Abstract

Heliostat alignment evaluation is among the main issues in solar tower concentration plant operation and maintenance. This paper describes a novel method used to evaluate heliostat misalignment and its experimental verification. This method provides a different way of visualizing beam centroid pointing errors by generating the complete deviation curve for each axis. This, for example, would be useful for verifying a heliostat’s correct alignment by using a measurement performed out of the receiver target, using these traces to calculate its reflection’s expected location, given a known misalignment. This measurement could be performed during operation simply by including a reflective element in the heliostat and two detector arrays on the tower’s surface. This model has been tested for various types of misalignments of a heliostat at different hours, dates, and heliostat locations. The simulation results have been validated by using an experimental setup at a scale of 1:100.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. C. K. Yang, T. C. Cheng, C. H. Cheng, C. C. Wang, and C. C. Lee, “Open-loop altitude-azimuth concentrated solar tracking system for solar-thermal applications,” Sol. Energy 147, 52–60 (2017).
    [Crossref]
  2. W. Huang, P. Hu, and Z. Chen, “Performance simulation of a parabolic trough solar collector,” Sol. Energy 86(2), 746–755 (2012).
    [Crossref]
  3. M. Coquand, F. Henault, and C. Caliot, “Backward-gazing method for measuring solar concentrators shape errors,” Appl. Opt. 56(7), 2029–2037 (2017).
    [Crossref] [PubMed]
  4. Y. Yao, Y. Hu, S. Gao, G. Yang, and J. Du, “A multipurpose dual-axis solar tracker with two tracking strategies,” Renew. Energy 72, 88–98 (2014).
    [Crossref]
  5. S. A. Jones and K. W. Stone, “Analysis of solar two heliostat tracking error sources,” Tech. Rep. SAND99–0239C Albuq. Sandia Natl. Lab. (1999).
  6. L. A. Díaz-Félix, M. Escobar-Toledo, J. Waissman, N. Pitalúa-Díaz, and C. A. Arancibia-Bulnes, “Evaluation of heliostat field global tracking error distributions by Monte Carlo simulations,” Energy Procedia 49, 1308–1317 (2014).
    [Crossref]
  7. M. Guo, Z. Wang, and F. Sun, “Simulations of reflected sun beam traces over a target plane for an azimuth elevation tracking heliostat with fixed geometric error sources,” Sol. Energy 97, 102–111 (2013).
    [Crossref]
  8. R. Alonso, C. Heras, J. Pelayo, I. Salinas, and J. Subias, “Closed-loop control system and method for heliostats in solar power towers,” U.S. patent ES2558847 (A1) Abstract of corresponding document: WO2016005620 (A1) (February 9, 2016).
  9. M. R. Convery, “Closed-loop control for power tower heliostats,” in High and Low Concentrator Systems for Solar Electric Applications Vi, K. VanSant and R. A. Sherif, eds. (Spie-Int Soc Optical Engineering, 2011), Vol. 8108, p. 81080M.
  10. H. Fathabadi, “Comparative study between two novel sensorless and sensor based dual-axis solar trackers,” Sol. Energy 138, 67–76 (2016).
    [Crossref]
  11. W. Nsengiyumva, S. G. Chen, L. Hu, and X. Chen, “Recent advancements and challenges in solar tracking systems (STS): A review,” Renew. Sustain. Energy Rev. 81, 250–279 (2018).
    [Crossref]
  12. J. A. Duffie and W. A. Beckman, Solar engineering of thermal processes (Wiley, 1991).
  13. M. Guo, F. Sun, Z. Wang, and J. Zhang, “Properties of a general azimuth-elevation tracking angle formula for a heliostat with a mirror-pivot offset and other angular errors,” Sol. Energy 96, 159–167 (2013).
    [Crossref]

2018 (1)

W. Nsengiyumva, S. G. Chen, L. Hu, and X. Chen, “Recent advancements and challenges in solar tracking systems (STS): A review,” Renew. Sustain. Energy Rev. 81, 250–279 (2018).
[Crossref]

