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MOWF_SchiTech_2015_Weiyang

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Wind farm development is an extremely complex process, most often driven by three im- portant performance criteria: (i) annual energy production, (ii) lifetime costs, and (iii) net impact on surroundings. Generally, planning a commercial scale wind farm takes several years. Undesirable concept-to-installation delays are primarily attributed to the lack of an upfront understanding of how different factors collectively affect the overall performance of a wind farm. More specifically, it is necessary to understand the balance between the socio-economic, engineering, and environmental objectives at an early stage in the design process. This paper proposes a Wind Farm Tradeoff Visualization (WiFToV) framework that aims to develop first-of-its-kind generalized guidelines for the conceptual design of wind farms, especially at early stages of wind farm development. Two major performance objectives are considered in this work: (i) cost of energy (COE) and (ii) land area per MW installed (LAMI). The COE is estimated using the Wind Turbine Design Cost and Scaling Model (WTDCS) and the Annual Energy Production (AEP) model incorporated by the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The LAMI is esti- mated using an optimal-layout based land usage model, which is treated as a post-process of the wind farm layout optimization. A Multi-Objective Mixed-Discrete Particle Swarm Optimization (MO-MDPSO) algorithm is used to perform the bi-objective optimization, which simultaneously optimizes the location and types of turbines. Together with a novel Pareto translation technique, the proposed WiFToV framework allows the exploration of the trade-off between COE and LAMI, and their variations with respect to multiple values of nameplate capacity.

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MOWF_SchiTech_2015_Weiyang

  1. 1. Simultaneously Optimizing COE and Land Footprint of Wind Farms under Different Land Plot Availability Weiyang Tong*, Souma Chowdhury#, and Achille Messac# * Syracuse University, Department of Mechanical and Aerospace Engineering # Mississippi State University, Department of Aerospace Engineering 11th Multi-Disciplinary Design Optimization Conference AIAA Science and Technology Forum and Exposition January 5 – 9, 2015 Kissimmee, Florida
  2. 2. Major Parties Involved 2  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 optimal design that balances the social, economic, and environmental objectives Project Investors Landowners Local Communities Power utilities Local public authorities Wind farm developer
  3. 3. Landowner Participation • In commercial wind farms, turbines generally appear in clusters due to considerations of land plot availability. • However, closer the turbines in an array, greater are the energy losses due to wake effects. • On the other hand, greater land usage increases the net impact on surroundings (e.g., impact on wildlife), and demands participation of more landowners. 3 Husum, Germanyhttp://www.sciencebuzz.org/ Thenetimpacton surroundings Cost of Energy
  4. 4. Research Motivation 4  Decision making of different factors is impractical and restrictive in conventional wind farm planning due to typically prescribed conditions:  Wind farm layouts are generally designed for prescribed land area or farm boundaries, and prescribed turbine configurations.  There exist very few instances (in the literature) of exploring how land plot availability impact wind farm layout planning (e.g., Chen and MacDonald, 2012, 2013).  Limited literature exists on exploring the trade-offs between COE/energy production and land footprint (e.g., Tong et al., 2012, 2013).  Exploration of such multiobjective wind farm layout optimization scenarios under different land plot availability also demands nonlinear MO optimizers that are fast, and can deal with constraints, multimodal functions, and mixed-discrete variables.
