1

Advanced CSP Teaching Materials

Chapter 7

Solar Dish Technology

Authors Matthias Günther1 Reza Shahbazfar1

Reviewers Thomas Fend2

Mohammad Hamdan3

1 Institute for Electrical Engineering, Rational Energy Conversion, University of Kassel, Wilhelmshöher

Allee 73, 34121 Kassel 2 German Aerospace Center (DLR) - Solar Research, Linder Höhe 51147 Cologne, Germany

3 Al-Zaytona University, P.O. Box 130, Amman, 11733 Jordan

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Table of Contents

Nomenclature ...................................................................................................................................3

Summary ...........................................................................................................................................4

1. General remarks about solar dish/engine systems ...............................................................5

2. Components ............................................................................................................................ 10

2.1. Collector ............................................................................................................................... 10

2.1.1. Geometrical considerations .................................................................................... 10

2.1.2. Geometrical collector errors ................................................................................... 18

2.1.3. Reflector materials .................................................................................................. 19

2.1.4. Collector structure ................................................................................................... 20

2.1.5. Secondary concentrator ......................................................................................... 26

2.1.6. Collector size ........................................................................................................... 27

2.1.7. Sun tracking ............................................................................................................. 28

2.2. Receiver ........................................................................................................................... 32

2.2.1. Direct illumination receiver ..................................................................................... 33

2.2.2. Indirect illumination receiver ................................................................................... 35

2.2.3. Thermal losses ........................................................................................................ 36

2.2.4. Hybridisation ............................................................................................................ 38

2.3. Heat engine ..................................................................................................................... 39

3. Efficiency considerations ....................................................................................................... 41

3.1. Efficiency parameters of a dish/engine system ................................................................ 41

3.2. Losses at the SBP 9kW dish/Stirling system .................................................................... 45

4. Comparison to other solar-to-electric conversion systems ................................................. 47

Reference List ................................................................................................................................ 48

Annex .............................................................................................................................................. 51

1. Demonstration that paraboloid mirrors with the same rim angle are geometrically

similar .......................................................................................................................................... 51

2. Derivation of the surface area of a rotational paraboloid mirror ..................................... 53

3. Some realized solar dish/Stirling systems ........................................................................ 55

Questions and exercises ............................................................................................................... 61

Questions .................................................................................................................................... 61

Answers ...................................................................................................................................... 61

Exercises..................................................................................................................................... 62

Solutions ..................................................................................................................................... 63

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Nomenclature

Symbol Meaning Unit

Latin letters A area m²

aperture area m²

Sun image area m²

C concentration ratio -

geometrical concentration ratio -

d aperture diameter m

direct normal irradiation W/m²

day of the year -

f focal length m

direct irradiance on the collector aperture W/m²

radiant flux density in the Sun image W/m²

Irradiance incident on a plane W/m²

reflected irradiance W/m²

electrical power W

input heat J

r radius of mirror aperture m

t time h W mechanical work J

theoretical maximum mechanical work output J

Greek letters

altitude angle °

azimuth angle °

solar azimuth angle °

declination °

ζ exergetic efficiency - ηC carnot efficiency -

heat engine efficiency -

system efficiency -

solar zenith angle °

λ wavelength nm, μm

reflectivity -

geographical latitude °

rim angle °

hour angle °

Acronyms

DLR German Aerospace Center DNI direct normal irradiation

DoY day of the year

SAIC Science Applied International Corporation SBP Schlaich Bergermann and Partner

SES Stirling Energy Systems, Inc.

UV ultraviolet

WGA Wilkingson, Goldberg, and Associates

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Summary

In this chapter we will get to know the most typical form of small scale CSP systems: solar dish

systems. We will understand their structure and how their components work. In the final part we will

learn how efficient they work and where energy may get “lost”.

Key questions

• What kind of CSP plants is appropriate for small scale applications?

• Which components does a solar dish/engine system consist of?

• How efficient are dish/engine systems?

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1. General remarks about solar dish/engine systems

Solar dish/engine systems are small energy conversion units compared to other CSP systems. Typical

system sizes are usually in the range of 5 kWe to 25 kWe. However, there are also smaller systems for

the domestic use.4 In general, solar dishes are equipped with Stirling engines as heat engines.

However, also micro gas turbines could be used. Because of the reduced size of solar dish/engine

systems they are in particular suitable for decentralized and off grid applications.

The following two images compare the different CSP systems according to their power. Solar trough

power plants are the largest power plants that were built until now. The largest until now (concerning

electric power) with 80 MWe are situated in the Mojave Desert in California. Larger projects are

planned (Solar Millennium, for instance, is planning 250 MWe power plants in California5). The

largest Fresnel power plant until now is the 30 MWe plant developed by Novatec Solar that is currently

constructed near Murcia/Spain.6 The largest solar tower power plant until now is PS 20 near Sevilla.

Much larger units (100 MWe and more) are planned by Bright Source Energy.7

Figure 1: Large-scale CSP systems (sources: www.zeit.de, www.dlr.de, www.paul-langrock.de)

4 Sunmachine is developing a 2kWe-system (www.sunmachine.com).

5 See http://www.energy.ca.gov/sitingcases/solar_millennium_blythe/.

6 See http://www.novatecsolar.de.

7 See http://www.brightsourceenergy.com/.

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Figure 2: Solar dish/engine systems as small-scale systems (sources:

www.sbp.de, www.energylam.sandia.gov, www.sunmachine.at)

The modular usability of solar dish systems allows also large scale applications. A large application

was realized in Shenandoah/Georgia in the early 1980s. 114 parabolic dish concentrators were

combined to provide electricity (450 kWe), air-conditioning, and process heat (at 173°C) for a

knitwear factory. The system worked until 1990.8

Figure 3: Power plant in Shenandoah/Georgia (source: www.energylam.sandia.gov)

In 2010 the 1.5 MW Maricopa Solar Plant (Peoria/Arizona) was built by Stirling Engine

Systems/Tessera Solar. It consists of 60 units of 25 kW dish/Stirling systems and is considered as a

demonstration plant and a model for much larger future projects.

8 See Goswami et al. 2000, p. 375.

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Figure 4: Maricopa Solar Plant (source: www.industcards.com)

However, generally solar dish/engine systems are considered as most suitable for smaller decentralized

and off-grid applications.

Dish technology is the oldest of the solar technologies, dating back to the 19th century when a number

of companies developed solar powered steam and Stirling-based systems. The geometrical properties

of paraboloid mirrors themselves, especially their concentrating and collimating properties, were

described already by the Greek mathematician and geometer Diocles around 200 BC.9 Nowadays the

dish geometry has a lot of applications: satellite dishes, reflecting telescopes, radio telescopes,

parabolic microphones, solar heater and many lighting devices such as spotlights, car headlights, par

cans and LED housings. By the way, the Olympic Flame is also kindled by sunlight, which is

concentrated with a parabolic dish. The actually largest solar dish with an aperture area of 494m2 was

built in 2009 at the Australian National University in Canberra.10

The Stirling engine was invented in 1816 by the Scottish clergyman and “part-time engineer” Robert

Stirling. It is the second oldest heat engine after the steam engine (18th

century). The first solar

application of the Stirling engine is attributed to the Swedish-American inventor and mechanical

engineer John Ericsson, who built in 1872 the dish/Stirling device shown in the following figure.

9 See Lienhard: http://www.uh.edu/engines/epi837.htm.

10 See Australian National University: http://solar-thermal.anu.edu.au/high-temperature/500-m2-dish/.

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Figure 5: Ericsson’s solar dish/Stirling device (source: www.stirlingengines.org.uk)

The modern dish/Stirling technology was developed in the late 1970s and in the early 1980s,

especially by United Stirling AB (Sweden), Advanco Corporation (USA), McDonnell Douglas

Aerospace Corporation (USA), NASA and the United States Department of Energy. In the early

1990s, the Cummins Engine Company (USA) offered a dish/Stirling system. In Germany, the

engineering office Schlaich, Bergermann und Partner in cooperation with DLR and other institutions

has done continuous development work in the field of dish systems since 1984.

In the USA, Science Applications International Corporation and Stirling Thermal Motors developed a

dish/Stirling system for utility-scale applications in the mid 1990s. In cooperation with the Arizona

Public Service Company it was developed further and installed in Arizona. The companies Stirling

Energy Systems, Tessera Solar and Stirling Thermal Motors and the investigation institution Sandia

National Laboratories are currently pushing the development further.

In Europe, Schlaich, Bergermann und Partner installed in 1984 two units with 17 m-collectors and 50

kWe Stirling engines in Saudi Arabia. In 1988 a system with a 7.5 m-collector and 9 kWe Stirling

engine was developed. Since 1992, these systems were tested at the Plataforma Solar de Almería in

Spain. In 1996 a new version with a larger collector (8.5 m diameter) and a fully automatic control

was tested in Almería. In 1998 started the development of the Euro Dish in cooperation with DLR and

other European partners. The prototypes are functioning since 2001 at the Plataforma Solar de Almería

in Spain.11

Solar dish systems are power conversion units that, as any CSP system, use direct radiation to provide

electricity. Their distinctive features are the paraboloid collector and a heat engine (Stirling engine or

micro gas turbine) that is connected directly to a receiver, which is located in the focal point of the

paraboloid mirror. The main components of a solar dish/engine system are a parabolic collector, a

receiver, a heat engine (Stirling engine, micro gas turbine) and a generator.

The parabolic collector, which concentrates the direct solar radiation in its focal point, is also referred

to as the parabolic dish. The receiver in (or closed to) the focal point of the parabolic dish receives the

concentrated radiation and converts it into thermal energy. The heat is subsequently transferred to the

11

See Laing et al. 2002, pp. 30-31.

