Optics of solar central receiver systems: a review

Lifeng Li; Joe Coventry; Roman Bader; John Pye; Wojciech Lipiński

doi:10.1364/OE.24.00A985

1. Introduction

Solar central receiver (SCR) systems are considered to be a promising technology for solar radiation collection and conversion into high-temperature thermal energy for electricity production and chemical processing. The pioneering experimental study of an SCR system was reported in 1957 by the Soviet researchers Baum et al. [1]. An optical system consisting of 1,293 mirrors was investigated to produce steam at 400°C. Another early use of an SCR system for steam generation was reported in 1968 by Francia [2], followed by numerous studies around the world. In an SCR system, individual mirrors, called heliostats, approximate elements of paraboloids of revolution with different focal lengths and with time-dependent orientation to follow the actual position of the sun in two-dimensions, and focus solar radiation on a common focal area of a receiver positioned on a central tower. Radiation absorbed by the receiver is converted into high-temperature thermal energy and transferred further to a heat transfer medium or used directly in chemical reactions. The heat transfer medium carries thermal energy to other sub-systems such as power blocks or chemical reactors, with a possible intermediate heat storage sub-system that allows for matching solar and demand transients. Figure 1 shows the basic components of an SCR system for power generation. The SCR system technology has attracted much attention due to its inherent suitability for energy storage, and the potential to achieve low overall levelized cost of energy through a combination of high optical and thermal performance, and high working temperature (up to 1000°C in state-of-the-art designs) that allows for efficient conversion of thermal energy to electrical or chemical form. Romero et al. [4] and Behar et al. [5] provided broad review studies on SCR systems, projects, and technologies. Full-scale SCR systems are included in the review study of global concentrating solar power (CSP) plants by Pavlovíc et al. [6] and Zhang et al. [7].

Fig. 1 Schematic of a SCR system consisting of a heliostat field, a central tower receiver, thermal energy storage system, and a power block [3].

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High capital cost of SCR systems still limits its commercial deployment. Improvements in optical and mechanical performance of the optical sub-system are crucial for capital cost reduction as the heliostat field typically represents 30–50% of the capital cost of the system and the required size of the heliostat field for a given nominal power level of a solar plant is reduced with an increased optical efficiency [8]. Similarly, increasing thermal performance of the receiver decreases the required size of the heliostat field and the associated capital cost.

The present article reviews pertinent studies related to optical modeling, design, optimization and demonstration of SCR systems. It focuses on optics of heliostats and heliostat fields as motivated by a need to understand the potential to adapt and improve state-of-the-art designs to meet the needs of emerging applications of the SCR technology [9,10]. Advancement of heliostat fields towards efficient and cost-effective collection and focusing of sunlight is pivotal to the advancement of SCR systems for electricity generation and chemical processing at large scale. A review of receiver optics and heat transfer is beyond the scope of this study. For a broader study in the field of concentrating solar power technologies, the reader is referred to [11].

2. Theoretical background

2.1 Radiative transfer

Macroscopic radiative transfer models of solar concentrating systems use the laws of geometrical (ray) optics and the classical radiative transfer theory based on the radiative transfer equation (RTE) [12]. A model SCR system used to elucidate the pertinent optics and radiative transfer concepts is depicted in Fig. 2.

Fig. 2 Simplified radiative transfer model of an SCR system.

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The spectral intensity and flux of solar radiation incident from direction $\hat{s}$ on an arbitrary surface element dA with a normal $\hat{n}$ and at position $\vec{r}$ are given by

I_{λ,solar} (\vec{r}, λ, \hat{s}, t) = \frac{d Q_{solar} (\vec{r}, λ, \hat{s}, t)}{| \hat{n} \cdot \hat{s} | ​ d A d λ d Ω d t} = \frac{d {\dot{Q}}_{solar} (\vec{r}, λ, \hat{s}, t)}{| \hat{n} \cdot \hat{s} | d A d λ d Ω}

{\dot{q}}_{λ, solar} (\vec{r}, λ, t) = \int_{Ω = 0}^{2 π} I_{λ, solar} (\vec{r}, λ, \hat{s}, t) | \hat{n} \cdot \hat{s} | d Ω

where

d Q_{solar} (\vec{r}, λ, \hat{s}, t)

and

d {\dot{Q}}_{solar} (\vec{r}, λ, \hat{s}, t)

are, respectively, the solar radiative energy and radiative power intercepted by dA within the wavelength interval dλ around the wavelength λ. In this work, the radiative transfer nomenclature is adopted from [12] unless stated otherwise. In the following text, the time notation t of radiative properties and transfer quantities is omitted for brevity. Detailed spectral optical models of solar concentrators typically use the air mass 1.5 spectral distribution (AM 1.5) as the reference spectrum, further modified according to local atmospheric conditions [13,14]. Simplified spectral optical models typically employ the spectral distribution of a blackbody at an effective temperature of the sun of approximately 5780 K [12]. The directional distribution of the incident solar irradiation results from the sun–earth geometry, with the solid and half-cone angles of the solar disk equal to 6.79 × 10⁻⁵ sr and 4.65 mrad (0.27°), respectively, and the effect of a sunshape, i.e. solar radiation distribution observed from the earth within the solar disk and the circumsolar aureole. The ratio of the amount of energy contained in the circumsolar aureole to the total amount of direct energy arriving from the sun is defined as the circumsolar ratio (CSR). It is an important parameter that directly influences the flux distribution and solar image size at the focal plane. Examples of sunshape models used in optical analyses of SCR systems are the pillbox, Kuiper [15], Biggs and Vittitoe [16], Rabl and Bendt [17], and Buie [18] distributions.

Solar radiation incident on a reflector surface element dA with a local normal $\hat{n}$ of a solar concentrator is partially reflected into a direction ${\hat{s}}_{r}$ . In geometrical optics, the most fundamental property describing the reflection process under the local thermodynamic equilibrium condition is the spectral bi-directional reflection function $ρ_{λ}^{''} (\vec{r}, λ, {\hat{s}}_{i}, {\hat{s}}_{r})$ , defined as [19,20]

ρ_{λ}^{''} (\vec{r}, λ, {\hat{s}}_{i}, {\hat{s}}_{r}) = \frac{d I_{λ} (\vec{r}, λ, {\hat{s}}_{i}, {\hat{s}}_{r})}{I_{λ} (\vec{r}, λ, {\hat{s}}_{i}) | \hat{n} \cdot {\hat{s}}_{i} | d Ω_{i}}

In the limiting cases of optically smooth and diffuse surfaces,

ρ_{λ}^{''} (\vec{r}, λ, {\hat{s}}_{i}, {\hat{s}}_{r}) = {\begin{cases} \infty, for θ_{r} = θ_{i}, ψ_{r} = ψ_{i} + π \\ 0, for all other {\hat{s}}_{r} \end{cases} optically smooth

ρ_{λ}^{''} (\vec{r}, λ) = ρ_{λ}^{' \cap} (\vec{r}, λ) / π diffuse

where the unit direction vector

\hat{s}

is expressed in terms of the polar angle θ (measured from the surface normal

\hat{n}

) and the azimuth angle ψ (measured between an arbitrary axis on the surface and the projection of

\hat{s}

on that surface). Minimum spectral attenuation and angular spread of the reflected intensity

I_{λ} (\vec{r}, λ, {\hat{s}}_{r})

are the desired reflection characteristics of a reflecting surface to maximize the total radiative power intercepted by the receiver aperture of an area A_rec,

{\dot{Q}}_{rec} (\vec{r}) = \int_{λ = 0}^{\infty} \int_{A_{rec}}^{} \int_{Ω = 0}^{2 π} I_{λ, rec} (\vec{r}, λ, \hat{s}) | \hat{n} \cdot \hat{s} | d Ω d A d λ

Note that the optical concentrator of an SCR system may consist of more than one reflector between the reference location of the incident solar radiation and the receiver.