2017 (2)

C. K. Yang, T. C. Cheng, C. H. Cheng, C. C. Wang, and C. C. Lee, “Open-loop altitude-azimuth concentrated solar tracking system for solar-thermal applications,” Sol. Energy 147, 52–60 (2017).
[Crossref]

M. Coquand, F. Henault, and C. Caliot, “Backward-gazing method for measuring solar concentrators shape errors,” Appl. Opt. 56(7), 2029–2037 (2017).
[Crossref] [PubMed]

2016 (1)

H. Fathabadi, “Comparative study between two novel sensorless and sensor based dual-axis solar trackers,” Sol. Energy 138, 67–76 (2016).
[Crossref]

2014 (2)

Y. Yao, Y. Hu, S. Gao, G. Yang, and J. Du, “A multipurpose dual-axis solar tracker with two tracking strategies,” Renew. Energy 72, 88–98 (2014).
[Crossref]

L. A. Díaz-Félix, M. Escobar-Toledo, J. Waissman, N. Pitalúa-Díaz, and C. A. Arancibia-Bulnes, “Evaluation of heliostat field global tracking error distributions by Monte Carlo simulations,” Energy Procedia 49, 1308–1317 (2014).
[Crossref]

2013 (2)

M. Guo, Z. Wang, and F. Sun, “Simulations of reflected sun beam traces over a target plane for an azimuth elevation tracking heliostat with fixed geometric error sources,” Sol. Energy 97, 102–111 (2013).
[Crossref]

M. Guo, F. Sun, Z. Wang, and J. Zhang, “Properties of a general azimuth-elevation tracking angle formula for a heliostat with a mirror-pivot offset and other angular errors,” Sol. Energy 96, 159–167 (2013).
[Crossref]

2012 (1)

W. Huang, P. Hu, and Z. Chen, “Performance simulation of a parabolic trough solar collector,” Sol. Energy 86(2), 746–755 (2012).
[Crossref]

Arancibia-Bulnes, C. A.

L. A. Díaz-Félix, M. Escobar-Toledo, J. Waissman, N. Pitalúa-Díaz, and C. A. Arancibia-Bulnes, “Evaluation of heliostat field global tracking error distributions by Monte Carlo simulations,” Energy Procedia 49, 1308–1317 (2014).
[Crossref]

Caliot, C.

Chen, S. G.

W. Nsengiyumva, S. G. Chen, L. Hu, and X. Chen, “Recent advancements and challenges in solar tracking systems (STS): A review,” Renew. Sustain. Energy Rev. 81, 250–279 (2018).
[Crossref]

Chen, X.

W. Nsengiyumva, S. G. Chen, L. Hu, and X. Chen, “Recent advancements and challenges in solar tracking systems (STS): A review,” Renew. Sustain. Energy Rev. 81, 250–279 (2018).
[Crossref]

Chen, Z.

W. Huang, P. Hu, and Z. Chen, “Performance simulation of a parabolic trough solar collector,” Sol. Energy 86(2), 746–755 (2012).
[Crossref]

Cheng, C. H.

C. K. Yang, T. C. Cheng, C. H. Cheng, C. C. Wang, and C. C. Lee, “Open-loop altitude-azimuth concentrated solar tracking system for solar-thermal applications,” Sol. Energy 147, 52–60 (2017).
[Crossref]

Cheng, T. C.

C. K. Yang, T. C. Cheng, C. H. Cheng, C. C. Wang, and C. C. Lee, “Open-loop altitude-azimuth concentrated solar tracking system for solar-thermal applications,” Sol. Energy 147, 52–60 (2017).
[Crossref]

Coquand, M.

Díaz-Félix, L. A.