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heat engine, where it is converted into mechanical energy. The mechanical energy drives the generator

that generates the electric energy. Receiver, heat engine and generator are assembled in many real

systems in one constructive unit, the power conversion unit. The power conversion unit is attached to

the collector because it always remains in the same position in relation to it (in the focus or slightly

behind it). Additional components of a solar dish/engine system are a bearing structure, a tracking

system and a control unit.

Figure 6: Main components of a dish/Stirling system (source: www.sbp.de)

A parabolic dish concentrates only the direct radiation that enters the system parallel to its optical axis.

So, the solar dish has to be oriented always towards the Sun. As it is a point-concentrating system, it

requires a two-axes tracking. Like other point-concentrating systems it reaches very high concentration

ratios, which are much higher than the ones of line-concentrating systems. These high concentration

ratios result in high receiver temperatures. Realized systems have reached temperatures above 800°C.

Such high operating temperatures allow a high thermal-mechanical energy conversion efficiency and,

consequently, high solar-to-electric efficiencies. Dish/Stirling systems have reached the highest solar-

to-grid peak efficiency among CSP systems: more than 30%.12

Nevertheless, under typical conditions

they have an average solar-to-electric efficiency between 16 and 25%.13

As solar dishes are equipped with Stirling engines or micro gas turbines, an important additional

advantage in comparison to Rankine-cycle systems is that the water consumption is minimal.

12

The highest value achieved is 31.25% (see Solarpaces et al. 2009, p. 28). 13

See Mohr et al. 1999, p. 91.

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2. Components

In the following, the different components will be described.

2.1. Collector

2.1.1. Geometrical considerations

Geometrically, the collector, the solar dish, is a rotationally symmetric section of a rotational

paraboloid or some kind of approximation to that. A paraboloid mirror has a focal point in which the

direct radiation is concentrated that reaches the mirror parallel to its optical axis. Direct solar radiation,

which has a certain beam spread (and is not exactly parallel to the optical axis), is concentrated in a

more or less extended focal spot in the focal plane.

Figure 7: Geometry of a solar dish (www.sbp.de, www.energylam.sandia.gov, www.solarcentral.org)

Like in any other concentrating system, the concentration ratio is one of the central parameters of the

collector. It is decisive for the possible operating temperatures of the Stirling engine. The

concentration ratio is defined as the ratio of the radiant flux density in the focal spot, or, what is the

same, in the Sun image, to the direct irradiance on the aperture of the collector . As the

direct irradiance at the collector aperture is just the direct normal irradiance, is the ratio of the

radiant flux density at the focal spot to the direct normal irradiance:

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On the one hand we can consider a mean concentration ratio, taking as the ratio of the mean radiant

flux density at the focal spot to the direct normal irradiance. On the other hand we also can consider a

punctual concentration ratio taking into account that the radiant flux density varies within the focal

spot. In the latter case, is taken at a point within the focal spot in order to determine the

concentration ratio in relation to that specific point. The uneven radiant flux density distribution within

the focal spot is a direct consequence of the beam spread of the direct solar radiation, which on its part

is a consequence of the extension of the Sun disc. The following figure demonstrates the radiant flux

density distribution in the focal spot of an experimental device at the DLR. As to be seen, the inner

part of the focal spot shows a much higher flux density and hence a higher punctual concentration

ratio than the outer parts. Supposing that the direct normal irradiance at the collector aperture is about

W/m2 (a typical value on a European summer day), the local concentration ratio in the centre of

the focal spot is between 5000 and 6000 (figure 8).

Figure 8: Radiant flux density distribution in the focal spot of an experimental device at the DLR

(source: DLR)

While the mere fact that the Sun disc has a certain extension is responsible for the shown general flux

density distribution, reflector imperfections, in particular slope errors, may cause more irregular

distributions than the one illustrated here.

Concerning the mean concentration ratio, contrary to the punctual one, there is an easy way to specify

it without any measurement: The geometrical concentration ratio is a useful approximation. is

the ratio of the (projected) collector aperture area to the focal spot area, i.e. to the area of the Sun

image or to the receiver aperture area (supposing that the receiver aperture has exactly the size of

the Sun image):

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Figure 9: Geometrical concentration

However, the geometrical concentration ratio is only an approximation of the real mean radiation

concentration. First, it does not take into consideration the limited reflectivity of the mirror. Second,

geometrical mirror imperfections may scatter a part of the incident light away from the receiver

aperture. Third, it does not take into account shading effects on the collector (caused by the energy

conversion unit and its bearing structure).

As mentioned above, a solar dish has the shape of a section of a paraboloid or some approximation to

it. While the geometrical figure of a paraboloid is infinite in its dimensions, a paraboloid mirror covers

just a section of a paraboloid. Thus, in order to define the shape and the size of a paraboloid mirror we

need, first, a description of the paraboloid and, second, a description of the section the paraboloid

mirror covers. We need, hence, two parameters for the determination of the shape and size of a

paraboloid mirror.

Concerning the geometrical figure of the paraboloid, we first determine that it is circular (neither

noncircular elliptic nor hyperbolic), i.e. it is a rotational paraboloid that can be generated by the

revolution of a parabola around its axis. The only parameter that remains is the focal length, which

determines a circular paraboloid completely. It determines how wide or how narrow it is. Analytically,

a circular paraboloid can be described in the Cartesian coordinate system as , where ,

the focal length, is the only parameter.

Figure 10: Focal length as shape parameter

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Concerning the section a paraboloid mirror covers, the first determination is that it covers a

rotationally symmetrical section of the paraboloid. That means that it covers a section around the

vertex such that all the rim points are at the same distance from the vertex. In order to describe the

dimension of the section the paraboloid mirror covers, we can use, for instance, the aperture area, the

aperture diameter, or the rim angle, which is the angle between the optical axis and the line between

the focal point and the mirror rim.

Figure 11: Geometrical dish parameters

Sometimes the absolute size of a collector is of no interest, but only its shape. Two collectors have the

same shape if they are geometrically similar, i.e. if one of them can be made congruent to the other by

a uniform scaling (enlarging or shrinking). In that case, one sole parameter is sufficient. This

parameter can be the rim angle , which determines completely the shape of a collector. To indicate

the rim angle is, hence, a short and efficient way to determine the shape of a paraboloid mirror. As it

may be surprising that the rim angle determines the mirror shape completely, a proof is elaborated in

the annex.

The rim angle is correlated to the ratio of the aperture diameter to the focal length (or to the ratio of the

focal length to the aperture diameter). The parabola in the following figure has the algebraic

representation

, so that the following relation holds (see figure 12):

. (1)

Figure 12: Representation of the rim angle in a cross-section of a paraboloid

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Taking into account that , where is the aperture diameter of the collector, equation (1) can

be transformed into:

, (2)

which represents the relation between the rim angle and ratio of the aperture diameter to the focal

length.

Equation (2) can be transformed in order to express the d-f ratio as a function of the rim angle:

(3)

The following diagram represents this dependence.

Figure 13: Relation between the rim angle and the d/f-value

If we take a fixed diameter, then, according to the equation (3), a relation between the focal length and

the rim angle results. The following figure represents this relation.

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Figure 14: Relation between the focal length and the rim angle for a constant reflector diameter.

As illustrated in this figure, small rim angles correspond to high focal lengths (at a given aperture

diameter) and vice versa.

The rim angle is an important constructive trait of collectors, especially because it has an effect on the

concentration ratio:

- First, we consider perfect paraboloid mirrors. In the chapter “Solar Radiation”, it was shown

that a rim angle of 45° results in the highest concentration ratio (for flat receivers). We want

now to add the following illustrative explication of the dependence of the concentration ratio

on the rim angle and the existence of some ideal rim angle (ideal in relation to the

concentration ratio):

If the rim angle is very small, then the mirror (with a given diameter) is far away from the

focal point. That means that the spread of the beam radiation, which is inevitable because of

the extension of the solar disc, will provoke a larger Sun image. At a given collector diameter,

this effect provokes that the concentration ratio must be lower for small rim angles. Mirrors

with a very small rim angle, hence, are not favourable for high radiation concentration ratios.

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Figure 15: Dependence of the focal spot size on the rim angle (at a given collector diameter)

On the other hand, there is another effect that provokes a widening of the focal spot for big

rim angles so that also very big rim angles affect negatively the concentration ratio. If we take

a receiver with a plane circular aperture in the focal plane (and, as we will see below, receivers

in dish systems generally have such an aperture geometry), then the beams reflected on the

outer parts of the mirror, which have a big incidence angle on the receiver aperture, provoke a

widening of the focal spot:

Figure 16: Dependence of the Sun image size on the rim angle (at a given focal length)

Therefore, not only mirrors with very small rim angles, but also mirrors with very big rim

angles are not favourable for a high radiation concentration ratio.

There are, hence, two effects that provoke a reduction of the concentration ratio: Small rim

angles provoke a widening of the focal spot (and, consequently, a reduction of the

concentration ratio) because of the higher focal distance and big rim angles provoke a

widening of the focal spot because of the tilted incidence of the reflected rays on the focal

plane. As these two effects are most notable at very large and very small rim angles, there

must be an ideal intermediate rim angle (considering perfect mirrors, taking into consideration

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only these effects and disregarding other criteria). In the chapter “Solar Radiation” it was

demonstrated that this ideal angle is 45°. At this rim angle the best trade-off between the two

effects is reached.

- The effect of slope errors shows a similar behaviour. On the one hand, slope errors generate a

higher absolute aberration in the focal plane at high focal distances. On the other hand, they

generate high radiation aberration in the focal plane at high incidence angles. Once more, very

big rim angles as well as very small rim angles are unfavourable for high radiation

concentration ratios.