The atmospheric transfer of radiation, and thus the spatial variation of radiative intensity between the reference location of incidence, reflectors and a receiver is modeled using the quasi-steady form of the radiative transfer equation, $\frac{d I_{λ} (\vec{r}, λ, \hat{s})}{d s} + β_{λ} I_{λ} (\vec{r}, λ, \hat{s}) = κ_{λ} I_{λ,b} (\vec{r}, λ) + \frac{σ_{s, λ}}{4 π} \int_{Ω_{i} = 0}^{4 π} I_{λ} (\vec{r}, λ, {\hat{s}}_{i}) Φ_{λ} (\vec{r}, λ, {\hat{s}}_{i}, \hat{s}) d Ω_{i}$ (6)

where κ_λ and σ_s,_λ are the spectral absorption and scattering coefficients, respectively, β_λ = κ_λ + σ_s,_λ is the extinction coefficient, and $Φ_{λ} (\vec{r}, λ, {\hat{s}}_{i}, \hat{s})$ is the scattering phase function of radiation from the direction ${\hat{s}}_{i}$ into $\hat{s}$ . The radiative properties are determined by employing atmospheric models that account for the actual composition of the gas, liquid and solid phases [21,22]. The quasi-steady form of RTE is employed as justified by the small characteristic radiation propagation times at length-scales associated with the overall dimensions of solar thermal systems.

2.2 Performance metrics

The performance metrics of concentrating solar thermal systems can be categorized as optical and thermodynamic. The basic optical performance metrics are the optical efficiency and the solar concentration ratio. The basic thermodynamic performance metrics are the absorption efficiency, the ideal thermodynamic conversion efficiency, and the receiver thermal efficiency.

2.2.1 Optical efficiency

The overall optical efficiency is defined as the ratio of the radiative energy intercepted by the receiver with an aperture area A_rec to the maximum possible energy that can be intercepted by the total concentrator (heliostat field) area for a given time period. The maximum possible radiative power that can be collected by the heliostat field is calculated as radiative power collected when solar rays are incident normally on an area equal to the total installed mirror area A_mirror of the heliostat field [23]. It should be noted that this efficiency is not based on the land area covered by the entire field, nor the heliostat field aperture area which takes into account the cosine effect (see below) and the open or opaque spaces among mirrors [24].

η_{optical} = \frac{\int_{Δ t} {\dot{Q}}_{rec} d t}{G A_{mirror} Δ t}

where G is the direct normal irradiance (DNI). The nomenclature for the irradiance G is adopted from [25]. For simulation or reference purposes, G is often taken equal to 1 kW m⁻² [25]. Hence, optical efficiency is a measure of how well the mirror surface performs in transferring radiation to the receiver, compared with an absolute upper bound based on the DNI and the total mirror area. This representation is useful, as heliostat field costs scale essentially linearly with total mirror area.

The overall optical efficiency accounts for cosine, shading, blocking, spillage, reflection, and atmospheric attenuation losses:

η_{optical} = η_{cosine} η_{shading} η_{reflection} η_{blocking} η_{spillage} η_{atmosphere}

The cosine effect refers to the fact that the amount of radiative power intercepted by the heliostat is proportional to the cosine of the angle between the heliostat surface normal and the direction of incident solar rays. The shading loss occurs when part of a heliostat surface is in shadow of a preceding heliostat, the tower or the receiver. The reflection loss results from the less-than-unity reflectivity of the heliostat surface. Some of the solar rays reflected from heliostats may hit the back surface of another heliostat instead of reaching the receiver, resulting in the blocking loss. The spillage loss occurs when solar rays reflected from the heliostat field miss the target. Spillage results from small receiver aperture size, heliostat surface error and heliostat misalignment. Atmospheric scattering and absorption result in the atmospheric attenuation loss, which increases with the distance between the heliostat and the receiver aperture and the water vapor or aerosol content in the atmosphere. A representative schematic showing each of these optical losses is shown in Fig. 3. A representative value for the annual overall optical efficiency of the PS10 solar power plant is approximately 67.5%, which is broken down as 84.4%, 96.6%, 88.0%, 99.1%, 99.4%, and 95.5% for cosine, shading, reflection, blocking, spillage, and atmospheric attenuation efficiencies [26]. This optical assessment was performed with winDELSOL (see Section 5.3).

Fig. 3 Optical losses in an SCR system that are pertinent to the definition of the optical efficiency [3].

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2.2.2 Concentration ratio

The commonly used definition of concentration ratio is the area (geometric) concentration ratio. It is defined as the ratio of the concentrator aperture area A_conc to the receiver aperture area A_rec [25],

C_{a} = \frac{A_{conc}}{A_{rec}}

The instaneous, area-average flux (energetic) concentration ratio is defined as the ratio of the area-average radiative flux incident at the receiver aperture to that on the concentrator aperture, which is normally referred to as the direct normal irradiance G,

C_{f} = \frac{{\dot{Q}}_{rec}}{A_{rec} G}

Due to the dramatic variation of the radiative flux over the receiver aperture, the local flux (energetic) concentration ratio can be defined as the ratio of the local radiative flux at any point of the receiver aperture to that on the concentrator aperture.

The time- and area-average flux concentration ratio over a time period Δt is obtained as:

{\bar{C}}_{f} = \frac{\int_{Δ t} {\dot{Q}}_{rec} d t}{G A_{rec} Δ t}

Higher temperatures at the receiver can be attained from higher concentration ratios that imply less radiation loss from a smaller receiver. However, there is a fundamental thermodynamic limit of achievable concentration. The ideal or maximum concentration ratio that a two-dimensional (linear concentrators) and three-dimensional (point-focus concentrators) concentrating system can achieve are

C_{a,ideal,2D} = \frac{1}{\sin θ_{c}},

C_{a,ideal,3D} = \frac{1}{\sin^{2} θ_{c}},

where θ_c is the acceptance half angle that is half of the angular range over which radiation is accepted without moving all or part of the receivers. The ideal concentration ratio cannot be infinitely large due to the actual angular size of the sun (half-cone angle 4.65mrad) giving the thermodynamic limit concentration for point-focus concentrators 46,250 and for linear concentrators 215 [23,25,27]. A multitude of practical issues further limit the concentration ratios of engineered systems. The solar flux concentration ratio typically varies between 30 and 100 for trough systems, 1000–10,000 for dish systems, and 500–5,000 for tower systems [9]. The concentration can be increased with the help of secondary concentrators (see Section 3). For SCR systems with two-axis tracking, the typical range of area concentration ratio and indicative temperature are 100–1500 and 150–2000°C, respectively [28].

