- Email: [email protected]
Cost of paraboloidal collectors for solar to thermal electric conversion
Solar Energy, Vo|. 17, pp. 351-358. Pergamon Press 1975. Printed in Great Britain
COST OF PARABOLOIDAL COLLECTORS FOR SOLAR TO THERMAL ELECTRIC CONVERSIONt W. W. SHANER MechanicalEngineeringDepartment,Colorado State University, Ft. Collins,CO 80523,U.S.A. and H. S. WILSON ManufacturingDevelopmentLaboratory, The WestinghouseElectric Corporation (Received 15 August 1974)
Abstract--Much is underway concerning technical and design aspects of solar collectors and associated costs of point designs. But little has been published on the tradeoffs between alternative designs and large-scale manufacturingpossibilities.To fillthis gap, close interchangeis needed among those versed in technical and systems design, manufacturing and costing. The solar to thermal electric power study funded by the National Science Foundation and carried out by Colorado State University and Westinghouse Electric Corporation has led to the assembly of such a team. This team is obtaining new data on large-scale production of concentrating collectors of widely varying parameters. Investment and other costs of paraboloidalcollectors with various aperture widths, reflectivities,rim angles, and accuracies of contour and tracking are reported herein. In studying alternative design-cost-performance relationships, emphasis is placed on breadth of coverage rather than on detailed accuracy. Alternative aperture widths led to preferences for differentproduction processes that are not particularly sensitiveto changes in rim angle or reflectivity. Significantcost relationships in the manufacture, installation and maintenance of collectors were found; other relationships are less certain. Besides the above, study results indicate directions for further study. INTRODUCTION A study currently underway involving the joint efforts of Colorado State University and the Westinghouse Electric Corporation on the conversion of solar to thermal electric energy calls for estimates of the costs of the components of alternative systems. These costs, together with the performances of the components and the overall systems, are expected to yield optimum designs for a wide range of system parameters. Important in the costing of these components is the estimate of values for concentrating collectors. Point designs by the Aerospace Corporation, for example, indicate that the costs of concentrating collectors account for about one half of the investment in converting solar to thermal electric energy[l]. Reliable estimates of the overall competitiveness of solar power systems therefore require careful study of the costs of collectors. To date literature on the application of solar energy contains little on which to base such estimates. Most of the cost estimates of collectors that have come to the authors' attention are only indicative of what collector costs might reasonably be. For example, Hildebrandt et al. [2] write that "We believe that large-scale fabrication procedures can produce the mirrors at $20 per m2. A specific approach would be to develop an aerodynamically sound structure that can be stamped or extruded continuously." Such gross estimates are appropriate during the initial stages of study, but eventually more detailed investigation is required. Considering the many possibilities of design, materials tThis paper was presented at the International Solar Energy Society's U.S. Section Meeting held in Fort Collins, Colorado (Aug. 1974).
and manufacturing techniques in producing concentrating collectors, it was felt that those knowledgeable in alternative manufacturing processes needed to be involved in the analysis. Accordingly, assistance was sought and obtained from the Westinghouse Manufacturing Development Laboratory on the design, manufacture and costs of producing large volumes of concentrating collectors. Results of this effort, together with concurrent studies by the faculty of Colorado State University, have produced estimates of installed costs for a large number of design parameters. This paper reports on results to date for paraboloids. While it is generally true that paraboloids, which require two axis tracking of high accuracy, are more expensive to build, they are also capable of producing higher temperatures. It was with the interest of covering the range of performance and cost possibilities that the paraboloid was selected for initial study. Other concentrator types, such as troughs and fresnel lenses, are also being studied and will be reported on as data are developed. Because large-scale production of paraboloidal reflectors does not now exist for the design conditions of interest, estimates of costs are only approximations to eventual costs. Thus, this paper can be considered as an interim report, with more precise cost estimates to be obtained as individual aspects of design, manufacture, installation and operation are studied in greater detail. OBJECTIVEOF THE STUDY The objective of this costing effort has been to estimate the full costs of as many different types of concentrating collectors as time and funds allow. These costs will be subsequently combined with performance characteristics through the use of an optimizing model to yield a set of
351
352
W. W. SHANER and H. S. WILSON
least cost values for alternative system designs. Results, when completed, will be in terms of dollars per kWh of electrical energy generated. SCOPE OF THE COST ANALYSIS
The thrust of this analysis has been on comprehensiveness of coverage, rather than on detailed accuracy for a limited number of alternatives. Data are derived from known technologies of processes either in actual use or reasonably likely to be used were the demand to exist for large-scale output of such collectors. Costs in 1972 dollars are to include the original equipment, installation, operation, maintenance and replacement. METHOD OF APPROACH
The first step in the investigation was a search of the literature concerning data on surfaces, shells, frame supports, structural bases and foundation, tracking, wind loading, maintenance and operation procedures, lives of components and methods of manufacture. Cost data were also recorded when available to be used as a check on subsequent calculations. Other than for this purpose, published cost data were not particularly useful since accompanying design information was seldom sufficient to allow for extrapolation of these data to other design parameters. Five design parameters were chosen to cover the performance characteristics to be incorporated in the optimization model. These are aperture width, reflectivity of surface, rim angle (angle obtained by a vertical line through the focus and another line from the focus to the edge of the paraboloid), contour error (gross errors due to major deviations in contour and minor errors due to surface roughness) and tracking error. Ranges of values are: Aperture width: from 10 cm to 10 m. Reflectivity: from 70 per cent to 90 per cent. Rim angle: from 45° to 115o. Contour error: from 0.1 ° to 3.0°. Tracking error: from 0.1 ° to 1.0°. Cost estimates were based on the assumption of large-scale production of solar-powered electrical energy. That is, if economically or otherwise feasible, solar energy plants were assumed to comprise a significant amount of new generating capacity. This led to an admittedly crude estimate of annual installations of 17.5 million m2 of projected surface areat. This level of installation is sufficiently large to confirm that installation of solar facilities at this rate indeed involves large-scale production on the part of potential manufacturers of concentrating collectors. Naturally, greater additions to annual generating capacity or higher percentages of total installations would lead to even larger levels of required annual production of solar collectors.
tThe authors arbitrarily selected 5 per cent of projected average annual additions to utility generating capacity for the 1970-80 period in the U.S.[3]. This amounts to 1750MW of solar generating capacity being installed on average each year, using a conversion ratio of 10 per cent from solar radiation of electrical energy and peak solar radiation of one kW/m~.
With the above data established, the Westinghouse staff selected the most suitable materials and processes for concentrating collectors over the foregoing ranges of parameters. Conceptual designs were set and from these estimates of quantities of materials, labor, and equipment were derived. Methods of production, such as in-house forming of structural frames and cutting of gears, large quantity costs for materials, labor rates and production equipment costs were obtained. Estimates of overhead rates, profit levels, and other costs of the manufactured collectors came from a variety of sources. In addition to the costs of the manufactured items were estimates of expenditures for transportation of materials and equipment to the solar site, supporting structures, foundations, installation, maintenance, operation and replacements. Wind loading, as would be expected, is a major factor in determining the size of supporting structures and the nature of the foundations. Structures were designed to withstand winds gusting to 100 mph when positioned vertically against the wind. Originally, 135 mph was selected as the design wind, but this was lowered on the assumption that some form of shearing pin device could be installed to protect the collectors from higher winds. Investment and replacement costs will eventually be annualized by means of a suitable discount factor that, among other things, reflects the electric utility industry's weighted average cost of capital after taxes. Annual maintenance and operating costs will be added to the annualized costs of investments and replacements to give an equivalent uniform annual cash flow. As of this writing it appears that, once installed, the solar plant will be operated to the maximum extent possible. This is because once the plant has been built, the marginal costs of its operation would be small and would therefore be preferred over alternative sources of energy. Total hours of operation would vary from year to year depending upon the amount of solar insolation rather than on demand for electrical energy. This being a random phenomenon, the expectation of annual output would be the same throughout the economic life of the investment, if properly maintained. These are the cost values to be fed into the optimization model to give a cost per kWh of electric energy supplied to some assumed load center. RESULTS TO DATE
Manufacturing processes have been selected for paraboloidal collectors over the range of assumed aperture diameters. Initial designs have been identified only in sufficient detail to allow first approximations of costs. Investment costs have been estimated for combinations of aperture diameters, rim angles and reflectivity, but not for alternative degrees of contour and tracking errors. Developing sensitive cost relationships for these latter two parameters proved more complex than originally anticipated. Maintenance and other operating costs have been only partially estimated. Lives of reflective materials are still under study by other groups and firm estimates must await the results of such studies. Consequently, estimates of the frequency and costs of replacements are subject to revision--possibly to a considerable extent--pending further developments.
