 5 presents an overall performance comparison between all four secondary designs; a more in-depth comparison between the adaptive and CPC designs are conducted in Section 6; finally, the conclusions are given in Section 7.
2 2 2 2 σtotal = σsun + σspecularity + (2σslope )2 + (2σtrack )2 + σreceiver .
(1)
Here, σspecularity , σslope , σtrack , and σreceiver are the RMS for mirror specularity, mirror slope error, mirror tracking error, and receiver-related optical error, respectively. The factor of 2 for the slope error and the tracking error comes from the law of reflection. It is mathematically convenient to assume Gaussian distributions for all error sources in order to approximate the size of the broadened sun beam as it approaches the secondary reflector. Knowing the beam spread can help determine the secondary-reflector aperture width [25]. 3. Secondary designs Four secondary designs are considered in the performance comparison in this work, each of which is briefly described below. 3.1. Adaptive design NREL’s proposed adaptive method does not assume a predefined analytical curve for the secondary profile [25]. Instead, the adaptive method accounts for the collector optical errors and aims to maximize the amount of power to the absorber by using the law of reflection to develop the optimal profile. The adaptive profile depends on the specific linear Fresnel configuration (both geometry and optics) such as absorber size and position, and collector-field size. As an adaptive method, the starting point for the secondary-reflector surface is determined by its pre-defined aperture width. As illustrated in Fig. 2, at the starting edge of the aperture, the principal incidence is determined based on the incoming ray intensity distribution. The principal incidence is the angle at which the maximum amount of sun ray power will be reflected to the absorber. The desirable reflection direction is set as the vector from the surface point to the absorber center. As Fig. 2 illustrates, with the known incoming principal incidence and the desirable reflection direction, the surface normal and tangent vectors are then determined. The next point along the secondary-reflector surface will advance along the surface tangent with a specified step per the required surface accuracy. The principal incidence, reflection, surface normal, and surface tangent for subsequent surface points can be determined by repeating the process for starting point. This algorithm has been improved since it was developed in an earlier publication [25]. While NREL’s adaptive method is applied to linear Fresnel systems in this study, it has the flexibility to assess one or more absorber tubes and various linear Fresnel configurations. It is also applicable to secondary optics in all solar thermal collectors such as parabolic trough, central receiver, and dish/engine collectors.
2. Aspects of linear Fresnel As illustrated in Fig. 1, the geometry of a typical linear Fresnel collector includes primary reflectors, a secondary reflector, and an absorber. The primary reflector is an array of flat or quasi-flat mirrors tilted to track the sun and concentrate the sun’s rays onto the absorber. The secondary reflector captures stray light from the primary reflector and reflects it onto the absorber. Solar collector optics aim to maximize energy collection by the absorber. Various optical error sources exist in a linear Fresnel system. Such errors include imperfect mirror specularity, primary mirror slope error, primary mirror tracking error, absorber position error, and similar associated errors on secondary reflectors. Designing a collector system starts by assuming a defined sun shape and, as the light is reflected through the system, the optical errors can distort the original image. In reality, the sun shape is always broadened when interacting
3.2. Compound parabolic concentrator (CPC) design The CPC design is commonly used in low-concentration stationary collectors and is a good candidate for a linear Fresnel secondary reflector due to the optical benefit of accepting light from a wide angular range. The CPC is defined by two separate curves: an ordinary involute near the absorber and a macro-focal parabola defining the edges [26,31,32]. Using polar coordinates as shown in Fig. 3, the CPC profile can be defined by:
r (θ) =
ra , cos(θ−tan−1 (I (θ)/ ra))
(2)
where ra is the radius of the absorber tube, θ is the polar coordinate angle, and I (θ) is the tangent distance from the absorber to the CPC 2
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Fig. 1. Linear Fresnel collector characteristics: (a) geometry and (b) optics images adapted from Zhu [25].
