# Development of an Elevation–Fresnel Linked Mini-Heliostat Array

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Theoretical Model

`SolTrace`software [21]. A program in

`C`was developed for the calculation of the solar $\widehat{\mathbf{s}}$ and normal vectors ${\widehat{\mathbf{n}}}_{j}$ of the mini-heliostats, used as inputs for

`SolTrace`.

#### 2.2. Experimental Methods

## 3. Results

#### 3.1. Theoretical Analysis

#### 3.2. Prototype

#### 3.3. Experimental Results and Comparison

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Vant-Hull, L. Central tower concentrating solar power (CSP) systems. In Concentrating Solar Power Technology; Elsevier: Amsterdam, The Netherlands, 2012; pp. 240–283. [Google Scholar] [CrossRef]
- Ho, C.K. Advances in central receivers for concentrating solar applications. Sol. Energy
**2017**, 152, 38–56. [Google Scholar] [CrossRef] - Behar, O.; Khellaf, A.; Mohammedi, K. A review of studies on central receiver solar thermal power plants. Renew. Sustain. Energy Rev.
**2013**, 23, 12–39. [Google Scholar] [CrossRef] - Li, L.; Coventry, J.; Bader, R.; Pye, J.; Lipiński, W. Optics of solar central receiver systems: A review. Opt. Express
**2016**, 24, A985–A1007. [Google Scholar] [CrossRef] [PubMed] - Ortega, J.I.; Burgaleta, J.I.; Téllez, F.M. Central receiver system solar power plant using molten salt as heat transfer fluid. J. Sol. Energy Eng.
**2008**, 130, 024501. [Google Scholar] [CrossRef] - Göttsche, J.; Hoffschmidt, B.; Schmitz, S.; Sauerborn, M.; Buck, R.; Teufel, E.; Badstübner, K.; Ifland, D.; Rebholz, C. Solar concentrating systems using small mirror arrays. J. Sol. Energy Eng.
**2010**, 132, 011003. [Google Scholar] [CrossRef] - Pfahl, A. Survey of Heliostat Concepts for Cost Reduction. J. Sol. Energy Eng.
**2013**, 136, 014501. [Google Scholar] [CrossRef] - Coventry, J.; Pye, J. Heliostat Cost Reduction—Where to Now? Energy Procedia
**2014**, 49, 60–70. [Google Scholar] [CrossRef][Green Version] - Pfahl, A.; Coventry, J.; Röger, M.; Wolfertstetter, F.; Vásquez-Arango, J.F.; Gross, F.; Arjomandi, M.; Schwarzbözl, P.; Geiger, M.; Liedke, P. Progress in heliostat development. Sol. Energy
**2017**, 152, 3–37. [Google Scholar] [CrossRef] - Schell, S. Design and evaluation of esolar’s heliostat fields. Sol. Energy
**2011**, 85, 614–619. [Google Scholar] [CrossRef] - Kolb, G.J.; Davenport, R.; Gorman, D.; Lumia, R.; Thomas, R.; Donnelly, M. Heliostat cost reduction. In Proceedings of the ASME 2007 Energy Sustainability Conference, Long Beach, CA, USA, 27–30 July 2007; pp. 1077–1084. [Google Scholar] [CrossRef][Green Version]
- Schramek, P.; Mills, D.R.; Stein, W.; Le Lièvre, P. Design of the Heliostat Field of the CSIRO Solar Tower. J. Sol. Energy Eng.