  5. 5. Research Objective 5  Investigate the capabilities of a new multi-objective mixed-discrete PSO to perform bi-objective optimization:  To simultaneously minimize the cost of energy (COE) and the land footprint per MW installed of the wind farm.  Investigate how different land plot availability scenarios impact the best trade-offs between COE and land footprint, and regulate the optimal wind farm layout designs. Cost of Energy ($/kWh) LandareaperMWinstalled(ha/MW) 0.035 0.04 0.045 0.05 10 20 30 40 50 60 70 80 90 100 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000
  6. 6. Outline 6 • Multi-Objective Wind Farm Layout Optimization • Wind Farm Cost and Energy Production Models • Conventional and Layout-based Land Usage Model • Multi-Objective Optimization Problem Definition • Multi-Objective Mixed-Discrete PSO (MO-MDPSO)  Highly nonlinear  High dimensional  Highly constrained  Non-convex Pareto frontier, and  Mixture of continuous and discrete design variables • Wind Farm Optimization under Land Plot Availability • Concluding Remarks
  7. 7. Outline 7 • Multi-Objective Wind Farm Layout Optimization • Wind Farm Cost and Energy Production Models • Conventional and Layout-based Land Usage Model • Multi-Objective Optimization Problem Definition • Multi-Objective Mixed-Discrete PSO (MO-MDPSO)  Highly nonlinear  High dimensional  Highly constrained  Non-convex Pareto frontier, and  Mixture of continuous and discrete design variables • Wind Farm Optimization under Land Plot Availability • Concluding Remarks
  8. 8. 𝐶𝑂𝐸 = 𝐼𝐶𝐶 × 𝐹𝐶𝑅 + 𝐿𝑅𝐶 𝐴𝐸𝑃 + 𝐿𝐿𝐶 + 𝑂&𝑀 where ICC – Initial Capital Cost LRC – Levelized Replacement Cost LLC – Land Lease Cost O&M – Operation & Maintenance Cost FCR – Fixed Charge Rate AEP – Annual Energy Production Wind Farm Cost of Energy 8 𝐸𝑓𝑎𝑟𝑚 = 365 × 24 𝑗=1 𝑁 𝑝 𝑃𝑓𝑎𝑟𝑚 𝑈𝑗, 𝜃𝑗 𝑓(𝑈𝑗, 𝜃𝑗)∆𝑈∆𝜃 1: Fingersh et al., 2006 NREL Tech. Report 2: Chowdhury et al., 2012 Renewable Energy Estimated using the Wind Turbine Design Cost and Scaling Model1  Rotor: Blades Hub Pitch mechanisms, etc;  Drive train nacelle Gearbox generator, etc;  Control, safety system, and monitoring  Tower  Balance of station Foundation Transportation Assembly and installation, etc Energy production model offered by UWFLO2:
  9. 9. 9 Energy Production Model in UWFLO  This model quantifies the power generation of an array of turbines as a function of the incoming wind conditions, turbine features, and the locations of turbines  It allows a variable induction factor: U: incoming wind speed; P: power generated, given by the power curve kg, kb: mechanical and electrical efficiencies, Dj: Rotor Diameter, 𝜌: Air density  The Katic’s model is used to account for wake merging and partial wake overlap 𝑢𝑗: Effective velocity deficit 𝐴 𝑘𝑗: Overlapping area bt.Turbine-j and Turbine-k
  10. 10. Conventional Wind Farm Layout Optimization 10 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
  11. 11. 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 11 • A given layout (siting of an array of turbines) is obtained. • 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 )
  12. 12. Optimal Layout-based Wind Farm Land Usage 12 • 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