3.3. Trapezoidal design
shape. The CPC acceptance angle (θa ) influences the range of accepted angles for the CPC design by defining the secondary’s aperture width (rw ) and distance from the absorber to the secondary’s edge (Δh ). The ideal involute would touch the absorber tube, but a gap typically exists between the absorber and the CPC cusp due to the glass envelope that often encompasses the absorber for high-temperature applications. The involute and parabolic shapes must be adjusted by a factor of θ0 ; if there were no gap, the value of θ0 would equal zero. The involute is defined π by the bounds ⎡0,θa + 2 ⎤ and is illustrated by the line segment AB in ⎣ ⎦ π 3π Fig. 3. The macro-focal parabola is bounded by ⎡θa + 2 , 2 −θa⎤ and is ⎣ ⎦ illustrated by the line segment BC in Fig. 3. The equation for I (θ) is detailed as follows:
ra (θ + θ0), 0 ⩽ θ ⩽ θa + ⎧ ⎪ I (θ) = ra θ + θa + π + 2θ0 − cos(θ − θa) ), θ + π < θ ⩽ ⎨ ( 2 ⎪ a 1 + sin(θ − θa) 2 ⎩
r θa = tan−1 ⎛ w ⎞ Δ ⎝ h⎠ ⎜
θ0 =
rg 2 ra
The trapezoidal design is well known for its simplistic design and ease of construction. The design may be used with a number of absorber tubes [29]; however, for this design validation, only one absorber tube will be used for comparison. Trapezoidal design may reach higher performance in multi-tube receivers. As shown in Fig. 4, the design is defined by the following equation: h
− rw ⩽ x ⩽ − tanθa ⎧ x ∗tan(θTC ), TC ⎪ h h − θ a < x < tanθa y = ha, TC TC ⎨ ⎪ (r −x ) ∗tan(θ ), ha ⩽ x ⩽ r w TC w tanθTC ⎩
π 2 3π −θa 2
Here, rw is the secondary-aperture width, ha is the secondary-reflector height, and θTC is the inclination of the side section of the secondary shape. When designing the trapezoidal geometry, the height must be selected to minimize the number of rays reflected and not captured by the absorber. The top-right corner of the trapezoid should be 45° from the origin to minimize missed rays.
(3)
⎟
−1 −cos−1
(4)
ra rg
(6)
3.4. Butterfly design
(5)
The butterfly design has two parabolic wings that are used to focus light on the absorber [33]. The wings are fashioned by rotating a parabola by an angle of (θB ). The parabola’s vertex is defined by focal length and the angle of rotation. In this case, the focal length is the
From these equations, the polar coordinates can be converted into Cartesian coordinates along the x and y axis to create the final shape file. Some variations of the CPC design exist to accommodate practical issues, but the one described here has the highest performance [32].
Fig. 2. Adaptive design methodology to optimize secondary reflector profile: (a) creation of the first two surface points and (b) the complete optimal surface. Adapted from Zhu [25].
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Fig. 3. Compound parabolic concentrator (CPC) design.
radius of the absorber outer layer. The parabola’s focal point is at the center of the absorber (0,0) and the vertex of the parabola is defined by ( x v ,yv ), as seen in Fig. 5. The one-side symmetric parabola is defined as below:
x = x ′cos(θB ) + y′sin(θB ); y = −x ′sin(θB ) + y′cos(θB )
(x ′−x v )2 y′ = yv + 4ra
θB =
tan−1
wfield h
(9)
2
x v = (−racos(θB )); yv = rasin(θB )
(10)
(7)
x max =
cos(θB ) ∗ 2ra 1−
(8)
Here, θB is defined by the primary field width and the height of the absorber tube above the primary mirrors. Other constants in Eqs. (7) and (8) are defined as follows:
1 1 + w 2field + h2
(11)
Here, wfield is the width of the primary mirror field and h is the height of the absorber above the primary mirrors.
Fig. 4. Trapezoid concentrator design.
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Fig. 5. Butterfly secondary design.