2.2.3 Absorption, ideal thermodynamic conversion, and receiver thermal efficiencies

The absorption efficiency of a solar receiver is defined as the ratio of radiative power absorbed by a perfectly insulated and isothermal receiver at tempereature T_H to the concentrated radiative power intercepted by the receiver aperture,

η_{absorption} = α - \frac{ε σ T_{H}^{4}}{G C}

where σ is the Stefan–Boltzmann constant equal to 5.67 × 10⁻⁸ W m⁻² K⁻⁴; α, ε and C are the total apparent absorptivity and emissivity at the receiver aperture, and the area-average flux concentration ratio, respectively. The receiver thermal efficiency is a generalization of the absorption efficiency definition (Eq. (14)) introduced above. The receiver thermal efficiency accounts for losses due to forced and natural convection, conduction through receiver walls, and thermal re-radiation through the aperture. It is defined as the ratio of the net heat rate gained in the receiver to the concentrated radiative power intercepted at the receiver aperture.

η_{thermal} = \frac{{\dot{Q}}_{net}}{A_{rec} G C}

The ideal thermodynamic conversion efficiency is defined as the ratio of work rate produced by a Carnot engine operating between a perfectly insulated and isothermal blackbody receiver and a cold reservoir at T_H and T_L, respectively, to the concentrated radiative power intercepted at the receiver aperture. It provides the upper theoretical limit of conversion of concentrated solar radiation into work, and is equal to the product of the blackbody-receiver absorption and Carnot efficiencies,

η_{ideal} = η_{absorption,bb} η_{Carnot} = (1 - \frac{σ T_{H}^{4}}{G C}) (1 - \frac{T_{L}}{T_{H}})

Figure 4 shows the blackbody absorption, Carnot, and ideal thermodynamic system efficiencies as functions of receiver temperature for selected values of the concentration ratio C in the range 100–10,000.

Fig. 4 Blackbody absorption, Carnot and ideal thermodynamic conversion efficiencies as functions of the receiver temperature for selected values of the solar concentration ratio [29].

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The upper overall theoretical efficiency limit of an SCR system is the product of the optical efficiency and the ideal thermodynamic conversion efficiency. It is a vector for coupled receiver and heliostat field optimization. The optical performance is maximized through rigorous design of individual heliostats, heliostat fields, and receivers by iterative optimization of their geometry, orientation, position and materials.

3. Classification of solar central receiver systems

Solar central receiver systems can be classified according to the geometrical configuration of secondary concentrator at the aperture of a receiver such as a compound parabolic concentrator (CPC). In the basic classification, tower-receiver and tower-reflector (beam-down) systems are distinguished. In a tower-receiver system, heliostats reflect radiation directly towards the receiver on a central tower. Figures 5(a)–5(d) shows the basic configurations of tower-receiver systems: (a) a single receiver with a single asymmetrically-located aperture and a polar heliostat field b) a single receiver with a circumferential aperture and a surround field c) a single receiver with multiple apertures/partitions and multiple polar fields located concentrically around the receiver, and (d) multiple receivers of any type located within a surround field constructed as a superposition of multiple fields or field segments. A multi-aperture cavity receiver system with each aperture equipped with a separate secondary concentrator and matched to a separate heliostat field was developed by Schmitz et al. and is shown in Fig. 5(c) left [31]. A “butterfly” field with six concentrators to match the multi-aperture receiver design was developed by Segal and Epstein and is shown in Fig. 5(c) right [32]. A multi-tower system (Fig. 5(d)) was developed by Schramek and Mills for the purpose of maximizing the ground area usage [33].

Fig. 5 Examples of SCR system configurations: (a) a single tower receiver with a single asymmetric aperture and a polar heliostat field (reprinted from [30], Copyright (2007), with permission from SolarPACES) b) a single tower receiver with a circumferential aperture and a surround field (reprinted from [4], Copyright (2002), with permission from the American Society of Mechanical Engineers) c) a single tower receiver with multiple apertures and multiple polar fields located concentrically around the receiver (left: reprinted from [31], Copyright (2006), with permission from Elsevier; right: reprinted from [32], Copyright (1999), with permission from Elsevier) d) multiple tower receivers immersed in a surround field constructed as a superposition of multiple fields (reprinted from [33], Copyright (2003), with permission from Elsevier), and (e) tower-reflector system (reprinted from [34], Copyright (1998), with permission from Elsevier).

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A tower-reflector system (Fig. 5(e) makes use of the Cassegrain optical configuration [35]. Heliostats reflect radiation towards a secondary reflector located on a tower, which in turn reflects radiation towards the receiver located on the ground level. The tower reflector approximates a hyperboloidal reflector if placed below the heliostat field focal point, or an ellipsoidal reflector if placed above the heliostat field focal point. A CPC is coupled with the receiver for increasing the concentration ratio at the expense of active cooling and additional optical losses [32]. Despite allowing for ground-level location of the receiver and related equipment as in the existing demonstration systems, no large-scale beam-down system has been built yet. Disadvantages of beam-down SCR systems include the decreased optical efficiency due to non-ideal mirror reflectivity, the increased beam spread, the large size of the secondary mirror, and the requirement to rigidly mount the secondary mirror near the primary focus [36].

Solar central receiver systems are designed by matching thermal requirements of thermal or thermochemical processes such as temperature, power level, transient variations, to thermal characteristics of a receiver. Receiver selection/design is inherently coupled to the selection/design of an optical concentrator. A broad variety of receiver designs specific to SCR systems have been conceptualized, designed and demonstrated as summarized by Ávila-Marín [37] and Ho and Iverson [38]. In this study, we omit a detailed discussion of receiver optics, and thus limit the classification to the basic receiver types, an external receiver and a cavity receiver, as schematically shown in Fig. 6. For an external receiver (Fig. 6(a)), radiation absorption, radiative and convective heat losses to the surrounding, and heat transfer to a working fluid or chemical reaction occur at the same surface. Due to the large surface area required for heat transfer, at high temperatures external receivers exhibit high radiative and convective losses. Radiative losses can be minimized by employing high-temperature selective coatings. Thus, the current use of external receivers is limited to applications with operating temperatures below approximately 1000 K. An external receiver can have a circumferential aperture to match a surround field as shown in Fig. 5(b), enabling very wide acceptance angles. Practical advantages are that it is conceptually simple, has light supporting structures, allows simpler maintenance, and reduces atmospheric attenuation losses by reducing the mean distance to heliostats.

Fig. 6 Basic receiver types: (a) external receiver and (b) cavity receiver. Reprinted from [38], Copyright (2014), with permission from Elsevier.

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For a cavity receiver (Fig. 6(b)), high-flux irradiation enters the receiver cavity through an open or windowed aperture, and is absorbed at internal surfaces or/and in a volume of a radiatively participating medium inside the cavity. Numerous cavity configurations and radiative absorption scenarios have been proposed, from direct irradiation of active heat transfer media or chemical reactions to indirect heating by heat transfer through absorbing solid elements of the cavity, from stationary designs to designs with moving internal parts and variable aperture sizes. Cavity receivers are preferred for high-temperature applications due to their high absorption efficiency. Because of the high-flux requirement, cavity receivers are best matched with polar (segment) heliostat fields of high optical efficiency. Multi-cavity receiver designs requiring moderate-flux concentration, such as at the Khi Solar One power plant [39,40] may have a hybrid polar-surround type heliostat layout (similar to Fig. 5(c) right).

