Isope topfarm

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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.

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Isope topfarm

  1. 1. TOPFARM: Multi-fidelity Optimization of Offshore Wind Farm<br />Pierre-Elouan Réthoré, Peter Fuglsang, <br />Gunner C. Larsen, Thomas Buhl, <br />Torben J. Larsen and Helge A. Madsen<br />Wind Energy Division<br />Risø DTU - National Laboratory for Sustainable Energy<br />Technical University of Denmark<br />ISOPE – 19-24 June 2011<br />
  2. 2. Outline<br /> Introduction – Vision and Philosophy<br /> The TOPFARM Modules<br /> The Wake “engine”<br /> The Load and Production “Engine”<br /> Cost Functions ... and Objective Function<br /> Results<br /><ul><li>Generic Offshore Wind Farm
  3. 3. Middelgrunden Offshore Wind Farm</li></ul>Conclusion<br />Outlook<br />
  4. 4. Conclusions<br />Introduction – Vision and Philosophy<br />Vision: A “complete” wind farm topology optimization taking into account <br />Loading- and production aspects in a realistic and coherent framework<br />Financial costs (foundation, grid infrastructure, ...)<br />... and subjected to various constraints (area, spacing,...) <br />Philosophy: The optimal wind farm layout reflects the optimal economical performance as seen over the lifetime of the wind farm<br />
  5. 5. Conclusions<br />Wind farm wind climate (in-stationary wake affected flow field)<br /> Production/loads (aeroelastic modeling)<br />Control strategies (WT/WF)<br />Cost models (financial costs, O&M, wind turbine degradation costs) <br />Verification of wind field and loads and production models<br />Optimization (synthesis of sub-model modules) <br />Proof-of-concept (1): Layout optimization of the offshore Middelgrunden wind farm<br />Proof-of-concept (2): Layout optimization of the on-shore Coldham /Stags Holt wind farm<br />The TOPFARM Modules<br />
  6. 6. Conclusions<br />Cost Functions … and Objective Function (1)<br /><ul><li>Only variable costs (i.e. costs depending on the wind farm topology) are included in the objective function (OF)</li></ul>OF formulated as a financial balance expressing the difference between the wind farm income (power production (WP)) and the wind farm expenses (i.e. O&M expenses (CM), cost of turbine fatigue load degradation (CD), and financial expenses (C) – in this case including grid costs (CG) and foundation costs (CF))<br />
  7. 7. Cost Functions … and Objective Function (2)<br />Gunner Larsens cost model<br />Maximize Finance balance<br />Maximize power production<br />Minimize cost<br />Minimize foundation cost<br />Minimize cable cost<br />Minimize maintenance<br />Minimize degradation<br />Maintenance cost<br />Degradation cost<br />Electrical Production Sales<br />Electrical infrastructure cost<br />Foundation cost<br />
  8. 8. Simple wake model<br />Fast and Simple Wake Model<br />From: G. C. Larsen, ”A simple stationary semi-analytical wake model. Risø-R-1713<br />
  9. 9. Conclusions<br />The Wake ”Engine” (1)<br /><ul><li>The dynamic wake meandering (DWM) model (“poor mans LES”) is an efficient model providing a realistic description of wake affected flow fields within wind farms
  10. 10. The core of the DWM model is a split in scalesin the wake flow field, with large turbulent scales being responsible for stochastic wake meandering (passive tracer analogy), and small scales being responsible for wake attenuation and expansion in the meandering frame of reference as caused by turbulent mixing (… LES sub-scale analogy)</li></li></ul><li>Conclusions<br />The Wake ”Engine” (2)<br />DWM main ingredients (2):<br /><ul><li>Wake down-stream transportation (meandering) by passive tracer analogy (... LES large-scale analogy)
