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Effective and time-efficient decision-making in the early stages of wind farm planning can lay the foundation of a successful wind energy project. Undesirable concept-to-installation delays in wind farm development is often caused by conflicting decisions from the major parties involved (e.g., developer, investors, landowners, and local communities), which in turn can be (in a major part) attributed to the lack of an upfront understanding of the trade-offs between the technical, socio-economic, and environmental-impact aspects of the wind farm for the given site. This paper proposes a consolidated visualization platform for wind farm planning, which could facilitate informed and co-operative decision-making by the parties involved. This visualization platform offers a GUI-based land shape chart, which provides the following information: the variation of the energy production capacity and of the corresponding required optimal land shape with different land area and nameplate capacity decisions. In order to develop this chart, a bi-objective optimization problem is formulated (using the Unrestricted Wind Farm Layout Optimization framework) to max- imize the capacity factor and minimize the land usage, subject to different nameplate capacity decisions. The application of an Optimal Layout-based land usage estimate allows the wind farm layout optimization to run without pre-specifying any farm boundaries; the optimal land shape is instead determined as a post process, using convex hull and minimum bounding rectangle concept, based on the optimal arrangement of turbines. Three land shape charts are generated under three characteristic wind patterns - (i) single dominant wind direction, (ii) two opposite dominant wind directions, and (ii) two orthogonal domi- nant wind directions, all three patterns comprising the same wind speed distribution. The results indicate that the optimal land shape is highly sensitive to the variation in LAMI for small-capacity wind farms (few turbines) and to the variation in nameplate capacity for small allowed land area. For the same decided nameplate capacity and LAMI values, we observe reasonable similarity in the optimal land shapes and the maximum energy pro- duction potentials given the “single dominant direction” and the “two opposite dominant directions” wind patterns; the optimal land shapes and the maximum energy production potentials yielded by the “two orthogonal dominant directions” wind pattern is however observed to be relatively different from the other two cases.

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  1. 1. A Consolidated Visualization of Wind Farm Energy Production Potential and Optimal Land Shapes under Different Land Area and Nameplate Capacity Decisions Weiyang Tong*, Souma Chowdhury#, and Achille Messac# * Syracuse University, Department of Mechanical and Aerospace Engineering # Mississippi State University, Bagley College of Engineering 10th Multi-Disciplinary Design Optimization Conference AIAA Science and Technology Forum and Exposition January 13 – 17, 2014 National Harbor, Maryland
  2. 2. Early Stage Wind Farm Development 2 Wind measurement • Site selection • Wind resource assessment Site selection • Landowner negotiation • Road access Feasibility analysis • Permitting • Power transmission • Economics analysis Environmental assessment • Noise impact • Impact on local wildlife  A complex process involving multiple objectives (e.g., cost and local impact)  Demands time-efficient decision-making  Often Suffers from lacking of transparency and cooperation among the parties involved Wind farm development at early stage
