HEURISTIC OPTIMIZATION TO DESIGN SOLAR POWER TOWER SYSTEMS

Transcription

1 HEURISTIC OPTIMIZATION TO DESIGN SOLAR POWER TOWER SYSTEMS Carmen-Ana Domínguez Bravo July 216

2 1. Introduction 2. Optimization problem 3. Analytical and computational model 4. Design of Heliostats Field 5. Design with multiple receivers

3 THE DESIGN OF A SOLAR POWER TOWER (SPT) z QE E O y H N x Thesis supervisors: Emilio Carrizosa (EIO-US), Enrique Fernández Cara (EDAN-US) Thesis tutor: Manuel Quero (Abengoa Solar) Research contract: CapTorSol (Abengoa Solar and FIUS)

4 Solar Power Plants Solar Thermal Photovoltaic Non-Concentrating Concentrating Linear Point Solar Chimney Linear Fresnel Parabolic Through Parabolic Dish Heliostat PV cell

5 Solar Power Plants Solar Thermal Photovoltaic Non-Concentrating Concentrating Linear Point Solar Chimney Linear Fresnel Parabolic Through Parabolic Dish Heliostat PV cell

6 SOLAR POWER TOWER PLANTS Heliostat: reflective mirror. Receiver: sunlight collector. 1. Sunlight is reflected by the heliostats field onto a receiver at the top of the tower. 2. Thermal energy is transferred through a thermodynamic cycle to produce electricity. vsun Source Abengoa

7 HELIOSTAT Helio: Greek word for sun. Stat: stationary (reflected image is fixed). Pedestal mounted mirror. Two-axis tracking system to follow the sun. Source Abengoa and CIEMAT-PSA

8 HELIOSTAT Helio: Greek word for sun. Stat: stationary (reflected image is fixed). Pedestal mounted mirror. Two-axis tracking system to follow the sun. Source Abengoa and CIEMAT-PSA

9 Tower-Receiver(s) Heliostats Field Θ := (h, ξ, α, r) S := {(x i, y i ) R 2 : i [1, N]} 8 Heliostat Field Layout N hel =

10 MATHEMATICAL MODELLING OPTIMIZATION PROBLEM (P) min Θ,S subject to F(Θ, S) = C(Θ, S)/E(Θ, S) Θ Θ S S Π Π Td (Θ, S) Π + Optimization criteria 2 objectives: total construction cost and collected annual energy. Deal with the aggregation function,

11 MATHEMATICAL MODELLING Tower ( height ), receiver aperture ( position and dimensions ), and heliostats field ( positions and number ). Main difficulties unknown number of variables, high number of heliostats in commercial plants (up to 2.), expensive objective function evaluation, nonclosed-form of the objective function, non-convex constraints. Assumptions circular aperture, the aim point is the aperture center and it is static, the receiver heat flux is homogeneous, shadowing & blocking effects consider parallel heliostats, costs associated with hel. are independent on the position.

12 ANALYTICAL AND COMPUTATIONAL MODEL COST FUNCTION C(h, r, S ) = β 1 (h + λ 1 ) λ 2 + β 2 πr 2 + cf + c S }{{}}{{} h: tower height. r: aperture radius. S : number of heliostats. Tower-receiver and heliostats field costs. Easy to compute and low number of variables.

13 1 L. Crespo and F. Ramos. NSPOC: A New Powerful Tool for Heliostat Field Layout and Receiver Geometry Optimizations. In: Proceedings of SolarPaces T. Wendelin. SolTRACE: A New Optical Modeling Tool for Concentrating Solar Optics. In: ASME Conference Proceedings. Vol ASME, 23. DOI: /ISEC F. J. Collado and J. Guallar. A review of optimized design layouts for solar power tower plants with campo code. In: Renewable and Sustainable Energy Reviews 2 (213), pp ANALYTICAL AND COMPUTATIONAL MODEL Analytical models ANNUAL THERMAL ENERGY FUNCTION Analytical formula and numeric algorithms to evaluate the plant performance. Accurate enough for the optimization process, e.g. Fortran code NSPOC 1. Source Article 3.

