Optical fibers and solar power generation

Optical fibers and solar power generation
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  Solar Energy  Vol. 68, No. 5, pp. 405–416, 20002000 Elsevier Science Ltd © Pergamon PII: S0038–092X(00)00009–8  All rights reserved. Printed in Great Britain0038-092X/00/$ - see front matter OPTICAL FIBERS AND SOLAR POWER GENERATION †,1 1 ABRAHAM KRIBUS , ORY ZIK and JACOB KARNI Environmental Sciences and Energy Research Department, Weizmann Institute of Science, Rehovot 76100,IsraelReceived 30 April 1999; revised version accepted 17 November 1999Communicated by LORIN VANT-HULL Abstract —A study of the potential use of optical fibers for solar thermal power generation is presented. Themain performance characteristics (numerical aperture and attenuation) and typical costs of currently availablefibers are discussed. Several approaches to the application of fibers are presented, for centralized (tower,central receiver) and distributed (dish–engine) systems. The overall system design-point efficiency and overallsystem cost are estimated. A scaling relation between system size and the cost of the fiber component isidentified, which severely limits the applicability of fibers to small systems only. The overall system cost forcentralized systems is found to be higher than the currently competitive range, even under optimisticassumptions of mass production of major components. A significant reduction in fiber cost is required beforethe use of fibers for centralized solar power generation can become competitive. In distributed generation usingdish/engine systems, however, the use of fibers does achieve competitive performance and costs, comparableto the costs for conventional dish systems.  ©  2000 Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION  paper reviews the possible marriage of opticalfibers and solar energy, and proposes possibleIn concentrating solar energy systems, theapproaches to make this match work.medium that transfers the concentrated light fromSeveral attempts and proposed concepts to usethe primary collectors (mirrors) to the receiver isoptical fibers with concentrated solar energy wereusually air. The main advantages of this mediumreported (Kato and Nakamura, 1976; Cariou  et  are low attenuation, and obviously low cost. The al . , 1982, 1985; Khatri  et al . , 1993; Nakamura  et  main disadvantage is the geometrical constraints al . , 1995; Liang  et al . , 1997; Peill and Hoffmann,placed on other system components to accommo-1997; Feuermann and Gordon, 1998a,b). How-date the optics. The receiver and additional hard-ever, these attempts have not yet been utilizedware (engine, heat exchangers, etc.) have to besuccessfully in major energy consuming applica-placed in awkward locations, such as on top of ations such as the power generation industry. Thetower, or hanging at the focus of a dish concen-reasons can be traced to the high cost of fibers;trator. The use of secondary optics near thelow numerical aperture (low solar energy con-receiver’s aperture introduces additional largecentration in the fiber) of the fibers that werecomponents at the same location. The receiver’sconsidered; and the absence of receiver technolo-design may also be constrained to fit the availablegy that can fully utilize the geometrical flexibilityradiation, rather than optimized, for example, forof optical fibers to improve the system efficiency.convective heat transfer. Replacing transmissionThese limitations may be alleviated due to recentthrough air by transmission through optical fibersadvances in fiber technology. The fiber industrycan address these issues, and offers an inherenthas grown significantly during the 1990s, drivengeometrical flexibility that can open novel possi-mostly by the communication market, leading to abilities for other solar energy concepts. On thesignificant reduction in fiber cost and improve-other hand, fibers add to the total cost of thement in fiber performance. The third issue issystem and are less transparent than air. Thisaddressed by recent developments in high tem-perature solar receivers (Karni  et al . , 1997),opening the way to benefit from the uniquegeometrical flexibility of optical fibers. A very † Author to whom correspondence should be addressed. Tel.: different application of solar energy in medicine 1 972-8-934-3766; fax:  1 972-8-934-4124; e-mail: was recently proposed (Feuermann and Gordon, 1 ISES member.  