  3. 3. Major Parties Involved 3  Undesirable concept-to-installation delays are caused by conflicting decisions from the major parties involved Wind farm developers need to address the concerns of the major parties involved Seek the balance between the social, economic, and environmental objectives Project Investors Landowners Local Communities Power utilities Local public authoritiesWind farm developer
  4. 4. Wind Farm Developers Landowners Project investors Local public authorities Local communities Power utilities Research Motivation 4  Nameplate capacity  Number of turbines  Land use  Land area  Land shape  Annual Energy Production  Capacity factor  Cost of Energy  Net Impact on Surroundings  Noise impact  Impact on wildlife  Turbine Survivability  Turbine type Many turbines Few turbines Small land per turbine Large land per turbine AEP AEP AEPAEP CoE CoE CoECoE NIS NIS NISNIS TS TS TSTS Preferred AEP Preferred NIS
  5. 5. Research Objective 5 Develop a Consolidated Visualization platform for wind farm planning Compare energy production potentials offered by different combinations of Nameplate Capacity and Land Area per MW Installed (LAMI) Show what exact optimal land shapes are demanded for these combinations
  6. 6. Outline 6 • Layout-based Land Usage • Multiple bi-objective optimizations • Consolidated Visualization Platform • Numerical Experiment • GUI-based land shape chart • Concluding Remarks
  7. 7. Conventional Wind Farm Layout Optimization 7 wind farm layout optimization flowchart Stop criterion Reach the best performance? Evaluate design objective functions Trade-off between design objectives Adjust the location of turbines Prescribed conditions Yes No Farm boundaries Land area Land orientation Number of turbines 𝐴𝑟𝑒𝑎𝑙𝑎𝑛𝑑 = 𝑓(𝑋 𝑚𝑖𝑛, 𝑌 𝑚𝑖𝑛, 𝑋 𝑚𝑎𝑥, 𝑌 𝑚𝑎𝑥) 𝑋 𝑁 ∈ [𝑋 𝑚𝑖𝑛, 𝑋 𝑚𝑎𝑥] 𝑌 𝑁 ∈ [𝑌 𝑚𝑖𝑛, 𝑌 𝑚𝑎𝑥] 𝑋 𝑚𝑖𝑛 𝑋 𝑚𝑎𝑥 𝑌 𝑚𝑖𝑛 𝑌 𝑚𝑎𝑥 Turbine location vector
  8. 8. Wind turbine 2D Convex hull SBR Buffer area Wind turbine 2D Convex hull SBR Buffer area Wind turbine 2D Convex hull SBR Buffer area Wind turbine 2D Convex hull SBR Buffer area Layout-based Wind Farm Land Usage 8 • The “2D Convex Hull” is applied to determine the land usage for a given set of turbines • The Smallest Bounding Rectangle (SBR) is fit based on the convex hull • A buffer zone is added to each side of the SBR to yield the final land usage 1D 𝐴𝑟𝑒𝑎𝑙𝑎𝑛𝑑 = 𝑓(𝑋 𝑁 , 𝑌 𝑁 ) 𝑆ℎ𝑎𝑝𝑒𝑙𝑎𝑛𝑑 = 𝑔(𝑋 𝑁 , 𝑌 𝑁 )
  9. 9. Optimal Layout-based Wind Farm Land Usage 9 • An Optimal Layout-based (OL-based) land use has the following features: • Farm boundaries are not assumed • Automatically determined by the layout optimization • Yield OL-based land area, 𝐴𝑟𝑒𝑎𝑙𝑎𝑛𝑑 ∗ • Yield OL-based land shape, 𝑆ℎ𝑎𝑝𝑒𝑙𝑎𝑛𝑑 ∗ Step 1: min 𝑋 𝑁,𝑌 𝑁 𝑓 𝑋 𝑁, 𝑌 𝑁 , 𝑔 𝑋 𝑁, 𝑌 𝑁 Step 2: 𝐴𝑟𝑒𝑎𝑙𝑎𝑛𝑑 ∗ = 𝑓 𝑋 𝑁 ∗ , 𝑌 𝑁 ∗ 𝑆ℎ𝑎𝑝𝑒𝑙𝑎𝑛𝑑 ∗ = 𝑔 𝑋 𝑁 ∗ , 𝑌 𝑁 ∗ Optimal layout
  10. 10. Multiple bi-objective optimizations 10 Land Area per MW Installed NameplateCapacity • The development of the consolidated visualization platform is based on a multiple performance of bi- objective layout optimizations • The number of turbines and the maximum allowed land area are specified for each case • The objectives are • Maximizing the wind farm capacity factor • Minimizing the unit land area Each bi-objective optimization problem is solved as multiple constrained single objective optimization problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area? shape? CF ? Area? shape? CF ? Area? shape? CF ? Area? shape? CF ? NC1NCm LAMI1 LAMIn
  11. 11. Multiple bi-objective optimizations 11 Stop criterion Evaluate design objective functions Trade-off between design objectives Adjust the location of turbines NCi AMWi Yes No max 𝐶𝐹(𝑉) = 𝐸𝑓𝑎𝑟𝑚 365 × 24 𝑁𝐶 𝑉 = {𝑋1, 𝑋2, ⋯ , 𝑋 𝑁, 𝑌1, 𝑌2, ⋯ , 𝑌𝑁} subject to 𝑔1 𝑉 ≤ 𝐴 𝑀𝑊𝑖 𝑔2 𝑉 ≤ 2𝐷 Estimated using the power generation model in UWFLO framework2 𝐸𝑓𝑎𝑟𝑚 = 365 × 24 𝑗=1 𝑁 𝑝 𝑃𝑓𝑎𝑟𝑚 𝑈𝑗, 𝜃𝑗 𝑓(𝑈𝑗, 𝜃𝑗)∆𝑈∆𝜃 Inter-Turbine Spacing layout-based land area constraint Solved by Mixed-Discrete Particle Swarm Optimization1 1: Chowdhury et al., 2013 Struct Multidisc Optim 2: Chowdhury et al., 2012 Renewable Energy