14 1 L. Crespo and F. Ramos. NSPOC: A New Powerful Tool for Heliostat Field Layout and Receiver Geometry Optimizations. In: Proceedings of SolarPaces T. Wendelin. SolTRACE: A New Optical Modeling Tool for Concentrating Solar Optics. In: ASME Conference Proceedings. Vol ASME, 23. DOI: /ISEC F. J. Collado and J. Guallar. A review of optimized design layouts for solar power tower plants with campo code. In: Renewable and Sustainable Energy Reviews 2 (213), pp ANALYTICAL AND COMPUTATIONAL MODEL Analytical models ANNUAL THERMAL ENERGY FUNCTION Analytical formula and numeric algorithms to evaluate the plant performance. Accurate enough for the optimization process, e.g. Fortran code NSPOC 1. Ray-tracing models Tracing light trajectories and simulate the effects of its interactions with digitized objects. Traditionally used to evaluate the plant performance, e.g. SolTRACE 2. Source Article 3.

15 ANNUAL THERMAL ENERGY FUNCTION E(Θ, S) = T Π t(θ, S) dt γ 1 I(t) ϕ(t, x, y, Θ, S)A(x, y) γ 2 πr 2 (x,y) S

16 ANNUAL THERMAL ENERGY FUNCTION E(Θ, S) = T Π t(θ, S) dt γ 1 I(t) ϕ(t, x, y, Θ, S)A(x, y) γ 2 πr 2 (x,y) S I solar radiation, A heliostat area, 5 ϕ solar efficiency functions: ν i with ν i [, 1]. i=1

17 ANNUAL THERMAL ENERGY FUNCTION SOLAR EFFICIENCY FUNCTIONS 1. Reflectivity constant 2. Cosine w(x,y) vsun(t) 2 w(x,y) 3. Interception f 1 (t, x, y) ( ) S exp f 2 (u,v,x,y) 2 f 3 2 du dv (t,x,y,θ) 4. Atmospheric α 1 α 2 w(x, y) + α 3 w(x, y) 2 5. Shading & blocking Sassi s algorithm 1 v Source Article 2. 1 G. Sassi. Some notes on shadow and blockage effects. In: Solar Energy 31.3 (1983), pp F. J. Collado and J. Guallar. A review of optimized design layouts for solar power tower plants with campo code. In: Renewable and Sustainable Energy Reviews 2 (213), pp

18 Field Distribution: IH 2 ID 3 Ef 2 [.88833,.99) [.78667,.88833) [.685,.78667) [.58333,.685) [.48167,.58333) [.38,.48167) Field Distribution: IH 2 ID 3 Ef 3 [.91833,1) [.83667,.91833) [.755,.83667) [.67333,.755) [.59167,.67333) [.51,.59167) Field Distribution: IH 2 ID 3 Ef 4 [.95333,.97) [.93667,.95333) [.92,.93667) [.9333,.92) [.88667,.9333) [.87,.88667) Field Distribution: IH 2 ID 3 Ef 6 [.915,1) [.83,.915) [.745,.83) [.66,.745) [.575,.66) [.49,.575) SOLAR EFFICIENCY FUNCTIONS VARIATIONS Cosine Atmospheric Interception Shading and blocking

19 OPTIMIZATION PROBLEM TOWER-RECEIVER AND HELIOSTATS FIELD (P) min Θ,S subject to F(Θ, S) = C(Θ, S)/E(Θ, S) Θ Θ S S Π Π Td (Θ, S) Separate (P) into 2 sub-problems: 1. (P S ): fixed heliostats field, optimize tower and receiver. 2. (P Θ ): fixed tower-receiver, optimize heliostat field.

20 DESIGN COMPLETE SPT SYSTEM Start Initial Tower-Receiver Design Optimal Design Calculate Initial Hel. Field (P) * Tower-Receiver Alternating algorithm Optimize Tower-Receiver Optimize Heliostat Field Yes * Heliostat Field Objective value improved? No Best Configuration Stop

21 DESIGN OF TOWER-RECEIVER Receiver variables and feasible set: Θ = (h, r, ξ, α), { Θ = Θ R 4 : r min r min(h, r max) h max }. RECEIVER ξ z z APERTURE Qe r h x-north y-west dap

22 DESIGN TOWER-RECEIVER (P S) S fixed max Θ subject to F(Θ, S) = C(Θ, S)/E(Θ, S) Θ Θ Π Π Td (Θ, S) Number of variables fixed and low. Non-convex objective function. Seems easy to solve (empirically unimodal).