4. Approach
Fresnel reflector that uses waterborne hollow plastic tubes to carry mini-size mirrors [36], as shown in Fig. 6. A basin holds 50 four-inchwide flat reflectors supported by these plastic tubes. One basin on each side of the receiver assembly forms a collector module. The geometrical and optical attributes of the current generation of Hyperlight reflectors are summarized in Tables 1 and 2. For the Hyperlight Energy linear Fresnel design, the secondary-reflector aperture is required to intercept 95% of reflected power for the outermost mirror and it is determined to be 0.35 m [25]. The inner primary mirrors are closer to the receiver assembly and will reflect higher percentage of light to the secondary aperture. The aperture of the secondary reflector is held constant for various secondary designs throughout the paper for a consistent performance comparison. The sun shape is assumed to have
A baseline linear Fresnel collector configuration is defined to compare the performance between different secondary designs described in Section 3. A performance metric, defined as the secondary intercept factor, is adopted to evaluate the optical performance of a secondary design. SolTrace, a ray-trace software package developed by NREL, is then used to calculate the secondary intercept factor for secondary reflectors and other relevant collector performance metrics [34,35]. 4.1. Baseline hyperlight energy linear Fresnel system Hyperlight Energy (Hyperlight) is developing a new type of linear
Fig. 6. Illustration of Hyperlight Energy Linear Fresnel reflectors [36].
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Table 1 Geometric specifications of Hyperlight collector. Total collector width (m) Total collector effective width (wfield , m)
12.8 12.5
Net reflector aperture width (wn , m) Number of basins along width Basin width (m) Basin length (m) Basin spacing along width (m) Basin spacing along length (m) Number of reflectors per basin Reflector width (m) Reflector spacing (m) Position of inner reflector relative to inner edge (m) Position of outer reflector relative to inner edge (m) Receiver assembly Absorber tube height (m) Absorber tube diameter (m) *(varied in 6.3)
10.5 2 6.1 15.7 1 0.67 50 0.105 0.115 0.15 5.9 7 0.09
Table 2 Optical properties of Hyperlight collector based on measurements or vendor’s specifications. Primary reflector Reflectance of primary reflector RMS of specularity (Gaussian, mrad) RMS of slope error and tracking error (Gaussian, mrad) Absorber tube Transmittance of glass envelope Absorptance of surface coating Position error (vertical, mm) Secondary reflector Reflectance of secondary reflector Specularity (Gaussian, mrad) *(varied in 6.2) Slope error (Gaussian, mrad) *(varied in 6.2)
0.94 1.5 3 0.97 0.96 [0, 30] Fig. 7. Transversal and longitudinal incidences angle for a linear Fresnel collector [38]. 0.94 1.5 2
reflectance, transmittance and the absorptance. 4.3. SolTrace
an annual average of circumsolar ratio of 10% and is represented by a Gaussian distribution with an RMS of 2.8 mrad [37].
The collector optical performance can be calculated using SolTrace [3] or other analytical methods [38]. SolTrace is a ray-tracing software tool developed by NREL to specifically model and analyze the optical performance of concentrating solar power systems. It uses a MonteCarlo algorithm to simulate sun shape and efficiently account for effects of various system optical errors. The software uses geometric optics to calculate ray intersections with various surfaces. At the same time, the model is statistically influenced to capture the probabilistic nature of sun angular intensity distributions and system optical errors. A series of SolTrace models was developed to recreate the Hyperlight Energy collector configuration and then simulate the optical performance of the different secondary-reflector profiles. Throughout the paper, the Hyperlight linear Fresnel collector is used as the baseline to compare performance of different secondaryreflector designs. Fig. 8 illustrates SolTrace model of a linear Fresnel collector with a secondary reflector at normal incidence. In all SolTrace models, one million rays were used for computing optical efficiency and secondary intercept factor, based on a preliminary convergence analysis. In the convergence analysis, a series of SolTrace simulations were performed with a wide range of number of rays. It is shown that the absorbed power changes less than 0.5% when the number of ray is more than 0.2 million. When 1 million rays are used, the convergence error is less than 0.1%. To be conservative, 1 million rays were used for all SolTrace models in the work presented.