  12. 12. Numerical Experiment: Description • Two design criteria: • Maximizing the wind farm capacity factor • Different specified constraints of Land Area per MW Installed (LAMI) • Identical turbines are used (GE-1.5 xle, rated power 1.5 MW) • The ambient turbulence over the entire farm site is assumed constant 12 LAMI (ha/MW) Number of turbines 40 60 80 100 50 (75 MW) 75 (112.5 MW) 100 (150 MW)
  13. 13. Numerical Experiment: Wind Distribution 13  The Weibull distribution is used for wind speed  Three characteristic wind patterns are generated with equal wind power density (WPD) 𝑓 𝑥 = 𝑘 𝑐 ( 𝑥 𝑐 ) 𝑘−1 where k = 2.022 C=5.247 0 0.05 0.1 0.15 0.2 0 5 10 15 𝑊𝑃𝐷 = 𝑖=1 𝑁 𝑝 1 2 𝜌𝑈𝑖 3 𝑓(𝑈𝑖, 𝜃1)Δ𝑈 = 𝑖=1 𝑁 𝑝 1 2 𝜌𝑈𝑖 3 1 2 𝑓 𝑈𝑖, 𝜃1 + 1 2 𝑓 𝑈𝑖, 𝜃2 Δ𝑈 = 𝑖=1 𝑁 𝑝 1 2 𝜌𝑈𝑖 3 1 2 𝑓 𝑈𝑖, 𝜃1 + 1 2 𝑓 𝑈𝑖, 𝜃3 Δ𝑈 where Δ𝑈 = 𝑈 𝑚𝑎𝑥 𝑁𝑝 Case 1: single dominant direction 𝜃1 = 30° Case 2: two opposite dominant directions 𝜃1 = 30°, 𝜃2 = 210° Case 3: two orthogonal dominant directions 𝜃1 = 30°, 𝜃3 = 120° m/s
  14. 14. 14 Case 1: single dominant direction Case 2: two opposite dominant directions Case 3: two orthogonal dominant directions 𝜃1 = 30° 𝜃1 = 30° 𝜃3 = 120° 𝜃1 = 30°
  15. 15. Numerical Experiment: Parallel Computing 15 . . . Start Task n Core n Task 2 Core 2 . . .Task 1 Core 1 End  For each combination, the optimization is run 5 times to compensate the impact of random parameters  Totally 180 optimizations are performed using parallel computing on 4 work stations (4/8 cores)
  16. 16. Results and Discussion: GUI-based Land Shape Chart 16 Single dominant direction  Most of land shapes are aligned with the dominant direction  The wind farm at the top-left cell predicted the lowest CF  The wind farm at the bottom-right cell predicted the highest CF
  17. 17. Results and Discussion: GUI-based Land Shape Chart 17 2 4 1 3
  18. 18. Results and Discussion: GUI-based Land Shape Chart 18 Two opposite dominant directions  The same trend for the predicted CF is observed  More closely aligned with the dominant directions  Some land shapes in this case are stretched
  19. 19. Results and Discussion: GUI-based Land Shape Chart 19 Two orthogonal dominant directions  The same trend for the predicted CF is observed  Most land plots have a square-like land shape
  20. 20. Land Shape Charts Comparison 20 Two opposite dominant directions Two orthogonal dominant directionsSingle dominant direction
  21. 21. Totally 375 optimizations were paralelly performed Land Shape Charts Comparison 21 Two opposite dominant directions Two orthogonal dominant directionsSingle dominant direction
  22. 22. Concluding Remarks • A Consolidated Visualization platform was developed to show • Energy production potentials with different combinations of land area and nameplate capacity • Optimal land shapes demanded for these combinations • Three components: (i) Optimal Layout-based land usage (convex hull and SBR) (ii) Multiple constrained single objective optimizations (iii) GUI-based land shape chart • Dominant directions have a strong impact, and land shapes are orientated along the dominant directions • The optimal-based land shape is highly sensitive to the number of turbines in the case of small allowed LAMI (vice versa) and to the LAMI in the case of small installed capacity ( few turbines installed) 22
  23. 23. Future Work • Enable the illustration of other important objectives, such as local impact and Cost of Energy • Adding one layer of map regarding land plot ownership and landowner participation 23
  24. 24. Acknowledgement  I would like to acknowledge my research adviser Prof. Achille Messac, and my co-adviser Dr. Souma Chowdhury for their immense help and support in this research.  I would also like to thank my friend and colleague Ali Mehmani for his valuable contributions to this paper.  Support from the NSF Awards is also acknowledged. 24