Radiative performance of cavity receivers in SCR systems can be further improved by applying secondary concentrators such as CPCs as in an example study by Segal and Epstein [41]. The use of a CPC increases the concentration ratio (ideally by a factor 1/sin²θ, where θ is the half-acceptance angle of a CPC), allows for utilization of spillage radiation directly around the hot spot, and spreads the angular distribution of the exiting radiation [42]. The latter allows for more uniform irradiation inside a receiver cavity, in particular for eliminating hot spots. Kribus et al. investigated performance limits of tower systems with four secondary concentrator options [43]: tower-top CPC, tailored edge-ray concentrator (TERC) approximated by a cone, and a Cassegrain system with ground-level CPC or compound elliptic concentrator (CEC). An annular compound parabolic concentrator (ACPC) was proposed by Lipiński and Steinfeld for utilization of low-grade spillage radiation outside the hot spot [44]. Except from conventional axi-symmetric secondary concentrators, secondary concentrators with non-regular cross sections were proposed and evaluated in tandem with heliostat fields with wider range of possible contours [45]. Beside improving overall optical system performance, the capture of spillage radiation helps protect outer walls of receivers from overheating, thus lowering the requirements for using protective shields and active cooling.

4. Optics of heliostats

An individual heliostat is composed of a reflector (one or more mirror facets), a supporting structure including foundations, and an actuation system. The specular reflectivity of the mirror facets, the alignment of the mirror facets, the alignment of the tracking system, and the structural rigidity (particularly under operational wind loads) must be optimized for best optical performance of an individual heliostat.

4.1 Classification

Heliostats can be classified in various ways, for example, by reflector type or by tracking arrangement. An extensive evaluation and classification of heliostat designs according to mirror type was conducted at Sandia National Laboratories in the 1980s [3]: glass-metal heliostats (Figs. 7(a) and 7(c)) utilize multiple individually curved glass mirror facets, supported by a rigid steel structure; stressed–membrane heliostats are based on two membranes (one reflective) with curvature provided by active control of the pressure between the membranes (Fig. 7(b)). Most recent heliostat designs include the Stellio heliostat developed by SBP Sonne [49], the proposed ASTRI sandwich-panel heliostat [50], and the suspension heliostat such as that proposed by Solaflect [48].

Fig. 7 Heliostat design examples: (a) flat glass–metal heliostat (1.14 m2 eSolar heliostat) (reprinted from [46], Copyright (2011), with permission from Elsevier) b) stressed–membrane heliostat (150 m2 metal membrane heliostat, PSA) (reprinted from [47], Copyright (1996), with permission from Schlaich Bergermann und Partner (SBP)), and (c) focusing glass–metal heliostat (16 m2 Solaflect’s suspension heliostat) (reprinted from [48], Copyright (2013), with permission from Solaflect Energy).

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A heliostat with a flat mirror produces a degraded focal spot at the receiver aperture, especially for large mirrors [51]. Thus, focusing (curved) heliostats have been developed that display optical performance nearly independent of their size. However, it is noted that astigmatic aberration (see Section 4.2.1) becomes worse for larger heliostats, which imposes optical constraints on large heliostats. The question of optimal heliostat size is debated by many authors [52,53] and is both an optical and cost related trade-off. The reflecting surface is divided into pre-aligned flat or curved and canted mirror facets. For any type of heliostats, decreasing their size is beneficial for ensuring a high optical quality of the reflecting surface, and minimizing shading and blocking losses in the field. A review of the state of the art in heliostat design and cost reduction is given by Coventry and Pye [53] and Pfahl [54].

4.2 Optical studies

The relevant optical losses associated with individual heliostats are due to imperfect reflection (reflectivity value less than unity, angular spread), cosine effect, and spillage. The reflectivity of the mirror depends on the surface material and its manufacturing precision. The non-normal orientation of a heliostat with respect to the directions of solar irradiation and towards the receiver results in the cosine loss. The spillage loss results from radiation incident at an area outside the prescribed receiver aperture. In seeking to achieve higher-temperature SCR systems, higher concentration ratios are required without increasing optical losses. This imposes challenging constraints on SCR system components.

4.2.1 Astigmatism

A key factor limiting the concentration ratio for a focusing collector system is the astigmatism effect, or off-axis aberration, from non-normal incidence. For tangential and sagittal rays, the focal lengths are shorter or longer than the nominal focal length, respectively, which results in degradation of the focal spot [55,56]. The astigmatism effect increases with increased slant range and increased cosine value of the angle between the heliostat surface normal and the incident rays [56]. The method used to correct the astigmatism effect in telescopes adapted to heliostats requires 2 m × n motors for a heliostat composed of m × n facets, which is impractical. A non-imaging focusing heliostat which manoeuvres the facets in a group manner so that the required number of motors can be reduced to m + n-2 or even 2 has been studied by Chen et al. [57,58] and Chong [59,60].

4.2.2 Aiming

The concentrated flux distribution at the receiver aperture requires controlling according to receiver geometry, lifetime and the specific requirements of thermal or thermal-chemical processes. Therefore, dynamic adjustment of flux distribution at the receiver aperture, i.e. aiming strategy, is indispensable for the optical sub-system design and optimization. A review study of aiming strategies for central receivers was performed by Grobler and Gauché [61]. Salomé et al. presented an open-loop approach to control the flux density distribution by selecting the best aiming point for each heliostat [62].

4.2.3 Canting and focusing

Mirrors or their individual facets of focusing heliostats are canted to focus solar irradiation on the receiver aperture. The canting concepts mainly include typical on- and off-axis canting, and newly proposed stretched-parabolic and target-aligned canting. Buck and Teufel presented a study to compare and optimize the canting methods [63]. In on-axis canting, heliostat elements are aligned while the sun and target vectors are perpendicular to the heliostat plane. In off-axis canting, the alignment is performed when the sun vector is oblique to the heliostat plane. Jones assessed the two approaches and concluded that on-axis canting consistently results in high optical performance while off-axis canting can lead to superior upper theoretical limit in optical performance with the actual performance strongly dependent on day and seasonal time [64]. Review studies of canting and focusing methods are published by Yellowhair and Ho [65] and Ren et al. [66]. Optical and mechanical canting methods were summarized, including the gauge blocks, inclinometers, photogrammetry, fringe reflection, imaging with theoretical image overlays, laser beam projections, camera look-back, and target reflection. New heliostat facet canting method was investigated for example by Yellowhair et al. by using a target in reflection [67]. Segal and Epstein investigated canting and focusing of facets of the hyperboloidal tower reflector at the Weizmann Institute of Science (WIS) by grouping facets to reduce the canting time [68].

4.2.4 Tracking

Tracking systems control movement of heliostats to align them according to the actual position of the sun. Accurate heliostat tracking is crucial to minimize the cosine loss and spillage loss on the receiver aperture. The tracking accuracy is characterized by the value of a tracking error. A good tracking system has a tracking error as low as 0.2 mrad (0.01°) as developed by Brown and Stone [69]. Based on the signal operation mode, closed-loop or open-loop tracking systems are distinguished, with the commercial systems opting for the latter with periodic closed-loop ‘alignment correction’ applied. Sun tracking systems were reviewed by Lee et al. [70] and Mousazadeh et al. [71]. The principle of spinning-elevation tracking or target-aligned tracking method was first discussed by Ries and Schubnell [72] and Zaibel et al. [73]. Performance of the two tracking methods, the azimuth-elevation method and the spinning-elevation method was compared by Chen et al. [74] and Chong and Tan [75]. The spinning-elevation method was found to offer a smaller image spread, as well as spatially and temporally more uniform radiative flux distributions, which in turn results in reduced spillage loss. An automated open-loop eight-dimensional tracking error characterization and correction method was presented by Khalsa et al. [76]. The method was demonstrated to lead to highly-reduced heliostat elevation and azimuth pointing errors using the National Solar Thermal Test Facilities (NSTTF) at Sandia National Laboratories [77]. In the study by Flesch et al., an auxiliary mirror attached to every heliostat in a field was used to create a small reflection image on a target, which in turn was used to automatically adjust the heliostat orientation [78].

