This is a paper presentation from the 2010 AIAA MAO conference, on Layout Optimization of a Wind Farm.

1. Exploring Key Factors Influencing Optimal Farm Design Using Mixed-Discrete Particle Swarm Optimization Souma Chowdhury*, Jie Zhang*, Achille Messac#, and Luciano Castillo* * Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering #Syracuse University, Department of Mechanical and Aerospace Engineering 13th AIAA/ISSMO Multidisciplinary Analysis Optimization (MAO) Conference September 13-15, 2010 Fort Worth, Texas

3. Objectives of this paper

4. Unrestricted Wind Farm Layout Optimization (UWFLO) framework

5. Mixed-Discrete Particle Swarm Optimization

6. Optimal use of a combination of available non-identical turbines

7. Exploring the influence of number of turbine and farm size

8. Concluding Remarks2

10. Number and types of turbines to be installed

11. Farm sizewww.prairieroots.org

12. Mixed-Discrete Non-Linear Optimization (MDNLO) 4 Wind farm layout optimization involving optimal selection of turbines: MDNLO with non-uniformly distributed discrete variables

18. Considers a variable induction factor and partial wake-rotor overlap

20. Simultaneously optimizes the selection of differing types of turbines

21. Maximizes the net power generation using the PSO algorithm8

22. 9

23. UWFLO Power Generation Model The flow pattern inside a wind farm is complex, primarily due to the wake effects and the highly turbulent flow. Rotor averaged velocity is determined from the flow profile* Step 1 Transformed co-ordinates are evaluated based on wind direction 10 * Cal et al., 2010

24. Mutual Influence of Turbines Step 2 An influence matrix is defined as where Turbine-i influences Turbine-j if Step 3 The turbines are ranked in the increasing order of their x-coordinate. Power generated by turbines is calculated in the increasing order of their rank. 11

25. Step 4 Effective velocity of wind approaching Turbine-j:* The power generated by turbine-j: Step 5 Power generated by the farm: Farm Efficiency: Power Generated by the Wind Farm 12 Coefficient of power Power generated by a standalone turbine * Katic et al., 1986

26. Wake Model UWFLO uses Frandsen’s wake model*,which calculates the diameter of the growing wake and the wake velocity as: Wake spreading constant However, UWFLO has the flexibility to use any standard wake model. 13 * Frandsen et al., 2006

27. 14

28. UWFLO – Problem Definition An unidirectional uniform wind at 7.09 m/s and at 0o to X-axis is considered. 15 Cost Constraint: Applied when optimizing the selection of wind turbines

29. Wind Farm Cost Model Quadratic response surface based cost models* are developed to represent the farm cost, as a function of the turbine rotor diameters and number of turbines. To this end we used data for wind farms in the state of New York* 16 For wind farm with non-identical turbines The cost per KW of power produced is given by * Chowdhury et al., IDETC2010

30. Particle Swarm Optimization (PSO) Swarm Motion* Solution Comparison The constraint dominance principle** is used. PSO can appropriately address the non-linearity and the multi-modality of the wind farm model. 17 * Kennedy and Eberhart, 1985 ** Deb et al., 2002 (NSGA-II)

31. Generalized Approach to MDNLO - Principles Divides the variable space into continuous and discrete variable spaces. Implements continuous optimization as the primary search strategy Approximates candidate solutions to nearby feasible discrete locations based on certain criterion. Saves computational expense by evaluating criterion functions only at feasible discrete locations. Implemented through non-gradient based optimization algorithms 18

32. Vertex Approximation Techniques In the discrete variable domain, the location of a candidate solution can be defined by a local hypercube Nearest Vertex Approach (NVA) Approximates to the nearest discrete location based on Euclidean distance. Shortest Normal Approach (SNA) Approximates to the discrete location with shortest normal to the connecting vector. 19

33. Experimental Scale Wind Farm The UWFLO model has been validated** against a wind tunnel experiment on a scaled down farm.* 20 Meanrotor diameter of commercial turbines: 75mScaled down to experimental dimensions: 0.12mResulting feasible set of diameters at the experimental scale: * Cal et al., 2010; ** Chowdhury et al., IDETC2010

34. Case 1 – Non-Identical Turbines 21 Using NVAUsing SNA Incoming Wind Speed

37. UWFLO – Influence of the Farm Size Cost information relating the farm size to the total cost was not readily available. 24

39. To this end the developed mixed-discrete PSO is found to be highly effective. The nearest vertex approach performs better than the shortest normal approach.

40. This wind farm optimization technique increases the power generation by 44% compared to the array layout (at no additional cost).

41. The determination of the appropriate number of turbines, and the farm size is crucial to optimal wind farm design. 25

43. Future research will also consider the variability of the speed and direction of wind, in the case of commercial wind farms.26

44. Selected References World Wind Energy Report 2008. Bonn, Germany, February 2009. Katic, I., Hojstrup, J., and Jensen, N. O. A Simple Model for Cluster Efficiency. In Proceedings of European Wind Energy Conference and Exhibition (Rome, Italy 1986). Frandsen, S., Barthelmie, R., Pryor, S, Rathmann, O, Larsen, S, Hojstrup, J, and Thogersen, M. Analytical Modeling of Wind Speed Deficit in Large Offshore Wind Farms. Wind energy, 9, 1-2 (2006), 39-53. Grady, S. A., Hussaini, M. Y., and Abdullah, M. M. Placement of Wind Turbines Using Genetic Algorithms. Renewable Energy, 30, 2 (February 2005). Sisbot, S., Turgut, O., Tunc, M., and Camdali, U. Optimal positioning of Wind Turbines on Gökçeada Using Multi-objective Genetic Algorithm. Wind Energy (2009). Mosetti, G., Poloni, C., and Diviacco, B. Optimization of Wind Turbine Positioning in Large Wind Farms by Means of a Genetic Algorithm. Journal of Wind Engineering and Industrial Aerodynamics, 54, 1 (January 1994), 105-116. Kennedy, J. and Eberhart, R. C. Particle Swarm Optimization. In Proceedings of the 1995 IEEE International Conference on Neural Networks ( 1995), 1942-1948. Cal, R. B., Lebron, J., Kang, H.S., Meneveau, C., and Castillo, L., “Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer”, Journal of Renewable and Sustainable Energy, 2, 1 (2010). Lebron, J., Castillo, Cal, R. B., Kang, H. S., and Meneveau, C., 2010, “Interaction Between a Wind Turbine Array and a Turbulent Boundary Layer,” Proceeding 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, January 4-9. 27

45. Acknowledgement 28 Thank you

46. QuestionsorComments 29