Besides these considerations concerning the concentration capacity of parabolic mirrors there are more

aspects in relation to the rim angle, which have to be taken into account:

- An advantage of mirrors with a very small rim angle is that their ideal parabolic shape can be

approximated quite well by a spherical one. The smaller the rim angle the smaller is the

difference between the optical quality of parabolic and spherical mirrors. This is an advantage

because it is easier to build spherical mirrors than parabolic ones.

This aspect has proven to be very important for real constructive solutions. However,

generally the consequence is not to construct collectors with a very small rim angle, but to

construct multi-facet collectors with a bigger rim angle, which are composed of a number of

small facets with a spherical shape. That means that the whole collector does not have a

spherical but approximately a parabolic shape, but the individual facets do have a spherical

shape (see below figure 19).

- There is an interrelation between the rim angle of the collector and the receiver type. Small

rim angles result in a low angular tolerance of the incident radiation at the receiver, big rim

angles result in a higher angular tolerance of the incident radiation at the receiver. As cavity

receivers accept the radiation only within smaller angular tolerances, they are used when the

rim angle is small (less than 50°), whereas external receivers can be used for higher rim

angles. Now, cavity receivers are more appropriate for high temperature applications because

of lower thermal losses (see below). This is an important motivation to limit the rim angle of

concentrators for dish/engine systems, which are high temperature applications.

- The surface area of a mirror with a big rim angle is larger than the surface area of a mirror

with the same diameter and smaller rim angle. This affects the material demand and the

weight of the collector. The mirror surface area amounts to

.

14 (4)

Here are the rim angles of some realized collectors15

:

SAIC (faceted stretched membrane construction) 29°

SBP 52°

SES 40°

WGA (model 10 kWe) 37°

The rim angles are closed to 45°, where a high concentration ratio is to be expected. The SAIC model

is an exception because it uses spherically shaped facets. This constructive solution does not allow

14

A derivation of the equation (4) is included in the annex. 15

See Fraser 2008, p. 9. Abbreviations: SAIC – Science Applications International Corporation, SBP –

Schlaich, Bergermann und Partner, SES – Stirling Energy Systems, WGA – Wilkingson, Goldberg,

and Associates.

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high rim angles of the complete collector because the aberration in relation to parabolic mirrors would

be too strong.

2.1.2. Geometrical collector errors

Optical collector losses result from geometrical errors and from the limited reflectivity of the

reflecting material. Among the geometrical errors we can distinguish between three types:

- Slope error: The surface of an ideal dish would have the shape of a circular paraboloid.

Angular aberrations of the mirror surface in relation to the ideal shape are called slope errors,

which may be the result of unavoidable shape tolerances in the production process as well as

of deformations because of the mounting on the bearing structure or because of gravitational

deformations due to the mirror weight.

The slope error can be determined for any point on the mirror surface. Additionally, an

average value for the whole mirror can be determined, which indicates the overall geometrical

quality of the mirror. A possible method in order to measure the slope error is deflectometry.

- Facet alignment error: In the case of multi facet reflectors, which are assembled with a number

of facets that are mounted to a supporting frame, geometrical errors can be caused by inexact

assembling, so that the light reflected on even perfectly shaped facets may partially or totally

miss the receiver.

- Positioning errors of the whole reflector: As the parabolic dish needs a two axis tracking in

order to maintain its optical axis in line with the Sun, it is prone to positioning and tracking

errors. Positioning errors imply that the optical system axis is not in line with the Sun.

Figure 17: Types of geometrical collector errors

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2.1.3. Reflector materials

The reflector should combine the following properties:

- Reflective surface: Most importantly, the reflector must have a highly reflective surface.

Typical average reflectivity values for mirror materials in the solar spectral range are between

and .16

Additionally, specularity must be high, i.e. the ability of the mirror surface to

reflect light without dispersing it at angles other than the incident angle. The reflecting surface

may be polished stainless steel or, which is more common, aluminium or silver coated glass or

plastic films.

- Climatic resistance: To ensure an enduring high reflectivity, the concentrator and its coating

have to be resistant to the climatic conditions at the respective location. Typical climatic stress

factors are UV light and high temperature variations, especially high frequent daily variations.

Also sandstorms may be a stress factor. The materials and the construction have to resist

temperature changes and mechanical influences by wind and possible drifting sand.

- Weight: A low weight is an advantage because of easier transportation, lighter and cheaper

bearing structure and foundation, and easier and cheaper tracking with less energy

consumption.

Further unspecific requirements are low costs and general environmental compatibility. The following

materials combine the mentioned requirements quite well:

- A simple possibility to provide a reflective surface is polished metal, aluminium or stainless

steel. It is economical and easy to produce. However, the main drawbacks of this method are

that the specularity is quite low and that the reflectivity decreases rapidly due to climatic and

other influences.

- Another option to provide a reflective surface is the use of backside coated glass mirrors. The

coating is normally silver or aluminium (similar to domestic mirrors). Reflectivity is high,

although decreasing at a higher glass thickness. Silver has the highest reflectivity of any metal

surface for the solar spectrum. Polished silver reaches a reflectivity of almost 98%. The

complete mirror has a lower reflectivity because the light has to pass twice through the mirror

glass. In order to minimize the absorption in the glass, special glass with low iron content is

used, so that a total reflectivity of about 95% is reached.17

Mirrors with aluminium coating

have a slightly lower reflectivity.

Glass mirrors are quite resistant to changing weather conditions. The most durable realized

collectors employ silver/glass mirrors.18

Disadvantages of the glass mirrors are the relatively

high weight and the lack of flexibility to fit into different given shapes.

- Plastic films are another option as bearing and protecting material for the reflective metal

layer, which is applied backside. Plastic films are flexible and allow fitting the mirror into a

given shape. Additionally, they are light and economic. Once more, aluminium and silver are

common reflective coatings. New silver coated plastic films reach a reflectivity of 96%. The

16

The reflectivity is the ratio of the reflected irradiance to the incident irradiance. Generally, it is a function of the wavelength: . Nevertheless, in technical applications, often an

average reflectivity is specified, which is quite exact for a spectral range. The reflectivity changes according to a number of influencing parameters like the material, the incidence angle and soiling. 17

Antireflection surfaces, on the other hand, are not important in CSP applications (contrary, for instance, to glass covers of photovoltaic modules). The numbers are taken from Stine/Diver 1994, p. 23. 18

See Fraser 2008, p. 6.

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main disadvantage of the plastic material is the low resistance to mechanical stress (scratches)

and an unfavourable aging behaviour especially as an effect of the exposure to UV radiation19

.

2.1.4. Collector structure

General constructive options – facets and segmentation

The collector can consist of one large continuous surface, like the collectors in the figures 18 and 20,

or of an assembly of a number of smaller, not directly connected reflectors, facets, which are fixed on

a conjoint bearing structure, like in the figures 19 and 21.

In a multi-facet construction, each facet has its own curvature and orientation characteristics in

accordance with its position within the system, and each facet is individually alignable. The complete

system, of course, needs one optical axis. This can be achieved assembling the facets in form of one

big paraboloid, as to be seen in figures 19 and 21.

A multi-facet construction has the advantage that it is not necessary to construct one big paraboloid

surface, which may be quite difficult and expensive. In the case of the constructions in figures 19 and

21, each facet is so small (in relation to the focal length) that they just need a very small spherical

curvature in order to form conjointly a sufficiently good approximation of a paraboloid.

Dishes that consist of one continuous paraboloid surface can be made out of one large piece, like the

collector in figure 18, or they can be composed of different segments that are connected to each other.

If they are made out of one large piece, the membrane type is chosen. If they are made out of segments

a space frame/glass mirror construction is chosen.

Figure 18: Membrane collector (source: SBP)

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In some plastics UV light can affect the molecular structure. Depending on the composition of the

material, mechanical as well as the optical properties, e.g. transparency, can be affected.

21

Figure 19: Multi facet stretched membrane collector (source: SBP)

Figure 20: Segmented space frame/glass mirror collector (source: SBP)

22

Figure 21: Multi facet space frame/glass mirror collector (source: www.solarcentral.org)

Space frame construction with glass mirrors

At modern larger solar dishes, optical and structural elements are clearly separated from each other.

One frequent constructive solution is the use of a space frame construction with glass mirrors, i.e. a

structure of tubular elements or truss segments that carry the mirror or the mirror facets.

In the case of large glass mirrors, the mirror is normally made of a number of pieces (facets, segments)

and not of one single piece. It is possible to produce a large glass mirror out of one single piece, but

the production of such large glass mirrors is expensive and technically difficult. Additionally, large

heavy non-segmented glass mirrors generate transportation and other handling problems. In

astronomical applications, where exact imaging properties are crucial, large non-faceted mirrors with a

very high geometrical quality are used. Only few firms in the world are able to construct such

extremely expensive mirrors. In CSP applications the quality requirements are not so high because

perfect imaging properties are not required to achieve high concentration ratios. Additionally, the

prices have to be maintained low in order to be able to compete with alternative energy conversion

systems. Large glass mirror solar dish collectors are, hence, composed of a number of facets or

segments.

A big parabolic glass mirror that is composed of segments is, for example, a version of the Euro Dish,

which was developed by Schlaich, Bergermann und Partner in Stuttgart/Germany in cooperation with

DLR and other partners (figure 20). It consists of 12 segments, which are produced separately. They

are sufficiently small to be transported in usual containers to the final location. There they are mounted

23

to the bearing structure. The segments are made of fibre-reinforced epoxy20

with thin glass mirrors

with a thickness of attached on their concave side (figure 22).

Figure 22: Production of the reflector segments of the Euro Dish (source: Keck/Schiel 2003)

The following figure shows how the segments are fixed on the bearing structure.21

Figure 23: Assembling of the Euro Dish (source: Keck/Schiel 2003, Schlaich Bergermann und Partner

(2002a))

Another possibility to construct a glass mirror solar dish is a multi-facet construction (figure 21). As

mentioned above, the facets are sufficiently small so that they can have slight spherical curvatures.