4.2.5 Wind load

Wind loads generate mirror instabilities degrading the optical quality of the image on the receiver aperture. Most studies have focused on mechanical analyses of wind load on heliostats [79,80], a subject beyond the scope of the present review. Addressing the issue of wind loads effects on optical performance of heliostats is crucial for optical performance improvement and cost reduction of heliostats [53]. Strachan and Houser experimentally investigated wind load effects on optical performance of Advanced Thermal Systems (ATS) and Solar Power Engineering Company (SPECO) heliostats [81].

5. Optics of heliostat fields

The optical design and optimization of a heliostat field are the culminating tasks in a SCR system designed for high optical efficiency. The optical losses associated with a heliostat field are due to shading, blocking and atmospheric attenuation. A general design process for a heliostat field with prescribed heliostat and receiver types is to (i) determine the basic system configuration, i.e. the heliostat field type, the relative position of the heliostat field and the receiver ii) generate and optimize the heliostat field layout by specifying the heliostat locations through a tradeoff between performance and cost via a simplified optical analysis, and (iii) iteratively obtain a high-fidelity heliostat field layout and accurate optical performance predictions through detailed optical/radiative transfer models of the system coupled to thermal and thermochemical models of receivers and receiver-reactors, respectively, and incorporating annual performance and overall techno-economic analyses of the system.

5.1 Classification

Based on the heliostat field layout boundary, polar fields and surround fields are distinguished as shown in Figs. 5(a) and 5(b), respectively. A surround heliostat field allows for circumferential irradiation of a central receiver, while a polar field results in highly-asymmetric irradiation. In a surround field, the east and west heliostats can collect solar radiation at lower values of the solar azimuth angle. For a given power level, the height of the central tower with a surround field is smaller as compared to that for a polar field, thus reducing thermal losses from the tower and piping, the amount of construction materials, and consequently the cost. Additionally, the distance between the most remote heliostats of a surround field and the receiver is smaller as compared to that for a polar field, reducing optical losses from atmospheric attenuation within the system. Alternatively, the heliostats in a polar field configuration (north or south field configuration for plants located in the norther or southern hemisphere, respectively) are all arranged on one side of the tower and operate with lower cosine losses. The polar field approach may generally be used when a cavity receiver is needed for high-temperature applications as discussed in Section 3.

5.2 Layout generation and optimization

Numerous studies on generation and refinement of heliostat layouts have been reported in literature. Basically, there are four categories of heliostat patterns: (a) radial cornfield b) radially-staggered field c) N–S cornfield, and (d) N–S staggered field [82]. The radially-staggered pattern is used in a majority of developments due to its proven superior performance over the other patterns from the above list. However, the biomimetic pattern developed by Noone et al. was found to have optical efficiency and ground coverage even higher than the radially-staggered pattern [83].

With the basic heliostat pattern selected, a field layout is generated and optimized. Examples of studies on generating heliostat field layouts include the cellwise method [82], the graphical method [84], the Yearly Normalized Energy Surface data based method [85], the method based on direct determination of heliostats position in the field as proposed by Collado [86], the Campo code [87], and the Heliostat Field Layout Design code [88].

More studies have been reported on heliostat field layout optimization. The optimization methods differ in fidelity (e.g. types of optical losses considered, weather conditions, and sunshape models), optimization criteria, and computation time. Pitz-Paal et al. published a study on heliostat field layout optimization for maximum annual solar-to-chemical energy conversion efficiency [89]. A computationally efficient method for designing and optimizing heliostat field layout was developed by Besarati and Goswami based on a new proposed method for calculating shading and blocking losses [90]. Further pertinent studies were published by Wei et al. [91], Pisani et al. [92], Buck [8], Dunham et al. [93], and Atif and Al-Sulaiman [94]. A comparative study of heliostat field layout characteristics designed and optimized with selected methods including dense radially-staggered layout, graphical method, Campo code, DELSOL software, and biomimetic pattern (see Fig. 8) was conducted by Mutuberria et al. [95]. The number of heliostats, annual optical efficiency and annual energy collected were used as the comparative criteria. It was found that for the three design power levels of 100, 120, and 150 MW_th, the layout generated with the dense radially-staggered method had the lowest optical efficiency of 71.1%, 68.9%, 61.0%, respectiviely, while among the other four methods, the highest optical efficiencies were achieved by the biomimetric pattern, 75.2%, 74.2%, 72.9%. The layout generated by the Campo code showed performance close to that of the biomimetic pattern in terms of the annual optical efficiency [95].

Fig. 8 Heliostat field layouts developed with different approaches: (a) dense radial staggered method b) Campo code c) graphical method d) DELSOL code and (e) biomimetic pattern. The color bar shows the annual optical efficiency values. Reprinted from [95], Copyright (2014), with permission from SolarPACES.

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5.3 Optical modeling

Detailed optical models are used to obtain accurate predictions of spatial and temporal radiative flux distributions at the receiver aperture. The cone optics, hermite polynomial expansion/convolution and Monte Carlo ray-tracing (MCRT)/statistical methods are used in optical simulations.

Monte Carlo ray-tracing methods are the most robust simulation techniques for optical and radiative transfer modeling of SCR systems [96]. As statistical methods, they can incorporate spatial, angular, spectral and temporal variations of radiative intensity, arbitrary spectral and directional properties of opaque and transmitting surfaces as well as participating media [12,97,98]. Monte Carlo ray-tracing methods come in multiple variants, from simple methods such as the basic collision-based method to advanced methods implementing various strategies towards increased computational efficiency and accuracy such as the energy partitioning and pathlength methods.

Hermite polynomial expansion/convolution method was used for flux calculation in codes such as DELSOL/winDELSOL [99,100], HFLCAL [101], and UHC/RCELL [82]. Monte-Carlo ray-tracing was used for developing codes such as MIRVAL [102] and SolTRACE [103]. HELIOS, an early model developed in late 1970s and based on cone optics, was used to predict a concentrated solar flux distribution on an arbitrary target grid obtained from a heliostat field [55]. Modeling tools for SCR systems can be found in review studies by Garcia et al. [104], Ho [105], and Bode and Gauché [106]. Yellowhair et al. compared DELSOL, HELIOS, SolTrace, Tonatiuh for modeling complex receiver geometries [107].

In the present study, selected modeling tools for SCR systems are summarized in Table 1. The tools differ in methods for radiative flux computations, types of optical losses accounted for, types of optical and radiative output characteristics, availability of user-defined field layout and receiver configurations, size limits of heliostat field and/or SCR systems, annual performance and optimization capabilities, and computational cost and efficiency.

Table 1. Tools for solar central receiver system modeling

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5.4 On-sun optical characterization and demonstration

This section reviews SCR systems at the research, demonstration and commercial scales. Listings of SCR research, demonstration and commercial systems are also available as Internet resources including crowdsourcing and include the most recent global developments (e.g [39,40,108,109].). A selection of systems designed for research and development purposes are listed in Table 2. Exemplary systems are shown in Fig. 9. Demonstration studies of tracking strategies were conducted by Smith and Ho at NSTTF [77], and by Flesch et al. at the Jülich Solar Tower of the German Aerospace Center (DLR) [78]. Examples of studies on investigating optical performance evaluated primarily through measurements of temperature and flux distribution at receiver or reactor apertures can be found in [110–114]. Other optical studies on heliostats include experimental analysis of heliostat surface deformation due to gravity in the Themis solar tower facility in France [115], wireless heliostat control system for self-powered heliostat fields in Jülich Solar Tower [116], on- and off-axis canting methods investigation in DAHAN tower plant [110], and the experimental study of the first fully automous heliostat field carried out with the Small Solar Power Systems (SSPS-CRS) facility in Spain [117].

