# Numerical Simulation and Design of Multi-Tower Concentrated Solar Power Fields

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}, nations at large are opting for and considering renewable energy technologies for their power generation. Solar energy, in particular, is seen as an extremely viable option, especially in areas with good solar insolation [1]. Solar thermal energy for electricity generation is typically referred to as Concentrated Solar Power (CSP) [2]. CSP can be a driving force in the cause of reducing CO

_{2}emission, thereby contributing to reducing and limiting the global temperature increase. Of the existing types of CSP, power tower systems are one of the most promising solar thermal technologies. This is mainly due to their ability to offer higher temperatures and, hence, higher efficiencies [2,3,4,5,6,7].

## 2. Model Description

#### 2.1. Solar Insolation, Time and Angles

_{s}). Figure 1 shows the angles defining the apparent position of the sun [12,31].

_{x}, S

_{y}, and S

_{z}denote the vector components $\overrightarrow{S}$ of the sun’s radiation. The solar altitude is given by Equation (1) [31]:

^{2}/day.

#### 2.2. Optical Efficiency

#### 2.2.1. Cosine Efficiency Loss

#### 2.2.2. Shadowing and Blocking Efficiency Loss

#### 2.2.3. Attenuation Efficiency Loss

#### 2.2.4. Interception Efficiency Loss

#### 2.2.5. Mirror Reflectivity Loss

#### 2.3. Field Layout Model

#### Model Validation

## 3. Design and Optimization

#### 3.1. Conventional Field

^{2}was chosen. The value represents a safe threshold of thermal rating, which the receiver will not exceed, thereby ensuring appropriate sizing.