The difference between the spherical curvature and the respective parabolic curvature (depending on

the exact position of the facets within the collector) is very small. The paraboloid shape is achieved by

the arrangement of the facets on the bearing structure and not by the curvature of the facets

themselves. The production of these small mirrors with a spherical shape may be cheaper and easier

than the production of large mirror segments with a parabolic shape.

Figure 24: Multi-facet construction (source: Stirling Energy Systems 2007)

20

Epoxy is a copolymer that is composed of a resin and a hardener.

24

A special case of a multi-facet construction is the central Fresnel collector. The working principle is

analogue to that of the linear Fresnel collector. While the linear Fresnel collector replaces a parabolic

trough by an array of mirror lines that are allocated in a plane, a central Fresnel collector replaces a

parabolic dish by a number of mirror facets that are allocated in a plane. Such a Fresnel paraboloid

concentrator was built in Latur/India (see figure 25).

Figure 25: Fresnel paraboloid concentrator, ARUN Solar, India (source: Garud 2010)

Stretched membrane construction

An alternative technique to produce an approximately parabolic curvature of a solar dish is the

application of pressure on membranes.

If a membrane is stretched like a drumhead on a hoop and a second stiffer one at the back side, and if

this collector body is evacuated slightly, the membrane receives a concave shape. With an appropriate

reflecting surface the membrane can be used for radiation concentration. This technique makes it

possible to manufacture very light collectors. A hoop in uniform compression is a highly stable

structure so that the whole supporting system can be very light. Additionally, the membrane with the

reflective surface can be also very light and needs only few (if any) additional stabilizing elements

besides the hoop. Stretched-membrane constructions, thus, can reduce the costs of design, fabrication

and alignment.22

22

See Stine/Diver 1994, pp. 23-24.

25

A disadvantage of the application of atmospheric pressure is that it does not produce a parabolic

shape, but a spherical one.23

One possibility to achieve high concentration ratios in spite of this is to

apply this technique only for mirrors with very small rim angles so that the difference between

parabolic and spherical shape is sufficiently small. Several of such small mirrors can be combined in

one collector. Figure 19 shows a collector where this solution was chosen.

Another possibility is to combine the described evacuation technique with some complementary

technique in order to approximate a parabolic shape. SBP shaped its membrane collector with

additional water load at the concave (overpressure) side.24

The combination of the atmospheric

pressure with the additional water pressure permitted to reach a very high geometrical quality.

Figure 26: Application of additional water load to form the parabolic shape (source: SBP)

A further proposal to get a high geometrical exactness at evacuated membrane constructions is to

subdivide the collector body (the low-pressure interior) into concentric sectors so that in each sector

the pressure can be adjusted separately in accordance with the desired curvature.25

SBP constructed the metal membrane reflector represented in figure 18. Stainless steel sheets with a

thickness of 0.23 mm and a width of 1m are welded together to a large membrane with 8.5 m

diameter. This membrane is attached to a hoop and forms the collector body. Subsequently, the

membrane is shaped plastically by pressure reduction within the reflector body and by additional

application of water pressure on the front membrane, which leads quite exactly to the shape of a

truncated paraboloid. Mirrors with a thickness of 0.9 mm and a size of 30 cm x 50 cm are attached on

the membrane.

23

A spherical shape has a minimal area-to-volume ratio. The stretched membrane adopts a spherical

shape so that an optimal balance of volume gain (at the concave, i.e. outer side) and low membrane

expansion is reached. 24

Schlaich Bergermann und Partner (2002b) 25

This was a proposal of the HTC-Solar research centre Lörrach/Germany. See http://www.patent-

de.com/19950928/DE4413056C1.html.

26

(1) (2) (3) (4) Figure 27: Construction of the metal membrane reflector (source: Schlaich Bergermann und Partner

2002b)

It is also possible to use a stretchable polymer membrane instead of a metal membrane (figure 28). A

reflective surface can be achieved by different techniques. Glass mirrors can be attached, a silvered

membrane can be used, aluminium can be vapour-deposited or the membrane itself can be reflective.26

In a way similar to the metal membrane construction, the polymer membrane is stretched over a

cylinder like a drumhead and forms the collector body. The pressure inside the cylinder is reduced and

the membrane receives a shape that makes it an appropriate solar dish.

A difference in relation to the metal-membrane construction is that the parabolic deformation of the

membrane is elastic so that the underpressure inside the reflector body has to be maintained. This

requires additional pressure control.

A typical problem with the polymer stretched membranes is that it wrinkles when it is stretched.

Possible solutions are additional stabilizing elements behind the membrane, like a foam body or a

metal sheet, or the attachment of thin glass mirrors on the front surface.27

Possible collector

deformations due to gravitational forces and wind loads may require additional stabilizing measures.

2.1.5. Secondary concentrator

A secondary concentrator can be attached at the receiver aperture. Such a secondary concentrator has a

highly reflective, trumpet-shaped surface that leads the reflected radiation from a wider area through

the cavity receiver aperture. The result is an increase in the capture fraction without an increase in the

26

See Kennedy et al. 2005. 27

See Simmers 2001.

Figure 28: polymer stretched membranes (source: Simmers 2001)

27

receiver aperture area (or a reduction of the aperture size for a given intercept factor). Thus, a

secondary concentrator can improve the performance of a parabolic dish. It is especially useful to

reduce the negative effects of optical errors because it leads an additional part of the scattered

radiation to the receiver aperture.

As the secondary concentrator is located in a high flux density region it must be made of a heat

resistant material and it needs a well-designed cooling.

Figure 29: Cross section of a secondary receiver with outer cooling coils

On the one hand, a secondary concentrator may reduce costs because the reflector can be accepted to

have a lower geometrical accuracy or it can be constructed smaller without losing system power. On

the other hand, the second concentrator is an additional component, which implies additional system

costs. Additionally, further maintenance may be required and additional energy may be needed for

cooling.

2.1.6. Collector size

The size of the collector depends basically on the desired electrical system power, the available

radiation and the efficiency of the conversion of radiation to electrical energy. At known direct normal

solar irradiance and system efficiency, the aperture area and the respective collector diameter can be

determined as follows:

(5)

(6)

where is the desired electrical system power, the solar-to-electric system efficiency and

the direct normal irradiance at the design point.

This equation can serve for the calculation of the aperture area at the design point, which is a point at

which the system reaches a high efficiency. A system should be designed in such a way that a high

28

efficiency is reached for typical environmental conditions at the respective location, especially for

typical solar irradiance values, but also for typical wind conditions.28

is determined by the general system purpose. Typical system efficiencies at the design point

are between 15 and 25%.29

The following figure illustrates the collector size in dependence on the

system power. A DNI of 1000 W/m2 is selected.

Figure 30: collector diameter at a DNI of 1000 W/m

2 and a system efficiency

between 15% and 25%

2.1.7. Sun tracking

Point concentrating collectors need a two axis tracking system so that the collector is always directed

towards the Sun and the direct solar radiation is always parallel to the optical axis of the system. There

are two different options to define the direction of the collector, which correspond to the two

coordinate systems (equatorial and horizontal coordinate system) that were introduced in chapter

“Solar Radiation” to describe the position of the Sun (in relation to an observer on Earth) as a function

of time:

- Polar tracking: One axis has the direction of the Earth’s rotational axis and the other is

perpendicular to it (at noon in east-west direction). The resulting determination of the collector

orientation is via hour angle and declination. This tracking system corresponds, thus, to the

equatorial coordinate system.

28

Wind may influence thermal losses on the receiver (see below). 29

See Stine/Diver 1994, p. 12 and Solarpaces, http://www.solarpaces.org/CSP_Technology/

docs/solar_dish.pdf.

29

Figure 31: Polar tracking system with hour angle and declination

The hour angle , which indicates the angular position of the Sun in relation to its apparent

daily east-west movement around the Earth’s axis (and thereby the angular orientation of the

collector in the east-west dimension around an axis parallel to the Earth’s axis) is determined

according to

, (7)

defining .30

The angular velocity of the mirror movement around the axis

parallel to the Earth’s axis is always nearly constant. Small adjustments have to be considered

due to the variance of solar time in relation to the local mean time (see chapter 2).

The declination, which indicates the angular position of the Sun in relation to the equatorial

plane is calculated according to

, (8)

where is the day of year (with on 1st January).

31 The movement of the collector

around the axis perpendicular to the Earth’s axis is very slow (maximum rate of 0.016 degrees

per hour).32

In a one-year periodicity it moves from to in relation to the

equatorial plane.

30

Remember that here means always solar time and not standard time. 31

A determination of the declination only in dependence on the day of year (and not additionally on

the exact solar time) may be sufficient because of very small variations during one day. 32

Stine/Diver 1994, p. 7.

30

Figure 32: dish/Stirling systems with polar tracking (source: SBP)

- Altitude-azimuth tracking: One axis has a horizontal orientation (at noon in east-west

direction) and the other one a vertical orientation. The resulting determination of the collector

orientation is via altitude angle and azimuth angle. This tracking system corresponds, thus, to

the horizontal coordinate system.

31

Figure 33: Altitude-azimuth tracking system with altitude angle and azimuth angle

The altitude angle indicates the altitude over the horizon, i.e. the angular orientation of the

collector with respect to the horizontal plane. It is identical to the solar altitude angle and is

determined as follows:

, (9)

where is the geographical latitude. It holds , where is the solar zenith angle.

The azimuth angle is identical to the solar azimuth angle , which indicates the angular

position of the Sun in relation to its apparent daily east-west movement around a vertical axis,

and indicates, thus, the angular orientation of the collector in relation to the south in the

horizontal plane. It is calculated as follows:

, (10)

where the sign function is equal to if is positive and it is if is negative.