4.2. Performance metrics The optical performance of a linear Fresnel collector can be characterized by optical efficiency with various forms:
η (θ⊥,θ∥) = ρ ·τ ·α·γ1st (θ⊥,θ∥)·γ2nd (θ⊥,θ∥) = ηo ·IAM (θ⊥,θ∥) ≅ ηo ·IAM t (θ⊥)·IAM l (θ∥)
(12)
Here, ρ is the primary mirror reflectance, τ is the absorber glass-envelope transmittance, and α is the average absorber coating absorptance. ηo is the nominal optical efficiency when the sun is at normal incidence and IAM is the incidence angle modifier, which can be approximated by decomposing IAM into two incidence angle modifiers (IAM t and IAM l ) along transversal and longitudinal directions [38]. IAM is equal to 1 at normal incidence. θ⊥ and θ∥ are the transversal and longitudinal incidence angle, respectively, as illustrated in Fig. 7. γ1st is the primary intercept factor accounting for the cosine loss, shading and blocking effect, and intercept accuracy of the primary reflector array with respect to the secondary-reflector aperture. It does not account for the primary reflector reflectance, the receiver glass envelope transmittance and the receiver absorptance. γ2nd is the secondary reflector factor and will be used to characterize the performance of different secondary-reflector designs. Because some rays reach the receiver without secondary reflection and some rays reach the receiver through secondary or multiple reflections, it is mathematically convenient to account for the secondary reflector reflectance in the secondary reflector. Thus, the secondary reflector reflectance does not appear in Eq. (12). The collector intercept factor is then the multiplication of the primary and secondary intercept factor without accounting for the
5. Comparison of four secondary designs at normal incidence The different secondary designs (Adaptive, CPC, Trapezoidal, and Butterfly) were first evaluated at normal incidence when the sun is directly above the collector. The secondary intercept factor and the overall collector optical efficiency are calculated for each of the designs. As shown in Fig. 9, the adaptive design outperformed the selected 6
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Fig. 8. Snapshots of SolTrace models to illustrate (a) entire linear Fresnel collector and (b) NREL’s adaptive secondary reflector with 100 rays plotted for visualization.
For a linear Fresnel collector, both transversal and longitudinal incidence angles are adopted to characterize its relative position of the sun. The secondary intercept factor for both adaptive and CPC designs is plotted as a function of transversal and longitudinal incidence angles in Fig. 10. It can be seen that the adaptive design continues to outperform the CPC secondary design through the entire range of incidence angles. The adaptive design’s secondary intercept factor average of 94.9% is 2.9% higher than the CPC’s average. An interesting phenomenon is the drop of the CPC performance at a transversal angle of 30°. The reason is as follows: because the involute shape does not intersect the absorber radius, the gap between the glass envelope and the secondary reflector allows for some rays to reflect past the absorber tube, instead of hitting the absorber tube [39]. Overall, both secondary-reflector designs exhibit high performance over a majority of incidence angles.
designs with a secondary intercept factor of 95%. The CPC performed 3% less than the adaptive-derived secondary, but outperformed both the Trapezoidal and Butterfly profiles. Moving forward, only the adaptive and CPC designs were used for more detailed comparison. 6. Comparisons of the adaptive and CPC designs In this section, a more in-depth comparison is conducted between the adaptive design and the CPC design, with respect to varying incidence angles, system optical error, and absorber size. 6.1. Impact of varying incidence angle During the actual operation of a CSP plant, a collector experiences a wide range of varying incidence angle while the sun moves in the sky. 7
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generate 3.1% more power than the CPC design. For the Hyperlight Energy baseline collector, an average 3.1% increase in the collector optical efficiency for the adaptive method will result into a 3.1% increase in energy production and then a 3.1% gain in annual revenue as well. If the target profit ratio is 8–10%, a 3.1% increase in the collector optical efficiency would indicate a 30–37.5% increase in the profit. 6.2. Impact of optical error The system optical error has a substantial impact on the collector performance. In general, the increasing optical error leads to decreasing collector performance. Here, the impact of increasing system error to the secondary-reflector performance is examined. The overall RMS of system optical error excluding the sun shape ranges from 0 to 20 mrad, as defined in Eq. (1). The secondary intercept factor and the collector optical efficiency at normal incidence are plotted as a function of the system error RMS for both adaptive and CPC designs in Fig. 13. It can be seen that the secondary intercept factor for both designs decreases with the increasing optical error RMS. It is noted that the adaptive design is consistently better than the CPC design through the whole range of optical error RMS, and the relative difference between two designs increases with the increasing optical error RMS.