353
Cost of paraboloidal collectors for solar to thermal electric conversion
Manu[acturing materials and processes Alternative materials and processes were systematically listed and described, followed" by a review of the most suitable combinations for the ranges of parameters being considered. Eight characteristics (e.g. reflectivity, costs per m2 of applied surface and useful life) for 19 surface materials (e.g. silver, aluminum, chromium and rhodium) were tabulated. Similarly, 22 characteristics (e.g. costs per kg, ease of forming, coetticients of thermal expansion and tensile strength) for 32 shell materials (e.g. aluminum, steel, cast iron, glass, epoxies and lightweight concrete) were also tabulated. For both categories of materials an initial weighting system was applied to the various characteristics to identify those materials apparently most favorable for the requisite conditions. The weighting served to highlight various possibilities rather than as the basis for the final selection. For example, thermally evaporated silver and chromium plating ranked high as potential surface materials, while pressed glass and fiber glass reinforced cement ranked high as shell materials. Descriptions of alternative manufacturing processes were obtained from published sources to identify the relevant possibilities. Of primary concern were accuracy of forming, rates of output per machine and costs per machine. Assuming that production of collectors is to come from 5 plants strategically located across the United States, annual output for 250 working days per year would be 14,000 m2 of projected area per dayt. By knowing the nominal production rate and the limits of a machine's capabilities to produce different aperture widths, the number of machines required for different aperture widths can be determined. Thirteen alternative processes are plotted in Fig. 1. By way of illustration, injection molding of collectors with one m aperture would call for about 10 machines each producing at the rate of 2 per min; whereas, the same process producing collectors with apertures of 10 cm would call for about 100 machines each
producing at the rate of 20 per min. The foregoing machines operating on a two-shift basis would in both cases turn out 14,000 m2 of projected surface area each day. The foregoing information was augmented by discussions with process technologists to arrive at production techniques and materials most suitable for the various sets of collector parameters. The choice for the smallest aperture range (10-30 cm) was pressed glass with vapor deposited aluminum for reflectivity of 85 per cent and silver for reflectivity of 90 per cent. Aluminum sheets were selected for the shell material for the paraboloids of medium (0.5-3 m) and large (3.5 and 7"5 m) apertures. Diaphragm hydro-drawing would be used in shaping the medium sizes and spin forming would be used for the larger sizes. Initially, explosion forming had been favored for this largest category, but was dropped because of excessive costs of fabrication. Aluminum alloy No. 3002-0 is reflector grade and when highly buffed and anodized will give reflectivities of 85 per cent for several years. A less expensive grade of aluminum, alloy No. 1100, gives reflectivities of 75-85 per cent when buffed and not anodized. Duration of such reflectivities are short, being on the order of only a few weeks. Anodizing the No. 1100 grade will give reflective lives comparable to the No. 3002-0 grade, but then reflectivity drops to about 60 per cent. This lower grade has been selected originally as a cheaper material for the lower reflectivity range of 70 per cent; however, it was subsequently learned that this level of reflectivity cannot be met. Consequently, some other material will have to be selected for the lower limits of reflectivity. Building paraboloids in excess of 7.5 m aperture width was found to be impracticable due to limitations in the size of aluminum sheets and to restrictions caused by bridge and other types of transportation clearances. Welding sheets together and shipping the paraboloids in sections would overcome these limitations, but then field erection costs would increase substantially. None of the processes are limited by variances in the rim angle. Altering the reflectivity by depositing different materials on glass does not seem to pose a problem. On
tl,750 MW per year at 10 per cent conversion would require about 17.5 million ms. Five plants operating 250 days per yr would each have a daily output of 14,000 ms. 1000.
..
/
/ o
\
PM
~ /
,
\
\]i
i \\
~1 \
i \-/, I
o.3
i
0.01
0.1
I ~
' ~CM S
\ \
Z
\A~¢~/
C
\
~,,, D.bI
~
NZ~O~
\
X
N
\
%
\
'~TP
-,
~
\
c~
1 10 Production Rate, I:~rts/min
\
,%
\ 100
Fig. 1. Production of paraboloidal collectors (14,000 m2/plant/day).
\ 1000
354
W.W. SHANERand H. S. WILSON
the other hand, ease and accuracy of shaping materials other than aluminum is still under study. Electroplating surface materials on steel does not now appear to be an attractive possibility due to the length of time it takes to carry out this process and to the difficulties of controlling quality. The use of more expensive materials, such as chromium and titanium, appears to be impracticable; but this is still being investigated. Conceptual, rather than detailed, designs were developed for the three processes: pressed glass, diaphragm hydro-drawing and spin forming. Paraboloids produced by the first two processes have been designed for installation on racks of from 4.5 to 6.1 m2 depending on the size of the paraboloids. These racks are made of structural steel in which the supports for the individual collectors are small welded box beams, which in turn are supported by a cross frame made of larger box beams. Collectors are positioned in the openings between the small box beams and attached by means of simple fasteners. In the case of the reflectors of 20 cm diameter, 625 of them would be positioned on a single rack. Each rack is mounted on balanced gimbled joints that are driven by either hightorque stepping motors or synchronous gear motors, depending on the particular tracking control system adopted. This whole assembly is mounted on heavy-walled pipe machined at the top to accept the assembly inserts. The pipe in turn is set in the ground and backfilled with a chemical foaming material with the trade name of Poleset. This material has long life, is easy to use, and develops strength greater than the surrounding soil at a cost competitive with conventional backfilling materials. The possibility of setting the pipe supports in heavy concrete slabs was eliminated because of the excessive amount of concrete required to resist overturning during high winds, if the slabs are at the surface. Buried slabs could be smaller, but would require substantial excavation. Also, the use of precast piles driven into the ground would generally be more expensive than angering and backfilling. Piles would therefore not be used except where soil conditions do not permit the cheaper method. Tracking would be accomplished by means of one or
more telescopic devices. Five were assumed for the cost estimates: one at each corner of the collector field and one in the middle, but further study might reduce this number. A single telescope could track the sun and feed the results into a central computer, which in turn would send the necessary signals to accurately guide individual modules. However, risks of failure would seem to dictate against reliance on a single sensing device. In fact, some argue that no sensor is needed, since the position of the sun is known. At the other extreme would be a sensor for each module; but the cost of this alternative would be high and should probably be avoided. Absorbers have not been incorporated into the design and costs of the foregoing system. They will be before the present costing effort is completed. Obviously, the choice of absorbers depends on the types of collectors being considered. There are many possibilities. The larger collectors will probably have individual absorbing units and the very small collectors may well be grouped in facet form to focus on a common absorbing surface. For intermediate sizes, both possibilities seem practicable. Even the very small collectors could have some form of individual absorbing units, if nothing more than a receiving segment of a continuous pipe. Realistic alternatives of shapes and materials (e.g. metal pipes and evacuated glass tubing) are influenced by the rim angle, since for angles greater than 900 the absorber would be below the edge of the rim. Preliminary estimates indicate that absorbers for larger-sized paraboloids are cheaper per unit area than those for smaller-sized paraboloids. In the latter case, insulation and piping costs increase substantially as the number of collectors per module increase. At the higher pressures and larger diameters of absorber pipe or tubing the flexible couplings and hoses become very costly. Total cost for installed paraboloids, exclusive of the absorber and in 1972 dollars, is approx. $50 per m2 of projected surface for the lower-cost designs. A breakdown for one of these is shown in Table 1. Costs are for 16 paraboloids of 1.5 m aperture width mounted on a single rack. Overall rack dimensions are 6.1 m2. Specular
Table 1. Costbreakdownfor paraboloidsof 1-5meteraperture; 16permodule*(85%reflectivity;80°rimangle) Item
$[M2
%of Total
Aluminum shell
13.00
25,5
Materials
Steel framing f o r shell
1.40
2.7
Gears and motors
6,50
12.7
Other
1,50
2.9
Labor and overhead to manufacture
3.80
7.4
Pipe supports
7.10
13.9
Foundation
6.60
12.9
Tracking mechanisms and controls
3.70
7.3
Transportation
1.10
2.2
Installation of modules
4.00
7.8
Contingency (5% of the above) Total
2.40
4._~7
$51.10
I00.0%
*Costs in 1972 dollars are per square meter of projected area, exclusive of the absorber.
355
Cost of paraboloidalcollectorsfor solarto thermalelectricconversion reflectivity of the surface is 85 per cent. Absorber costs for this particular design might add another $10 per m2 to the total. Materials, labor and overhead constitute the costs of the manufactured modules, which would be partially assembled and crated for shipment to the solar site. As is apparent, materials dominate manufacturing costs. Labor and overhead costs are a small percentage because of the highly automated process and the large volume of through-put. According to Westinghouse, it is not uncommon for the most highly automated processes to have direct labor costs less than 5 per cent of total manufacturing costs, as is the case in this estimate. Overhead costs include general and administrative costs, plant maintenance and services, building rental and return on investment in equipment and working capital. The costs representing return on investment were calculated assuming equipment lives of 8 yr for light equipment and 16 yr for heavy equipment and an after-tax opportunity cost of capital of 10 per cent. Annual output per factory would be 3.5 million ms of projected surface area. Transportation costs for the modules and other materials were based on the assumption that the solar site would be approx. 350 miles from the factory producing the modules and that the average rate for this distance would be $20 per ton. These are admittedly only general and approximate figures, but the relative magnitude of transportation costs is not critical to the overall estimate. In contrast, field construction and installation costs proved to be much higher than originally anticipated. While it is possible that these costs can be reduced through more careful analysis and consideration of other alternatives, their overall significance to the total estimate is expected to remain. The contingency factor of 5 per cent is included to cover oversights and unexpected difficulties in production and installation. It is an estimate reflecting expectations that the costs will actually be higher than those tabulated; it is not an allowance to cover whatever financial difficulties might arise should costs exceed the estimate or to provide for inflation.