L. A. Díaz-Félix, M. Escobar-Toledo, J. Waissman, N. Pitalúa-Díaz, and C. A. Arancibia-Bulnes, “Evaluation of heliostat field global tracking error distributions by Monte Carlo simulations,” Energy Procedia 49, 1308–1317 (2014).
[Crossref]

Du, J.

Y. Yao, Y. Hu, S. Gao, G. Yang, and J. Du, “A multipurpose dual-axis solar tracker with two tracking strategies,” Renew. Energy 72, 88–98 (2014).
[Crossref]

Escobar-Toledo, M.

L. A. Díaz-Félix, M. Escobar-Toledo, J. Waissman, N. Pitalúa-Díaz, and C. A. Arancibia-Bulnes, “Evaluation of heliostat field global tracking error distributions by Monte Carlo simulations,” Energy Procedia 49, 1308–1317 (2014).
[Crossref]

Fathabadi, H.

H. Fathabadi, “Comparative study between two novel sensorless and sensor based dual-axis solar trackers,” Sol. Energy 138, 67–76 (2016).
[Crossref]

Gao, S.

Y. Yao, Y. Hu, S. Gao, G. Yang, and J. Du, “A multipurpose dual-axis solar tracker with two tracking strategies,” Renew. Energy 72, 88–98 (2014).
[Crossref]

Guo, M.

M. Guo, Z. Wang, and F. Sun, “Simulations of reflected sun beam traces over a target plane for an azimuth elevation tracking heliostat with fixed geometric error sources,” Sol. Energy 97, 102–111 (2013).
[Crossref]

M. Guo, F. Sun, Z. Wang, and J. Zhang, “Properties of a general azimuth-elevation tracking angle formula for a heliostat with a mirror-pivot offset and other angular errors,” Sol. Energy 96, 159–167 (2013).
[Crossref]

Henault, F.

Hu, L.

W. Nsengiyumva, S. G. Chen, L. Hu, and X. Chen, “Recent advancements and challenges in solar tracking systems (STS): A review,” Renew. Sustain. Energy Rev. 81, 250–279 (2018).
[Crossref]

Hu, P.

W. Huang, P. Hu, and Z. Chen, “Performance simulation of a parabolic trough solar collector,” Sol. Energy 86(2), 746–755 (2012).
[Crossref]

Hu, Y.

Y. Yao, Y. Hu, S. Gao, G. Yang, and J. Du, “A multipurpose dual-axis solar tracker with two tracking strategies,” Renew. Energy 72, 88–98 (2014).
[Crossref]

Huang, W.

W. Huang, P. Hu, and Z. Chen, “Performance simulation of a parabolic trough solar collector,” Sol. Energy 86(2), 746–755 (2012).
[Crossref]

Lee, C. C.

C. K. Yang, T. C. Cheng, C. H. Cheng, C. C. Wang, and C. C. Lee, “Open-loop altitude-azimuth concentrated solar tracking system for solar-thermal applications,” Sol. Energy 147, 52–60 (2017).
[Crossref]

Nsengiyumva, W.

W. Nsengiyumva, S. G. Chen, L. Hu, and X. Chen, “Recent advancements and challenges in solar tracking systems (STS): A review,” Renew. Sustain. Energy Rev. 81, 250–279 (2018).
[Crossref]

Pitalúa-Díaz, N.

L. A. Díaz-Félix, M. Escobar-Toledo, J. Waissman, N. Pitalúa-Díaz, and C. A. Arancibia-Bulnes, “Evaluation of heliostat field global tracking error distributions by Monte Carlo simulations,” Energy Procedia 49, 1308–1317 (2014).
[Crossref]

Sun, F.

M. Guo, F. Sun, Z. Wang, and J. Zhang, “Properties of a general azimuth-elevation tracking angle formula for a heliostat with a mirror-pivot offset and other angular errors,” Sol. Energy 96, 159–167 (2013).
[Crossref]

M. Guo, Z. Wang, and F. Sun, “Simulations of reflected sun beam traces over a target plane for an azimuth elevation tracking heliostat with fixed geometric error sources,” Sol. Energy 97, 102–111 (2013).
[Crossref]

Waissman, J.

