http://windenergyresearch.org/?p=2836 A wind farm layout optimization framework based on a multi-fidelity model approach is applied to the offshore test case of Middelgrunden, Denmark. While aesthetic considerations have heavily influenced the famous curved design of Middelgrunden wind farm, this work focuses on testing a method that optimizes the profit of offshore wind farms based on a balance of the energy production, the electrical grid costs, the foundations cost, and the wake induced lifetime fatigue of different wind turbine components. The multi-fidelity concept uses cost function models of increasing complexity (and decreasing speed) to accelerate the convergence to an optimum solution. In the EU TopFarm project, three levels of complexity are considered. The first level uses a simple stationary wind farm wake model to estimate the Annual Energy Production AEP, a foundations cost function based on the water depth, and an electrical grid cost function. The second level calculates the AEP and adds a wake induced fatigue cost function based on the interpolation of a database of simulations done for various wind speed and wake setups with the aero-elastic code HAWC2 and the Dynamic Wake Meandering (DWM) model. The third level includes directly the HAWC2 and DWM models in the optimization loop in order to estimate both the fatigue costs and the AEP. The novelty of this work is the implementation of the multi-fidelity, the inclusion of the fatigue costs in the optimization framework, and its application on an existing offshore wind farm test case. Paper presented at ISOPE 19-14 June 2011, Maui, Hawaii, USA P.-E. Réthoré, P. Fuglsang, G.C. Larsen, T. Buhl, T.J. Larsen, H.A. Madsen. TopFarm: Multi-fidelity Optimization of Offshore Wind Farm<. (2011-TCP-1012). ISOPE conference. Maui, Hawaii, USA. 19-24 June 2011.

1. TOPFARM: Multi-fidelity Optimization of Offshore Wind Farm Pierre-Elouan Réthoré, Peter Fuglsang, Gunner C. Larsen, Thomas Buhl, Torben J. Larsen and Helge A. Madsen Wind Energy Division Risø DTU - National Laboratory for Sustainable Energy Technical University of Denmark ISOPE – 19-24 June 2011

3. Middelgrunden Offshore Wind FarmConclusion Outlook

4. Conclusions Introduction – Vision and Philosophy Vision: A “complete” wind farm topology optimization taking into account Loading- and production aspects in a realistic and coherent framework Financial costs (foundation, grid infrastructure, ...) ... and subjected to various constraints (area, spacing,...) Philosophy: The optimal wind farm layout reflects the optimal economical performance as seen over the lifetime of the wind farm

5. Conclusions Wind farm wind climate (in-stationary wake affected flow field) Production/loads (aeroelastic modeling) Control strategies (WT/WF) Cost models (financial costs, O&M, wind turbine degradation costs) Verification of wind field and loads and production models Optimization (synthesis of sub-model modules) Proof-of-concept (1): Layout optimization of the offshore Middelgrunden wind farm Proof-of-concept (2): Layout optimization of the on-shore Coldham /Stags Holt wind farm The TOPFARM Modules

7. Cost Functions … and Objective Function (2) Gunner Larsens cost model Maximize Finance balance Maximize power production Minimize cost Minimize foundation cost Minimize cable cost Minimize maintenance Minimize degradation Maintenance cost Degradation cost Electrical Production Sales Electrical infrastructure cost Foundation cost

8. Simple wake model Fast and Simple Wake Model From: G. C. Larsen, ”A simple stationary semi-analytical wake model. Risø-R-1713

12. Foundation Costs (CF) Different models investigated. Discontinuous model chosen (green): 20 % of turbine price For each meter above 8 meters an additional cost of 2% Above 20 meters very expensive (20% pr m) Simple and fast Could be refined easily

13. Electrical Grid Costs (CG) Simple model for electrical grid costs: Finding the shortest connection between all the turbines. Fixed cost per meter: C=675 €/m

14. Optimization Algorithms Genetic Algorithm (SGA) Structured grid Slow (Many iterations necessary) Global optimum Gradient Based Search (SLP) Unstructured grid (good for refinements) Faster (Few iterations for converging) Local minimum SGA+SLP: Good combination for finding a refined global optimum. Example of Structured grid

15. Multifidelity Approach

17. Water depth between 4 and 20 mWind direction probability density distribution Gray color: Water depth [m] Yellow line: Electrical grid

18. Results – Generic Offshore Wind Farm (2) Result of a gradient based optimization (SLP)

19. Results – Generic Offshore Wind Farm (3) Result of a genetic algorithm + gradient based optimization (Simplex)

20. Results - Middelgrunden (1) Photo: Andreas Johansen

21. Results - Middelgrunden (2)

22. Results - Middelgrunden (3) Ambient wind climate:

23. Results - Middelgrunden (4) Iterations: 1000 SGA + 20 SLP

24. Results - Middelgrunden (5) Before After

25. Conclusions Results - Middelgrunden (4) The baseline layout was largely based on visual considerations The optimized solution is fundamentally different from the baseline layout ... the resulting layout makes use of the entire feasible domain, and the turbines are not placed in a regular pattern The foundation costs have not been increased, because the turbines have been placed at shallow water The major changes involve energy production and electrical grid costs ... both were increased A total improvement of the financial balance of 2.1 M€ was achieved compared to the baseline layout

27. Including financial costs (foundation, grid infrastructure, etc.) in the optimization problemThe performance of the platform has been demonstrated for offshore and on-shore example sites

29. Full DWM based optimization (presently only the closest upstream turbine is considered load generating) ...

30. Better foundation cost model

31. Parallization of the code … improved computational speed

32. Aeroelastic computations in the frequency domain … improved computational speed

33. Cheapest rather than shortest cabling between turbines

34. Inclusion of extreme load aspects

35. Eddy viscosity model consistent with the DWM split in scales … improved description of the wake deficit