Fig. 9. Comparison of the secondary intercept factor and the collector optical efficiency for four different secondary-reflector designs. Secondary intercept factors are 94.8% for the adaptive, 92.1% for the CPC, 81.4% for the trapezoidal, and 48.5% for the butterfly.
6.3. Impact of absorber size
In Fig. 11, the collector optical efficiency is also plotted as a function of transversal and longitudinal incidence angles for both secondary designs. In addition to the performance of the secondary reflector, the collector optical efficiency takes into account the cosine loss, primary reflector performance (such as shading and blocking), and optical loss due to the components’ optical properties (such as primary reflector reflectance, absorber surface absorptance, and absorber glass envelope transmittance). Thus, it is more sensitive to the sun incidence than that of the secondary reflector. At the high incidence angles, the primary intercept loss such as the shading and blocking loss and the cosine loss starts to dominate [25] so that the difference of the collector optical efficiency between two methods becomes minimal. A performance comparison is also conducted for a representative day of May at Imperial, CA. The weather data comes from the TMY3 data from NREL’s System Advisor Model (SAM) program [40]. As shown in Fig. 12, the transversal and longitudinal incidence angles are plotted as a function of time of day and both incidence angles change during the day. The DNI, the absorbed power by receiver per unit area of primary reflector for two secondary designs are also plotted as a function of time of day. The adaptive design performs consistently better than the CPC design. For the whole day, the adaptive design can
With a fixed reflector array, a decreasing absorber diameter corresponds to an increasing concentration ratio and leads to a decreasing absorber surface—thus resulting in a decreasing thermal loss. At the same time, a smaller absorber may accept less solar power due to the narrowed acceptance angle of the absorber, as illustrated in Fig. 1(b). The absorber diameter will also affect secondary-reflector design. When an absorber diameter changes, both adaptive and CPC designs need to be re-optimized. For a selected absorber diameter, the secondary-reflector aperture is re-calculated based on the criterion of 95% intercept power [25]. Once the secondary aperture is determined, the secondaryreflector shape can be derived based on either the adaptive method or the CPC method. Here, the optical performance of secondary-reflector designs is plotted as a function of the absorber diameter in Fig. 14. With the decreasing absorber diameter, the secondary intercept factor decreases for both secondary designs. Once again, the adaptive design has a better performance than the CPC design for the entire range of absorber diameters. The relative performance difference increases with decreasing absorber diameter and varies between 2.7% and 6.5%. Please note that the optimization of absorber size is out of scope here because the
Fig. 10. Comparison of the secondary intercept factor for both adaptive and CPC designs as a function of (a) transversal incidence angle (setting longitudinal angle to be zero) and (b) longitudinal incidence angle (setting transversal angle to be zero).
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Fig. 11. Comparison of the collector optical efficiency for both adaptive and CPC designs as a function of (a) transversal incidence angle (setting longitudinal angle to be zero) and (b) longitudinal incidence angle (setting transversal angle to be zero).
Fig. 12. Performance comparison in a day of May at Imperial, CO: (a) transversal and longitudinal incidence angles as a function of time of day; (b) DNI, absorbed power by receiver for two secondary designs as a function of time of day. 1
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Fig. 13. (a) The secondary intercept factor of the adaptive and CPC designs and (b) their relative performance difference as a function of the collector optical error RMS.
7. Conclusions
increasing absorber size leads to a decrease in the concentration ratio and the change in the overall heat transfer coefficient between the absorber and the ambient.