23 DESIGN TOWER-RECEIVER (P S) S fixed max Θ subject to F(Θ, S) = C(Θ, S)/E(Θ, S) Θ Θ Π Π Td (Θ, S) Resolution Cyclic coordinate method and local searches for each variable. F(, S) h [h min,h max ] r [r min,r max ]

24 DESIGN OF HELIOSTATS FIELD Heliostat Field Layout N hel = 624 Heliostats positions { } S = (x i, y i ) R 2 : i [1, N] Feasible set S r min xi 2 + yi 2 r max (x i, y i ) (x j, y j ) δ

25 DESIGN OF HELIOSTATS FIELD Heliostat Field Layout N hel = 624 Heliostats positions { } S = (x i, y i ) R 2 : i [1, N] Feasible set S r min xi 2 + yi 2 r max (x i, y i ) (x j, y j ) δ

26 DESIGN OF HELIOSTATS FIELD (P Θ ) Θ fixed min F(Θ, S) = C(Θ, S)/E(Θ, S) S subject to S S Π Π Td (Θ, S) Non-fixed number of variables (expected to be high). Non-convex objective function. Non-convex constraints. Many local optima. packing problem with interactions between circles

27 DESIGN OF HELIOSTATS FIELD STATE-OF-THE-ART METHODS: PATTERN-BASED Select a geometric pattern (radial-stagger, spiral, grid, etc.) Pattern described by a low number of parameters. Optimize the parameters with standard procedures (Powell, Genetic, etc.) 8 Heliostat Field Layout N hel = Fig: Source Abengoa

28 DESIGN OF HELIOSTATS FIELD PATTERN-FREE Solve future challenges ( flexible algorithm ) Fig: Multiple Receivers. Source Abengoa (Patent US 212/125) Fig: Multi Tower Solar Array. Source Schramek, 213.

29 DESIGN OF HELIOSTATS FIELD PATTERN-FREE Solve future challenges ( flexible algorithm ) greedy-based heuristic Greedy algorithm pattern free to be flexible multi-start to avoid local optima

30 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern.

31 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. Step k: optimization pb in 2 variables. Locate heliostat number k k 1 heliostats in the field S k 1 Constraints involving S k 1 (P ) max Ẽ(x, y, S k 1 ) k (x,y) F S subject to Π Π Td (Θ, S) (x, y) (x i, y i ) δ for i = 1,... k 1

32 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. Step k: optimization pb in 2 variables. Locate heliostat number k. k 1 heliostats in the field. Constraints involving S k 1. Multi-start strategy to avoid local optima. N ini initial solutions. Final solution with highest energy value. Avoid local optima due to shadowing & blocking. Annual Energy Values per unit area

33 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. Step k: optimization pb in 2 variables. Locate heliostat number k. k 1 heliostats in the field. Constraints involving S k 1. Multi-start strategy to avoid local optima. N ini initial solutions. Final solution with highest energy value. Avoid local optima due to shadowing & blocking. Annual Energy Values per unit area with S and B

34 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. Step k: optimization pb in 2 variables. Locate heliostat number k. k 1 heliostats in the field. Constraints involving S k 1. Multi-start strategy to avoid local optima. N ini initial solutions. Final solution with highest energy value. Avoid local optima due to shadowing & blocking effects. Heliostat Field Layout N hel = 624 Heliostat Field Layout N hel =

35 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. Step k: optimization pb in 2 variables. Locate heliostat number k. k 1 heliostats in the field. Constraints involving S k 1. Multi-start strategy to avoid local optima. N ini different random solutions. Perform local search. Final solution, the one with highest energy value. Determine the final number of heliostats. Π Π Td (x, y, S k 1 ) feasible solution. Continue locating heliostats. Stop when the objective function C/E does not improve. Final N.