32

Figure 34: dish/Stirling systems with altitude-azimuth tracking

Generally, the mechanical structure is simpler for altitude-azimuth tracking while the control

algorithm is simpler for polar tracking. That is why larger dish systems use normally altitude-azimuth

tracking, while smaller systems use more often polar tracking.33

2.2. Receiver

The receiver of a solar dish system is the interface between the concentrator and the heat engine. It has

two functions: First, it absorbs a large part or the radiation reflected by the collector and converts it

into heat. Second, it transfers the heat to the working gas of the heat engine. Important requirements

for the receiver are, thus, high absorption rates and good heat transfer characteristics.

Stirling engines and micro gas turbines need different receivers. The most successful receivers for

micro gas turbines use “volumetric absorption” in which the concentrated solar radiation passes

through a fused silica quartz window and is absorbed by a porous matrix. Honeycombs and reticulated

open-cell ceramic foam structures offer large heat transfer areas within quite a small space. More

about volumetric receivers is explained in the chapter about tower power plants.

In the following we will concentrate on receivers for dish/Stirling systems. In general, two types of

receiver geometries could be used with parabolic dish collectors: external receivers and cavity

receivers. Externals receivers are usually spherical and absorb radiation coming from different

directions. Cavity receivers have an aperture through which the radiation passes.

33

See Solarpaces: http://www.solarpaces.org/CSP_Technology/docs/solar_dish.pdf.

33

Figure 35: Schematical representation of an external receiver (left) and a cavity receiver (right)

As the external receiver receives the radiation from different directions, while the cavity aperture of a

cavity receiver faces to only one direction, to the vertex of the collector, the external receiver could be

interesting for collectors with a large rim angle. However, the heat losses, especially radiative heat

losses, at the unprotected external receivers are quite high at the high operating temperatures of dish

systems. In a cavity receiver, on the contrary, a big part of the emitted radiation remains inside the

cavity and is absorbed again so that the total radiative heat loss is lower. The effective absorptance of

the cavity is higher than the absorptance of its interior surface. This is possible because of the concave

shape of the absorber surface. Additionally, the convective heat loss is also lower at cavity receivers

than at unprotected external receivers.

An important advantage of a cavity receiver is that the absorber size may be different from the size of

the aperture. The aperture is located normally at the focus of the concentrator, while the absorber is

located behind the focus. That means that the highly concentrated flux spreads inside the cavity before

encountering the larger absorbing surface area. This spreading reduces the flux that is incident on the

absorber surface so that the materials are not thermally overstressed. However, as the aperture area is

much smaller than the absorber surface area, the thermal losses are reduced. Cavity receivers have,

thus, favourable absorption characteristics at minimized thermal losses.

Because of these favourable properties of cavity receivers, only this type of receivers has been used in

dish/Stirling systems to date. External receivers, on the contrary, have been used in parabolic dish

applications that operate at a lower temperature. As we concentrate here on high temperature

applications, we will present now the different types of cavity receivers. We will distinguish between

direct illumination receivers and indirect illumination receivers.

2.2.1. Direct illumination receiver

At direct illumination receivers the concentrated radiation heats directly the working gas of the Stirling

engine in a bundle of thin pipes. It is the simpler type of receivers compared to indirect illumination

receivers. Most realized systems operate with direct illumination receivers.34

The following figures show two different direct illumination receivers and their integration in a

Stirling engine.

34

See Stine/Diver 1994, p. 12.

34

The first one belongs to the SBP Euro Dish system. It consists of 78 tubes, which are connected to the

working space of the engine. The tubes are made of a heat and corrosion resistant nickel alloy.

Thermocouples are attached at the back side that control the receiver temperature. The maximal

temperature on the illuminated tube sectors is about 900°C. The receiver is allocated about 15 cm

behind the focal spot of the concentrator, which reduces the radiation flux. A water-cooled aluminium

cylinder forms the cavity in front of the receiver tubes. At the back side, the receiver is thermally

isolated by a ceramics body and a stainless steel cover.35

The second receiver in the figure belongs to the SunCatcher System developed by SES.

35

See Laing et al. 2002, pp. 32-33.

Figure 36: Direct illumination cavity receivers and their integration into Stirling engines. (sources:

Schiel 2007 (above) Stirling Energy Systems 2007 (below))

35

2.2.2. Indirect illumination receiver

In an indirect illumination receiver the working gas is heated indirectly through an intermediate heat

transfer fluid. This fluid is heated at the absorber where it evaporates. It condenses at the heater tubes

that contain the working gas of the Stirling engine, releases the corresponding condensation heat to the

working gas and flows back by gravity to the absorber. Because of this evaporation-condensation

cycle, this type of receivers is also called reflux receiver. The working fluid is normally a liquid metal

like sodium.

Figure 37: Indirect illumination receiver

Indirect illumination receivers have certain advantages compared to direct illumination receivers. An

important advantage is that they operate at uniform temperatures, while directly illuminated heater

tubes can experience strong temperature gradients from front to back and along the tube length that

degrade performance and limit life.36

It also permits to tolerate and equilibrate more easily

nonuniformities in concentrator flux profiles.

Additionally, indirect illumination receivers permit generally higher heat transfer rates. This and the

smaller differences between receiver peak temperature and engine working gas temperature make

possible a higher engine efficiency.37

Furthermore, the use of an intermediate heat-transfer fluid decouples the design of the receiver from

the engine. This makes it possible to design more efficient receivers while at the same time optimizing

the Stirling engine design.

Finally, it is easier to add a gas burner for hybrid solar/fossil-fuel operation than it would be in a direct

illumination receiver.38

On the other hand, indirect illumination receivers are more complex and they imply additional

problems, which require consideration39

:

36

This is not valid for the startup process, when high temperature gradients can be registered along

the vapour ducts (see Adkins et al. 1999, p. 3). 37

According to Adkins et al. the use of a reflux receiver can boost the system performance by twenty

percent when compared to directly illuminating the engine heater tubes (Adkins et al. 1999, p. 1). 38

See Stine/Diver 1994, p. 69. 39

See Adkins et al. 1999, p. 2.

36

- There is a capillary pumping limit where gravitational and frictional forces exceed the wick’s

ability to distribute the liquid working fluid by capillary forces.

- There is a boiling limit where superheat conditions cause vapour bubbles to form in the wick.

- There is an entrainment limit where liquid is suspended by the vapour flow and prevented

from returning to the evaporator wick.

- There is a vapour velocity limit where friction causes large pressure drops in the vapour ducts

between the evaporator and the condenser, which cools the vapour.

- The integrity of the system can be compromised by corrosion of the wick or envelope

materials or the mechanical failure of components at high temperatures.

A difference among indirect illumination receivers can be made between pool-boiler receivers and

heat-pipe receivers. The difference refers to the way how the liquid metal is transported to the

absorber: Either the absorber surface is always directly immersed in a pool of liquid metal (pool-boiler

receiver) or a connecting wick draws the liquid metal up from a small sump to wet the absorber

surface (heat-pipe receiver).

The principal advantage of the heat-pipe receiver over the pool-boiler receiver is the added safety

associated with smaller inventories of liquid metal heat transfer fluid. As it has less thermal mass than

the pool-boiler receiver, the heat-pipe receiver responds more rapidly to changes in the solar

irradiance. Heat loss associated with transient cloud cover is therefore lower with the heat-pipe

receiver. On the other hand, the heat-pipe receiver has an increased number of thermal stress cycles on

the receiver and engine during cloudy days, and a greater variation in output power.40

2.2.3. Thermal losses

High operation temperatures allow higher heat engine efficiencies. Temperature limitations exist

because of the limited thermal tolerances of the receiver material. Many realized dish/Stirling systems

are operated in the temperature range between 700°C and 800°C; the absorber temperature normally

does not exceed 900°C. Such high temperature levels make the receivers prone to high thermal losses,

which reduce the system efficiency. Thermal losses at the receiver are produced due to all three basic

heat transfer effects, i.e. conduction, radiation and convection.

The most important thermal loss process is radiation. Generally, at high temperature applications the

radiative heat loss is more important than convective and conductive heat losses. The radiative heat

loss grows proportionally to the surface temperature to the fourth power (Stefan-Boltzmann law),

while the convective and conductive heat losses grow in a linear way in relation to the difference of

ambient and receiver temperature. Therefore, the radiative loss grows much more if the receiver

temperature rises than the convective and conductive heat loss. At high temperature applications it is,

hence, very important to reduce the radiative heat loss. As already mentioned, cavity receivers, thanks

to their concave shape, reduce the radiative loss from the absorber surface through reabsorption of a

part of the emitted radiation. An effective heat loss reduction can be reached if the absorptance of the

cavity is high, if the surface area of the cavity is large, if an aperture cover is added, or if the aperture

diameter is reduced. Concerning the reduction of the aperture diameter, a trade-off must be made

between the reduction of radiative losses on the one hand and the possible reduction of the intercept

factor on the other hand.

The absorber surface is normally coated in a dull black. Selective coatings, which are used in low

temperature applications and also in medium temperature applications like parabolic trough power

plants (at about 400°C) in order to reduce radiation emission in the infrared range, are not so

40

See Stine/Diver 1994, p. 69.

37

frequently used in high temperature systems. First, many of these coatings degrade rapidly in the high-

flux environment of a parabolic dish receiver. Second, the coatings work less effectively at high

temperatures because there is a significant overlap of the solar spectrum being absorbed and the

emission spectrum of the absorber at 700°C to 800°C.41

Third, in cavity receivers the optical properties

of the inner absorber surface are little important because the cavity geometry anyway provokes that the

optical aperture properties are similar to the optical properties of a black body.42

The second most important heat loss process is convection. Forced convection is caused by wind;

natural convection is caused by the temperature difference (and resulting air density differences)

between the receiver surface and the ambient air. Both convection types depend quite strongly on the

orientation of the receiver. Obviously, forced convection depends additionally on wind speed.

