# Considering Wake Effects in a Mixed Integer Linear Programming Model for Optimizing Wind Farm Layout

[Examensarbete på avancerad nivå]

In this thesis is an already existing mixed integer linear programming (MILP) model for designing wind power farms developed further. The development is focused on the wake effects, since those are not linear and most of the variables in the problem are due to wakes. The new models were tested on a potential site Moskogen, nearby Jarpen in Jamtland, Sweden. Mathematical optimization is a powerful tool, which unlike most used methods for designing wind power farms, controls that it actually have found the best solution for the stated problem. The largest drawback is that only some groups of mathematical optimization problems can be solved, and those mostly require a lot of time. MILP do have methods to find the best solution. When designing wind power farms it is important to maximize the power extraction, at the same time as environmental and other restrictions are respected. In the MILP model is the maximum number of turbines restricted due to budget reasons and there are sound limits on some nearby positions. Wind power turbines extract energy from and are obstacles for the wind, which means that they decrease the wind speed and increase the turbulence downwind. This change of speed and turbulence is called a wake. Measurements from existing farms and simulations show that for turbines standing close to other turbines the stress on the structure is substantial and the losses in productivity are large. Therefore a minimum distance is applied, which is calculated to 5 rotor diameters. From 5 to 12 rotor diameters the wake causes an extraction loss in power. Further away the extraction losses due to a wake are assumed negligible. The first development of the MILP-model is that no wakes are accounted for if there is more than 12 rotor diameters between two turbines. Then the model were developed into three different modifications: i) The wake losses are not calculated, instead it has to be at least 12 rotor diameters between the turbines in dominant wind directions, ii) The wakes are only in constraints limiting the wake effect and the wakes are excluded from the objective function and iii) The wake effects are scaled so that the sum of all wakes might be more correct, but single wakes will be less correct. Due to time limits on the project no tests were ran more than 24 hours. The standard model without wake losses gave the highest extraction, 16% higher than previous results, but also had a lower capacity factor. Model i) without wake losses and model ii) with the wake losses constrained to 5% of the extraction gave 9 and 3% higher extraction, respectively. The other models gave lower extraction than previous results, probably due to the time limit.

Publikationen registrerades 2014-12-09. Den ändrades senast 2014-12-09

CPL ID: 207753

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