36 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. 8 Heliostat Field Layout

37 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. 8 Heliostat Field Layout

38 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. 8 Heliostat Field Layout

39 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. 8 Heliostat Field Layout

40 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. 8 Heliostat Field Layout

41 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. 8 Heliostat Field Layout

42 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. 8 Heliostat Field Layout

43 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. 8 Heliostat Field Layout

44 GREEDY ALGORITHM Heliostats located one by one, without fixed pattern. 8 Heliostat Field Layout

45 1 L. L. Vant-Hull. Layout of optimized Heliostat Field. Tech. rep. University of Houston, C. J. Noone, M. Torrilhon, and A. Mitsos. Heliostat field optimization: A new computationally efficient model and biomimetic layout. In: Solar Energy 86 (212), pp E. Carrizosa et al. A heuristic method for simultaneous tower and pattern-free field optimization on solar power systems. In: Computers & Operations Research 57 (215), pp DESIGN OF HELIOSTATS FIELD COMPARATIVE RESULTS Radial-staggered 1 Heliostat Field Layout N hel = Spiral 2 Heliostat Field Layout N hel = Greedy 3 Heliostat Field Layout N hel =

46 DESIGN OF HELIOSTATS FIELD COMPARATIVE RESULTS Field N Π Td E F PS Spiral GPS1 Requirement Phase GPS1 Completion Phase Thermal power at T d, Π Td (MWth 1 2 ). Annual thermal energy, E (GWHth 1 3 ). Cost function, C (Me), Cost per unit of annual thermal energy, F = C/E.

47 DIFFERENT FEASIBLE REGIONS RECTANGULAR, PERFORATED AND VALLEY REGIONS Feasible Region 1 Feasible Region 2 Feasible Region 3

48 Heliostat Field Layout N hel = 611 Heliostat Field Layout N hel = 67 Heliostat Field Layout N hel = (d) PS1 (e) Requirement (f) Completion Heliostat Field Layout N hel = 611 Heliostat Field Layout N hel = 612 Heliostat Field Layout N hel = (g) RPS1 (h) Requirement (i) Completion

49 DIFFERENT FEASIBLE REGIONS RECTANGULAR, PERFORATED AND VALLEY REGIONS PS1 Reg S S Π Td Π + E F F sep R P V Orig Req Compl. (Π + ) Compl Orig Req Compl.(Π + ) Compl Orig Req Compl. (Π + ) Compl Thermal power at T d, Π Td (MWth 1 2 ). Annual thermal energy, E (GWHth 1 3 ). Cost function, C (Me), Cost per unit of annual thermal energy, F = C/E.

50 MORE PROBLEMS Heliostat pods 1 Multi-size-heliostats 2 Multiple receivers 3 Genetic based Heliostat Field Layout 8 7 Heliostat Field Layout N1 hel = 491 N2 hel = Heliostat Field Layout N hel = 1872 (South) y coordinate (North) (West) x coordinate (East) C. Domínguez-Bravo et al. Field-design optimization with triangular heliostat pods. In: Proceedings of SolarPaces E. Carrizosa et al. An Optimization Approach to the Design of Multi-Size-Heliostat fields. Tech. rep. IMUS, E. Carrizosa et al. Optimization of multiple receivers Solar Power Tower systems. In: Energy 9 (215), pp

51 MULTIPLE RECEIVERS One receiver (northern or southern field) Circular receiver (surrounding field) Multiple receivers (separate fields) Source Abengoa (SP2) Source TorresolEnergy (Gemasolar) Source Abengoa (Patent US 212/125)

52 MULTIPLE RECEIVERS OPTIMIZATION PROBLEM (P) min Θ,S subject to F(Θ, S) Θ Θ S S Π i Π Td (Θ i, S) Π + i i = 1, 2, 3 F = C/E. i = 1, 2, 3, receivers. Θ = (Θ 1, Θ 2, Θ 3 ) with Θ i = (r i, h i, ξ i, α i ) t R 4 i.

53 MULTIPLE RECEIVERS TOWER-RECEIVER(S): VARIABLES AND CONSTRAINTS RECEIVER ξ z z APERTURE Qe r x- North +α -α h α 2 α 1 α 3 y-west x-north y-west dap (j) height h, tilt ξ and radius r (front-lateral) (k) orientation α (top) x- North ς 1 ς 2 y-west ς 3 (l) constraints (top)

54 MULTIPLE RECEIVERS HELIOSTATS FIELD PROBLEM (P Θ ) Θ fixed min F(Θ, S) S subject to S S Π i Π Td (Θ i, S) Π + i i = 1, 2, 3 Assumptions: 1. Separate fields: each receiver have a separate field region. S = S 1 S 2 S 3 and S 1 S 2 S 3 = S i = {(x, y) S : heliostat at (x, y) aims at receiver i} 2. Static aiming strategy: heliostats always aim to the same receiver.