  13. 13. Evaluate Performance Objectives Cost of Energy Land Footprint MO-MDPSO Multi-Objective Wind Farm Optimization Framework 13 1. Turbine Locations 2. Turbine Config. Trade-off bt. objectives Optimal designs: o Location of turbines o Selection of turbine types o Site orientation 𝑚𝑖𝑛 {𝐶𝑂𝐸 𝑉 , 𝐴 𝑀𝑊 𝑉 } 𝑉 = 𝑥1, 𝑥2, ⋯ , 𝑥 𝑁, 𝑦1, 𝑦2, ⋯ , 𝑦 𝑁, 𝑇 𝑇 = {1,2, ⋯ , 16} subject to 𝑔1 𝑉 𝑔2 𝑉 ≤ 2𝐷 Inter-Turbine Spacing Binary-decision landowner participation Highly nonlinear and multimodal Mixed-Integer Variables Nonlinear constraints
  14. 14. Outline 14 • Multi-Objective Wind Farm Layout Optimization • Wind Farm Cost and Energy Production Models • Conventional and Layout-based Land Usage Model • Multi-Objective Optimization Problem Definition • Multi-Objective Mixed-Discrete PSO (MO-MDPSO)  Highly nonlinear  High dimensional  Highly constrained  Non-convex Pareto frontier, and  Mixture of continuous and discrete design variables • Wind Farm Optimization under Land Plot Availability • Concluding Remarks
  15. 15. 1 2 3 4 5 1 2 3 4 5 f1 f2 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Infeasible R egion Actual Boundary Local Pareto set Multi-Objective Mixed-Discrete PSO Position update: 𝒙𝑖 𝑡 + 1 = 𝒙𝑖 𝑡 + 𝒗𝑖 𝑡 + 1 Velocity update: 𝒗𝑖 𝑡 + 1 = 𝑤𝒗𝑖 𝑡 + 𝑟1 𝐶1 𝑷𝑖 𝑙 (𝑡) − 𝒙𝑖 + 𝑟2 𝐶2 𝑷𝑖 𝑔 (𝑡) − 𝒙𝑖 + 𝑟3 𝛾 𝑐,𝑖 𝒗𝑖(𝑡) 15 𝑷𝑖 𝑙 – local leader of particle-i, which is selected from the local Pareto set 𝑷𝑖 𝑔 – global leader of particle-i that is determined by a stochastic process Crowding Distance – to manage the size of local/global Pareto set Multiple global leaders Inertia Local search Global search Applied w.r.t. each particle’s global leader Current particle Stored particle Highly constrained High dimensional Non-convex Pareto frontier Highly nonlinear Mixed types of variables
  16. 16. Hypercube enclosing 72 candidate solutions X1 X2 0 1 2 3 0 1 2 3 Particles Global leaders Multiple λ-Fractional Domains 16 • 7 global leaders are observed • Ideally, each fractional domain should enclose 10 particles • Particles located in the overlapping regions are uniformly re-allocated between domains • This method uniquely exploits diversity preservation to both prevent particle stagnation and accomplish a desirable distribution of Pareto solutions. 13 10 14 𝜆 = 0.25 Design Variable Space
  17. 17. Outline 17 • Multi-Objective Wind Farm Layout Optimization • Wind Farm Cost and Energy Production Models • Conventional and Layout-based Land Usage Model • Multi-Objective Optimization Problem Definition • Multi-Objective Mixed-Discrete PSO (MO-MDPSO)  Highly nonlinear  High dimensional  Highly constrained  Non-convex Pareto frontier, and  Mixture of continuous and discrete design variables • Wind Farm Optimization under Land Plot Availability • Concluding Remarks
  18. 18. Case Study Setup: Assumptions and Prescriptions Assumptions: • A wind distribution (based on 10yr measured data) is used • 16 square land plots are considered • Identical turbines are used with 16 candidate turbine types • Landowner participation is assumed to be Binary (deterministic) 18 User-defined parameters in MO-MDPSO Parameter Mixed-discrete constrained problems 𝑤 0.5 𝐶1 1.5 𝐶𝑐0 1.5 𝛾 𝑐0 2.0 𝛾 𝑚𝑖𝑛 1e-5 𝛾 𝑑0 1.0 𝜆 0.1 Local set size 10 Global set size Up to 100 Population size 1000 Particle Velocity parameters Diversity parameters Multi-objective Search parameters
  19. 19. Three Case Studies: Based on Land Plot Availability 19 Parameter Case Study I Case Study II Case Study III Number of turbines 50 50 50 Plots allowed to be used All 16 plots 8 specified plots No more than any 6 plots No. of design variables 101 101 101 Max. Function Evaluations 250,000 250,000 250,000 Case I Case II Case III