Generally, the aperture area and cavity properties have an influence on convection losses: Small

aperture areas, larger internal cavity diameters with respect to the aperture diameter and a larger cavity

surface area reduce thermal losses.43

- In relation to natural convection, thermal losses are lower when the receiver is closed to a

vertical position with the aperture oriented downwards, i.e. at noon. They are higher in the

morning and in the evening. Besides the variations during the day, this also provokes a

dependence of the thermal losses on the season and on the geographical location (latitude).

- Forced convection losses may be much higher than natural convection losses. Total

convection losses have been measured to be up to four times that of natural convection with a

4.5 m/s wind directly facing the aperture opening.44

The losses depend on wind speed, cavity

temperature and geometry, effectiveness of a protecting wind skirt (if existing) and on the

orientation of the receiver aperture in relation to the wind direction (being highest if the wind

is oriented towards the aperture).45

The following diagram is the result of measurements that were made at the SBP 50kWe

dish/Stirling system. It shows the enormous influence of the wind speed on the system

efficiency.46

41

See Stine/Diver 1994, p. 26. 42

In a completely closed cavity, the radiation emission and absorption of the walls are the same as if

the cavity had perfectly black surfaces (i.e. with the radiant absorptance/emittance 1). They do not

depend on the radiant absorptance and emittance of the walls if they were the surface of a convex

body. 43

See Fraser 2008, p. 21. 44

See Harris/Lenz 1985. 45

See Fraser 2008, p. 20. 46

See Mohr et al. 1999, pp. 103-104. Wind affects the system efficiency not only because of

convective losses but also, as Mohr et al. mention, because of additional optical losses (due to the

mechanical load on the components). The measurements were done at a constant irradiance of 1000

W/m2.

38

Figure 38: Influence of wind speed on the efficiency of

a dish/Stirling system (source: Mohr et al. 1999, p. 104)

Convection losses can be reduced significantly by placing a glass or quartz window over the receiver

aperture. However, the cover will diminish slightly the irradiance on the absorber.

Conductive heat losses from the absorber through the receiver housing, finally, represent only a small

portion of the total system losses and they can be effectively controlled by modifying the receiver’s

insulation thickness.47

2.2.4. Hybridisation

Dish/Stirling systems as well as dish/Brayton systems are appropriate for hybridisation. Any system

that uses a heat engine has an inherent ability to operate on fossil fuels. For the acceptation of

dish/engine systems in the market, hybridisation may be a very important argument in favour of them,

because this allows the generation of electricity on demand. This is especially important because until

now there are no thermal storage systems for dish/engine systems.

In the case of dish/Brayton systems, the addition of a fossil fuel combustor can be done with minimal

expense or complication.48

The hybrid combustor is downstream of the solar receiver and has no

adverse impact on the system performance. Hybridisation does not only permit the delivery of

electricity on demand, but it also can help to avoid part load operation of the gas turbine and to

increase, hence, the overall system efficiency.

Hybridisation of dish/Stirling systems is a bit more difficult although the Stirling engine, as an engine

with external heat supply, is compatible with a large number of heat sources.

DLR with different partners developed at the end of the 1990s a hybrid heat pipe receiver for the

SBP/LCS 10-kWe dish/Stirling system with the SOLO-161 Stirling engine.49

An indirect illumination receiver is used because it allows a separation of the different heat transfer

surfaces, absorber surface, Stirling heater head and gas heat exchanger. This gives more freedom in

designing all components according to their specific requirements. Additionally, as mentioned above,

non-uniform heat fluxes are tolerated more easily than at a direct illumination receiver.

47

See Fraser 2008, p. 17. 48

See Solarpaces. 49

See Laing et al. 1999.

39

Figure 39: Schematic representation of the hybrid heat pipe receiver (source: Laing et al. 1999)

The figure shows how the different heat transfer components are separately arranged. The heat pipe

with a wick structure is located around the cavity. The whole cavity serves as absorber surface. The

outer heat pipe mantle is the heat transfer surface for the gas heat flow, equipped with a high number

of fins. The Stirling heater tubes are brazed in the plate at the rear of the heat pipe. The two different

heating zones (for solar and combustion heating) and the condenser zone are separated from each

other. The system can be operated by solar heating, by combustion heating or by a combination of

both.

Figure 40: Foto of the hybrid heat pipe receiver (source: Laing et al. 1999)

At the hybrid operation mode, the required engine pressure and consequently output power has to be

pre-set in the control unit. The burner is automatically turned on, once the engine pressure falls below

this level.

2.3. Heat engine

Solar dishes can be combined with many kinds of heat engines, which convert heat into mechanical

power in order to drive an electric generator. A number of thermodynamic cycles and working fluids

40

have been considered for dish/engine systems. These include Rankine cycles (using water or an

organic working fluid), Brayton cycles and Stirling cycles.

Generally, the Stirling cycle is favoured. All the systems that are presented in the annex are

dish/Stirling systems.

Only few projects make use of the Brayton cycle. In Arizona there is currently a project by

Southwest Solar Technologies Inc. and Brayton Energy LLC to deliver utility-scale electricity

with dish/Brayton systems. The project includes a compressed air energy storage. Off-peak

energy from a power plant or from renewable energy source is used to run air compressors

that pump air into storage tanks or underground caverns where it is stored under pressure.

When electricity is needed and direct solar radiation is available, the air is delivered to a

network of parabolic dishes, where the compressed air is heated and where it drives micro gas

turbines.

The Rankine cycle was finally not applied in the existing prototypes.

41

3. Efficiency considerations

3.1. Efficiency parameters of a dish/engine system

The overall efficiency of a dish/Stirling system, i.e. the solar-to-electric efficiency, depends on the

following parameters: (a) solar irradiance, (b) radiation concentration, (c) intercept factor, (d) thermal

receiver efficiency, (f) engine efficiency, (g) generator efficiency.

a) Solar irradiance: Concerning the dependence of the electrical power output and the respective

system efficiency of dish/engine systems at different solar radiation conditions we should

expect, of course, a higher power output at higher direct normal irradiance values.

Additionally, a higher Carnot efficiency at higher receiver temperatures could be an argument

for a higher system efficiency at higher solar irradiance. However, higher thermal receiver

losses at higher operating temperatures should weaken this effect. Actually, at realized

systems quite a linear dependence of power output on solar irradiance has been identified. The

following diagram represents measuring results taken from the SBP 9kWe dish/Stirling system

at the Plataforma Solar in Almería/Spain.50

Other realized systems have shown a similar

behaviour.

Figure 46: Electric power output of the SBP 9kWe dish/Stirling system in dependence on the

direct normal irradiance

The system efficiency shows a corresponding asymptotic run. At high irradiance values the

system reaches a certain maximum efficiency:

50

See Mohr et al. 1999, 105.

42

Figure 47: System efficiency of the SBP 9kWe dish/Stirling system in dependence on the

direct normal irradiance

As to be seen, the system efficiency reaches high levels at a high direct normal irradiance. The

highest efficiency is reached at the highest possible irradiance. Now, the highest possible

irradiance is reached only exceptionally. The most common direct normal irradiance levels are

far below the maximal values. The following diagram shows the hourly average direct normal

irradiance during the year on a place in Spain.51

We see that even average values between 800

and 900 W/m2 are to be expected only during a couple of weeks at midsummer during few

hours. Even higher values are rather exceptional.

Figure 48: Hourly average direct normal irradiance during the year on a example location in

Spain. 52

That means that a system with the highest efficiency at around 900 W/m2 would run only

during a very small time fraction during the year at its highest efficiency. In order to avoid that

the system is run at a relatively low system efficiency during a large part of the year and that

its annual capacity factor is quite low, the EuroDish/Stirling system, for instance, was

equipped with a bigger solar dish so that the Stirling motor runs at its highest efficiency

already at lower irradiance conditions. The collector was enlarged by 25 %. While the former

system configuration permitted to run the Stirling engine at maximal irradiance at its design

point, the new configuration with the enlarged collector permitted to run the Stirling engine

51

The diagram is taken from Schillings et al. 2004, p. 19. The exact location is not specified. It has to

be taken into account that these are average values of the DNI, i.e. also cloudy days are considered.

The average DNI under clear-sky conditions is higher than indicated in the diagram.

43

already at lower irradiance values at its design point. Using the terminology for large scale

CSP plants, we can say that the system is operated at a solar multiple of 1.25. At a DNI above

850W/m2 the excess heat that cannot be processed by the Stirling engine has to be dumped. In

parabolic trough power plants, the dumping of thermal energy is done by a slight defocusing

of the parabolic troughs. In the dish/Stirling system, however, the excess heat is dissipated by

a small blower that is directed to the receiver tubes. The advantage of the larger dish is that the

Stirling engine is operated at a high efficiency also quite below the peak irradiance. The

annual energy yield can be raised by until 30%.52

The power and efficiency run of the system with the enlarged collector has qualitatively the

following form:

Figure 49: Power output pattern at solar multiple 1.25 (with

ventilator regulation at the receiver)

Figure 50: System efficiency pattern at solar multiple 1.25

b) Radiation concentration ratio: The higher the concentration ratio is, the higher is the possible

absorber temperature and the higher can be the thermal-to mechanic efficiency of the system.

The concentration ratio depends on the following collector properties:

52

See Laing et al. 2002, p. 33.