Table 2. Demonstration solar central receiver systems [39,40]

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Fig. 9 Selected SCR demonstration systems: (a) NSTTF, USA (reprinted from [77], Copyright (1999), with permission from Elsevier) b) DAHAN tower plant, China (reprinted from [110], Copyright (2014), with permission from solar thermal group of Chinese Academy of Sciences) c) Daegu Solar Power Tower, South Korea (reprinted from [111], Copyright (2015), with permission from Elsevier) d) Jülich Solar Tower, Germany (reprinted from [133], Copyright (2011), with permission from the American Society of Mechanical Engineers) e) Heliostat Test Field, Sonora, Mexico (reprinted from [112], Copyright (2011), with permission from SolarPACES) f) SSPS-CRS facility, Spain (reprinted from [134], Copyright (1991), with permission from Springer).

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Table 3 gives an overview of selected commercial SCR systems that are in operation or under development/construction [108]. These SCR systems are generally used to provide heat to steam turbine power cycles operating at up to 565°C. Consequently, these systems typically use external receivers, which are suitable at this temperature level. There is a larger number of demonstration SCR systems designed to achieve higher temperatures for the research purpose on optics, materials, thermochemistry, and/or thermophysics. At higher temperature levels, cavity receivers and/or secondary concentrators are required to reduce the re-radiation losses from the receiver.

Table 3. Commercial solar central receiver systems [39,40]

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The size of commercial SCR systems varies greatly. Currently, the largest reported SCR system, used in the Ivanpah Solar Power Facility generating up to 377 MW_e of electric power, has a solar field aperture area of 2.6 km². Commercial SCR systems use a range of heliostat types with heliostat aperture areas ranging from ~1 m² (eSolar heliostat) to 140 m² (Abengoa Solar heliostat).

6. Summary and conclusions

In this study, we have reviewed basic concepts associated with optics of solar central receiver systems. Typical system configurations were discussed along with the main components, heliostat, heliostat field, secondary concentrator, and receiver. A review of research studies on optical design, optimization and characterization of heliostats and heliostat fields was conducted. A large variety of optical analysis tools have been developed, and applied to design and optimization of demonstration and commercial facilities. A relatively small number of published studies report experimental results of on-sun optical characterization of central receiver systems. Modeling the optical performance of central receiver systems is an efficient and accurate approach for the design and optimization without incurring substantial costs associated with construction of early-stage prototype systems. The large number of available tools allows optical engineers to reduce the development time. However, the specific configurations of individual designs typically necessitate extension or development of new, advanced tools that allow for increased simulation accuracy and flexibility, in particular for problems coupling optics, thermophysics and thermochemistry in plant sub-systems. Optical design and optimization of SCR systems is the key to reduce their capital cost.

Acknowledgments

Financial support by the Australian Renewable Energy Agency (ARENA), grant Solar R&D 2014/RND005, is gratefully acknowledged. We thank Dr Keith Lovegrove of IT Power Australia Pty Ltd for numerous discussions related to solar central receiver system design, performance and economics.

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Tool	Year	Full name	Developed by	Programming language¹	Flux calculation methods	Applications²	Refer-ences
CAMPO	2011	-	Zaragoza University	MATLAB	-	CRS	[87]
CRS4-2	2011	Crs4 Research Software for Central Receiver Solar System SimulationS	Center for Advanced Studies, Parco Scientifico e Tecnologico, Italy	Fortran	-	CRS,BD	[118]
DELSOL	1979	-	Sandia National Laboratories (SANDIA)	FORTRAN77	Hermite polynomial expansion/convolution	CRS	[99]
winDELSOL	1986	-	SANDIA	FORTRAN77	Hermite polynomial expansion/convolution	CRS	[100]
EnerTracer	2000	-	Plataforma Solar de Almeria (PSA)	C + +	MCRT	Light reflecting system	[119]
Fiat_Lux	1997	-	PSA	MATLAB	MCRT	CRS	[120]
HELIOS	1981	-	SANDIA	FORTRAN extended - version 4	Cone optics	CRS, PT, DS	[55]
HFLCAL	1986	Heliostat Field Layout CALculations	DLR	-	Convolution	CRS	[101]
HFLD	2010	Heliostat Field Layout Design	Chinese Academy of Sciences (CAS)	MATLAB	MCRT	CRS	[88]
Koikari & Yoshida	2012	-	Institute of Appliend Energy, Tokyo	CUDA, GPU by NVIDIA	MCRT	Tower reflector system	[121]
MIRVAL	1978	-	SANDIA	Fortran	MCRT	CRS	[102]
MIT code /Biomimetic	2012	-	Massachusetts Institute of Technology (MIT)	Fortran	Convolution	CRS	[83]
MUEEN	2000	-	Center for Solar Energy studies, Tripoli, Libya	C + +	Graphical	CRS	[84]
NSPOC	2009	New Solar Plant Optimization Code	-	Fortran	-	CRS	[122]
Raytrace3D-PowerTower	2010	-	Fraunhofer Institute for Solar Energy Systems (ISE)	-	MCRT	CRS	[123]
SCT	2006	Solar Concentration Toolbox	Centro de Investigaciones Energéticas Medioambientalesy Tecnológicas (CIEMAT) lab	MATLAB	MCRT	CRS	[85]
SENSOL	2005	-	SENER	Fortran	-	CRS, PT, PV, BD	[124]
SoFiA	2015	Solar Field Assessment	-	-	MCRT	CRS	[125]
SOLFAST	2012	SOLar Facilities Simulation Tools	HPC-SA and PROMES-CNRS lab	-	MCRT	CRS, PT, DS,	[126]
SolTRACE	2003	-	National Renewable Energy Laboratory (NREL)	C + +	MCRT	Solar power optical systems	[103]
SPRAY	-	-	DLR	Fortran90	MCRT	CRS, PT, BD, Linear-Fresnel	[127]
STRAL	2009	Solar Tower Ray-tracing Laboratory	DLR	C + + , assembler	MCRT	CRS	[128]
TieSOL	2011	-	Tietronix Software Inc.	C, C + + , C#, OpenGL	MCRT	CRS	[129]
Tracer	2009	-	Tel Aviv University, Australian National University (ANU)	Python	MCRT	Optical systems	[130]
Tonatiuh	2009	-	National Renewable Energy Centre (CENER), Spain	C + +	MCRT	Solar concentrating systems	[131]
UHC-RCELL	1974	University of Houston Code	University of Houston	FORTRAN77, C + +	Hermite polynomial expansion/convolution	CRS	[82]
VEGAS	2010	-	ETH Zurich	Fortran90	MCRT	Reflector geometries	[132]

