Article | Proceedings of The 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016, The 57th SIMS Conference on Simulation and Modelling SIMS 2016 | Mathematical Conditions in Heliostat Models for Deterministic Computation of Setpoints Linköping University Electronic Press Conference Proceedings
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Title:
Mathematical Conditions in Heliostat Models for Deterministic Computation of Setpoints
Author:
Moisés Villegas-Vallecillos: Departamento de Matemáticas, Universidad de Cádiz, Spain Luis J. Yebra: Plataforma Solar de Almería, CIEMAT, Spain / CIESOL, Joint Centre of the University of Almería-CIEMAT, Spain
DOI:
10.3384/ecp17142919
Download:
Full text (pdf)
Year:
2018
Conference:
Proceedings of The 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016, The 57th SIMS Conference on Simulation and Modelling SIMS 2016
Issue:
142
Article no.:
135
Pages:
919-925
No. of pages:
7
Publication type:
Abstract and Fulltext
Published:
2018-12-19
ISBN:
978-91-7685-399-3
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press, Linköpings universitet


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In this paper a set of mathematical conditions on heliostat models is presented. Its purpose is to guarantee a deterministic computation of the heliostat setpoints in azimuth (ß) and elevation (a). In Central Receiver (CR) Concentrating Solar Power (CSP) plants, thousands of heliostats are continuously operated, and the updating of their setpoints is required frequently. For this reason, the ful?llment of some mathematical conditions of the mentioned type is important. In a simpli?ed approach, during the operation, each heliostat re?ects in its mirror a ray from the sun that impacts on a given aiming point P. This aiming point is assumed to be higher than the heliostat position, in the tower receiver. If v is the incident solar vector, x is the orthogonal vector of the heliostat re?ective plane and f (x) is the center of the heliostat mirror, then a system of equations with unknown x is arisen. Imposing certain conditions on f , we can ensure the existence and uniqueness of solution of this system, and provide a sequence converging to such solution. Furthermore, we offer a numerical method for approximating the solution in a deterministic form, which can be computed with the requirements of hard real time systems.

Keywords: central receiver concentrating solar thermal plants, heliostat setpoint, Banach’s fixed point theorem, Newton-Raphson’s numerical method, deterministic computation

Proceedings of The 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016, The 57th SIMS Conference on Simulation and Modelling SIMS 2016

Author:
Moisés Villegas-Vallecillos, Luis J. Yebra
Title:
Mathematical Conditions in Heliostat Models for Deterministic Computation of Setpoints
DOI:
http://dx.doi.org/10.3384/ecp17142919
References:
No references available

Proceedings of The 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016, The 57th SIMS Conference on Simulation and Modelling SIMS 2016

Author:
Moisés Villegas-Vallecillos, Luis J. Yebra
Title:
Mathematical Conditions in Heliostat Models for Deterministic Computation of Setpoints
DOI:
https://doi.org10.3384/ecp17142919
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Last updated: 2019-10-02