55 4 Y. Luo, X. Du, and D. Wen. Novel design of central dual-receiver for solar power tower. In: Applied Thermal Engineering 91 (215), pp R. Ben-Zvi, M. Epstein, and A. Segal. Simulation of an integrated steam generator for solar tower. In: Solar Energy 86 (212), pp M. Schmitz et al. Assesment of the potencial improvement due to multiple apertures in central receiver systems with secondary concentrators. In: Solar Energy 8 (26), pp MULTIPLE RECEIVERS STATE-OF-THE-ART Dual receiver 4 Two integrated receivers (external and cavity) 5 Multiple apertures 6

56 MULTIPLE RECEIVERS Algorithm steps 1. Calculate aiming regions: S 1, S 2 and S Locate the heliostats: 2.1 Complete North region. 2.2 Update boundaries. 2.3 Complete West & East simultaneously.

57 MULTIPLE RECEIVERS Calculate aiming regions: 1. Discretization of the feasible region. 2. At each point, calculate energy values for each receiver. 3. Select boundary points and obtain polynomial boundaries. 4. Different possibilities applying weights. Best Annual Energy Values

58 MULTIPLE RECEIVERS Calculate aiming regions: 1. Discretization of the feasible region. 2. At each point, calculate energy values for each receiver. 3. Select boundary points and obtain polynomial boundaries. 4. Different possibilities applying weights. Best Annual Energy Values 1 Regions of a Multi receiver Field

59 MULTIPLE RECEIVERS Calculate aiming regions: 1. Discretization of the feasible region. 2. At each point, calculate energy values for each receiver. 3. Select boundary points and obtain polynomial boundaries. 4. Different possibilities applying weights. 1 Regions of a Multi receiver Field

60 MULTIPLE RECEIVERS Calculate aiming regions: 1. Discretization of the feasible region. 2. At each point, calculate energy values for each receiver. 3. Select boundary points and obtain polynomial boundaries. 4. Different possibilities applying weights. 1 Regions of a Multi receiver Field 1 Field Regions with Three Receivers p(x) W q(x) E Data W Data E

61 MULTIPLE RECEIVERS Calculate aiming regions: 1. Discretization of the feasible region. 2. At each point, calculate energy values for each receiver. 3. Select boundary points and obtain polynomial boundaries. 4. Different possibilities applying weights. 1 Field Regions with Three Receivers 5 5 p(x) W q(x) E Data W Data E

62 MULTIPLE RECEIVERS Calculate aiming regions: 1. Discretization of the feasible region. 2. At each point, calculate energy values for each receiver. 3. Select boundary points and obtain polynomial boundaries. 4. Different possibilities applying weights. 1 Field Regions with Three Receivers 1 Field Regions with Three Receivers 5 5 p(x) W q(x) E Data W Data E W 1.1 E 1.5 W 1.5 E 1 W 1 E.995 W.995 E.99 W.99 E Data W Data E

63 MULTIPLE RECEIVERS Heliostats location: North, West & East. 1. Pattern-free location with greedy algorithm. 2. Until Π i is reached. 3. Complete the field while objective function improves. 9 Heliostat Field Layout N hel =

64 MULTIPLE RECEIVERS Heliostats location: North, West & East. 1. Pattern-free location with greedy algorithm. 2. Until Π i is reached. 3. Complete the field while objective function improves. 9 Heliostat Field Layout N hel =

65 MULTIPLE RECEIVERS Heliostats location: North, West & East. 1. Pattern-free location with greedy algorithm. 2. Until Π i is reached. 3. Complete the field while objective function improves. 9 Heliostat Field Layout N hel =

66 MULTIPLE RECEIVERS ALTERNATING ALGORITHM Step Pb S Π Td E C F k = 1 : (Θ, S ) : (Θ 1, S ) k = 1 3 : (Θ 1, S 1 ) : (Θ 2, S 1 ) k = 2 5 : (Θ 2, S 2 ) Thermal power at T d, Π Td (MWth). Annual thermal energy, E (GWHth). Cost function, C (Me). Cost per unit of annual thermal energy, F = C/E.

67 MULTIPLE RECEIVERS ALTERNATING ALGORITHM: RECEIVERS Step h ξ α r Θ Θ Θ Θ Θ Θ 1 Θ Θ Θ 2 Θ Θ Θ Tower height, h (m). Receiver aperture tilt ξ (grad), orientation α (grad) and radius r (m).