Cost-parameter relationships Sensitivity of collector costs to changes in aperture width are shown in Fig. 2. Rim angle is 80° and reflectivity is 85 per cent in each case. Costs vary because of differences in module size, number of reflectors per module and methods of manufacture. But taking the lowest cost possibility for each manufacturing type gives strikingly similar results of roughly $50 per m2 of projected area. Incorporation of absorber costs with collector costs, however, will tend to favor the larger aperture sizes. Sharply decreasing costs of the small, pressed glass reflectors occur because of the reduction in framing steel as the number of reflectors per module is reduced. Module size for this type of collector remains roughly constant at about 6 ms over this range of aperture widths. These dimensions allow a module to be fabricated in 2 sections, to meet transportation clearance requirements, and to be quickly assembled in the field. Little advantage would be
SE Vol. 17, No. 6-42
/
0
~
4
8o ~-
~
60
40
i i
--
-•• ~ ) Pressed Gloss ~ Hydro-drawn : ~ Hydro-drawn ~ Hydro drawn ~) Sp,n-~ot~d (~ Sp,n {ormed :
20 ~_
i
:
4,0
50
61 × 6 I me~er modules 144,36,&~6 unlts/mcxiule 9 uniTs/module 4 un,ts/module 4 unlts/module singly mounted l
10 0
10
20
3D Aperture
60
i 70
8.0
Diameter, meters
Fig. 2. Paraboloidalcost-aperturerelationships(85% ref., 80° rim angle). gained by going to smaller-sized modules, since the costs of pipe supports, foundations, motors and gears would increase. Larger-sized modules would lead to either clearance difficulties or higher costs of field assembly. It should be noted that plant manufacturing has been favored over field assembly whenever possible because of the higher costs of field labor and the difficulties of quality control. Diaphragm hydro-drawn paraboloids in the 0.5-1.5 m range do not vary in cost significantly as long as the module size is kept approx. 6 m2. But going to smaller module sizes produces increasingly higher costs. For example, paraboloids of 1.5 m width cost $51 per m2 when 16 are mounted per module, $64 per m2 when 9 are mounted per module, and $88 per m2 for modules of 4. Spin-formed paraboloids that are multiply mounted have slightly lower costs than do the diaphragm hydrodrawn paraboloids. This is due primarily to the somewhat lower scrap associated with the spin-formed process. The large, singly mounted paraboloids would be manufactured at the site by the spin-forming process. On-site production eliminates the difficulties of transporting the large, bulky and monolithically finished product. The somewhat higher costs of modules of comparable size results from the greater difficulty and expense of field operations. But as noted earlier, the lower expected costs of absorbers should make the singly mounted collectors competitive with the other types. Figure 3 shows that as rim angles are decreased or increased from 80o the costs vary accordingly. Changes in the amount of material required for shells with different rim angles are primarily responsible for these cost changes. Equipment selected for each of the processes are for the most part capable of producing the different rim angles without difficulty and at essentially the same speed. Figure 4 shows the effect on costs of changing the reflectivity from 85 per cent. These changes also are the result of different material costs. Increasing the reflectivity to 90 per cent by applying evaporated silver instead of aluminum to the pressed glass reflectors raises the costs from between $1.00 and $1.50, depending on the rim angle. Reflective costs increase with larger rim angles
356
W . W . SHANER a n d H . S . WILSON
+6.00 •
P,essedGlass
I
•
Aluminum: Soin-formod, 3 0 meters ]
+5,00 +400 !
Aluminum:
/
Spln.~otmed, 7.32~ters i
i
+3.00 b- +2.00 +1.00
~
o
¢'4 b. O"
-1.00
200
300
!
J
45
55
i
I
]
65
i
?
-
i
75 85 95 Rim Angle, degrees
-
I
105
115
Fig. 3. Paraboloidalcost-rimanglerelationships (85%ref., 80°rim angle). +200
! i Pressed Glass (90 %)
+ 1.00
~
~"
-1.00
'1' Aluminum (60%)
o £
-2oc
I
I i
r
r
-
-
Costs of maintenance and operations
I
I
Spi~4o,,~ea( 15 m) -3.00
~o,~a (
:
~
.
H a,o.d,ow.
-70v45n
55
65
involves adding $54 from Fig. 2 and $5.30 from Fig. 3 and subtracting $6.40 from Fig. 4. Or, if reflectivity of 85 per cent were desired, the cost would be the sum of the first 2 values, namely $59.30 per m2. Establishing reliable estimates of the tradeoffs between contour and tracking accuracies with costs have proved more difficult than originally anticipated. Contour errors of 0.1 ° in the shape of the surface appear to be within the capabilities of the manufacturing processes selected. On the other hand, blemishes and roughnesses caused by the forming processes create conditions tending to reduce the inherent specular reflectivity of the surface reflective material. Moreover, when paraboloids are set in racks and focus on a common absorber, the structural accuracy of the rack itself becomes a factor. Contraction and expansion due to temperature changes, deflections due to weight of the structure and warping during fabrication will add to contour errors. In somewhat similar fashion, the accuracy of tracking is a combination of a number of factors. Sensing is reported to easily meet the 0.1 ° error set as one of the parameters for tracking, but driving the modules or single collectors is quite another question. Accuracy of mounting, shafts, gearing or hydraulic controls, deviations due to thermal conditions and other problems of field installation require further analysis before the relationships between performance and costs are adequately understood.
75 85 95 Rim Angle, degrees
105
115
Fig. 4. Paraboloidal cost-reflectivityrelationships (85% ref., 80° rim angle). since the amount of actual surface area per unit of projected area is greater. Reduced costs result from using aluminum alloy No. 1100 that yields reflectivities on the order of 60 per cent. Cost reductions are greater as the rim angles increase and as the size of the spin-formed paraboloids increase. A single curve is shown for hydro-drawn paraboloids because the thickness of the shell material is approximately the same over the relevant range of 0.5-1.5 m aperture width; but for the spin-formed paraboloids shell thickness increases with the larger diameters. Figures 2--4 can therefore be used to obtain costs for various aperture widths, reflectivities and rim angles. For example, the cost of a spin-formed paraboloid of 7.32 m width, reflectivity of 60 per cent, and rim angle of 115° would cost about $53 per m 2 of projected area. This
Two uncertainties loom large in estimating the costs of maintaining and operating the collector field once it is installed. One of these is the level of reflectivity of the surface materials over time and the other is the economic lives of the reflective surfaces. Dirt and other foreign particles are deposited on the surface with the passage of time and thus reduce reflectivity from the initial state. Little has been published on the rate of degration from this cause. A notable exception are reports on the experiments currently underway by the Honeywell Systems and Research Center[4]. Field tests in Arizona on 9 different samples showed an average reduction in reflectivity due to dirtiness of about I0 per cent. By eliminating 2 of the samples whose surfaces appeared to be deteriorating, since the original reflectivity was not restored after washing, the average reduction was approx. 8 per cent. Interestingly enough, the reduction for samples tested 23 weeks was not materially different from the reduction for those tested only 9 weeks. This suggests that initial reductions in reflectivity may occur fairly rapidly and then stabilize until the surfaces begin to break down. The significance of this rather limited information is that frequent cleaning of the surface to restore reflectivity would be required. On the other hand, once the surfaces become dirty, they could be left in that state without much further loss in reflectivity. This leads to two plausible extremes in maintenance procedures: one is to clean the surfaces frequently, and the other is to not clean them at all. The data available do not allow one to conclude how frequently cleaning is necessary, other than to know that
Cost of paraboloidal collectors for solar to thermal electric conversion it would be at least every 9 weeks--the length of the shorter Honeywell tests. Despite the lack of information, a tentative conclusion can be reached on the choice between these two extremes in maintenance procedures. The solution involves the use of a breakeven point, i.e. the economic tradeoff between additional investment in collectors to make up for the reduction in reflectivity due to the dirty surface and the maintenance costs of keeping the surfaces clean. The results, worked out in the Appendix indicate that neither manual nor automatic cleaning can be justified by the increase in reflectivity. The economic alternative is to leave the reflectors dirty and build the extra surface area needed to make up for the loss. Accordingly, maintenance costs for cleaning would be limited to periodic spot checks as needed and not for a program of regular cleaning. It is worth noting, however, that these conclusions are based on limited information. As results of current and future tests become known and as other cleaning possibilities such as portable sprayers are developed, a re-examination of this issue will be in order. Estimating the lives of reflective surfaces is not so readily solved. Lives of mirror and anodized surfaces have relatively long lives when not exposed to the elements; but damage due to sand storms could be serious. Operational procedures could probably be instituted to position the reflective surfaces downwind. Nevertheless, lives for anodized surfaces--which represent a durable surface compared with some other types of materials---could be substantially reduced from the 8 to 10 yr normally expected for interior installations. Suffice it to say that this is an area requiring further consideration, as longer field trials begin to reveal both the lengths of lives of various surfaces, and the rates of degradation due to the accumulation of dirt. For the current analysis, procedures and costs for repairing and replacing damaged surfaces are still under study. The lives of other components of the collector installations will be estimated using information obtained from industrial sources experienced in operating outdoor facilities. Overall economic life of 30 yr for the solar installations will probably be chosen, since this figure is commonly used for electric utility installations. Maintenance and operating costs will also have to be established before the final optimization runs can be completed. These costs have been difficult to estimate because of the lack of experience with similar facilities. However, their overall importance may not be great. The recent Aerospace study [5] shows operating and maintenance costs as being less than 5 per cent of busbar energy costs. CONCLUSIONS