44

a. Collector geometry: Different collector shapes result in different concentration ratios,

being the paraboloid shape the one that makes possible the highest concentration

ratios. Among paraboloid mirrors, furthermore, different rim angles imply different

concentration ratios.

b. Geometrical mirror quality: Slope errors and other geometrical mirror errors provoke

radiation aberration and reduce the concentration ratio.

c. Mirror reflectivity: High reflectivity means low transmission and absorption losses at

the mirror. The following diagram shows the dependence of the system efficiency on

the reflectivity at different geometrical concentration ratios for a specific system:

Figure 51: System efficiency depending on geometrical concentration ratio and

collector reflectivity for a concrete system (source: Mohr et al. 1999, p. 100)

According to this diagram, we can also see that the system efficiency rises only slightly for

concentration ratios over 2000. Taking the effect of a higher concentration ratio, the

consequent higher receiver temperature and the higher thermal-to-mechanic efficiency

isolated, we could suppose that the system efficiency should show a stronger dependence on

the concentration ratio. However, higher thermal losses at higher temperatures reduce this

dependence considerably. Taking this into consideration and taking into account the

expectable higher costs for the construction of dishes with a higher concentration ratio it may

be not economical to aspire to concentration ratios higher than 2000.

c) Intercept factor: The intercept factor is the ratio of the radiation that hits the receiver aperture

to the radiation that is reflected on the mirror. It depends, once more, on the geometrical

mirror quality, but additionally on the shape, size and position of the receiver aperture and also

on the tracking accuracy. A reduced intercept factor reduces always the energy flow to the

receiver, but it may increase the mean radiant flux density when only the central parts of the

Sun image, which have a higher radiant flux density, hit the receiver aperture.

d) Thermal efficiency of the receiver: As explained above, especially radiative and convective

heat losses affect the receiver efficiency.

45

e) Heat engine efficiency: The total efficiency of the heat engine is determined by the

Carnot-efficiency ηC and the exergetic efficiency ζ. The Carnot-efficiency ηC is defined by the

temperature levels at which the engine works. It indicates the highest possible ratio of

obtained work to supplied heat (in a perfect heat engine). The exergetic efficiency is the

ratio of the obtained work (in a real engine) to the work that would be obtained if the engine

efficiency was equal to the respective Carnot efficiency.

(11)

(12)

(13)

The Carnot efficiency is determined by the temperature levels. Especially interesting is the

high temperature level because it can be influenced by higher concentration ratios and high

thermal receiver efficiencies. The low temperature level is normally fixed by the

environmental conditions, but effective cooling systems can also improve the engine

efficiency.

The exergetic efficiency is the parameter that can be optimized by the engine construction.

f) Generator efficiency: The generator efficiency normally is quite high (above 0.9). The

established technology and the high efficiency that is reached do not leave much space for

improvements.

g) Parasitic energy use: The system efficiency also depends on the own power consumption, for

instance for the tracking system requirements. This parasitic energy use reduces the usable

electric energy that is generated by the system.

3.2. Losses at the SBP 9kW dish/Stirling system

The following diagrams show the losses at a dish-Stirling system. The data were acquired at a solar

irradiance of 1000W/m2 at a SBP 9kW dish/Stirling system.

53 They are valid for only this system, but

other realized systems have shown comparable characteristics.

The losses that have to be considered are the following:

h) Optical losses due to limited mirror reflectivity

i) Losses due to limited intercept factor

j) Thermal losses at the receiver

k) Energy conversion losses at the Stirling engine (composed of temperature-constrained Carnot

efficiency and constructively conditioned exergetic efficiency)

l) Energy conversion losses at the generator

m) Losses due to parasitic power requirements

The following diagram shows the different losses quantitatively and it relates them to the usable

electrical energy:

53

The data are taken from Fraser 2008, p. 17.

46

Figure 52: Losses and usable energy at the SBP 9kW dish/Stirling system

The second diagram shows a waterfall chart illustrating the successive reduction of the solar energy to

the final usable electric energy:

Figure 53: Energy waterfall chart for the SBP 9kW dish/Stirling system

collector reflection losses;

6.0%

receiver intercept losses ; 9.5%

receiver thermal losses; 9,9%

Stirling engine conversion

losses; 50.8%

generator conversion losses; 2.2%

parasitics; 2.1%

usable electrical energy ; 19,5%

47

4. Comparison to other solar-to-electric conversion systems

In the following, advantages and disadvantages of dish/engine systems in relation to other solar-to-

electric conversion systems are presented. PV is included in this comparison (besides other CSP

technologies), which is motivated by the following consideration: Some CSP technologies have the

essential advantage over PV that they offer the possibility to include thermal storage systems and to

deliver power on demand. However, until now there are no thermal storage systems for dish/engine

systems, which is why they are in a special competition situation with PV.

Advantages:

- The system efficiency can be higher than in other systems. This is valid as well for other CSP

systems as for (commercially available) PV.

- Dish/engine systems need little water for their operation. This is a very important advantage

over Rankine-cycle based systems, especially if they have wet cooling systems.

- Dish/engine systems do not need any heat transfer fluid. This is a cost-reducing factor.

Additionally, energy losses in heat transfer processes associated to systems with a special heat

transfer fluid are avoided.

- Dish/engine systems can be used for small and off-grid applications. Additionally, they can be

used in a modular way, which is not possible in the same flexible and efficient way with large-

scale CSP systems.

Disadvantages:

- There are still no thermal storage systems for dish/engine systems. The possibility to integrate

a thermal storage is a crucial advantage of some other CSP systems over PV. However,

hybridization is possible in order to deliver power on demand.

- Dish/engine systems have movable parts, while PV systems do not need moving parts.

- Like any CSP system, dish/engine systems use only direct radiation, while PV systems make

use of diffuse radiation too.

- Dish/engine systems still have a prototype status. The investment costs (€/kW) and the

electricity generation costs (€/kWh) are still above that of large-scale central receiver or

parabolic trough power plants. They have successfully demonstrated that they can produce

electrical power for extended periods of time, and even large scale applications were built. It is

important now to establish high levels of system reliability and thereby to reduce the operating

and maintenance costs. The initial costs of the systems are still a barrier to the market entry,

which may decrease in the future in the case that serial production is reached. The potential for

future cost reduction is considered to be high.54

54

Sea A.T. Kearney 2010, p. 22.

48

Reference List

A.T. Kearney (2010): “Solar Thermal Electricity 2025” June 2010

Adkins, D.R. et al. (1999): “Heat Pipe Solar Receiver Development Activities at Sandia National

Laboratories”.

http://www.osti.gov/bridge/purl.cover.jsp?purl=/3248-3rhhgP/webviewable/

[July 2011]

Australian National University: “SG4 500m2 paraboloidal dish solar concentrator at ANU”.

http://solar-thermal.anu.edu.au/high-temperature/500-m2-dish/ [July 2011]

Bean J.R., Diver J.R. (1995): “Technical Status of the Dish/Stirling Joint Venture Program”

http://www.osti.gov/bridge/purl.cover.jsp?purl=/79749-A3FdGz/webviewable/

[July 2011]

Beninga, K. J.: “Solar Power Technologies”. Science Applications International Corporation.

http://iranscope.ghandchi.com/Anthology/AlternativeEnergy/Beninga.pdf

[July 2011]

Garud, S. (2010): “Concentrating solar power in India” TERI.

http://www.solarthermalworld.org/files/ShirishGarud.pdf . [July 2011]

Fraser, P. R. (2008): “Stirling Dish System Performance Prediction Model”. University of Wisconsin.

https://www.nrel.gov/analysis/sam/pdfs/thesis_fraser08.pdf. [July 2011]

Goswami, D.Y./Kreith, F./Kreider, J.F. (2000): Principles of Solar Engineering. Second edition.

Philadelphia: Taylor & Francis

Herdin, R. “Seminar Alternative Energien - Dish Stirling”.

http://www.prof-ges.com/lectures/Seminar_Alternative_Energien-Solar_Dish.pdf .

[July 2011]

Keck, T./Schiel, W. (2003): “EnviroDish and EuroDish System and Status”. ISES 2003.

http://www.fika.org/jb/resources/EuroDish%20Presentation%20ises2003%20draft.p

df. [July 2011]

Kennedy, C., Terwilliger, K., Lundquist, C. (2005): „CSP FY 2005 Milestone Report”.

http://www.abetterfocus.com/files/Reflector_Milestone_Report_9-05.pdf. [July

2011]

Laing, D. et al. (1999): “Hybrid Sodium Heat Pipe Receiver for Dish/Stirling Systems – Design and

Test Results”.

http://www.vok.lth.se/~ce/Research/stirling/papers/ISEC99047.pdf. [August 2010]

Laing, D. et al. (2002): „Dish-Stirling-Systeme“. In: FVS Themen 2002, pp. 30-34.

http://www.fvee.de/fileadmin/publikationen/Themenhefte/th2002/th2002_02.pdf.

[July 2011]

49

Lienhard, J.H.: “Diocles”. www.uh.edu/engines/epi837.htm. [July 2011]

Mohr, M., Svoboda, P., Unger, H. (1999): Praxis solarthermischer Kraftwerke. Berlin, Heidelberg:

Springer

Nepveu, F. (2006). „Thermal modelling of the Dish/Stirling system”. Sollab.

http://home.ku.edu.tr/kunsal/public_html/stirlin/25_Nepveu_Sollab_2006.pdf [July

2011]

Reinalter W. (2010): “Experiencias con discos parabólicos en el mundo”. Master in Solar Energy at

Universidad de Almería/Spain

Schiel, W. (2007): „Dish Stirling Activities at Schlaich Bergermann und Partner“. SBP.

http://www.nrel.gov/csp/troughnet/pdfs/2007/geyer_sbp_dish_stirling.pdf. [July

2011]

Schillings, C. et al. (2004): „Projektbericht. Sokrates-Projekt Solarthermische Kraftwerkstechnologie

für den Schutz des Erdklimas. AP 3“

http://www.dlr.de/tt/Portaldata/41/Resources/dokumente/institut/system/projects/AP

3_2_Solarenergieressource.pdf. [July 2011]

Schlaich Bergermann und Partner (2002a): „EuroDish – Stirling System Description. A new

decentralised Solar Power Technology”.

http://www.1000friendsofflorida.org/Solar/EuroDish_System_Description.pdf [July

2011]

Schlaich Bergermann und Partner (2002b): „Ein neues solares Dish-Stirling Kleinkraftwerk mit

Metallmembran-Konzentrator für Gruppenaufstellung“.

http://www.sbp.de/de/fla/contact/download/sbp_dish_membran.pdf. [August 2010]

Simmers, D. E. (2001): “A Low-Cost Solar Dish Design Utilizing a Stretched Membrane Reflector”.