L. A. Díaz-Félix, M. Escobar-Toledo, J. Waissman, N. Pitalúa-Díaz, and C. A. Arancibia-Bulnes, “Evaluation of heliostat field global tracking error distributions by Monte Carlo simulations,” Energy Procedia 49, 1308–1317 (2014).
[Crossref]

Wang, C. C.

C. K. Yang, T. C. Cheng, C. H. Cheng, C. C. Wang, and C. C. Lee, “Open-loop altitude-azimuth concentrated solar tracking system for solar-thermal applications,” Sol. Energy 147, 52–60 (2017).
[Crossref]

Wang, Z.

M. Guo, F. Sun, Z. Wang, and J. Zhang, “Properties of a general azimuth-elevation tracking angle formula for a heliostat with a mirror-pivot offset and other angular errors,” Sol. Energy 96, 159–167 (2013).
[Crossref]

M. Guo, Z. Wang, and F. Sun, “Simulations of reflected sun beam traces over a target plane for an azimuth elevation tracking heliostat with fixed geometric error sources,” Sol. Energy 97, 102–111 (2013).
[Crossref]

Yang, C. K.

C. K. Yang, T. C. Cheng, C. H. Cheng, C. C. Wang, and C. C. Lee, “Open-loop altitude-azimuth concentrated solar tracking system for solar-thermal applications,” Sol. Energy 147, 52–60 (2017).
[Crossref]

Yang, G.

Y. Yao, Y. Hu, S. Gao, G. Yang, and J. Du, “A multipurpose dual-axis solar tracker with two tracking strategies,” Renew. Energy 72, 88–98 (2014).
[Crossref]

Yao, Y.

Y. Yao, Y. Hu, S. Gao, G. Yang, and J. Du, “A multipurpose dual-axis solar tracker with two tracking strategies,” Renew. Energy 72, 88–98 (2014).
[Crossref]

Zhang, J.

M. Guo, F. Sun, Z. Wang, and J. Zhang, “Properties of a general azimuth-elevation tracking angle formula for a heliostat with a mirror-pivot offset and other angular errors,” Sol. Energy 96, 159–167 (2013).
[Crossref]

Appl. Opt. (1)

Energy Procedia (1)

L. A. Díaz-Félix, M. Escobar-Toledo, J. Waissman, N. Pitalúa-Díaz, and C. A. Arancibia-Bulnes, “Evaluation of heliostat field global tracking error distributions by Monte Carlo simulations,” Energy Procedia 49, 1308–1317 (2014).
[Crossref]

Renew. Energy (1)

Y. Yao, Y. Hu, S. Gao, G. Yang, and J. Du, “A multipurpose dual-axis solar tracker with two tracking strategies,” Renew. Energy 72, 88–98 (2014).
[Crossref]

Renew. Sustain. Energy Rev. (1)

W. Nsengiyumva, S. G. Chen, L. Hu, and X. Chen, “Recent advancements and challenges in solar tracking systems (STS): A review,” Renew. Sustain. Energy Rev. 81, 250–279 (2018).
[Crossref]

Sol. Energy (5)

H. Fathabadi, “Comparative study between two novel sensorless and sensor based dual-axis solar trackers,” Sol. Energy 138, 67–76 (2016).
[Crossref]

M. Guo, F. Sun, Z. Wang, and J. Zhang, “Properties of a general azimuth-elevation tracking angle formula for a heliostat with a mirror-pivot offset and other angular errors,” Sol. Energy 96, 159–167 (2013).
[Crossref]

C. K. Yang, T. C. Cheng, C. H. Cheng, C. C. Wang, and C. C. Lee, “Open-loop altitude-azimuth concentrated solar tracking system for solar-thermal applications,” Sol. Energy 147, 52–60 (2017).
[Crossref]