**2009**, 131, 024505. [Google Scholar] [CrossRef] - Domínguez-Bravo, C.A.; Bode, S.J.; Heiming, G.; Richter, P.; Carrizosa, E.; Fernández-Cara, E.; Frank, M.; Gauché, P. Field-design optimization with triangular heliostat pods. AIP Conf. Proc.
**2016**, 1734, 070006. [Google Scholar] [CrossRef][Green Version] - Dunham, M.; Kasetty, R.; Mathur, A.; Lipiński, W. Optical analysis of a heliostat array with linked tracking. J. Sol. Energy Eng.
**2013**, 135, 034501. [Google Scholar] [CrossRef] - Amsbeck, L.; Buck, R.; Pfahl, A.; Uhlig, R. Optical performance and weight estimation of a heliostat with ganged facets. J. Sol. Energy Eng.
**2007**, 130, 011010. [Google Scholar] [CrossRef] - Yellowhair, J.; Andraka, C.; Armijo, K.; Ortega, J.; Clair, J. Optical performance modeling and analysis of a tensile ganged heliostat concept. In Proceedings of the ASME 2019 13th International Conference on Energy Sustainability, ES 2019, Collocated with the ASME 2019 Heat Transfer Summer Conference, Washington, DC, USA, 14–17 July 2019. [Google Scholar] [CrossRef]
- Mills, D.R. Linear Fresnel reflector (LFR) technology. In Concentrating Solar Power Technology; Lovegrove, K., Stein, W., Eds.; Woodhead Publishing Series in Energy; Woodhead Publishing: Cambridge, UK, 2012; pp. 153–196. [Google Scholar] [CrossRef]
- Buck, R.; Teufel, E. Comparison and Optimization of Heliostat Canting Methods. J. Sol. Energy Eng.
**2009**, 131, 011001. [Google Scholar] [CrossRef] - Grena, R. An algorithm for the computation of the solar position. Sol. Energy
**2008**, 82, 462–470. [Google Scholar] [CrossRef] - Dopos, A. LK Scripting Language Reference; NREL: Golden, CO, USA, 2017. [Google Scholar]
- Wendelin, T.; Dobos, A.; Lewandowski, A. SolTrace: A Ray-Tracing Code for Complex Solar Optical Systems. Contract
**2013**, 303, 275–3000. [Google Scholar] - Martínez-Manuel, L.; Peña-Cruz, M.; Villa-Medina, M.; Ojeda-Bernal, C.; Prado-Zermeño, M.; Prado-Zermeño, I.; Pineda-Arellano, C.; Carrillo, J.; Salgado-Tránsito, I.; Martell-Chavez, F. A 17.5 kWel high flux solar simulator with controllable flux-spot capabilities: Design and validation study. Sol. Energy
**2018**, 170, 807–819. [Google Scholar] [CrossRef] - Moreno-Cruz, I. Análisis de un Sistema de Seguimiento Solar Para Arreglos de Helióstatos Acoplados. Ph.D. Thesis, Instituto de Energías Renovables, UNAM, Temixco, Mexico, 2019. [Google Scholar]
- Chong, K. Optical analysis for simplified astigmatic correction of non-imaging focusing heliostat. Sol. Energy
**2010**, 84, 1356–1365. [Google Scholar] [CrossRef] - Renzi, M.; Bartolini, C.M.; Santolini, M.; Arteconi, A. Efficiency assessment for a small heliostat solar concentration plant. Int. J. Energy Res.
**2015**, 39, 265–278. [Google Scholar] [CrossRef] - Díaz-Félix, L.; Escobar-Toledo, M.; Waissman, J.; Pitalúa-Díaz, N.; Arancibia-Bulnes, C. Evaluation of Heliostat Field Global Tracking Error Distributions by Monte Carlo Simulations. Energy Procedia
**2014**, 49, 1308–1317. [Google Scholar] [CrossRef][Green Version] - Bonanos, A.; Faka, M.; Abate, D.; Hermon, S.; Blanco, M. Heliostat surface shape characterization for accurate flux prediction. Renew. Energy
**2019**, 142, 30–40. [Google Scholar] [CrossRef] - Iriarte-Cornejo, C.; Arancibia-Bulnes, C.; Hinojosa, J.; Peña-Cruz, M.I. Effect of spatial resolution of heliostat surface characterization on its concentrated heat flux distribution. Sol. Energy
**2018**, 174, 312–320. [Google Scholar] [CrossRef] - Sánchez-González, A.; Caliot, C.; Ferrière, A.; Santana, D. Determination of heliostat canting errors via deterministic optimization. Sol. Energy
**2017**, 150, 136–146. [Google Scholar] [CrossRef]