1998b); however, we restrict the discussion here 405  406 A. Kribus  et al . to the major application of solar thermal electrici- would still reach the fiber’s sidewall at the criticalty generation. angle for total internal reflection. The numericalTwo common approaches to solar concentration aperture (NA) is a measure of the fiber’s accept-optics seem suitable for application of optical ance angle  u   : A fibers: solar tower and parabolic dish. Line focus-  ]]] ] 2 2 NA 5 sin u   5  n  2 n  . (1)ing systems (parabolic trough) seem less appro-  œ  A core clad priate, since they provide low concentration andtherefore the required cross-section area of the NA values for several commercially availablelight transporting medium is too large to consider fibers are presented in Table 1. Most typical fibersoptical fibers. The tower and dish systems, on the have a NA of 0.2–0.4; NA 5 0.4 corresponds toother hand, produce much higher concentration  u  5 24 8 , leading to a low concentration of light inand lower cross-section area needed for guiding the fiber. For example, if we assume the sun’sthe light. The tower and dish systems are often effective half-angle to be  u   5 7 mrad (including S coupled to high-temperature receivers that can primary mirror errors), then the maximum con-benefit from the additional degrees of freedom centration that can be carried in a fiber of NA 5 2 provided by fiber light guides. 0.4 is about  C   5 (sin  u   /sin  u   )  5 3000. The max A S The paper is divided as follows: we first discuss highest value we found for a commercially avail-some essential properties of optical fibers, andable fiber is NA 5 0.86, leading to an acceptancetheir significance in possible solar applications.half-angle of 59 8  and maximum concentration of We then present several possible application15,000. This represents a reduction by a factor of concepts. An approximate performance and econ-5 in the amount of material (and hence cost)omic analysis is provided to assess the conditionsrelative to the former value. The easiest way tothat could make a solar application of opticalincrease NA up to the limit of NA 5 1 is to usefibers commercially viable.unclad fibers, where  n  5 1. However, the clad- clad ding serves to preserve the surface quality of thereflective surface. The quality of the glass–air 2. OPTICAL FIBERS FOR SOLAR ENERGY interface in a fiber without cladding could de- 2.1.  Overview  teriorate quickly and losses will increase. A fiberwith protective sleeve spaced away from the glassOptical fibers have a range of commercialby thin spacers, creating an air gap, was proposedapplications, notably in communication and light-by Feuermann and Gordon (1998a,b). The prac-ing. Fibers consist of a coaxial arrangement of aticality of this design has yet to be shown. Ourcore that serves as the light conduit, a cladding of focus is the commercially available fibers witha lower refractive index to provide internal reflec-proven applicability and a comparison to a hypo-tion at the boundary of the core, and an externalthetical fiber having NA 5 1 is given as a refer-protective sheet. Fibers used in solar energyence.applications should have a broad transmissionspectrum (multi-mode fibers) and a large cross- 2.3.  Transmission efficiency section area, similar to fibers used for lighting(Sikkens and Ansems, 1993). Lighting fibers are Energy passing through a fiber may be lost inusually made up to a diameter of 70  m m, to several ways: scattering and absorption in the corepreserve flexibility, and are bundled if higher material; ‘leaks’ in the core-cladding interface;power is needed. However, larger diameter fibersare also available (up to 10 mm) if flexibility is  Table 1. Data for several commercial fibers. Attenuation is anintegral over a typical solar radiation spectrum for a 1-m-long not required. The fiber diameter is not a crucial fiber parameter in solar energy, since we may use a Manufacturer Model Attenuation (dB) NA bundles with fused ends (Cariou  et al . , 1982; 1 Schott W 2.348 0.860 Liang  et al . , 1997). Alternatively, we may scale 2 Schott B3 1.767 0.540 the primary collector to match the fiber size  3 Spectran HCP-M1000T 0.168 0.3704 Spectran HCN-H1000T 0.348 0.480 (Feuermann and Gordon, 1998a,b). The fiber 5 Spectran HCL-M940T 0.067 0.220 material for solar application should be restricted 6 3M FP-1.0-LHT 0.050 0.400 to silica, which offers the best transmittance  7 3M FT-1.0-URT 0.291 0.4808 3M FG-100-GLA 0.216 0.365 properties and the best resistance to heating. 