Wednesday, 26 January 2011
We study the problem of choosing the optimal layout of individual turbines within the boundaries of a wind farm subject to proximity constraints and maximizing energy production. We present a mathematical model for wind turbine placement based on the wind distribution at the wind farm site. At present, this model considers the problem in two dimensions and can utilize estimates of the distribution of wind speed and direction at turbine hub height. Ideally, such distributions would be representative of the climatology of potential wind farm site, if the required instrumentation is in operation. Alternatively, the data can be derived from simulation via the application of numerical weather prediction. In this case, we use the WRF-ARW community model configured to provide detailed wind estimates at an arbitrary target site.
The layout model takes into consideration the hard constraints on turbine placement imposed by budget and turbine operational limitations. The objective is to maximize energy production subject to energy losses incurred due to wake effects between turbines. As opposed to existing approaches based on heuristic and global search methods, we describe an exact search method based on Branch and Bound that provides optimality guarantees. If given enough time, our solving method is guaranteed to find the optimal solution and if terminated early it provides a feasible solution together with an optimality gap. Existing methods find progressively better solutions but have no way of determining how far the best solution found so far is from the optimal and hence, provide solutions that may be arbitrarily bad.
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