W. Huang, P. Hu, and Z. Chen, “Performance simulation of a parabolic trough solar collector,” Sol. Energy 86(2), 746–755 (2012).
[Crossref]

M. Guo, Z. Wang, and F. Sun, “Simulations of reflected sun beam traces over a target plane for an azimuth elevation tracking heliostat with fixed geometric error sources,” Sol. Energy 97, 102–111 (2013).
[Crossref]

Other (4)

R. Alonso, C. Heras, J. Pelayo, I. Salinas, and J. Subias, “Closed-loop control system and method for heliostats in solar power towers,” U.S. patent ES2558847 (A1) Abstract of corresponding document: WO2016005620 (A1) (February 9, 2016).

M. R. Convery, “Closed-loop control for power tower heliostats,” in High and Low Concentrator Systems for Solar Electric Applications Vi, K. VanSant and R. A. Sherif, eds. (Spie-Int Soc Optical Engineering, 2011), Vol. 8108, p. 81080M.

S. A. Jones and K. W. Stone, “Analysis of solar two heliostat tracking error sources,” Tech. Rep. SAND99–0239C Albuq. Sandia Natl. Lab. (1999).

J. A. Duffie and W. A. Beckman, Solar engineering of thermal processes (Wiley, 1991).

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Figures (8)

Fig. 1
Fig. 1 Cylindrical surface for the error in the elevation of an heliostat.
Fig. 2
Fig. 2 Cylindrical surfaces for the error in elevation and azimuth of a heliostat.
Fig. 3
Fig. 3 Local coordinate system.
Fig. 4
Fig. 4 Deviation curves for different hours (solar hour) and locations (placed on the lower right side of each graph in meters) of the heliostat (simulations for June 21).
Fig. 5
Fig. 5 Evolution of the deviation for different hours of the day as a function of errors in azimuth and elevation. Each graph belongs to a heliostat location on a certain date.
Fig. 6
Fig. 6 Experimental setup.
Fig. 7
Fig. 7 Traces resulting from two different misalignment conditions in our experimental setup.
Fig. 8
Fig. 8 Results of the experimental setup at 1: 100 scale versus the simulation results.

Equations (18)

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S =( S x , S y , S z )=( cosδcosω,cosδsinω,sinδ ).
O=( x o , y o , z o )=( 0,0,0 )
T x ( α )=( 1 0 0 0 cos( α ) sin( α ) 0 sin( α ) cos( α ) ),
T y ( β )=( cos( β ) 0 sin( β ) 0 1 0 sin( β ) 0 cos( β ) ),
T z ( γ )=( cos( γ ) sin( γ ) 0 sin( γ ) cos( γ ) 0 0 0 1 ),
S local = T z ( φ ) S
C=( x C , y C , z C )
r =( r x , r y , r z )
P=( x P , y P , z P )=( x C , y C , z C )+( r x , r y , r z ).
n = r r =( n x , n y , n z )
R = I 2 I n n 2 n =( R x , R y , R z )
{ Y= y p R y x P R x Z= z p R z x P R x
R P =( R Px , R Py , R Pz )=OP=( x 0 , y 0 , z 0 )( x P , y P , z P )=( x 0 , y 0 , z 0 )( x C , y C , z C )( r x , r y , r z ).
S R P R P = 2 S n P n P 2 n P =λ n P .
λ( n Px , n Py , n Pz )= λ r ( r x , r y , r z )=( S x , S y , S z )+ ( x C , y C , z C )+( r x , r y , r z ) ( x C + r x ) 2 + ( y C + r y ) 2 + ( z C + r z ) 2 .
λ´( n Px , n Py , n Pz )( S x , S y , S z )+ ( x C , y C , z C ) ( x C ) 2 + ( y C ) 2 + ( z C ) 2
λ ´ i n Pi = λ ´ i r r Pi = S R i1 R i1 ,
R 0 =( x 0 , y 0 , z 0 )( x C , y C , z C ).

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