#### 3.2. Multi-Tower Field

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- 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] - IEA. Technology Roadmap Solar Thermal Electricity. Int. Energy Agency
**2014**, 52. [Google Scholar] [CrossRef] - Weinrebe, G.; von Reeken, F.; Wöhrbach, M.; Plaz, T.; Göcke, V.; Balz, M. Towards Holistic Power Tower System Optimization. Energy Procedia
**2014**, 49, 1573–1581. [Google Scholar] [CrossRef] [Green Version] - Mills, D. Advances in solar thermal electricity technology. Sol. Energy
**2004**, 76, 19–31. [Google Scholar] [CrossRef] - IRENA. Renewable Energy Technologies Cost Analysis Series: Concentrating Solar Power. Compr. Renew. Energy
**2012**, 3, 595–636. [Google Scholar] [CrossRef] [Green Version] - Kolb, G.; Ho, C.; Mancini, T.; Gary, J. Power tower technology roadmap and cost reduction plan. Sandia
**2011**, 38. [Google Scholar] [CrossRef] [Green Version] - International Renewable Energy Agency (IRENA). Renewable Power Generation Costs in 2018; IRENA: Abu Dhabi, UAE, 2018. [Google Scholar]
- Noone, C.J.; Torrilhon, M.; Mitsos, A. Heliostat field optimization: A new computationally efficient model and biomimetic layout. Solar Energy
**2012**, 86, 792–803. [Google Scholar] [CrossRef] - Kolb, G.J.; Jones, S.A.; Donnelly, M.W.; Gorman, D.; Thomas, R.; Davenport, R.; Lumia, R. Heliostat Cost Reduction Study; Sandia National Laboratories: Albuquerque, NM, USA, 2007; Volume SAND2007-3. [Google Scholar] [CrossRef] [Green Version]
- Cádiz, P.; Frasquet, M.; Silva, M.; Martínez, F.; Carballo, J. Shadowing and Blocking Effect Optimization for a Variable Geometry Heliostat Field. Energy Procedia
**2015**, 69, 60–69. [Google Scholar] [CrossRef] [Green Version] - Wei, X.; Lu, Z.; Wang, Z.; Yu, W.; Zhang, H.; Yao, Z. A new method for the design of the heliostat field layout for solar tower power plant. Renew. Energy
**2010**, 35, 1970–1975. [Google Scholar] [CrossRef] - Cruz, N.C.; Redondo, J.L.; Berenguel, M.; Álvarez, J.D.; Becerra-Teron, A.; Ortigosa, P.M. High performance computing for the heliostat field layout evaluation. J. Supercomput.
**2016**, 73, 1–18. [Google Scholar] [CrossRef] - Collado, F.J.; Guallar, J. Campo: Generation of regular heliostat fields. Renew. Energy
**2012**, 46, 49–59. [Google Scholar] [CrossRef] - Aldulaimi, K.M.; Söylemez, M.S. Performance Analysis of Multilevel Heliostat Field Layout. Turk. J. Sci. Technol.
**2016**, 11, 11–20. [Google Scholar] - Besarati, S.M.; Yogi Goswami, D.; Stefanakos, E.K. Optimal heliostat aiming strategy for uniform distribution of heat flux on the receiver of a solar power tower plant. Energy Convers. Manag.
**2014**, 84, 234–243. [Google Scholar] [CrossRef] - Buck, R. Heliostat Field Layout Improvement by Nonrestricted Refinement. J. Sol. Energy Eng.
**2013**, 136, 21014. [Google Scholar] [CrossRef] - Carrizosa, E.; Domínguez-Bravo, C.; Fernández-Cara, E.; Quero, M. A heuristic method for simultaneous tower and pattern-free field optimization on solar power systems. Comput. Oper. Res.
**2015**, 57, 109–122. [Google Scholar] [CrossRef] - Carrizosa, E.; Domínguez-Bravo, C.-A.; Fernández-Cara, E. An optimization tool to design the field of a solar power tower plant allowing heliostats of different sizes. Int. J. Energy Res.
**2017**. [Google Scholar] [CrossRef] [Green Version] - Lazardjani, M.Y.; Kronhardt, V.; Dikta, G.; Göttsche, J. Simultaneous optimization of micro-heliostat geometry and field layout using a genetic algorithm. In Proceedings of the AIP Conference, Cape Town, South Africa, 14–18 May 2016; Volume 1734. [Google Scholar] [CrossRef] [Green Version]
- Danielli, A.; Yatir, Y.; Mor, O. Improving the optical efficiency of a concentrated solar power field using a concatenated micro-tower configuration. Sol. Energy