Country	Developed by	SCR systems	Turbine power/ Thermal power	Tower height (m)	Heliostats number	Solar field maximum aperture area (m²)	Storage	Heat transfer medium	Location	Start year
Australia	CSIRO	CSIRO solar tower	-	30	450	800	-	Water/Steam	Newcastle, New South Wales	2006
	Solastor	Cooma tower	-	-	-	-	-	-	Cooma, New South Wales	2007
	Graphite Energy	Lake Cargelligo	3 MW_e	-	620	6,080	Yes	Water/Steam	Lake Cargelligo, New South Wales	2011
	Vast Solar	Jemalong Solar Thermal Station	1.1 MW_e	25 (5x)	3500	15,000	Yes	Sodium	Jemalong, New South Wales	2016
China	CAS	DAHAN tower plant	1 MW_e	120	100	10,000	Yes	Water/Steam	Yanqing, Beijing	2012
Cyprus	Cyprus Institute	Pentakomo solar field	-	-	50	-	-	-	Cyprus	-
France	CNRS-PROMES	Themis solar tower	2 MW_e	104	201	11,800	Yes	Molten salts	Targasonne	1983
Germany	DLR	Jülich solar tower	1.5 MW_e	60	2153	17,650	Yes	Air	Jülich	2008
Germany	DLR	Algeria CSP tower pilot plant	7 MW_e	-	-	-	-	Air	Boughzoul, Medea	2013
Greece	-	MINOS CSP tower	50 MW_e	-	-	-	-	Water/Steam	Crete	-
India	ACME	Acme solar thermal tower	2.5 MW_e	46	14,280	16,222	No	Water/Steam	Bikaner, Rajasthan	2011
Israel	AORA	AORA Solar Tulip Tower - Samar	0.1 MW_e + 0.17 MW_e	-	-	-	Yes	-	Samar	2009
	BrightSource	Solar Energy Development Center (SEDC)	6 MW_t	60	1,600	-	-	-	Rotem	2008
	WIS	WIS solar tower	-	54	64	-	-	-	Rehovot	1988
Italy	-	EURELIOS	1 MW_e	55	182	-	Yes	Water/Steam	Adrano	1981
Mexico	-	Heliostat test facility	-	32	16	-	-	-	Sonora	2010
Saudi Arabia	Solar Tower Technologies (STT)	-	-	-	66	528	-	-	Riyadh	2015
South Korea	Daesung Energy	Daegu Solar Power Tower	0.2 MW_e	50	450	1,800	-	Air	Daegu	2011
Spain	Abengoa Solar	Eureka	2 MW_e	50	35	4,200	-	Water/Steam	Sanlucar la Mayor, Sevilla	-
		CTAER variable geometry solar test facility	8 MW_t	-	13	1,560	-	-	Tabernas, Almeria	2012
		Solugas	4.6 MW_e	-	-	-	No	Air	Sanlucar la Mayor, Sevilla	2013
	AORA	AORA Solar Tulip Tower - Almeria	0.1 MW_e	-	-	-	-	-	Tabernas, Almeria	2012
	PSA	CESA-1	7 MW_t	80	300	82,500	Yes	-	Tabernas, Almeria	1983
	PSA	SSPS-CRS	2.7 MW_t	43	111	-	-	Air	Tabernas, Almeria	1981
Turkey	Greenway CSP	Greenway CSP Mersin Solar Tower Plant	5 MW_t	60	510	-	Yes	Water/Steam	Mersin	2012
UAE	Cosmo Oil, Masdar, Tokyo Institute of Technology	Solar Beam Down Plant	0.1 MW_t	16	33	280.5	-	-	Masdar City	2010
USA	eSolar	Sierra SunTower	5 MW_e	55	24,360	27,670	No	Water/Steam	Lancaster, California	2009
	-	Solar One	10 MW_e	-	1,818	72,650	-	Water	Daggett, California	1982-1986
	-	Solar Two	10 MW_e	-	1,926	82,750	-	Molten Salt	Daggett, California	1995-2009
	SANDIA	NSTTF	6 MW_t	61	218	2,800	-	-	Albuquerque, New Mexico	-

Country	Developed by	SCR systems	Turbine power (MW)	Tower height (m)	Heliostats number	Solar field maximum aperture area (m²)	Storage	Heat transfer medium	Location	Start or planned start year	Status
Australia	Aalborg CSP	Sundrop CSP Project	1.5	127	23,000	51,500	No	Water/Steam	Port Augusta	2016	Under construction
Chile	Abengoa Solar	Atacama-1	110	243	10,600	1,484,000	Yes	Molten Salt	Calama	2018	Under construction
Chile	Solar Reserve	Copiapó	260	-	-	-	Yes	-	Copiapó	2019	Under development
China	BrightSource Energy, Shanghai Electric Group	Qinghai Delingha Solar Thermal Generation Project	270	-	-	-	Yes	Molten Salt	Qinghai	2017	Under development
	Qinghai CSP Electric Power Group	Golmud	200	-	-	-	Yes	Molten Salt	Qinghai	2018	Under construction
	Supcon Solar	Delingha Supcon Tower Plant	50	80	217,440	434,880	Yes	-	Qinghai	-	Under construction
Israel	Megalim Solar Power Ltd	Ashalim Plot B	121	250	50,600	1,052,480	No	Water/Steam	Ashalim	2017	Under construction
Morocco	ACWA	NOOR III	150	-	-	-	Yes	-	Ouarzazate	2017	Under construction
South Africa	Abengoa Solar	Khi Solar One	50	205	4,120	576,800	Yes	Water/Steam	Upington	2016	Operational
South Africa	ACWA, Solar Reserve	Redstone Solar Thermal Power Plant	100	-	-	-	Yes	Molten Salt	Postmasburg	2018	Under development
Spain	Abengoa Solar	PS10 Solar Power Plant	11	115	624	75,000	Yes	Water/Steam	Seville	2007	Operational
	Abengoa Solar	PS20 Solar Power Plant	20	165	1,255	150,000	Yes	Water/Steam	Seville	2009	Operational
	Torresol Energy	Gemasolar	20	140	2,650	304,750	Yes	Molten salts	Seville	2011	Operational
USA	BrightSource Energy, Google, NRG Energy	Ivanpah Solar Power Facility	377	137	175,000	2,600,000	No	Water/Steam	San Bernardino County, California	2014	Operational
	eSolar	Sierra SunTower	5	55	24,360	27,670	No	Water/Steam	Lancaster, California	2009	Operational
	Solar Reserve	Crescent Dunes Solar Energy Project	110	160	10,347	1,197,148	Yes	Molten salts	Nye County, Nevada	2015	Operational