Fairly reliable estimates have been obtained on the large-scale production and installation of paraboloidal collectors over a wide range of collector designs. The dominance of materials in the overall manufacturing costs is typical of large-scale, highly automated production of products destined for industrial use. Field costs, such as pipe supports, foundations and installation, make up nearly half of the total costs. This is not unexpected
357
considering the high cost of on-site labor and other contractor costs. Estimates of component lives, operation and maintenance costs may have to be provisionally made to complete the optimization runs, since firmer estimates of some of these factors depend on the results of further research. Cost functions were developed for reflectors of varying aperture widths and for different rim angles. As it turned out, module size exerts much more influence on overall costs than does the choice of shell materials or methods of manufacture. Nor did the size of rim angle take on particular improtance in total costs. Cost-performance relationships were developed for reflectivity. But little could be concluded at this state of the analysis on the trade-offs between costs on the one hand and contour and tracking errors on the other. Finally, initial investment and maintenance costs lend themselves to optimization in that higher initial costs should lead to lower maintenance costs and visa versa; but this too must await firmer estimates of maintenance procedures and costs. In short, much still remains to be accomplished in fully understanding the cost relationships for even this relatively limited area of study. Acknowledgements--This paper is the result of research carried out by the authors as part of the study of Solar Thermal Electric Power Systems funded by the National Science Foundation for its program of Research Applied to National Needs. REFERENCES
1. The Aerospace Corporation, Task 1 Report: Comparative Systems Analyses. El Segundo, California (1972). 2. A. F. Hildebrandt et al., Large-scale concentration and conversion of solar energy. EOS, Trans. Am. Geophys. Union 53(7), 684-691 (1972). 3. The Federal Power Commission, The 1970 National Power Survey: Part L Washington, D.C. (1971). 4. University of Minnesota and Honeywell, Research Applied to Solar-Thermal Power Systems: Progress Report No. 2. Minneapolis, Minnesota (1973). 5. The Aerospace Corporation, Solar Thermal Conversion Mission Analysis, Volume IV: Mission~System and Economic Analysis. E1 Segundo, California (1974). 6. E. L. Grant and W. G. Ireson. Principles of Engineering Economy, 5th Edn. Ronald Press, New York (1970). APPENDIX
Breakeven analyses on whether or not to clean the reflective surfaces When reasonably accurate estimates of costs are difficult to make, a breakeven analysis will sometimes yield sufficient information for choosing among alternatives. This proved to be the case in the choice between cleaning the reflective surfaces of the collectors and allowing them to remain dirty. The question of cleaning the surfaces arises as a result of the degradation of reflectivity due to the accumulation of dirt and other foreign matter. The approach, described below, consists of setting the equivalent uniform annual cost of investing in additional collectors equal to the annual cost of cleaning them. The results show that neither manual nor automatic washing is as cheap as allowing the surfaces to remain dirty and providing additional surface area to obtain comparable levels of radiation. Additional surface vs manual washing Assume installed collector and absorber costs of $60 per m2 broken down as follows: surface and shells with a cost of $15 per m2 and lives of 5 yr; motors, gears and similar items with a cost of $15 per ms and lives of 10 yr; and basic structure and other
358
W . W . SHANERand H. S. WILSON
components with a cost of $30 per m 2 and lives of 30 yr. Let the required before-tax return on investment for the typical electric utility by 15 per cent. Then, the equivalent uniform annual cost per m 2 of projected area would be:t $30(A/P, 15%, 30 yr) = 30 × 0.1523 = $4.57 $15(A/P, 15%,10yr)=15×0.1993= 2.99 $15(A/P, 15%, 5 yr) = 15 x 0.2983 = 4.48 Total = $12.04/m 2 where, for example, the term (A/P, 15 per cent, 30 yr) is the capital recover factor that converts an initial amount P into an equivalent uniform annual amount A using an interest rate of 15 per cent and a life of 30 yr. The formula for obtaining the value of 0.1523 is 15%(1+ 15%)3°.((1+ 15%)3°- 1)-1. In this case P = $30 and A = $4.57. Additional to investment are the costs of maintaining the extra surface area and the labor to replace the worn out shells, motors and other items having lives of 5 and 10 yr. Equivalent uniform annual costs per square meter of projected area are as follows: Labor to replace reflectors every 5 yr: $2.00(A/F, 15%, 5 yr) = 2 x 0.148 = $0.30 Labor to replace motors, etc. every 10 yr: $1.00(A/F, 15%, 10 yr) = 1 × 0.049 = $0.05 Marginal maintenance cost for extra surface area: 5% × $60 (original investment) = $3.00
the surface that is cleaned every 9 weeks would be 81-6 per cent, provided the rate of degradation is uniform over this 9-week period. This last assumption actually favors cleaning, since it is more likely that the degradation is more rapid at the outset so that the average reflectivity of the washed surface would be less than 81.6 per cent. Comparable radiation would result from the two maintenance procedures (i.e. washing and no washing) if the projected surface area for the case of no washing were increased by 4.3 per cent (i.e. 81.6% + 78.2%-1). The equivalent uniform annual cost of this increased area is $0.66 per m 2 (i.e. 4.3% × $15.39). For a module of 16 collectors of 1.5 m aperture width, the projected surface area is 28.2 m 2 and the equivalent uniform annual cost would be $18.61 per module (i.e. $0.66 x 28.2). The foregoing value can now be compared with the cost of manually washing the surfaces. Assume a comprehensive field labor cost of $8.00 per hour in which the hours of actual cleaning are 80 per cent of total hours on the job. With the modules being cleaned every 9 weeks, the total number of cleanings per yr would be 5.8. One can now find the breakeven point in terms of the length of time to clean such a module: ($8.00/hr × 5.8 times per yr x H hr/module) + 80% = $18.61/yr H = 0.32 hr or about 19 min of washing time per module. Nineteen minutes per module is quite a short time and certainly does not allow for the type of hand cleaning assumed for the Honeywell experiments. Thus, it seems safe to conclude that hand cleaning of the reflector surfaces is not justified.
Total= $3.35/m2 where the term (A/F, 15%, 5) is the sinking fund factor that converts a future amount F into an equivalent uniform annual amount A using an interest rate of 15 per cent and a life of 5 yr. The formula for obtaining the value of 0.148 is 15%((1 + 15%)5 1)-1. In this case F = $2.00 and A = $0.30. Combining the annualized investment costs of $12.04 with maintenance and replacement costs of $3.35 gives a total of $15.39 per m 2 of projected area. With an average reflectivity of 85 per cent when initially installed and a reduction of 8 per cent to a level of 78.2 per cent in 9 weeks that stabilizes at this level, then the average reflectivity of
tThe following notation is more or less standard for calculations in engineering economy. For example, see the text by Grant and Ireson[6].
Additional surface vs automated washing Assume that a simple system of 1-in. dia. piping is placed adjacent to the reflectors in 4 rows of approx. 6.0 m length each for a total of 24 m of piping for each module and that about 16 m of connecting pipe are required, giving a total of 40 m per reflector. With an installed cost for such a piping system of $6.50 per m and a cost of $40 for valves and solenoids, the total costs per module would be $300. The equivalent uniform annual cost of this installation, assuming an interest rate of 15 per cent and a life of 15 yr, would be: $300 × (A/P, 15%, 15 yr) = 300 × 0.17102 = $51.30. This annual amount, which excludes costs of water and other services, is greater than the annual cost of $18.61 per mz for increasing the area of collector surface. In conclusion, automated washing would also appear to be an inferior alternative, even if the washing were to be so frequent as to raise the reflectivity to approximately its original value.