**2011**, 85, 931–937. [Google Scholar] [CrossRef] - Cruz, N.C.; Salhi, S.; Redondo, J.L.; Álvarez, J.D.; Berenguel, M.; Ortigosa, P.M. Design of a parallel genetic algorithm for continuous and pattern-free heliostat field optimization. J. Supercomput.
**2018**, 1–16. [Google Scholar] [CrossRef] [Green Version] - Arrif, T.; Benchabane, A.; Germoui, M.; Bezza, B.; Belaid, A. Optimisation of heliostat field layout for solar power tower systems using iterative artificial bee colony algorithm: A review and case study. Int. J. Ambient Energy
**2018**, 1–16. [Google Scholar] [CrossRef] - Deng, L.; Wu, Y.; Guo, S.; Zhang, L.; Sun, H. Rose pattern for heliostat field optimization with a dynamic speciation-based mutation differential evolution. Int. J. Energy Res.
**2019**, 1–20. [Google Scholar] [CrossRef] - Romero, M.; Marcos, M.J.; Téllez, F.M.; Blanco, M.J.; Fernández, V.; Baonza, F.; Berger, F. Distributed power from solar tower systems: A MIUS approach. Sol. Energy
**1999**, 67, 249–264. [Google Scholar] [CrossRef] - Schramek, P.; Mills, D.R. Multi-tower solar array. Sol. Energy
**2003**, 75, 249–260. [Google Scholar] [CrossRef] - Augsburger, G.; Favrat, D. From Single- to Multi-Tower Solar Thermal Power Plants: Investigation of the Thermo-Economic Optimum Transition Size. In Proceedings of the SolarPACES 2012 Conference on Concentrating Solar Power and Chemical Energy Systems, Marrakesh, Morocco, 11–14 September 2012. [Google Scholar]
- Pacheco, J.E.; Moursund, C.; Rogers, D.; Wasyluk, D. Conceptual Design of a 100 MWe Modular Molten Salt Power Tower Plant; eSolar, Inc.: Burbank, CA, USA, 2011. [Google Scholar]
- Tyner, C.; Wasyluk, D. eSolar’s Modular, Scalable Molten Salt Power Tower Reference Plant Design. Energy Procedia
**2014**, 49, 1563–1572. [Google Scholar] [CrossRef] [Green Version] - Piroozmand, P.; Boroushaki, M. A computational method for optimal design of the multi-tower heliostat field considering heliostats interactions. Energy
**2016**, 106, 240–252. [Google Scholar] [CrossRef] - Wood, C.; Drewes, K. Vast Solar: Improving performance and reducing cost and risk using high temperature modular arrays and sodium heat transfer fluid. In Proceedings of the SolarPaces Conference, Daegu, South Korea, 1–4 October 2019. [Google Scholar]
- Duffie, J.A.; Beckman, W.A. Solar Engineering of Thermal Processes, 4th ed.; John Wiley & Sons Inc.: Hoboken, NJ, USA, 2013. [Google Scholar]
- National Aeronautic and Space Agency (NASA). Surface Metreology and Solar Energy. Available online: http://eosweb.larc.nasa.gov/cgi-bin/sse/sse.cgi?+s01#s01 (accessed on 9 September 2011).
- Ogunmodimu, O.; Marquard, A. CSP Technology and its Potential Contribution to Electricity Supply in northern Nigeria. Int. J. Renew. Energy Res.
**2013**, 3, 529–537. Available online: http://www.ijrer.com/index.php/ijrer/article/view/688 (accessed on 20 February 2020). - Habib, S.L.; Idris, N.; Ladan, M.; Mohammad, A. Unlocking Nigeria’s Solar PV and CSP Potentials for Sustainable Electricity Development. Int. J. Sci. Eng. Res.
**2012**, 3, 1–8. [Google Scholar] - Ortega, G.; Rovira, A. Proposal and analysis of different methodologies for the shading and blocking efficiency in central receivers systems. Sol. Energy
**2017**, 144, 475–488. [Google Scholar] [CrossRef] - Stine, B.W.; Geyer, M. Power from the Sun. 2001. Available online: http://www.powerfromthesun.net/book.html (accessed on 16 June 2017).
- Besarati, S.M.; Yogi Goswami, D. A computationally efficient method for the design of the heliostat field for solar power tower plant. Renew. Energy
**2014**, 69, 226–232. [Google Scholar] [CrossRef] - Wagner, M.J. Simulation and Predictive Performance Modeling of Utility-Scale Central Receiver System Power Plants. 2008. Available online: http://sel.me.wisc.edu/publications/theses/wagner08.zip (accessed on 12 November 2019).
- Weijie, D.; Xuemei, Z. Modeling and Simulation of Heliostats Field in Solar Power Tower. In Proceedings of the 29th Chinese Control And Decision Conference (CCDC), Chongqing, China, 28–30 May 2017; pp. 3246–3251. [Google Scholar]
- Sassi, G. Some notes on shadow and blockage effects. Sol. Energy