Tool	Year	Full name	Developed by	Programming language¹	Flux calculation methods	Applications²	Refer-ences
CAMPO	2011	-	Zaragoza University	MATLAB	-	CRS	[87]
CRS4-2	2011	Crs4 Research Software for Central Receiver Solar System SimulationS	Center for Advanced Studies, Parco Scientifico e Tecnologico, Italy	Fortran	-	CRS,BD	[118]
DELSOL	1979	-	Sandia National Laboratories (SANDIA)	FORTRAN77	Hermite polynomial expansion/convolution	CRS	[99]
winDELSOL	1986	-	SANDIA	FORTRAN77	Hermite polynomial expansion/convolution	CRS	[100]
EnerTracer	2000	-	Plataforma Solar de Almeria (PSA)	C + +	MCRT	Light reflecting system	[119]
Fiat_Lux	1997	-	PSA	MATLAB	MCRT	CRS	[120]
HELIOS	1981	-	SANDIA	FORTRAN extended - version 4	Cone optics	CRS, PT, DS	[55]
HFLCAL	1986	Heliostat Field Layout CALculations	DLR	-	Convolution	CRS	[101]
HFLD	2010	Heliostat Field Layout Design	Chinese Academy of Sciences (CAS)	MATLAB	MCRT	CRS	[88]
Koikari & Yoshida	2012	-	Institute of Appliend Energy, Tokyo	CUDA, GPU by NVIDIA	MCRT	Tower reflector system	[121]
MIRVAL	1978	-	SANDIA	Fortran	MCRT	CRS	[102]
MIT code /Biomimetic	2012	-	Massachusetts Institute of Technology (MIT)	Fortran	Convolution	CRS	[83]
MUEEN	2000	-	Center for Solar Energy studies, Tripoli, Libya	C + +	Graphical	CRS	[84]
NSPOC	2009	New Solar Plant Optimization Code	-	Fortran	-	CRS	[122]
Raytrace3D-PowerTower	2010	-	Fraunhofer Institute for Solar Energy Systems (ISE)	-	MCRT	CRS	[123]
SCT	2006	Solar Concentration Toolbox	Centro de Investigaciones Energéticas Medioambientalesy Tecnológicas (CIEMAT) lab	MATLAB	MCRT	CRS	[85]
SENSOL	2005	-	SENER	Fortran	-	CRS, PT, PV, BD	[124]
SoFiA	2015	Solar Field Assessment	-	-	MCRT	CRS	[125]
SOLFAST	2012	SOLar Facilities Simulation Tools	HPC-SA and PROMES-CNRS lab	-	MCRT	CRS, PT, DS,	[126]
SolTRACE	2003	-	National Renewable Energy Laboratory (NREL)	C + +	MCRT	Solar power optical systems	[103]
SPRAY	-	-	DLR	Fortran90	MCRT	CRS, PT, BD, Linear-Fresnel	[127]
STRAL	2009	Solar Tower Ray-tracing Laboratory	DLR	C + + , assembler	MCRT	CRS	[128]
TieSOL	2011	-	Tietronix Software Inc.	C, C + + , C#, OpenGL	MCRT	CRS	[129]
Tracer	2009	-	Tel Aviv University, Australian National University (ANU)	Python	MCRT	Optical systems	[130]
Tonatiuh	2009	-	National Renewable Energy Centre (CENER), Spain	C + +	MCRT	Solar concentrating systems	[131]
UHC-RCELL	1974	University of Houston Code	University of Houston	FORTRAN77, C + +	Hermite polynomial expansion/convolution	CRS	[82]
VEGAS	2010	-	ETH Zurich	Fortran90	MCRT	Reflector geometries	[132]

Country	Developed by	SCR systems	Turbine power/ Thermal power	Tower height (m)	Heliostats number	Solar field maximum aperture area (m²)	Storage	Heat transfer medium	Location	Start year
Australia	CSIRO	CSIRO solar tower	-	30	450	800	-	Water/Steam	Newcastle, New South Wales	2006
	Solastor	Cooma tower	-	-	-	-	-	-	Cooma, New South Wales	2007
	Graphite Energy	Lake Cargelligo	3 MW_e	-	620	6,080	Yes	Water/Steam	Lake Cargelligo, New South Wales	2011
	Vast Solar	Jemalong Solar Thermal Station	1.1 MW_e	25 (5x)	3500	15,000	Yes	Sodium	Jemalong, New South Wales	2016
China	CAS	DAHAN tower plant	1 MW_e	120	100	10,000	Yes	Water/Steam	Yanqing, Beijing	2012
Cyprus	Cyprus Institute	Pentakomo solar field	-	-	50	-	-	-	Cyprus	-
France	CNRS-PROMES	Themis solar tower	2 MW_e	104	201	11,800	Yes	Molten salts	Targasonne	1983
Germany	DLR	Jülich solar tower	1.5 MW_e	60	2153	17,650	Yes	Air	Jülich	2008
Germany	DLR	Algeria CSP tower pilot plant	7 MW_e	-	-	-	-	Air	Boughzoul, Medea	2013
Greece	-	MINOS CSP tower	50 MW_e	-	-	-	-	Water/Steam	Crete	-
India	ACME	Acme solar thermal tower	2.5 MW_e	46	14,280	16,222	No	Water/Steam	Bikaner, Rajasthan	2011
Israel	AORA	AORA Solar Tulip Tower - Samar	0.1 MW_e + 0.17 MW_e	-	-	-	Yes	-	Samar	2009
	BrightSource	Solar Energy Development Center (SEDC)	6 MW_t	60	1,600	-	-	-	Rotem	2008
	WIS	WIS solar tower	-	54	64	-	-	-	Rehovot	1988
Italy	-	EURELIOS	1 MW_e	55	182	-	Yes	Water/Steam	Adrano	1981
Mexico	-	Heliostat test facility	-	32	16	-	-	-	Sonora	2010
Saudi Arabia	Solar Tower Technologies (STT)	-	-	-	66	528	-	-	Riyadh	2015
South Korea	Daesung Energy	Daegu Solar Power Tower	0.2 MW_e	50	450	1,800	-	Air	Daegu	2011
Spain	Abengoa Solar	Eureka	2 MW_e	50	35	4,200	-	Water/Steam	Sanlucar la Mayor, Sevilla	-
		CTAER variable geometry solar test facility	8 MW_t	-	13	1,560	-	-	Tabernas, Almeria	2012
		Solugas	4.6 MW_e	-	-	-	No	Air	Sanlucar la Mayor, Sevilla	2013
	AORA	AORA Solar Tulip Tower - Almeria	0.1 MW_e	-	-	-	-	-	Tabernas, Almeria	2012
	PSA	CESA-1	7 MW_t	80	300	82,500	Yes	-	Tabernas, Almeria	1983
	PSA	SSPS-CRS	2.7 MW_t	43	111	-	-	Air	Tabernas, Almeria	1981
Turkey	Greenway CSP	Greenway CSP Mersin Solar Tower Plant	5 MW_t	60	510	-	Yes	Water/Steam	Mersin	2012
UAE	Cosmo Oil, Masdar, Tokyo Institute of Technology	Solar Beam Down Plant	0.1 MW_t	16	33	280.5	-	-	Masdar City	2010
USA	eSolar	Sierra SunTower	5 MW_e	55	24,360	27,670	No	Water/Steam	Lancaster, California	2009
	-	Solar One	10 MW_e	-	1,818	72,650	-	Water	Daggett, California	1982-1986
	-	Solar Two	10 MW_e	-	1,926	82,750	-	Molten Salt	Daggett, California	1995-2009
	SANDIA	NSTTF	6 MW_t	61	218	2,800	-	-	Albuquerque, New Mexico	-

Optics of solar central receiver systems: a review

Abstract

1. Introduction

2. Theoretical background

2.1 Radiative transfer

2.2 Performance metrics

2.2.1 Optical efficiency

2.2.2 Concentration ratio

2.2.3 Absorption, ideal thermodynamic conversion, and receiver thermal efficiencies

3. Classification of solar central receiver systems

4. Optics of heliostats

4.1 Classification

4.2 Optical studies

4.2.1 Astigmatism

4.2.2 Aiming

4.2.3 Canting and focusing

4.2.4 Tracking

4.2.5 Wind load

5. Optics of heliostat fields

5.1 Classification

5.2 Layout generation and optimization

5.3 Optical modeling

5.4 On-sun optical characterization and demonstration

6. Summary and conclusions

Acknowledgments

References and links

Cited By

Figures (9)

Tables (3)

Equations (16)

Optics Express