  25. 25. Questions and Comments 25 Thank you
  26. 26. Lower-level: CF-LAMI Trade-off Exploration 26 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 optimal layout with land area of 180 ha optimal layout with land area of 900 ha optimal layout with land area of 3000 ha Optimal layouts of 20 turbines with different land area constraints
  27. 27. Numerical Experiment: Wind Data 27
  28. 28. CF Response Surface Obtained  Even if turbines are allowed the same land area per MW installed, a greater number of turbines (higher nameplate capacity) would lead to greater wake losses, leading to lower energy production.  A contour plot of the function can provide the “LAMI vs. nameplate capacity” cutoff curve that corresponds to the threshold CF. LandAreaperMWinstalled(m2/MW) Nameplate Capacity (MW) 28
  29. 29. Mid-level: Quantification of Trade-offs between Design Objectives 29 • The wind distribution is unique • A group of Pareto curves can be obtained from the multi-objective wind farm layout optimization at the bottom-level • Based on observation, use an appropriate form of function to fit all the Pareto curves, for example, a form of power function with 3 coefficients • Once the global design factors are specified, a trade-off curve between two objectives can be generated 𝑜𝑏𝑗2 𝑛 = 𝑎(𝑝1, 𝑝2, ⋯ , 𝑝 𝐾)𝑜𝑏𝑗1 𝑛 𝑏(𝑝1,𝑝2,⋯,𝑝 𝑁) + 𝑐(𝑝1, 𝑝2, ⋯ , 𝑝 𝐾) where 𝑛 = 1,2, ⋯ , 𝑁 representing 𝑁 sets of samples of global design factors; and 𝐾 is the total number of global design factors accounted for
  30. 30. 30 Single Wake Test: Comparing Wake Growth  Frandsen model and Larsen model predict greater wake diameters  Jensen model has a linear expansion  The difference between wake diameters predicted by each model can be as large as 3D, and it can be larger as the downstream distance increases 3D
  31. 31. 31 Single Wake Test: Comparing Wake Speed  Frandsen model predicts the highest wake speed  Ishihara model predicts a relatively low wake speed; however, as the downstream distance increases, the wake recovers fast owing to the consideration of turbine induced turbulence in this model
  32. 32. wind direction Numerical Experiments 32  An array-like wind farm with 9 GE 2.5 MW – 100m turbines is considered.  A fixed aspect ratio is selected; the streamwise spacing is ranged from 5D to 20D, while the lateral spacing is no less than 2D.  The farm capacity factor is given by Prj: Rated capacity, Pfarm: Farm output
  33. 33. 33 Layout-based Power Generation Model  In this power generation model, the induction factor is treated as a function of the incoming wind speed and turbine features: U: incoming wind speed; P: power generated, given by the power curve kg, kb: mechanical and electrical efficiencies, Dj: Rotor Diameter, 𝜌: Air density  A generalized power curve is used to represent the approximate power response of a particular turbine 𝑈𝑖𝑛, 𝑈 𝑜𝑢𝑡, and 𝑈𝑟: cut-in speed, cut-out speed, and rated speed 𝑃𝑟: Rated capacity, 𝑃𝑛: Polynomial fit for the generalized power curve* *: Chowdhury et al , 2011
  34. 34. 34 Layout-based Power Generation Model  Turbine-j is in the influence of the wake of Turbine-i, if and only if Considers turbines with differing rotor-diameters and hub-heights  The Katic model* is used to account for wake merging and partial wake overlap 𝑢𝑗: Effective velocity deficit 𝐴 𝑘𝑗: Overlapping area between Turbine-j and Turbine-k Partial wake-rotor overlap *: Katic et al , 1987
  35. 35. Mixed-Discrete Particle Swarm Optimization (PSO)  This algorithm has the ability to deal with both discrete and continuous design variables, and  The mixed-discrete PSO presents an explicit diversity preservation capability to prevent premature stagnation of particles.  PSO can appropriately address the non-linearity and the multi- modality of the wind farm model. 35