A Better Focus Co.

http://www.abetterfocus.com/files/Paper0167_stretched_Membrane_R1.pdf. [July

2011]

Solarpaces: “Solar Dish Engine”. www.solarpaces.org/CSP_Technology/docs/solar_dish.pdf [July

2011]

Solarpaces/Estela/Greenpeace (2009): Concentrating Solar Power. Global Outlook 09

Stine W.B., Diver R.B. (1994): “A Compendium of Solar Dish/Stirling Technology”. Albuquerque,

Livermore: Sandia National Laboratories.

http://www.osti.gov/bridge/servlets/purl/10130410-xiVU1V/native/10130410.pdf.

[July 2011]

Stirling Energy Systems, Inc. (2007): “Solar Dish Stirling Systems Report” NREL CSP Technology

Workshop.

50

http://www.nrel.gov/csp/troughnet/pdfs/2007/liden_ses_dish_stirling.pdf. [July

2011]

The California Energy Commission: Solar Millennium Blythe Solar Power Project

http://www.energy.ca.gov/sitingcases/solar_millennium_blythe/. [July 2011]

Tessera Solar (2010): “SunCatcher. The Next Generation of CSP Electricity Generation Technology“

http://www.tesserasolar.com/north-america/advantages.htm.

[July 2011]

51

Annex

1. Demonstration that paraboloid mirrors with the same rim angle are

geometrically similar

In order to show that paraboloid mirrors with the same rim angle are geometrically similar it is

demonstrated that the slope of paraboloid mirrors with the same rim angle is identical at points that

correspond to each other. In other words, it will be show that the slope characteristics of a paraboloid

mirror depend exclusively on its rim angle. In order to do that, we reduce the problem to a two-

dimensional one, considering a parabola

.

In a first step we want to show that the slope angle at the rim is exclusively a function of the rim angle

. As to be seen in the foregoing figure, we can formulate the following relation:

. (1)

From (1) we get:

(2)

We consider only the positive value of and reduce (2) to:

(3)

The slope of the parabola is described by the derivation of

with respect to x:

(4)

The slope at is then:

52

, (5)

which depends only on the rim angle and which is, consequently, independent from .

In a second step we can show that parabolas with different have also the same slope at all the points

between and , i.e. at the points , with . The parabola between the two

points takes the form

and the derivation with respect to takes the form

.

Taking into consideration (3), the slope is, then:

(6)

which, once more, depends only on the rim angle and on the factor , but not on . That means that all

rotationally symmetrical sections around the vertex of any circular paraboloid with the same rim angle

are geometrically similar. And that means that all paraboloid mirrors with the same rim angle have the

same shape, i.e. are geometrically similar.

53

2. Derivation of the surface area of a rotational paraboloid mirror

The total area is the integration over all angular segments of the mirror, with a radius between

and

, where is the radius of the mirror aperture:

(1)

The angular segments at the distance have the area:

(2)

As to be seen in the following figure, can be determined as follows:

(3)

From (2) and (3) we get:

(4)

and with (1):

(5)

54

Taking into consideration that

, (5) is transformed into:

55

3. Some realized solar dish/Stirling systems

In the following a selection of realized solar dish/Stirling systems are presented.55

1) Advanco/Vanguard (1984)

Collector diameter: 10.5 m

Collector aperture area: 86.7 m²

Structure weight: approximately 10 tns

336 glass/silver mirrors facets

Power: 25 kWe

Maximal system efficiency: 30%

2) McDonnell Douglas (1984)

Collector diameter: 10.5 m

Collector aperture area 87.7 m²

82 curved glass mirror facets

Structure weight: approximately 7 tns

Altitude-azimuth tracking

Power: 25 kWe

Maximal system efficiency: 30%

55

Sources: Reinalter 2010, Tessera Solar 2010 (3), Bean/Diver 1995 (5), (10), SBP (6), (8), (10).

56

3) SES-Tessera Solar

Collector diameter: 11.6m

Power: 25 kWe

Curved glass mirror facets

Maximal system efficiency: 31.25%

4) SBP, Riad (1986)

Collector diameter: 17 m

Collector surface area: 227m²

Glass/silver mirrors on membrane reflector

Altitude-azimuth tracking

Power: 50 kWe

Maximal system efficiency: 23%

57

5) SAIC/STM (1991)

Collector diameter: 10.4 m

Surface 84.8 m²

16 facets of stainless steel membrane with silvered

polymer reflective film

Altitude-azimuth tracking

Power: 22 kWe

Maximal system efficiency: 20%

6) SBP/DISTAL I (1991)

Collector diameter: 7.5 m

Collector aperture area: 42 m²

Steel membrane with silver coated glass mirrors

Polar tracking

Power: 9 kWe

Maximal system efficiency: 20%

7) SBP/DISTAL II (1997)

Collector diameter: 8.5 m

Collector aperture area: 53 m²

Steel membrane with silver coated glass mirrors

Altitude-azimuth tracking

Power: 10 kWe

Maximal system efficiency: 21%

58

8) Euro Dish (2001)

Collector diameter: 8.5 m

Collector aperture area: 53 m²

Fibre-reinforced epoxy with silver coated

glass mirrors

Altitude-azimuth tracking

Power: 10 kWe

Maximal system efficiency: 24%

9) WGA/Sandia (2000)

Collector diameter: 7.5 m

Collector aperture area: 41 m²

Silver coated glass mirrors

Altitude-azimuth tracking

Power: 10 kWe

Maximal system efficiency: 24%

59

10) Cummins CPG 460 (1992)

Collector diameter: 7.3 m

Collector aperture area: 41.5 m²

24 facets of stretched membrane silvered

polymer film mirrors

Polar tracing

Power: 7 kWe

11) Infinia Corporation (2007)

Collector diameter: 4.6 m

Glass fiber reinforced plastic with silver

coated glass mirrors

Altitude-azimuth tracking

Power: 3 kWe

Free-piston Stirling engine

Maximal system efficiency: 24%

60

12) Big Dish/Australian National University (1994)

Collector area 400 m2

Sun tracing azimuth/elevation

Power: approx. 50 kWe

61

Questions and exercises

Questions

1. All other things being equal, what parameter the concentration ratio of a paraboloid collector does

not depend on? (Take as the concentration ratio the ratio of the mean normal radiant flux at the

focal spot to the normal radiant flux at the collector aperture.)

a) rim angle

b) collector size

c) reflecting material

2. A dish/Stirling system needs a two-axis tracking. A developer wants to design a dish/Stirling

system such that, for simplicity, the continuous automatic tracking works only around one axis.

How can he achieve this?

Answers

1. The concentration ratio does not depend on the collector size. A bigger collector collects more

solar radiation, but the concentration ratio is not bigger if the shape (rim angle), the reflecting

material and the optical collector quality are the same.

2. He uses polar tracking and installs a continuous automatic one-axis tracking, which moves the

dish around the polar axis. The tracking around the east-west axis is done in an intermittent way

once a day (automatically or manually).

62

Exercises

1. Your task is to design a dish/Stirling system for an off-grid application in the central part of Algeria.

a) The system should reach 12kWe at optimal conditions. Based on plausible assumptions, what

is the minimal diameter of the collector (circular paraboloid)?

b) You decide to modify the collector size such that the system reaches its design point already at

a DNI of 800W/m2 (at higher irradiance, a convective cooling device at the receiver avoids

stronger heating of the absorber). What is the collector diameter now?

c) Suppose that the collector has a rim angle that permits the highest medium concentration ratio

at the focal spot. What is the focal length of the mirror in a) and in b)?

2. In chapter “Solar radiation” the mean concentration ratio for a paraboloid mirror and a plane

receiver was indicated to be

. Consider a collector with a rim angle

of 40° and a focal length of 6m.

a) What is the mean concentration ratio, if the reflectivity is 0.9, shading due to the Stirling

engine and the bearing structure 8%, and scattering losses 20%?

b) What is the mean radiant flux density at the receiver aperture at a DNI of 800W/m2? Suppose

that the receiver aperture has the size of the Sun image.

c) What is the diameter of the Sun image?

d) The absorber has the shape of a spherical cap with the radius of 10cm and is situated 10cm

behind the focal plane. Its extension is such that it receives the incident radiation completely

and that there is no non-illuminated part:

What is the mean radiant flux density at the absorber surface?

63

Solutions

1. a)

,

,

at high irradiance: we take the value of the SBP system in 3.2., which is about

19%,

DNI at good irradiance conditions in the Sahara: about 1000W/m2.

From these suppositions we get: and

b) We suppose that the system efficiency will reach the same value at 800W/m2

like the system under the conditions of a):

,

c)

The rim angle that permits the highest concentration ratio is 45°.

For the system in a), the diameter is 9m:

The same for the system in b):

2. a)

b)

c)

d)

( : mean radiant flux density on the absorber, : absorber surface area)

(surface area of a spherical cap),

Applying some analytical geometry permits to determine h: