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Research Papers

# Probabilistic Analysis to Quantify Optical Performance and Error Budgets for Next Generation Heliostats

[+] Author and Article Information
Joshua Christian

Concentrating Solar Technologies Department,
Sandia Staffing Alliance,
P.O. Box 5800, MS-1127,
Albuquerque, NM 87185
e-mail: jmchris@sandia.gov

Adam Moya, Clifford Ho, Charles Andraka, James Yuan

Concentrating Solar Technologies Department,
Sandia National Laboratories,
P.O. Box 5800, MS-1127,
Albuquerque, NM 87185

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received February 28, 2013; final manuscript received November 25, 2014; published online January 15, 2015. Assoc. Editor: Markus Eck.

The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

J. Sol. Energy Eng 137(3), 031014 (Jun 01, 2015) (8 pages) Paper No: SOL-13-1072; doi: 10.1115/1.4029376 History: Received February 28, 2013; Revised November 25, 2014; Online January 15, 2015

## Abstract

Current heliostats cost ∼$200/m2 of reflective area and are estimated to contribute up to 50% of the total solar power tower plant costs. A drastic overall cost reduction is required in order for concentrated solar thermal power to be economically viable. The Department of Energy has set forth the SunShot initiative targeting a levelized cost of energy (LCOE) of$0.06/kWh by the year 2020. The cost of each heliostat must be brought down to an estimated $75/m2 to achieve this rigorous goal. One of the driving aspects of heliostat design and cost are the heliostat optical errors. At the moment, it is relatively unclear about the amount of error that can be present in the system while still maintaining low cost and high optical accuracy. The optical errors present on heliostat mirror surfaces directly influence the plant LCOE by causing beam spillage. This can result in an increase in the number of heliostats, an increased receiver size, and decreased thermal efficiency. Assuming a fixed heliostat cost of$75/m2, the effects of optical errors on LCOE were evaluated within the software delsol. From a probabilistic analysis, beam quality errors (i.e., slope error, alignment errors, etc.) were shown to have more importance on the LCOE than tracking errors. This determination resulted in a realization that the tracking errors and beam quality errors could be combined into a “bundled” root-sum-square (RSS) error value and produce similar results in delsol. A “bundled” error value of 2 mrad resulted in an LCOE of \$0.06/kWh. This “bundled” value was the basis for a new optical error budget and is decomposed into five individual errors. These five errors can be used as design specifications for new generation heliostats.

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Topics: Errors , Mirrors , Design

## References

Kolb, G. J., Jones, S. A., Gorman, D., Thomas, R., Davenport, R., and Lumia, R., 2007, “Heliostat Cost Reduction Study,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2007-3293.
National Renewable Energy Laboratory (NREL), 2012, SunShot Vision Study, Department of Energy.
Zavoico, A. B., 2001, “Solar Power Tower: Design Basis Document,” Sandia National Laboratories, Albuquerque, NM/Livermore, CA, Report No. SAND2001-2100.
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Yellowhair, J., Christian, J., and Ho, C., 2014, “Evaluation of Solar Optical Modeling Tools for Modeling Complex Receiver Geometries,” ASME Paper No. ES2014-6620.
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## Figures

Fig. 1

Standardized regression coefficients (beta values); cylindrical receiver with 14.87 m diameter and 18.62 m height; sigsx and sigsy had a range of 1–4 mrad; sigaz and sigel had a range of 0.25–1.5 mrad

Fig. 2

Delta R2 values; cylindrical receiver with 14.87 m diameter and 18.62 m height; sigaz and sigel had a range of 0.25–1.5 mrad

Fig. 3

Standardized regression coefficients (beta values); cylindrical receiver with 12 m diameter and 10 m height; sigaz and sigel had a range of 0.25–1.5 mrad

Fig. 4

Delta R2 values; cylindrical receiver with 12 m diameter and 10 m height; sigaz and sigel had a range of 0.25–1.5 mrad

Fig. 5

Bundled error versus LCOE for different receiver sizes; The same azimuth and elevation bundled errors were used for this analysis

Fig. 6

Sample triangular distribution used in the optical performance analysis, the shaded region represents the range of values sampled

Fig. 7

Cumulative probability function plot of the bundled slope errors for a receiver size of 14.87 m diameter × 18.62 m height, each CDF has a varying triangular distribution range centered about the nominal error value for which the errors were sampled from

Fig. 8

Cumulative probability function plot of the bundled slope errors for a receiver size of 12 m diameter × 10 m height, each CDF has a varying triangular distribution range centered about the nominal error value for which the errors were sampled from

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