9 3M FG-550-LER 0.014 0.22010 3M FT-1.0-DMT 0.090 0.390 2.2.  Numerical aperture 11 Sumita SON-60 0.325 0.50012 Fujikura GC 800/1000L 0.038 0.250 A fiber’s acceptance angle  u   is the largest angle a of incident light relative to the optical axis, which  NA, numerical aperture.  Optical fibers and solar power generation 407 and entrance and exit losses. Attenuation occurs attenuation. We use the AM1 spectrum as thealong the fiber and depends on its length, while spectral distribution  I   ( l ) of the solar input, AM1 entrance and exit losses are independent of length. multiplied by the spectral reflectance  r  ( l ) of aThe flux  F   leaving a fiber of length  L  may be typical silvered glass reflector. The total transmis- out modeled as follows (Snyder and Love, 1983): sion efficiency h   of a fiber of length  L  is then: fiber 2 g   L  F   5 F T T e  (2)  2 g l  L  s d out in in out E  I   l r l  e  d l s d s d AM1 ]]]]]] ] h   L  5 T T   . (3) s d fiber in out where  L  is the average optical path through the E  I   l r l  d l s d s d AM1 fiber,  F   is the flux incident on the fiber inlet, and in T   ,  T   and the exponent represent the effects of  in out entrance and exit losses and attenuation, respec- Fig. 1a shows the attenuation (in the commonlytively. Eq. (2) assumes that the attenuation coeffi- used units of dB, computed from the transmissioncient  g   is constant along the fiber. However,  g   as:  2 10 ? log  h   ) for a 1-m length sample of  10 fiber does depend on wavelength and angle of the several commercial fibers versus the numericalincident radiation, so Eq. (2) is strictly correct for aperture (data are presented in Table 1). Wecollimated monochromatic incident light. ignore here the uncertainty related to large-angleThe entrance and exit losses include Fresnel radiation described above, and assume that allreflection, which is about 4% on each side for a radiation within the formal NA stated by theplain interface. An anti-reflective coating of the manufacturer undergoes the same attenuation. Weentrance and exit interfaces can reduce these note a clear correlation between the NA andlosses to 1–2% each. Surface imperfections can attenuation. The increase of NA usually impliesalso cause additional losses. In addition, the introduction of doping to increase the index of entrance loss includes spillage, i.e. radiation col- refraction of the fiber core; apparently, this alsolected by the primary optics that misses the fiber increases the attenuation. If we repeat the integralaperture; typically, this can amount to a few for different lengths, we find an interesting spec-percentage points. We use the values  T   5 0.94 in and  T   5 0.96 as reasonable estimates for these out transmission factors.The attenuation coefficient  g   is usuallyspecified by fiber manufacturers as a function of wavelength. The spectral behavior roughly fol-lows the properties of the core material, indicatingthat the attenuation is mostly caused by internalscattering and absorption, and only to a lesserdegree by the cladding interface. However, at-tenuation figures are usually measured usingcollimated laser light, and do not specify depen-dence on the numerical aperture. This dependenceis crucial for the solar application, where we wishto increase the angular range of light as much aspossible. Available measurements (Cariou  et al . ,1982; Liang  et al . , 1997) show a significantincrease in attenuation at angles approaching thenominal acceptance angle of the fiber. An increaseis indeed expected at large angles due to theincreased optical path that the light passes in thefiber. However, the expected gradual increase(proportional to 1/cos  u  ) cannot justify the trendshown in Cariou  et al .  (1982). This is a criticalissue for solar applications and should be ex-plored in detail, both analytically and experimen- Fig. 1. (a) Numerical aperture and attenuation of solar light in tally, to find a rationale for this behavior. a 1-m fiber for commercial fibers. Fiber details are given by We have carried out a spectral integral of  the corresponding numbers in Table 1. (b) Variation of the spectral transmission over a typical solar input for  average attenuation of solar light as a function of fiber length the fibers listed in Table 1, to obtain the overall  due to spectral selectivity of the fiber.  