COST OF PARABOLOIDAL COLLECTORS FOR SOLAR TO THERMAL ELECTRIC CONVERSIONt W. W. SHANER MechanicalEngineeringDepartment,Colorado State University, Ft. Collins,CO 80523,U.S.A. and H. S. WILSON ManufacturingDevelopmentLaboratory, The WestinghouseElectric Corporation (Received 15 August 1974)
Abstract--Much is underway concerning technical and design aspects of solar collectors and associated costs of point designs. But little has been published on the tradeoffs between alternative designs and large-scale manufacturingpossibilities.To fillthis gap, close interchangeis needed among those versed in technical and systems design, manufacturing and costing. The solar to thermal electric power study funded by the National Science Foundation and carried out by Colorado State University and Westinghouse Electric Corporation has led to the assembly of such a team. This team is obtaining new data on large-scale production of concentrating collectors of widely varying parameters. Investment and other costs of paraboloidalcollectors with various aperture widths, reflectivities,rim angles, and accuracies of contour and tracking are reported herein. In studying alternative design-cost-performance relationships, emphasis is placed on breadth of coverage rather than on detailed accuracy. Alternative aperture widths led to preferences for differentproduction processes that are not particularly sensitiveto changes in rim angle or reflectivity. Significantcost relationships in the manufacture, installation and maintenance of collectors were found; other relationships are less certain. Besides the above, study results indicate directions for further study. INTRODUCTION A study currently underway involving the joint efforts of Colorado State University and the Westinghouse Electric Corporation on the conversion of solar to thermal electric energy calls for estimates of the costs of the components of alternative systems. These costs, together with the performances of the components and the overall systems, are expected to yield optimum designs for a wide range of system parameters. Important in the costing of these components is the estimate of values for concentrating collectors. Point designs by the Aerospace Corporation, for example, indicate that the costs of concentrating collectors account for about one half of the investment in converting solar to thermal electric energy[l]. Reliable estimates of the overall competitiveness of solar power systems therefore require careful study of the costs of collectors. To date literature on the application of solar energy contains little on which to base such estimates. Most of the cost estimates of collectors that have come to the authors' attention are only indicative of what collector costs might reasonably be. For example, Hildebrandt et al. [2] write that "We believe that large-scale fabrication procedures can produce the mirrors at $20 per m2. A specific approach would be to develop an aerodynamically sound structure that can be stamped or extruded continuously." Such gross estimates are appropriate during the initial stages of study, but eventually more detailed investigation is required. Considering the many possibilities of design, materials tThis paper was presented at the International Solar Energy Society's U.S. Section Meeting held in Fort Collins, Colorado (Aug. 1974).
and manufacturing techniques in producing concentrating collectors, it was felt that those knowledgeable in alternative manufacturing processes needed to be involved in the analysis. Accordingly, assistance was sought and obtained from the Westinghouse Manufacturing Development Laboratory on the design, manufacture and costs of producing large volumes of concentrating collectors. Results of this effort, together with concurrent studies by the faculty of Colorado State University, have produced estimates of installed costs for a large number of design parameters. This paper reports on results to date for paraboloids. While it is generally true that paraboloids, which require two axis tracking of high accuracy, are more expensive to build, they are also capable of producing higher temperatures. It was with the interest of covering the range of performance and cost possibilities that the paraboloid was selected for initial study. Other concentrator types, such as troughs and fresnel lenses, are also being studied and will be reported on as data are developed. Because large-scale production of paraboloidal reflectors does not now exist for the design conditions of interest, estimates of costs are only approximations to eventual costs. Thus, this paper can be considered as an interim report, with more precise cost estimates to be obtained as individual aspects of design, manufacture, installation and operation are studied in greater detail. OBJECTIVEOF THE STUDY The objective of this costing effort has been to estimate the full costs of as many different types of concentrating collectors as time and funds allow. These costs will be subsequently combined with performance characteristics through the use of an optimizing model to yield a set of
351
352
W. W. SHANER and H. S. WILSON
least cost values for alternative system designs. Results, when completed, will be in terms of dollars per kWh of electrical energy generated. SCOPE OF THE COST ANALYSIS
The thrust of this analysis has been on comprehensiveness of coverage, rather than on detailed accuracy for a limited number of alternatives. Data are derived from known technologies of processes either in actual use or reasonably likely to be used were the demand to exist for large-scale output of such collectors. Costs in 1972 dollars are to include the original equipment, installation, operation, maintenance and replacement. METHOD OF APPROACH
The first step in the investigation was a search of the literature concerning data on surfaces, shells, frame supports, structural bases and foundation, tracking, wind loading, maintenance and operation procedures, lives of components and methods of manufacture. Cost data were also recorded when available to be used as a check on subsequent calculations. Other than for this purpose, published cost data were not particularly useful since accompanying design information was seldom sufficient to allow for extrapolation of these data to other design parameters. Five design parameters were chosen to cover the performance characteristics to be incorporated in the optimization model. These are aperture width, reflectivity of surface, rim angle (angle obtained by a vertical line through the focus and another line from the focus to the edge of the paraboloid), contour error (gross errors due to major deviations in contour and minor errors due to surface roughness) and tracking error. Ranges of values are: Aperture width: from 10 cm to 10 m. Reflectivity: from 70 per cent to 90 per cent. Rim angle: from 45° to 115o. Contour error: from 0.1 ° to 3.0°. Tracking error: from 0.1 ° to 1.0°. Cost estimates were based on the assumption of large-scale production of solar-powered electrical energy. That is, if economically or otherwise feasible, solar energy plants were assumed to comprise a significant amount of new generating capacity. This led to an admittedly crude estimate of annual installations of 17.5 million m2 of projected surface areat. This level of installation is sufficiently large to confirm that installation of solar facilities at this rate indeed involves large-scale production on the part of potential manufacturers of concentrating collectors. Naturally, greater additions to annual generating capacity or higher percentages of total installations would lead to even larger levels of required annual production of solar collectors.
tThe authors arbitrarily selected 5 per cent of projected average annual additions to utility generating capacity for the 1970-80 period in the U.S.[3]. This amounts to 1750MW of solar generating capacity being installed on average each year, using a conversion ratio of 10 per cent from solar radiation of electrical energy and peak solar radiation of one kW/m~.
With the above data established, the Westinghouse staff selected the most suitable materials and processes for concentrating collectors over the foregoing ranges of parameters. Conceptual designs were set and from these estimates of quantities of materials, labor, and equipment were derived. Methods of production, such as in-house forming of structural frames and cutting of gears, large quantity costs for materials, labor rates and production equipment costs were obtained. Estimates of overhead rates, profit levels, and other costs of the manufactured collectors came from a variety of sources. In addition to the costs of the manufactured items were estimates of expenditures for transportation of materials and equipment to the solar site, supporting structures, foundations, installation, maintenance, operation and replacements. Wind loading, as would be expected, is a major factor in determining the size of supporting structures and the nature of the foundations. Structures were designed to withstand winds gusting to 100 mph when positioned vertically against the wind. Originally, 135 mph was selected as the design wind, but this was lowered on the assumption that some form of shearing pin device could be installed to protect the collectors from higher winds. Investment and replacement costs will eventually be annualized by means of a suitable discount factor that, among other things, reflects the electric utility industry's weighted average cost of capital after taxes. Annual maintenance and operating costs will be added to the annualized costs of investments and replacements to give an equivalent uniform annual cash flow. As of this writing it appears that, once installed, the solar plant will be operated to the maximum extent possible. This is because once the plant has been built, the marginal costs of its operation would be small and would therefore be preferred over alternative sources of energy. Total hours of operation would vary from year to year depending upon the amount of solar insolation rather than on demand for electrical energy. This being a random phenomenon, the expectation of annual output would be the same throughout the economic life of the investment, if properly maintained. These are the cost values to be fed into the optimization model to give a cost per kWh of electric energy supplied to some assumed load center. RESULTS TO DATE
Manufacturing processes have been selected for paraboloidal collectors over the range of assumed aperture diameters. Initial designs have been identified only in sufficient detail to allow first approximations of costs. Investment costs have been estimated for combinations of aperture diameters, rim angles and reflectivity, but not for alternative degrees of contour and tracking errors. Developing sensitive cost relationships for these latter two parameters proved more complex than originally anticipated. Maintenance and other operating costs have been only partially estimated. Lives of reflective materials are still under study by other groups and firm estimates must await the results of such studies. Consequently, estimates of the frequency and costs of replacements are subject to revision--possibly to a considerable extent--pending further developments.