  20. 20. 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 88 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Case Study I: All 16 Land Plots 20 𝑔1 𝑉 = min max(𝑥 − 𝑋 𝑚𝑖𝑛, 0)+max(𝑋 𝑚𝑎𝑥 − 𝑥, 0), max 𝑦 − 𝑌 𝑚𝑖𝑛, 0 +max(𝑌 𝑚𝑎𝑥 − 𝑦, 0) Cost of Energy ($/kWh) LandareaperMWinstalled(ha/MW) 0.035 0.04 0.045 0.05 10 20 30 40 50 60 70 80 90 100 COE – LAMI Tradeoff Major turbine features Land plot availability constraint Optimal wind farm layout: Max. Land, Min. COE Min. Land, Max. COE
  21. 21. Cost of Energy ($/kWh) LandareaperMWinstalled(ha/MW) 0.035 0.04 0.045 0.05 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Case Study II: 8 Specified Land Plots 21 𝑔1 𝑉 = 𝑖=1 𝑁 𝑝 ∀𝑝∈𝑃 min max(𝑥 − 𝑋 𝑚𝑖𝑛 𝑝 , 𝑋 𝑚𝑎𝑥 𝑝 − 𝑥, 0) +max(𝑦 − 𝑌 𝑚𝑖𝑛 𝑝 , 𝑌 𝑚𝑎𝑥 𝑝 − 𝑦, 0) where 𝑃={3, 4, 6, 7, 9, 10, 11, 13} COE – LAMI Tradeoff Major turbine features Land plot availability constraint Optimal wind farm layout: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 Max. Land, Min. COE Min. Land, Max. COE
  22. 22. Cost of Energy ($/kWh) LandareaperMWinstalled(ha/MW) 0.035 0.04 0.045 0.05 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Case Study III: No More than 6 Land Plots 22 COE – LAMI Tradeoff Major turbine features Land plot availability constraint Optimal wind farm layout: 𝑔1 𝑉 = 𝑖=1 𝑁 1 16 𝑢(𝑥, 𝑦) ≤ 6, and 𝑢 𝑥, 𝑦 = 1, 𝑖𝑓 𝑋 𝑚𝑖𝑛 𝑝 ≤ 𝑥 ≤ 𝑋 𝑚𝑎𝑥 𝑝 𝑎𝑛𝑑 𝑌 𝑚𝑖𝑛 𝑝 ≤ 𝑦 ≤ 𝑌 𝑚𝑎𝑥 𝑝 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 Max. Land, Min. COE Min. Land, Max. COE
  23. 23. WFLO Cases with Non-Identical Turbines 23 1 9 8 16 4 7 1 12 3 6 6 6 8 12 2 1 8 16 16 16 7 8 7 8 2 8 9 16 8 8 10 1 8 1 9 16 2 4 13 6 8 3 8 13 5 10 16 16 2 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 1 9 12 5 14 7 3 10 11 4 8 15 6 13 9 2 13 5 1 9 3 11 15 7 8 16 12 4 10 2 6 14 7 15 11 4 9 2 5 13 14 6 3 10 5 12 16 8 11 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 Cost of Energy ($/kWh) LandareaperMWinstalled(ha/MW) 0.035 0.04 0.045 0.05 10 20 30 40 50 60 70 80 90 100 Case I Case II Case III 1 12 9 16 16 13 2 12 9 11 6 16 5 11 11 5 16 5 1 16 3 7 16 8 15 16 16 5 16 1 16 16 9 13 16 7 5 7 12 5 16 16 8 13 15 16 16 10 16 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 1 8 9 8 14 6 2 8 9 1 7 16 6 9 8 1 16 9 1 3 3 9 16 9 8 16 8 4 8 1 13 16 8 16 11 6 8 3 8 16 14 8 3 8 3 7 16 9 7 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 1 16 11 8 16 8 1 8 12 2 8 16 8 16 8 3 16 3 1 8 1 8 16 5 8 16 5 8 9 1 9 16 8 16 7 2 9 3 8 16 11 5 2 16 1 15 16 9 8 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 1 16 9 9 15 8 1 8 16 2 7 16 8 16 8 2 16 1 1 7 1 9 16 16 9 16 12 1 9 1 3 16 16 16 6 2 5 4 3 16 16 16 2 16 1 16 16 9 9 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X (m) Y(m) -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 Rated Power (W) 2.4E+06 2.2E+06 2E+06 1.8E+06 1.6E+06 1.4E+06 1.2E+06 1E+06 800000 • Each turbine can take any of the 16 configurations. • No. of variables = 150 • Max function calls = 250 × 1500 • As before Case I results are not fully converged. • Beyond a certain land footprint per MW, additional land area provides marginal benefit
  24. 24. Outline 24 • Multi-Objective Wind Farm Layout Optimization • Wind Farm Cost and Energy Production Models • Conventional and Layout-based Land Usage Model • Multi-Objective Optimization Problem Definition • Multi-Objective Mixed-Discrete PSO (MO-MDPSO)  Highly nonlinear  High dimensional  Highly constrained  Non-convex Pareto frontier, and  Mixture of continuous and discrete design variables • Wind Farm Optimization under Land Plot Availability • Concluding Remarks