408 A. Kribus  et al . tral selectivity feature that causes the average We also present in Fig. 2 results for a hypotheticalattenuation per unit length to depend on fiber fiber having NA 5 1, and the attenuation prop-length. The parts of the spectrum that possess erties of Spectran HCN-H1000T. The maximumhigh attenuation decay more rapidly than the parts concentration achievable with this hypotheticalthat possess low attenuation, and therefore their case is much higher than with existing fibers,weight in the integral diminishes for long fibers. showing the available potential for improvement.The effective attenuation coefficient diminishes We conclude that: (1) the choice of the ‘best’therefore as the fiber becomes longer. The effect fiber is not an intrinsic choice, but depends on thecan be quite significant, as seen in Fig. 1b. specific design and required length; and (2) thereWe computed the upper bound on the exit flux is considerable room for improvement in opticalconcentration of the 12 commercial fibers listed in fiber performance.Table 1, including the aforementioned spectral 2.4.  Cost  effects. The exit flux concentration may be con-sidered as the ‘carrying capacity’ of the fiber, and Commercial mass-produced communicationsdetermines the total fiber cross-section (hence the fibers have low cost, typically a few cents peramount of material) that is needed to guide a linear metre. However, fibers suitable for solarcertain amount of power. We assume that an ideal applications, having large diameter, high NA andprimary reflector concentrates the radiation from low attenuation, are currently not mass producedthe sun’s angle  u   to the fiber’s acceptance angle and their cost is much higher. We assume solar- S u   . The change in flux between the fiber inlet and optimized fibers that are produced on a large scale A exit is only due to attenuation, Eq. (3), so that the using techniques similar to those in use forupper bound on the exit flux concentration is: communications fibers today. In communicationfibers, the cost is dominated by the production 2 sin  u   process, and the material accounts for a small A ] ] C   5  h   L  . (4) s d out 2 fiber fraction only (around 10%). For thick solar fibers,sin  u  S we assume that the production cost is about theFig. 2 presents the maximum exit flux con- same as thin fibers, but the amount of material iscentration as a function of fiber length. We have much higher. A common mass-produced single-assumed that the entrance and exit transmission mode silica fiber with outer diameter of 125  m mfactors are  T   5 0.94 and  T   5 0.96 for all fibers. costs about $0.08/m. Allocating 10% of the cost in out We note that several ‘winners’ stand out: for very to the material leads to  | $300/kg of silica. For ashort fibers (  L , 3 m), the Schott W fiber is best 1-mm-diameter solar fiber the total cost is thendue to its high NA. However, for  L . 10 m, the $0.58/m. Without the mass production assump-Spectran HCN-H1000T provides the highest con- tion, typical material cost would probably becentration. In the intermediate range, 3 ,  L , 10, around $2000/kg, production cost would be high-the Sumita SON-60 is best. Both of the latter er, and fiber cost should be at least $4/m. In thefibers have a moderate NA but superior transmitt- following section we use a cost of $0.5/m as aance, and are therefore better over long distances. reference estimate. It is reasonable to assume thatif massive demand arises for this type of fibers,then the fiber cost could be driven even lower. Inthe analysis below, we also consider what rangeof fiber costs will make the solar application of fibers competitive. 3. SYSTEM MODELS 3.1.  Performance model The total efficiency  h   of a solar plant is a total composite of the efficiencies of the major com-ponents in the energy conversion chain: h   5 h   ? h   ? h   ? h   . (5) total primary fiber receiver PCU Fig. 2. Flux concentration at fiber exit as a function of fiberlength for representative commercially available fibers (see h   is the transmission efficiency of the fiber Table 1) and a hypothetical unclad fiber with attenuation  fiber identical to commercial fiber  [ 4.  based on Eq. (3).  