353
Cost of paraboloidal collectors for solar to thermal electric conversion
Manu[acturing materials and processes Alternative materials and processes were systematically listed and described, followed" by a review of the most suitable combinations for the ranges of parameters being considered. Eight characteristics (e.g. reflectivity, costs per m2 of applied surface and useful life) for 19 surface materials (e.g. silver, aluminum, chromium and rhodium) were tabulated. Similarly, 22 characteristics (e.g. costs per kg, ease of forming, coetticients of thermal expansion and tensile strength) for 32 shell materials (e.g. aluminum, steel, cast iron, glass, epoxies and lightweight concrete) were also tabulated. For both categories of materials an initial weighting system was applied to the various characteristics to identify those materials apparently most favorable for the requisite conditions. The weighting served to highlight various possibilities rather than as the basis for the final selection. For example, thermally evaporated silver and chromium plating ranked high as potential surface materials, while pressed glass and fiber glass reinforced cement ranked high as shell materials. Descriptions of alternative manufacturing processes were obtained from published sources to identify the relevant possibilities. Of primary concern were accuracy of forming, rates of output per machine and costs per machine. Assuming that production of collectors is to come from 5 plants strategically located across the United States, annual output for 250 working days per year would be 14,000 m2 of projected area per dayt. By knowing the nominal production rate and the limits of a machine's capabilities to produce different aperture widths, the number of machines required for different aperture widths can be determined. Thirteen alternative processes are plotted in Fig. 1. By way of illustration, injection molding of collectors with one m aperture would call for about 10 machines each producing at the rate of 2 per min; whereas, the same process producing collectors with apertures of 10 cm would call for about 100 machines each
producing at the rate of 20 per min. The foregoing machines operating on a two-shift basis would in both cases turn out 14,000 m2 of projected surface area each day. The foregoing information was augmented by discussions with process technologists to arrive at production techniques and materials most suitable for the various sets of collector parameters. The choice for the smallest aperture range (10-30 cm) was pressed glass with vapor deposited aluminum for reflectivity of 85 per cent and silver for reflectivity of 90 per cent. Aluminum sheets were selected for the shell material for the paraboloids of medium (0.5-3 m) and large (3.5 and 7"5 m) apertures. Diaphragm hydro-drawing would be used in shaping the medium sizes and spin forming would be used for the larger sizes. Initially, explosion forming had been favored for this largest category, but was dropped because of excessive costs of fabrication. Aluminum alloy No. 3002-0 is reflector grade and when highly buffed and anodized will give reflectivities of 85 per cent for several years. A less expensive grade of aluminum, alloy No. 1100, gives reflectivities of 75-85 per cent when buffed and not anodized. Duration of such reflectivities are short, being on the order of only a few weeks. Anodizing the No. 1100 grade will give reflective lives comparable to the No. 3002-0 grade, but then reflectivity drops to about 60 per cent. This lower grade has been selected originally as a cheaper material for the lower reflectivity range of 70 per cent; however, it was subsequently learned that this level of reflectivity cannot be met. Consequently, some other material will have to be selected for the lower limits of reflectivity. Building paraboloids in excess of 7.5 m aperture width was found to be impracticable due to limitations in the size of aluminum sheets and to restrictions caused by bridge and other types of transportation clearances. Welding sheets together and shipping the paraboloids in sections would overcome these limitations, but then field erection costs would increase substantially. None of the processes are limited by variances in the rim angle. Altering the reflectivity by depositing different materials on glass does not seem to pose a problem. On
tl,750 MW per year at 10 per cent conversion would require about 17.5 million ms. Five plants operating 250 days per yr would each have a daily output of 14,000 ms. 1000.
..
/
/ o
\
PM
~ /
,
\
\]i
i \\
~1 \
i \-/, I
o.3
i
0.01
0.1
I ~
' ~CM S
\ \
Z
\A~¢~/
C
\
~,,, D.bI
~
NZ~O~
\
X
N
\
%
\
'~TP
-,
~
\
c~
1 10 Production Rate, I:~rts/min
\
,%
\ 100
Fig. 1. Production of paraboloidal collectors (14,000 m2/plant/day).
\ 1000
354
W.W. SHANERand H. S. WILSON
the other hand, ease and accuracy of shaping materials other than aluminum is still under study. Electroplating surface materials on steel does not now appear to be an attractive possibility due to the length of time it takes to carry out this process and to the difficulties of controlling quality. The use of more expensive materials, such as chromium and titanium, appears to be impracticable; but this is still being investigated. Conceptual, rather than detailed, designs were developed for the three processes: pressed glass, diaphragm hydro-drawing and spin forming. Paraboloids produced by the first two processes have been designed for installation on racks of from 4.5 to 6.1 m2 depending on the size of the paraboloids. These racks are made of structural steel in which the supports for the individual collectors are small welded box beams, which in turn are supported by a cross frame made of larger box beams. Collectors are positioned in the openings between the small box beams and attached by means of simple fasteners. In the case of the reflectors of 20 cm diameter, 625 of them would be positioned on a single rack. Each rack is mounted on balanced gimbled joints that are driven by either hightorque stepping motors or synchronous gear motors, depending on the particular tracking control system adopted. This whole assembly is mounted on heavy-walled pipe machined at the top to accept the assembly inserts. The pipe in turn is set in the ground and backfilled with a chemical foaming material with the trade name of Poleset. This material has long life, is easy to use, and develops strength greater than the surrounding soil at a cost competitive with conventional backfilling materials. The possibility of setting the pipe supports in heavy concrete slabs was eliminated because of the excessive amount of concrete required to resist overturning during high winds, if the slabs are at the surface. Buried slabs could be smaller, but would require substantial excavation. Also, the use of precast piles driven into the ground would generally be more expensive than angering and backfilling. Piles would therefore not be used except where soil conditions do not permit the cheaper method. Tracking would be accomplished by means of one or
more telescopic devices. Five were assumed for the cost estimates: one at each corner of the collector field and one in the middle, but further study might reduce this number. A single telescope could track the sun and feed the results into a central computer, which in turn would send the necessary signals to accurately guide individual modules. However, risks of failure would seem to dictate against reliance on a single sensing device. In fact, some argue that no sensor is needed, since the position of the sun is known. At the other extreme would be a sensor for each module; but the cost of this alternative would be high and should probably be avoided. Absorbers have not been incorporated into the design and costs of the foregoing system. They will be before the present costing effort is completed. Obviously, the choice of absorbers depends on the types of collectors being considered. There are many possibilities. The larger collectors will probably have individual absorbing units and the very small collectors may well be grouped in facet form to focus on a common absorbing surface. For intermediate sizes, both possibilities seem practicable. Even the very small collectors could have some form of individual absorbing units, if nothing more than a receiving segment of a continuous pipe. Realistic alternatives of shapes and materials (e.g. metal pipes and evacuated glass tubing) are influenced by the rim angle, since for angles greater than 900 the absorber would be below the edge of the rim. Preliminary estimates indicate that absorbers for larger-sized paraboloids are cheaper per unit area than those for smaller-sized paraboloids. In the latter case, insulation and piping costs increase substantially as the number of collectors per module increase. At the higher pressures and larger diameters of absorber pipe or tubing the flexible couplings and hoses become very costly. Total cost for installed paraboloids, exclusive of the absorber and in 1972 dollars, is approx. $50 per m2 of projected surface for the lower-cost designs. A breakdown for one of these is shown in Table 1. Costs are for 16 paraboloids of 1.5 m aperture width mounted on a single rack. Overall rack dimensions are 6.1 m2. Specular
Table 1. Costbreakdownfor paraboloidsof 1-5meteraperture; 16permodule*(85%reflectivity;80°rimangle) Item
$[M2
%of Total
Aluminum shell
13.00
25,5
Materials
Steel framing f o r shell
1.40
2.7
Gears and motors
6,50
12.7
Other
1,50
2.9
Labor and overhead to manufacture
3.80
7.4
Pipe supports
7.10
13.9
Foundation
6.60
12.9
Tracking mechanisms and controls
3.70
7.3
Transportation
1.10
2.2
Installation of modules
4.00
7.8
Contingency (5% of the above) Total
2.40
4._~7
$51.10
I00.0%
*Costs in 1972 dollars are per square meter of projected area, exclusive of the absorber.
355
Cost of paraboloidalcollectorsfor solarto thermalelectricconversion reflectivity of the surface is 85 per cent. Absorber costs for this particular design might add another $10 per m2 to the total. Materials, labor and overhead constitute the costs of the manufactured modules, which would be partially assembled and crated for shipment to the solar site. As is apparent, materials dominate manufacturing costs. Labor and overhead costs are a small percentage because of the highly automated process and the large volume of through-put. According to Westinghouse, it is not uncommon for the most highly automated processes to have direct labor costs less than 5 per cent of total manufacturing costs, as is the case in this estimate. Overhead costs include general and administrative costs, plant maintenance and services, building rental and return on investment in equipment and working capital. The costs representing return on investment were calculated assuming equipment lives of 8 yr for light equipment and 16 yr for heavy equipment and an after-tax opportunity cost of capital of 10 per cent. Annual output per factory would be 3.5 million ms of projected surface area. Transportation costs for the modules and other materials were based on the assumption that the solar site would be approx. 350 miles from the factory producing the modules and that the average rate for this distance would be $20 per ton. These are admittedly only general and approximate figures, but the relative magnitude of transportation costs is not critical to the overall estimate. In contrast, field construction and installation costs proved to be much higher than originally anticipated. While it is possible that these costs can be reduced through more careful analysis and consideration of other alternatives, their overall significance to the total estimate is expected to remain. The contingency factor of 5 per cent is included to cover oversights and unexpected difficulties in production and installation. It is an estimate reflecting expectations that the costs will actually be higher than those tabulated; it is not an allowance to cover whatever financial difficulties might arise should costs exceed the estimate or to provide for inflation.