**Figure 3.**Global reference system showing the solar vector $\widehat{\mathbf{s}}$, the mirror normal $\widehat{\mathbf{n}}$, and the target vector $\widehat{\mathbf{t}}$ (

**a**). The ${\xi}_{0}$ and ${\psi}_{0}$ rotations of the central facet for the heliostat array tracking (

**b**).

**Figure 4.**Impact points of the central reflected ray of each facet, for the four mini-heliostats ${f}_{1}$, ${f}_{2}$, ${f}_{3}$ and ${f}_{4}$ of the H4 array, on the receiver, for 21 March. The positions are (

**a**) $0.75h$ (26.25 m) and (

**b**) $4h$ (140 m).

**Figure 5.**Central rays’ impact points of each facet on the target for an H4 array, and for the 21st day of each month from June to December. The array is located at 0.75h (26.25 m).

**Figure 6.**Daily standard deviation of facet impact points in x (

**a**) and z (

**b**), for H4 arrays located at $0.75h$ (26.25 m), $2h$ (70 m), and $4h$ (140 m).

**Figure 7.**Daily standard deviations of facet impact points for the heliostat arrays H2, H4, H8, H16, H24, and H32 throughout the year, along the x (

**a**) and z (

**b**) axes. The arrays are located at $2h$ (70 m).

**Figure 8.**Concentrated solar flux distribution on the receiver ($6\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\times 6\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$) for an H8 array located at $0.75h$ (26.25 m). Solar noon the 21st of June (

**a**) and December (

**b**).

**Figure 9.**Concentrated solar flux distribution on the receiver ($6\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\times 6\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$) for an H32 array, on 21 June at 8:30 (

**a**) and 12:30 (

**b**), solar time, for a distance of 2h (70 m).

**Figure 10.**Variation throughout the year of the daily standard deviations of the concentrated radiative flux distribution ${\overline{S}}_{x}$ and ${\overline{S}}_{z}$ along the x (

**a**) and z (

**b**) axes, respectively, for arrays with different number of facets, placed at a distance of 2h (70 m).

**Figure 11.**Behavior of the daily standard deviations $\overline{S}$ (

**a**) and the peak flux (

**b**) for H8 arrays with and without concentrating mirrors. Location is at 37 m from the tower.

**Figure 12.**Energy contributed per mirror throughout the year for different arrays. Distance of $0.75h$ (26.25 m).

**Figure 15.**Photographs of the heliostat array prototype (

**a**), and the concentrated solar flux distribution reflected on the target (

**b**).

**Figure 17.**Experimental radiative flux distribution (

**a**) and ray tracing simulation with SolTrace (

**b**) for the heliostat array prototype. The isolines $0.500$, $1.00$, $3.00$, and $5.00$ correspond to irradiance in $\mathrm{kW}/{\mathrm{m}}^{2}$.

**Figure 18.**Irradiance distributions along the x (

**a**) and z (

**b**) directions through the distribution centroids.

Parameter | Value | Units |
---|---|---|

Number of facets | 8 | – |

Facet length | 1.00 | m |

Facet width | 0.60 | m |

Mirror material | Back silvered glass | – |

Mirror thickness | 6 | mm |

Structure material | ASTM A36 Steel | – |

Spacing between facets | 0.02 | m |

Length of the elevation frame | 5.062 | m |

Width of the elevation frame | 1.13 | m |

Height of the array | 1.6 | m |

Type of actuator | Linear jack /stepper motor | – |

Elevation range | [5, 80] | deg |

Facet rotation range | [−53.71, 53.71] | deg |

Facet | ${\mathit{f}}_{8}$ | ${\mathit{f}}_{6}$ | ${\mathit{f}}_{4}$ | ${\mathit{f}}_{2}$ | ${\mathit{f}}_{1}$ | ${\mathit{f}}_{3}$ | ${\mathit{f}}_{5}$ | ${\mathit{f}}_{7}$ |
---|---|---|---|---|---|---|---|---|

Canting angle (deg) | 1.884 | 1.346 | 0.808 | 0.269 | −0.269 | −0.808 | −1.346 | −1.884 |

Slope error (mrad) | 1.36 | 0.75 | 1.41 | 1.68 | 0.87 | 1.26 | 1.32 | 0.77 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Moreno-Cruz, I.; Castro, J.C.; Álvarez-Brito, O.; Mota-Nava, H.B.; Ramírez-Zúñiga, G.; Quiñones-Aguilar, J.J.; Arancibia-Bulnes, C.A. Development of an Elevation–Fresnel Linked Mini-Heliostat Array. *Energies* **2020**, *13*, 4012.
https://doi.org/10.3390/en13154012

**AMA Style**

Moreno-Cruz I, Castro JC, Álvarez-Brito O, Mota-Nava HB, Ramírez-Zúñiga G, Quiñones-Aguilar JJ, Arancibia-Bulnes CA. Development of an Elevation–Fresnel Linked Mini-Heliostat Array. *Energies*. 2020; 13(15):4012.
https://doi.org/10.3390/en13154012

**Chicago/Turabian Style**

Moreno-Cruz, Isaías, Juan Carlos Castro, Omar Álvarez-Brito, Hilda B. Mota-Nava, Guillermo Ramírez-Zúñiga, José J. Quiñones-Aguilar, and Camilo A. Arancibia-Bulnes. 2020. "Development of an Elevation–Fresnel Linked Mini-Heliostat Array" *Energies* 13, no. 15: 4012.
https://doi.org/10.3390/en13154012