h   is the efficiency of the PCU  Optical fibers and solar power generation 409 power conversion unit (PCU) composed of the specific costs, $/kW and $/kW . The fixed and t e heat engine and generator. We assume that it is indirect costs are added as percentages of thefixed regardless of size for the various systems component costs, as described below.compared here, to provide a common basis of The plant overall cost is normalized to the plantcomparison of the solar part of the plant. rating to provide the total specific investment cost,The primary collector efficiency  h   in- $/kW . We did not attempt to generate a more primary e cludes several contributions, depending on the sophisticated measure of plant economic perform-choice of primary design: ance, such as levelized energy cost, since thiswould have required a much more detailed h   5 r   ? r   ? h   ? h   (6) primary primary hyp intercept shade evaluation of plant life, maintenance costs, andfinancing environment. This level of detail iswhere  r   is the reflectivity of the first primary premature in the current analysis, where the mainreflector, dish or heliostat;  r   is the reflectivity hyp technology considered (fibers carrying concen-of a secondary hyperboloid reflector, in casetrated solar energy) is not yet reasonably de-where a Cassegrainian design is employed (other-veloped, and operational aspects of such plantswise it is set to one);  h   is the intercepted intercept are unknown.fraction of the focal spot, to account for spillage;and  h   is the fraction of the primary reflector shade not shaded by the secondary in Cassegrainiandesigns.  4. APPLICATIONS The receiver efficiency  h   is based on a receiver 4.1.  Overview simple model of a black absorber:In the following sections we consider and 4 s   T   1D T  s d air compare several options to employ optical fibers ]]] ] h   5 1 2 2  L  . (7) receiver con F  in a solar power generation system. We estimatethe efficiency of conversion from solar to elec-Receiver emission losses are according to thetricity under nominal conditions (design-pointtemperature of the absorber, which is higher thanefficiency), and the specific cost per kilowatt of the working gas temperature  T   by an estimated air rated generation capacity. The competitive rangeamount  D T  . The flux incident on the receiverfor power production, according to current marketaperture,  F  , is computed from the geometricconditions, is roughly in the range of $2000–concentration of the optical subsystem (primary3000/kW for on-grid power production, and e collector and fibers), and the overall optical$4000–8000/kW for remote, off-grid applica- e efficiency. The fractional loss due to conductiontions. We consider the feasibility of solar plantand convection  L  is estimated for the various con designs against these based on the receiver design. 3.2.  Cost model  4.2. ‘   Mini - dish ’   fields with a central receiver  The total cost of the solar plant is the sum of  First Cariou  et al .  (1982) and then Feuermannthe major subsystem costs: and Gordon (1998a) proposed to construct largecollection systems from a multitude of small C   5 C   1 C   1 C   1 C  total primary tower fiber receiver dishes, each concentrating solar radiation into a 1 C   1 C   1 C   . (8) single fiber. Many such mini-dishes can be in- PCU fixed indirect stalled on a single heliostat-like frame and track The cost of the primary collector  C   is the sun as a unit. The concentrated radiation from primary computed from the reflector area (including the many frames is channeled via the fiber bundles tosecondary hyperboloid in a Cassegrainian design) a single central site and converted in a manner 2 and a specific cost for the reflector, $/m . The similar to a central receiver system. Fig. 3 pre-cost of the tower  C   , when present, is propor- sents a schematic view of a possible mini-dish tower tional to the height; more sophisticated non-linear system. This proposal could produce severalmodels were not used since the systems consid- major benefits. Mass production of the mini-dishered here are small. The cost of the fiber  C   is element should lead to considerable cost reduc- fiber calculated from the total length of fibers in the tion. The receiver and power conversion unit cansystem and a specific cost per metre length, be located in a protected, easily accessible loca-assuming all fibers are 1 mm diameter. The costs tion, instead of on the tower top or in the focus of of the receiver and PCU are based on fixed a tracking dish. In addition, the layout of the
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