Cost-parameter relationships Sensitivity of collector costs to changes in aperture width are shown in Fig. 2. Rim angle is 80° and reflectivity is 85 per cent in each case. Costs vary because of differences in module size, number of reflectors per module and methods of manufacture. But taking the lowest cost possibility for each manufacturing type gives strikingly similar results of roughly $50 per m2 of projected area. Incorporation of absorber costs with collector costs, however, will tend to favor the larger aperture sizes. Sharply decreasing costs of the small, pressed glass reflectors occur because of the reduction in framing steel as the number of reflectors per module is reduced. Module size for this type of collector remains roughly constant at about 6 ms over this range of aperture widths. These dimensions allow a module to be fabricated in 2 sections, to meet transportation clearance requirements, and to be quickly assembled in the field. Little advantage would be
SE Vol. 17, No. 6-42
/
0
~
4
8o ~-
~
60
40
i i
--
-•• ~ ) Pressed Gloss ~ Hydro-drawn : ~ Hydro-drawn ~ Hydro drawn ~) Sp,n-~ot~d (~ Sp,n {ormed :
20 ~_
i
:
4,0
50
61 × 6 I me~er modules 144,36,&~6 unlts/mcxiule 9 uniTs/module 4 un,ts/module 4 unlts/module singly mounted l
10 0
10
20
3D Aperture
60
i 70
8.0
Diameter, meters
Fig. 2. Paraboloidalcost-aperturerelationships(85% ref., 80° rim angle). gained by going to smaller-sized modules, since the costs of pipe supports, foundations, motors and gears would increase. Larger-sized modules would lead to either clearance difficulties or higher costs of field assembly. It should be noted that plant manufacturing has been favored over field assembly whenever possible because of the higher costs of field labor and the difficulties of quality control. Diaphragm hydro-drawn paraboloids in the 0.5-1.5 m range do not vary in cost significantly as long as the module size is kept approx. 6 m2. But going to smaller module sizes produces increasingly higher costs. For example, paraboloids of 1.5 m width cost $51 per m2 when 16 are mounted per module, $64 per m2 when 9 are mounted per module, and $88 per m2 for modules of 4. Spin-formed paraboloids that are multiply mounted have slightly lower costs than do the diaphragm hydrodrawn paraboloids. This is due primarily to the somewhat lower scrap associated with the spin-formed process. The large, singly mounted paraboloids would be manufactured at the site by the spin-forming process. On-site production eliminates the difficulties of transporting the large, bulky and monolithically finished product. The somewhat higher costs of modules of comparable size results from the greater difficulty and expense of field operations. But as noted earlier, the lower expected costs of absorbers should make the singly mounted collectors competitive with the other types. Figure 3 shows that as rim angles are decreased or increased from 80o the costs vary accordingly. Changes in the amount of material required for shells with different rim angles are primarily responsible for these cost changes. Equipment selected for each of the processes are for the most part capable of producing the different rim angles without difficulty and at essentially the same speed. Figure 4 shows the effect on costs of changing the reflectivity from 85 per cent. These changes also are the result of different material costs. Increasing the reflectivity to 90 per cent by applying evaporated silver instead of aluminum to the pressed glass reflectors raises the costs from between $1.00 and $1.50, depending on the rim angle. Reflective costs increase with larger rim angles
356
W . W . SHANER a n d H . S . WILSON
+6.00 •
P,essedGlass
I
•
Aluminum: Soin-formod, 3 0 meters ]
+5,00 +400 !
Aluminum:
/
Spln.~otmed, 7.32~ters i
i
+3.00 b- +2.00 +1.00
~
o
¢'4 b. O"
-1.00
200
300
!
J
45
55
i
I
]
65
i
?
-
i
75 85 95 Rim Angle, degrees
-
I
105
115
Fig. 3. Paraboloidalcost-rimanglerelationships (85%ref., 80°rim angle). +200
! i Pressed Glass (90 %)
+ 1.00
~
~"
-1.00
'1' Aluminum (60%)
o £
-2oc
I
I i
r
r
-
-
Costs of maintenance and operations
I
I
Spi~4o,,~ea( 15 m) -3.00
~o,~a (
:
~
.
H a,o.d,ow.
-70v45n
55
65
involves adding $54 from Fig. 2 and $5.30 from Fig. 3 and subtracting $6.40 from Fig. 4. Or, if reflectivity of 85 per cent were desired, the cost would be the sum of the first 2 values, namely $59.30 per m2. Establishing reliable estimates of the tradeoffs between contour and tracking accuracies with costs have proved more difficult than originally anticipated. Contour errors of 0.1 ° in the shape of the surface appear to be within the capabilities of the manufacturing processes selected. On the other hand, blemishes and roughnesses caused by the forming processes create conditions tending to reduce the inherent specular reflectivity of the surface reflective material. Moreover, when paraboloids are set in racks and focus on a common absorber, the structural accuracy of the rack itself becomes a factor. Contraction and expansion due to temperature changes, deflections due to weight of the structure and warping during fabrication will add to contour errors. In somewhat similar fashion, the accuracy of tracking is a combination of a number of factors. Sensing is reported to easily meet the 0.1 ° error set as one of the parameters for tracking, but driving the modules or single collectors is quite another question. Accuracy of mounting, shafts, gearing or hydraulic controls, deviations due to thermal conditions and other problems of field installation require further analysis before the relationships between performance and costs are adequately understood.
75 85 95 Rim Angle, degrees
105
115
Fig. 4. Paraboloidal cost-reflectivityrelationships (85% ref., 80° rim angle). since the amount of actual surface area per unit of projected area is greater. Reduced costs result from using aluminum alloy No. 1100 that yields reflectivities on the order of 60 per cent. Cost reductions are greater as the rim angles increase and as the size of the spin-formed paraboloids increase. A single curve is shown for hydro-drawn paraboloids because the thickness of the shell material is approximately the same over the relevant range of 0.5-1.5 m aperture width; but for the spin-formed paraboloids shell thickness increases with the larger diameters. Figures 2--4 can therefore be used to obtain costs for various aperture widths, reflectivities and rim angles. For example, the cost of a spin-formed paraboloid of 7.32 m width, reflectivity of 60 per cent, and rim angle of 115° would cost about $53 per m 2 of projected area. This
Two uncertainties loom large in estimating the costs of maintaining and operating the collector field once it is installed. One of these is the level of reflectivity of the surface materials over time and the other is the economic lives of the reflective surfaces. Dirt and other foreign particles are deposited on the surface with the passage of time and thus reduce reflectivity from the initial state. Little has been published on the rate of degration from this cause. A notable exception are reports on the experiments currently underway by the Honeywell Systems and Research Center[4]. Field tests in Arizona on 9 different samples showed an average reduction in reflectivity due to dirtiness of about I0 per cent. By eliminating 2 of the samples whose surfaces appeared to be deteriorating, since the original reflectivity was not restored after washing, the average reduction was approx. 8 per cent. Interestingly enough, the reduction for samples tested 23 weeks was not materially different from the reduction for those tested only 9 weeks. This suggests that initial reductions in reflectivity may occur fairly rapidly and then stabilize until the surfaces begin to break down. The significance of this rather limited information is that frequent cleaning of the surface to restore reflectivity would be required. On the other hand, once the surfaces become dirty, they could be left in that state without much further loss in reflectivity. This leads to two plausible extremes in maintenance procedures: one is to clean the surfaces frequently, and the other is to not clean them at all. The data available do not allow one to conclude how frequently cleaning is necessary, other than to know that
Cost of paraboloidal collectors for solar to thermal electric conversion it would be at least every 9 weeks--the length of the shorter Honeywell tests. Despite the lack of information, a tentative conclusion can be reached on the choice between these two extremes in maintenance procedures. The solution involves the use of a breakeven point, i.e. the economic tradeoff between additional investment in collectors to make up for the reduction in reflectivity due to the dirty surface and the maintenance costs of keeping the surfaces clean. The results, worked out in the Appendix indicate that neither manual nor automatic cleaning can be justified by the increase in reflectivity. The economic alternative is to leave the reflectors dirty and build the extra surface area needed to make up for the loss. Accordingly, maintenance costs for cleaning would be limited to periodic spot checks as needed and not for a program of regular cleaning. It is worth noting, however, that these conclusions are based on limited information. As results of current and future tests become known and as other cleaning possibilities such as portable sprayers are developed, a re-examination of this issue will be in order. Estimating the lives of reflective surfaces is not so readily solved. Lives of mirror and anodized surfaces have relatively long lives when not exposed to the elements; but damage due to sand storms could be serious. Operational procedures could probably be instituted to position the reflective surfaces downwind. Nevertheless, lives for anodized surfaces--which represent a durable surface compared with some other types of materials---could be substantially reduced from the 8 to 10 yr normally expected for interior installations. Suffice it to say that this is an area requiring further consideration, as longer field trials begin to reveal both the lengths of lives of various surfaces, and the rates of degradation due to the accumulation of dirt. For the current analysis, procedures and costs for repairing and replacing damaged surfaces are still under study. The lives of other components of the collector installations will be estimated using information obtained from industrial sources experienced in operating outdoor facilities. Overall economic life of 30 yr for the solar installations will probably be chosen, since this figure is commonly used for electric utility installations. Maintenance and operating costs will also have to be established before the final optimization runs can be completed. These costs have been difficult to estimate because of the lack of experience with similar facilities. However, their overall importance may not be great. The recent Aerospace study [5] shows operating and maintenance costs as being less than 5 per cent of busbar energy costs. CONCLUSIONS