  25. 25. Concluding Remarks  A Multi-Objective Wind Farm Layout Optimization framework was developed: 1. UWFLO Energy Production Model and Layout-based Land Usage Model 2. WTDCS/NREL Cost Model 3. A new Multi-Objective Mixed-Discrete PSO algorithm  This framework provides optimal turbine locations, turbine types, and the land plots to be used for turbine installation.  Three different land plot availability scenarios were explored, while minimizing COE and land-footprint per MW installed. Findings include: 1. Under frugal land usage, the most productive land plots are automatically selected. 2. Layout pattern for “max COE/min land” solutions remained similar across specified, limited, and unlimited land plot availabilities scenarios. 3. Most desirable results were obtained under limited land plot availability, where – for a 66% increase in land footprint (15 to 25 Ha/MW), a 15% reduction in COE is obtained. 25
  26. 26. Future Work • Further fine-tune the optimizer to accomplish greater convergence. • Consider a probabilistic model of landowner participation and a benefit model for landowners. • Develop a strategy to assign a utility value to each land plot, based on their potential productivity for given wind conditions. 26
  27. 27. Acknowledgement  I would like to thank the co-authors Prof. Achille Messac and Weiyang Tong.  Support from the NSF Awards (CMMI-1437746) is also acknowledged. 27
  28. 28. Questions and Comments 28 Thank you
  29. 29. Comparison of Performance Indicators 24 Performance of Accuracy Performance of Diversity ZDT 4 0 1 2 3 ZDT 3 0 0.01 0.02 0.03 0.04 0.05 ZDT 1 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 ZDT 2 0 0.0002 0.0004 0.0006 0.0008 0.001 ZDT 6 0 0.1 0.2 0.3 0.4MO- MDPSO NSGA2 MO- MDPSO NSGA2 MO- MDPSO NSGA2 MO- MDPSO NSGA2 MO- MDPSO NSGA2 ZDT 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ZDT 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ZDT 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ZDT 4 0 5 10 ZDT 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 MO- MDPSO NSGA2 MO- MDPSO NSGA2 MO- MDPSO NSGA2 MO- MDPSO NSGA2 MO- MDPSO NSGA2 The lower the better
  30. 30. 30 • The MINLP problem adopted from Dimkou and Papalexandri* No. of design variables 6 No. of discrete variables 3 (binary) Function evaluations 10,000 Population size 100 Elite size of NSGA-II 78 Elite size of MO-MDPSO 100 *: Dimkou and Papalexandri (1998) Mixed-Discrete Constrained Test Problem 1 f1 f2 -60 -50 -40 -30 -20 -10 0 -20 0 20 40 60 80 100 Pareto solution by NSGA-II Pareto solution by MO-MDPSO
  31. 31. 31 • The design of disc brake problem adopted from Osyczka and Kundu* No. of design variables 4 No. of discrete variables 1 (integer) Function evaluations 10,000 Population size 100 Elite size of NSGA-II 87 Elite size of MO-MDPSO 100 *: Osyczka and Kundu (1998) Mixed-Discrete Constrained Test Problem 2
  32. 32. Optimal layout-based land usage 32 -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
  33. 33. 33 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
  34. 34. Wind Farm Cost of Energy 34 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

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