68 MULTIPLE RECEIVERS ALTERNATING ALGORITHM: FIELDS 1 Heliostat Field Layout N hel = Heliostat Field Layout N hel = 233 Heliostat Field Layout N hel =

69 Eskerrik Asko

70 REFERENCES I [1] Pat. US A [2] L. Alon et al. Computer-Based Management of Mirror-Washing in Utility-Scale Solar Thermal Plants. In: Proceedings of ASME 214 (8th International Conference on Energy Sustainability and 12th International Conference on Fuel Cell Science, Engineering and Technology). Vol. 1. ES [3] L. Amsbeck et al. Optical Performance and Weight Estimation of a Heliostat With Ganged Facets. In: Journal of Solar Energy Engineering (28), (3 Pages). [4] R. Ben-Zvi, M. Epstein, and A. Segal. Simulation of an integrated steam generator for solar tower. In: Solar Energy 86 (212), pp [5] S. M. Besarati, D. Y. Goswami, and E. K. Stefanakos. Optimal heliostat aiming strategy for uniform distribution of heat flux on the receiver of a solar power tower plant. In: Energy Conversion and Management 84 (214), pp [6] J. B. Blackmon. Parametric determination of heliostat minimum cost per unit area. In: Solar Energy 97 (213), pp [7] P. Cádiz et al. Shadowing and blocking effect optimization for a variable geometry heliostat field. In: Energy Procedia 69 (215), pp [8] E. Carrizosa et al. A heuristic method for simultaneous tower and pattern-free field optimization on solar power systems. In: Computers & Operations Research 57 (215), pp [9] E. Carrizosa et al. An Optimization Approach to the Design of Multi-Size-Heliostat fields. Tech. rep. IMUS, 214. [1] E. Carrizosa et al. Optimization of multiple receivers Solar Power Tower systems. In: Energy 9 (215), pp [11] F. J. Collado and J. Guallar. A review of optimized design layouts for solar power tower plants with campo code. In: Renewable and Sustainable Energy Reviews 2 (213), pp [12] L. Crespo and F. Ramos. NSPOC: A New Powerful Tool for Heliostat Field Layout and Receiver Geometry Optimizations. In: Proceedings of SolarPaces [13] C. Domínguez-Bravo et al. Field-design optimization with triangular heliostat pods. In: Proceedings of SolarPaces [14] M. Izygon et al. TieSOL A GPU-based suite of fsoftware for central receiver solar power plants. In: Proceedings of SolarPaces [15] J. Larmuth, K. J. Malan, and P. Gauché. Design and Cost Review of 2 m2 Heliostat Prototypes. Tech. rep. STERG, Stellenbosch University, 214. [16] Y. Luo, X. Du, and D. Wen. Novel design of central dual-receiver for solar power tower. In: Applied Thermal Engineering 91 (215), pp

71 REFERENCES II [17] T. R. Mancini. Catalog of Solar Heliostats. Tech. rep. III 1/. SolarPaces, 2. URL: [18] C. J. Noone, M. Torrilhon, and A. Mitsos. Heliostat field optimization: A new computationally efficient model and biomimetic layout. In: Solar Energy 86 (212), pp [19] C. J. Noone et al. Site selection for hillside central receiver solar thermal plants. In: Solar Energy 85 (211), pp [2] A. Ramos and F. Ramos. Heliostat blocking and shadowing efficiency in the video-game era. arxiv: v URL: [21] P. Ricklin et al. Commercial readiness of esolar next generation heliostat. In: Energy Procedia 49 (214). SolarPaces 213, pp [22] G. Sassi. Some notes on shadow and blockage effects. In: Solar Energy 31.3 (1983), pp [23] M. Schmitz et al. Assesment of the potencial improvement due to multiple apertures in central receiver systems with secondary concentrators. In: Solar Energy 8 (26), pp [24] P. Schramek and D. R. Mills. Multi-tower solar array. In: Solar Energy 75.3 (23), pp [25] J. Spelling et al. Thermoeconomic optimization of a combined-cycle solar tower power plant. In: Energy 41 (212), pp [26] L. L. Vant-Hull. Layout of optimized Heliostat Field. Tech. rep. University of Houston, [27] T. Wendelin. SolTRACE: A New Optical Modeling Tool for Concentrating Solar Optics. In: ASME Conference Proceedings. Vol ASME, 23. DOI: /ISEC