  11. 11. A sequence of “deficit-releases” is considered ... and described in space and time</li></li></ul><li>Conclusions<br />The wake ”engine” (4)<br /><ul><li>Does it work? ... a full-scale verification (based on LiDAR measurements) </li></li></ul><li>Conclusions<br />The load and production ”engine” (1)<br /><ul><li>Dynamic wake meandering (DWM) model (“poor mans LES”) – module1 – combined with aeroelastic simulations of the individual turbines – modules 2, 3</li></li></ul><li>Conclusions<br />The load and production ”engine” (2)<br /><ul><li>Does it work? ... a full-scale verification (based on WT7) </li></li></ul><li>Damages Costs (CD) & Maintenance Costs (CM)<br />Damages costs (CD) are accumulated damage of an element ’s’ (Ds) X the price of the element (Ps).<br />Ds is a linear function of the fatigue loads.<br />Maintenance Costs are based on the probability of occurrence of a failure multiplied by the replacement cost.<br />
  12. 12. Foundation Costs (CF)<br />Different models investigated.<br />Discontinuous model chosen (green):<br />20 % of turbine price<br />For each meter above 8 meters an additional cost of 2%<br />Above 20 meters very expensive (20% pr m)<br />Simple and fast<br />Could be refined easily<br />
  13. 13. Electrical Grid Costs (CG)<br />Simple model for electrical grid costs:<br />Finding the shortest connection between all the turbines.<br />Fixed cost per meter: <br />C=675 €/m<br />
  14. 14. Optimization Algorithms<br />Genetic Algorithm (SGA)<br />Structured grid <br />Slow (Many iterations necessary)<br />Global optimum<br />Gradient Based Search (SLP)<br />Unstructured grid (good for refinements)<br />Faster (Few iterations for converging)<br />Local minimum<br />SGA+SLP:<br />Good combination for finding a refined global optimum.<br />Example of Structured grid<br />
  15. 15. Multifidelity Approach<br />
  16. 16. Results – Generic Offshore Wind Farm (1)<br /><ul><li> 6 5MW offshore wind turbines.
  17. 17. Water depth between 4 and 20 m</li></ul>Wind direction probability<br />density distribution<br />Gray color: Water depth [m]<br />Yellow line: Electrical grid<br />
  18. 18. Results – Generic Offshore Wind Farm (2)<br />Result of a gradient based optimization (SLP)<br />
  19. 19. Results – Generic Offshore Wind Farm (3)<br />Result of a genetic algorithm + gradient based optimization (Simplex)<br />
  20. 20. Results - Middelgrunden (1)<br />Photo: Andreas Johansen<br />
  21. 21. Results - Middelgrunden (2)<br />
  22. 22. Results - Middelgrunden (3)<br /> Ambient wind climate:<br />
  23. 23. Results - Middelgrunden (4)<br />Iterations: 1000 SGA + 20 SLP<br />
  24. 24. Results - Middelgrunden (5)<br />Before<br />After<br />
  25. 25. Conclusions<br />Results - Middelgrunden (4)<br />The baseline layout was largely based on visual considerations<br />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 <br />The foundation costs have not been increased, because the turbines have been placed at shallow water <br />The major changes involve energy production and electrical grid costs ... both were increased<br />A total improvement of the financial balance of 2.1 M€ was achieved compared to the baseline layout<br />
  26. 26. Conclusions<br />Conclusion(s)<br />A new optimization platform has been developed that allow for wind farm topology optimization in the sense that the optimal economical performance, as seen over the lifetime of the wind farm, is achieved<br />This is done by:<br /><ul><li>Taking into account both loading (i.e. degradation), operational costs (i.e. O&M) and production of the individual turbines in the wind farm in a realistic and coherent framework .... and by
  27. 27. Including financial costs (foundation, grid infrastructure, etc.) in the optimization problem</li></ul>The performance of the platform has been demonstrated for offshore and on-shore example sites<br />
  28. 28. Conclusions<br />Outlook<br />(Possible) future model extensions:<br /><ul><li>Inclusion of atmospheric stability effects (… important for production; cf. L. Jensen & R. Barthelmie)
  29. 29. Full DWM based optimization (presently only the closest upstream turbine is considered load generating) ...
  30. 30. Better foundation cost model
  31. 31. Parallization of the code … improved computational speed
  32. 32. Aeroelastic computations in the frequency domain … improved computational speed
  33. 33. Cheapest rather than shortest cabling between turbines
  34. 34. Inclusion of extreme load aspects
  35. 35. Eddy viscosity model consistent with the DWM split in scales … improved description of the wake deficit</li>

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