**1983**, 31, 331–333. [Google Scholar] [CrossRef] - Collado, F.J.; Turégano, J.A. Calculation of the annual thermal energy supplied by a defined heliostat field. Sol. Energy
**1989**, 42, 149–165. [Google Scholar] [CrossRef] - Ballestrín, J.; Marzo, A. Solar radiation attenuation in solar tower plants. Sol. Energy
**2012**, 86, 388–392. [Google Scholar] [CrossRef] - Leary, P.L.; Hankins, J.D. User’s Guide for MIRVAL: A Computer Code for Comparing Designs of Heliostat-Receiver Optics for Central Receiver Solar Power Plants; Sandia National Lab.: Livermore, CA, USA, 1976. [Google Scholar] [CrossRef]
- Schmitz, M.; Schwarzbözl, P.; Buck, R.; Pitz-Paal, R. Assessment of the potential improvement due to multiple apertures in central receiver systems with secondary concentrators. Sol. Energy
**2006**, 80, 111–120. [Google Scholar] [CrossRef] [Green Version] - García, L.; Burisch, M.; Sanchez, M. Spillage Estimation in a Heliostats Field for Solar Field Optimization. Energy Procedia
**2015**, 69, 1269–1276. [Google Scholar] [CrossRef] [Green Version] - Collado, F.J.; Gómez, A.; Turégano, J.A. An analytic function for the flux density due to sunlight reflected from a heliostat. Sol. Energy
**1986**, 37, 215–234. [Google Scholar] [CrossRef] - Collado, F.J. One-point fitting of the flux density produced by a heliostat. Sol. Energy
**2010**, 84, 673–684. [Google Scholar] [CrossRef] - Schwarzbözl, P.; Pitz-Paal, R.; Schmitz, M. Visual HFLCAL—A Software Tool for Layout and Optimisation of Heliostat Fields. 2009. Available online: http://elib.dlr.de/60308/ (accessed on 19 June 2017).
- Collado, F.J.; Guallar, J. A review of optimized design layouts for solar power tower plants with campo code. Renew. Sustain. Energy Rev.
**2013**, 20, 142–154. [Google Scholar] [CrossRef] [Green Version] - Siala, F.M.F.; Elayeb, M.E. Mathematical formulation of a graphical method for a no-blocking heliostat field layout. Renew. Energy
**2001**, 23, 77–92. [Google Scholar] [CrossRef] - Collado, F.J.; Guallar, J. Quick design of regular heliostat fields for commercial solar tower power plants. Energy
**2019**, 178, 115–125. [Google Scholar] [CrossRef] - Gabbrielli, R.; Castrataro, P.; Del Medico, F.; Di Palo, M.; Lenzo, B. Levelized cost of heat for linear Fresnel concentrated solar systems. Energy Procedia
**2014**, 49, 1340–1349. [Google Scholar] [CrossRef] - Louvet, Y.; Fischer, S.; Furbo, S.; Giovanetti, F.; Mauthner, F.; Mugnier, D.; Veynandt, F. LCOH for Solar Thermal Applications. 2017. Available online: http://task54.iea-shc.org/ (accessed on 4 December 2019).
- Baez, M.J.; Martinez, T.L. Technical Report on the Elaboration of a Cost Estimation Methodology. Available online: http://www.front-rhc.eu/wp-content/uploads/2014/11/FROnT_D3.1_elaboration-of-a-cost-estimation-methodology_2015.07.22.pdf (accessed on 5 November 2019).
- Collado, F.J.; Guallar, J. Two-stages optimised design of the collector field of solar power tower plants. Sol. Energy
**2016**, 135, 884–896. [Google Scholar] [CrossRef] [Green Version] - Taylor, M.; Daniel, K.; So, E.Y. IRENA: Renewable Power Generation Costs in 2014. 2014. Available online: https://www.irena.org/documentdownloads/publications/irena_re_power_costs_2014_report.pdf (accessed on 12 November 2019).
- Kistler, B.L. A User’s Manual for DELSOL3: A Computer Code for Calculating the Optical Performance and Optimal System Design for Solar Thermal Central Receiver Plants; SANDIA National Laboratories: Albuquerque, NM, USA, 1986. [Google Scholar]
- NREL. System Advisor Model (SAM); NREL: Golden, CO, USA, 2014. [Google Scholar]
- Turchi, C.S.; Heath, G.A. Molten Salt Power Tower Cost Model for the System Advisor Model (SAM) Molten Salt Power Tower Cost Model for the System Advisor Model (SAM). Energy
**2013**. [Google Scholar] [CrossRef] [Green Version] - Talebizadeh, P.; Mehrabian Ali, M.; Rahimzadeh, H. Optimization of Heliostats Layout in Central Receiver Solar Power Plants. J. Energy Eng.
**2014**, 140, 04014005. [Google Scholar] [CrossRef] - Atashkari, K.; Nariman-Zadeh, N.; Pilechi, A.; Jamali, A.; Yao, X. Thermodynamic Pareto optimization of turbojet engines using multi-objective genetic algorithms. Int. J. Therm. Sci.
**2005**, 44, 1061–1071. [Google Scholar] [CrossRef] - Pitz-Paal, R.; Botero, N.B.; Steinfeld, A. Heliostat field layout optimization for high-temperature solar thermochemical processing. Sol. Energy
**2011**, 85, 334–343. [Google Scholar] [CrossRef]