Fairly reliable estimates have been obtained on the large-scale production and installation of paraboloidal collectors over a wide range of collector designs. The dominance of materials in the overall manufacturing costs is typical of large-scale, highly automated production of products destined for industrial use. Field costs, such as pipe supports, foundations and installation, make up nearly half of the total costs. This is not unexpected
357
considering the high cost of on-site labor and other contractor costs. Estimates of component lives, operation and maintenance costs may have to be provisionally made to complete the optimization runs, since firmer estimates of some of these factors depend on the results of further research. Cost functions were developed for reflectors of varying aperture widths and for different rim angles. As it turned out, module size exerts much more influence on overall costs than does the choice of shell materials or methods of manufacture. Nor did the size of rim angle take on particular improtance in total costs. Cost-performance relationships were developed for reflectivity. But little could be concluded at this state of the analysis on the trade-offs between costs on the one hand and contour and tracking errors on the other. Finally, initial investment and maintenance costs lend themselves to optimization in that higher initial costs should lead to lower maintenance costs and visa versa; but this too must await firmer estimates of maintenance procedures and costs. In short, much still remains to be accomplished in fully understanding the cost relationships for even this relatively limited area of study. Acknowledgements--This paper is the result of research carried out by the authors as part of the study of Solar Thermal Electric Power Systems funded by the National Science Foundation for its program of Research Applied to National Needs. REFERENCES
1. The Aerospace Corporation, Task 1 Report: Comparative Systems Analyses. El Segundo, California (1972). 2. A. F. Hildebrandt et al., Large-scale concentration and conversion of solar energy. EOS, Trans. Am. Geophys. Union 53(7), 684-691 (1972). 3. The Federal Power Commission, The 1970 National Power Survey: Part L Washington, D.C. (1971). 4. University of Minnesota and Honeywell, Research Applied to Solar-Thermal Power Systems: Progress Report No. 2. Minneapolis, Minnesota (1973). 5. The Aerospace Corporation, Solar Thermal Conversion Mission Analysis, Volume IV: Mission~System and Economic Analysis. E1 Segundo, California (1974). 6. E. L. Grant and W. G. Ireson. Principles of Engineering Economy, 5th Edn. Ronald Press, New York (1970). APPENDIX
Breakeven analyses on whether or not to clean the reflective surfaces When reasonably accurate estimates of costs are difficult to make, a breakeven analysis will sometimes yield sufficient information for choosing among alternatives. This proved to be the case in the choice between cleaning the reflective surfaces of the collectors and allowing them to remain dirty. The question of cleaning the surfaces arises as a result of the degradation of reflectivity due to the accumulation of dirt and other foreign matter. The approach, described below, consists of setting the equivalent uniform annual cost of investing in additional collectors equal to the annual cost of cleaning them. The results show that neither manual nor automatic washing is as cheap as allowing the surfaces to remain dirty and providing additional surface area to obtain comparable levels of radiation. Additional surface vs manual washing Assume installed collector and absorber costs of $60 per m2 broken down as follows: surface and shells with a cost of $15 per m2 and lives of 5 yr; motors, gears and similar items with a cost of $15 per ms and lives of 10 yr; and basic structure and other
358
W . W . SHANERand H. S. WILSON
components with a cost of $30 per m 2 and lives of 30 yr. Let the required before-tax return on investment for the typical electric utility by 15 per cent. Then, the equivalent uniform annual cost per m 2 of projected area would be:t $30(A/P, 15%, 30 yr) = 30 × 0.1523 = $4.57 $15(A/P, 15%,10yr)=15×0.1993= 2.99 $15(A/P, 15%, 5 yr) = 15 x 0.2983 = 4.48 Total = $12.04/m 2 where, for example, the term (A/P, 15 per cent, 30 yr) is the capital recover factor that converts an initial amount P into an equivalent uniform annual amount A using an interest rate of 15 per cent and a life of 30 yr. The formula for obtaining the value of 0.1523 is 15%(1+ 15%)3°.((1+ 15%)3°- 1)-1. In this case P = $30 and A = $4.57. Additional to investment are the costs of maintaining the extra surface area and the labor to replace the worn out shells, motors and other items having lives of 5 and 10 yr. Equivalent uniform annual costs per square meter of projected area are as follows: Labor to replace reflectors every 5 yr: $2.00(A/F, 15%, 5 yr) = 2 x 0.148 = $0.30 Labor to replace motors, etc. every 10 yr: $1.00(A/F, 15%, 10 yr) = 1 × 0.049 = $0.05 Marginal maintenance cost for extra surface area: 5% × $60 (original investment) = $3.00
the surface that is cleaned every 9 weeks would be 81-6 per cent, provided the rate of degradation is uniform over this 9-week period. This last assumption actually favors cleaning, since it is more likely that the degradation is more rapid at the outset so that the average reflectivity of the washed surface would be less than 81.6 per cent. Comparable radiation would result from the two maintenance procedures (i.e. washing and no washing) if the projected surface area for the case of no washing were increased by 4.3 per cent (i.e. 81.6% + 78.2%-1). The equivalent uniform annual cost of this increased area is $0.66 per m 2 (i.e. 4.3% × $15.39). For a module of 16 collectors of 1.5 m aperture width, the projected surface area is 28.2 m 2 and the equivalent uniform annual cost would be $18.61 per module (i.e. $0.66 x 28.2). The foregoing value can now be compared with the cost of manually washing the surfaces. Assume a comprehensive field labor cost of $8.00 per hour in which the hours of actual cleaning are 80 per cent of total hours on the job. With the modules being cleaned every 9 weeks, the total number of cleanings per yr would be 5.8. One can now find the breakeven point in terms of the length of time to clean such a module: ($8.00/hr × 5.8 times per yr x H hr/module) + 80% = $18.61/yr H = 0.32 hr or about 19 min of washing time per module. Nineteen minutes per module is quite a short time and certainly does not allow for the type of hand cleaning assumed for the Honeywell experiments. Thus, it seems safe to conclude that hand cleaning of the reflector surfaces is not justified.
Total= $3.35/m2 where the term (A/F, 15%, 5) is the sinking fund factor that converts a future amount F into an equivalent uniform annual amount A using an interest rate of 15 per cent and a life of 5 yr. The formula for obtaining the value of 0.148 is 15%((1 + 15%)5 1)-1. In this case F = $2.00 and A = $0.30. Combining the annualized investment costs of $12.04 with maintenance and replacement costs of $3.35 gives a total of $15.39 per m 2 of projected area. With an average reflectivity of 85 per cent when initially installed and a reduction of 8 per cent to a level of 78.2 per cent in 9 weeks that stabilizes at this level, then the average reflectivity of
tThe following notation is more or less standard for calculations in engineering economy. For example, see the text by Grant and Ireson[6].
Additional surface vs automated washing Assume that a simple system of 1-in. dia. piping is placed adjacent to the reflectors in 4 rows of approx. 6.0 m length each for a total of 24 m of piping for each module and that about 16 m of connecting pipe are required, giving a total of 40 m per reflector. With an installed cost for such a piping system of $6.50 per m and a cost of $40 for valves and solenoids, the total costs per module would be $300. The equivalent uniform annual cost of this installation, assuming an interest rate of 15 per cent and a life of 15 yr, would be: $300 × (A/P, 15%, 15 yr) = 300 × 0.17102 = $51.30. This annual amount, which excludes costs of water and other services, is greater than the annual cost of $18.61 per mz for increasing the area of collector surface. In conclusion, automated washing would also appear to be an inferior alternative, even if the washing were to be so frequent as to raise the reflectivity to approximately its original value.