In this work, four different secondary-reflector designs are summarized, and their performance is carefully compared under various conditions by assuming a commercial linear Fresnel collector as the 9
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Fig. 14. (a) The secondary intercept factor of the adaptive and CPC designs and (b) their relative performance difference as plotted as a function of absorber diameter.
that the receiver assembly cost is not a dominating cost item, and thus the design with highest optical performance – the adaptive design – is selected as the optimal solution. Its performance will be further validated through the next phase of the project.
baseline. It is shown that NREL’s newly developed adaptive design presents the best performance among all four designs. At normal incidence, the secondary intercept factor for the adaptive is 2.7%, 13.4% and 46.3% (in the absolute value) higher than that of the CPC, the trapezoid and the butterfly, respectively. The butterfly design has the worst optical performance because it does not take into account the sun shape in the derivation process. The trapezoid concentrator design has poor performance as well because its simple geometry was intended for thermal insulation of the linear Fresnel receiver assembly. The CPC design was determined to be efficient, along with NREL’s adaptive design. The comparison is conducted for receiver assembly designs using one single receiver tube and it should be noted that the comparison results may vary for different concentration ratios or multi-tube receiver design. The adaptive and CPC designs are shown to be much superior to the other designs, so they were further compared with respect to various system aspects such as varying incidence angles, system optical error, and absorber diameter. The results indicate that NREL’s adaptive design has consistently better performance than the CPC design under all scenarios. For the baseline collector configuration, the adaptive is about 2.9% higher for varying transversal and longitudinal incidence angles. For a given day in May at Imperial, CA, the adaptive design can generate 3.1% more power than the CPC design. With the increasing optical error and decreasing absorber size, the relative advantage of the adaptive increases from 2.9% to about 7%. The key reason is that NREL’s adaptive method takes into account the fact that not all reflected light will reach the absorber, whereas the CPC design inherently assumes the completeness of the broadened sun cone through each stage of a linear Fresnel collector. An increasing optical error or a decreasing absorber tube would lead to an increasing departure from the assumption that the complete broadened sun cone will be absorbed by the receiver tube, so that the advantage of the adaptive method becomes more pronounced. With respect to the manufacturability, although the trapezoid design stands for the easiest solution, one identified manufacture entity has stated that new irregular shape of a secondary reflector will not incur a substantial cost increase. A demonstration Hyperlight Energy linear Fresnel loop adopting the new adaptive design is planned to be completed in a near future and a collector performance campaign will be conducted. System cost and economics may also play a role in determining the optimal solution. If the receiver assembly cost is relatively high compared with the overall system cost, a life economic analysis would be essential to determine the final optimal solution. Otherwise, the receiver design with highest performance most likely becomes the optimal solution. For the Hyperlight collector development, it is found
Acknowledgement The work was supported by the United States Department of Energy under Contract No. DE-AC36-08GO28308 to the National Renewable Energy Laboratory, Southern California Gas Company through CEC/ EPIC Subtier Funds-In Agreement FIA-15-1809 and Combined Power LLC (Hyperlight Energy) through the Cooperative Research and Development Agreement CRD-16-625. References [1] Desideri U, Campana PE. Analysis and comparison between a concentrating solar and a photovoltaic power plant. Appl Energy 2013;113:422–33. [2] NREL. Available from:
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2010;87:541–50. [30] Grena R, Tarquini P. Solar linear Fresnel collector using molten nitrates as heat transfer fluid. Energy 2011;36:1048–56. [31] Reddy KS, Prasad GSC, Sundararajan T. Optimization of solar linear fresnel reflectors system with secondary concentrator for uniform flux distribution over absorber tube. Indian Institute of Technology Madras: Solar Energy; 2016. [32] Rabl A. Active solar collectors and their applications. New York: Oxford University Press; 1985. [33] Mathur SS, Kandpal TC, Negi BS. Optical design and concentration characteristics of linear Fresnel reflector solar concentrators – I mirror elements of varying width. Energy Convers Manage 1991;31(3):205–19. [34] Wendelin T. SolTrace: a new optical modeling tool for concentrating solar optics. In: 2003 International solar energy conference, Hawaii, USA; 2003. [35] SolTrace. Available from:
[19] NREL. The NREL concentrating solar power program; 2015. Available from:
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