**Figure 3.**Blocking showing the contour of the representative heliostat and the projected contour of two adjacent heliostats in the first-row.

**Figure 8.**(

**a**) Position of the four identified quadrants in the field. (

**b**) Description of the region in which the additional tower would be sighted.

**Figure 9.**(

**a**) Levelized Cost of Heat (LCOH) and energy output with one additional multi-tower system (

**b**) thermal power and mean annual efficiency with one additional multi-tower system.

**Figure 10.**(

**a**) Heliostats aiming at the auxiliary tower through the year; (

**b**) Heliostats aiming at the auxiliary tower during sunshine hours at the design point date.

**Figure 11.**(

**a**) Total monthly energy output, conventional and one additional tower field; (

**b**) Total monthly mean efficiency output, conventional and one additional tower field.

**Figure 12.**(

**a**,

**c**,

**g**,

**i**) Conventional field: mean annual efficiency, cosine, attenuation, shadowing & blocking and interception efficiency respectively. (

**b**,

**d**,

**f**,

**h**,

**j**) Multi-tower field, one additional tower: mean annual efficiency, cosine, attenuation, shadowing and blocking and interception efficiency respectively.

Zones | Zone 1 | Zone 2 | Zone 3 | ||||||
---|---|---|---|---|---|---|---|---|---|

Field Efficiency | |||||||||

Row Spacing (m) | Ref Model (%) | Model (%) | Diff (%) | Ref Model (%) | Model (%) | Diff (%) | Ref Model (%) | Model (%) | Diff (%) |

$\Delta $R1 = 0.866DM | 65.34 | 65.21 | 0.20 | 55.42 | 55.12 | 0.54 | 37.54 | 37.34 | 0.53 |

$\Delta $R2 = 0.866DM | |||||||||

$\Delta $R3 = 0.866DM | |||||||||

$\Delta $R1 = 0.866DM | 65.36 | 65.21 | 0.23 | 58.45 | 58.59 | −0.24 | 48.05 | 47.79 | 0.54 |

$\Delta $R2 = 1.4DM | |||||||||

$\Delta $R3 = 1.4DM | |||||||||

$\Delta $R1 = 0.866DM | 65.36 | 65.21 | 0.23 | 57.85 | 57.86 | −0.02 | 48.35 | 48.27 | 0.17 |

$\Delta $R2 = 1.6DM | |||||||||

$\Delta $R3 = 1.6DM | |||||||||

$\Delta $R1 = 0.866DM | 65.36 | 65.21 | 0.23 | 58.66 | 58.79 | −0.22 | 50.26 | 49.98 | 0.56 |

$\Delta $R2 = 1.4DM | |||||||||

$\Delta $R3 = 1.6DM | |||||||||

$\Delta $R1 = 0.866DM | 65.36 | 65.21 | 0.23 | 58.77 | 58.89 | −0.20 | 51 | 50.78 | 0.43 |

$\Delta $R2 = 1.4DM | |||||||||

$\Delta $R3 = 1.8DM | |||||||||

$\Delta $R1 = 0.866DM | 65.36 | 65.21 | 0.23 | 58.75 | 58.89 | −0.24 | 51.07 | 50.69 | 0.74 |

$\Delta $R2 = 1.4DM | |||||||||

$\Delta $R3 = 2.0DM | |||||||||

$\Delta $R1 = 0.866DM | 65.36 | 65.21 | 0.23 | 58.68 | 58.89 | −0.36 | 50.9 | 50.58 | 0.63 |

$\Delta $R2 = 1.4DM | |||||||||

$\Delta $R3 = 2.2DM |

Design Variables | Variables Range |
---|---|

Number of Heliostats in 1st row (Zone 1) | 10–46 |

Heliostat Area (m^{2}) | 25–120 |

Receiver Dimensions (m^{2}) | 25–226 |

Tower Height (m) | 25–140 |

Heliostat Row Separation Distance Zone 1 (m) | (0.866 − 1.666) × DM |

Heliostat Separation Distance Zone 2 (m) | (0.866 − 2.666) × DM |

Heliostat Separation Distance Zone 3 (m) | (0.866 − 3.666) × DM |

**Table 3.**Summary of key results from the 50 MWth Conventional Power Tower field from the model developed and System Advisor Model (SAM).

Parameter | Model | System Advisor Model (SAM) |
---|---|---|

Heliostat Area (m^{2}) | 95.17 | 95.17 |

Central Tower Height (m) | 91.48 | 83.98 |

Central Receiver Area (m^{2}) | 55.84 | 91.43 |

Levelized Cost of Heat, LCOH ($/kWht) | 0.0474 | 0.0481 |

Power (MWth) | 49.89 | 50 |

Efficiency Design Point (%) | 60.01 | - |

Mean Annual Efficiency (%) | 54.80 | 55.63 |

Reflective Surface Area (m^{2}) | 152,270.72 | 136,011.51 |

Annual Energy (MWht) | 150,768.00 | 149,560.720 |

System Cost ($) | 40,652,834.350 | 41,253,240.000 |

Averaged Annual Efficiency in the 1st Quadrant (%) | Averaged Annual Efficiency in the 2nd Quadrant (%) | Averaged Annual Efficiency in the 3rd Quadrant (%) | Averaged Annual Efficiency in the 4th Quadrant (%) |
---|---|---|---|

57.14 | 56.24 | 54.37 | 53.37 |

**Table 5.**Multi-tower (one additional tower) field model design variables with lower and upper bounds.

Design Variables | Variables Range |
---|---|

Number of Heliostats in 1st row (Zone 1) | 10–46 |

Heliostat Area (m^{2}) | 25–120 |

Receiver Dimensions (m^{2}) | 25–226 |

Tower Height (m) | 25–140 |

Heliostat Row Separation Distance Zone 1 (m) | (0.866–1.666) × DM |

Heliostat Separation Distance Zone 2 (m) | (0.866–2.666) × DM |

Heliostat Separation Distance Zone 3 (m) | (0.866–3.666) × DM |

Additional Tower Placement Distance (m) | ((0.866–1.666) × DM) + Df |

Additional Tower Height (m) | 25–140 |

Additional Tower Receiver Dimensions (m^{2}) | 25–226 |

Parameter | Conventional Field | Multi-Tower Field (One Additional Tower) |
---|---|---|

Heliostat Area (m^{2}) | 95.17 | 93.99 |

Central Tower Height (m) | 91.48 | 92.91 |

Central Receiver Area (m^{2}) | 55.84 | 40.36 |

Auxiliary Tower Height (m) | - | 92.94 |

Auxiliary Receiver Area (m^{2}) | - | 66.38 |

LCOH ($/kWht) | 0.0474 | 0.0579 |

Field Power (MWth) | 49.89 | 49.79 |

Efficiency Design Point (%) | 60.01 | 62.95 |

Mean Annual Efficiency (%) | 54.80 | 58.44 |

Mean Annual Attenuation Efficiency (%) | 96.52 | 97.07 |

Mean Annual Shadowing and Blocking Efficiency (%) | 95.96 | 96.84 |

Mean Annual Cosine Efficiency (%) | 77.84 | 84.47 |

Mean Annual Interception Efficiency (%) | 87.82 | 92.70 |

Reflective Surface Area (m^{2}) | 152,270.72 | 140,987.00 |

Number of Heliostats | 1600 | 1500 |

Annual Energy (MWht) | 150,768.00 | 153,788.27 |

Auxiliary Receiver Thermal Power (MWth) | - | 11.51 |

System Cost ($) | 40,652,834.35 | 57,198,009.00 |

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**MDPI and ACS Style**

Hussaini, Z.A.; King, P.; Sansom, C.
Numerical Simulation and Design of Multi-Tower Concentrated Solar Power Fields. *Sustainability* **2020**, *12*, 2402.
https://doi.org/10.3390/su12062402

**AMA Style**

Hussaini ZA, King P, Sansom C.
Numerical Simulation and Design of Multi-Tower Concentrated Solar Power Fields. *Sustainability*. 2020; 12(6):2402.
https://doi.org/10.3390/su12062402

**Chicago/Turabian Style**

Hussaini, Zaharaddeen Ali, Peter King, and Chris Sansom.
2020. "Numerical Simulation and Design of Multi-Tower Concentrated Solar Power Fields" *Sustainability* 12, no. 6: 2402.
https://doi.org/10.3390/su12062402