Wind turbine placement in a wind farm can be optimized to limit power losses due to wakes and improve the economic value of the plant. Seeing as wind farms are increasing in number and size, fast methods to generate good quality layouts can be beneficial for designers. Wind Farm Layout Optimization (WFLO) consists in finding a layout that maximizes the Annual Energy Production (AEP) of a wind farm. The procedure is driven by an algorithm that generates possible layouts and by a framework that evaluates their AEP. If the traditional method to assess AEP is adopted, layout optimization is computationally demanding due to the impact of each turbine's position on the productivity of the surrounding ones. Indeed, for any change in the layout, this inter-dependency forces designers to calculate wake effects and the wind resource-average energy production of the wind farm. This thesis proposes an approach to reduce the computational load of WFLO by pre-computing the power losses. Indeed, the approach avoids recalculating the expected power loss among turbines during the optimization procedure. This optimization strategy employs a novel approach, called Pre-Averaged Model (PAM), that expresses the expected power loss of a wake source at representative points around it. Firstly, the wind farm is discretized, and fictitious turbines are placed at each given spot. Secondly, PAM calculates the expected power loss caused by each fictitious turbine for the surrounding ones. Discontinuities introduced by wind resource discretization and top-hat wake deficit profiles affect PAM's accuracy substantially. Binning wind measurements in 72 wind directions solves the problem for typical engineering wake models. Then, a greedy algorithm uses the power losses of the fictitious turbines to build layouts constructively by adding an extra turbine per iteration. The effect of multiple wake sources on a wake target is modelled by linear superimposition of the pre-computed power losses. PAM is tested in combination with three greedy algorithms, namely, Basic Greedy (BG), Add-Remove-Move Greedy (ADREMOG), and ADREMOG II. This research demonstrates that the PAM and the superposition of the power losses can be reliably used for WFLO. Also, the joint use of PAM and greedy algorithms achieve an interesting trade-off between speed and quality of the layouts. Indeed, PAM is beneficial as it speeds up greedy algorithms. Furthermore, greedy algorithms allow generating better layouts at the cost of slowing down the algorithm. The balance between speed and quality can be regulated by using a finer discretization, testing different locations for the first turbine placement, or acting on the nature of the algorithm. In particular, the use of a re-location stage at each constructive iteration increases the quality of the layouts substantially but reduces the speed of execution. As a result, the proposed algorithms present different characteristics: the BG is the fastest but its median layout is the worst; ADREMOG produces the best layouts in the longest time; ADREMOG II is a compromise between the two former algorithms.

Surrogate models are used to approximate the expensive ‘true’ simulation codes and thus have the potential to speed up the wind farm layout optimisation problem (WFLOP). One technique to make surrogate models is Polynomial Chaos Expansion (PCE). PCE can approximate a (wind farm) model by using orthogonal polynomials which are constructed based on input variables. In case of a wind farm model, these are wind speed and wind direction. The technique sounds promising, but up till now, PCE has mainly been used as an uncertainty quantification method and not as much in order to help with optimisation problems. This thesis research project aims to implement the PCE method in WFLOP by implementing a multivariate polynomial basis based on the wind speed and wind direction. The usability of the method will be determined based on a comparison between the WFLOP results of the PCE surrogate model and the conventional approach.

Surrogate modeling is a family of engineering techniques that attracts great interest today and can be applied in many challenging fields. A big advantage of it is that surrogate models (models based on these techniques) offer reliable results by being computationally cheaper than other candidate models. The savings in computational time is usually paramount for problems that involve a lot of variables and parameters and many iterative processes.

In the wind energy industry in particular, the design of the best layout of the wind farm is a problem that has been presented in the literature as an optimization problem; that is, a problem to optimize the wind farm layout in respect to some objective the modeler deems appropriate. More often than not, maximizing the expected power of the layout is mainly considered as this objective. The layout's expected power is -- among other things -- heavily dependent on the layout and the wake interactions between the turbines. The iterative search among many layouts to find the best one can be done with the help of a well-known optimization tool, the binary genetic algorithm. However, this tool cannot work alone, it solely facilitates the search over an adequate number of candidate solutions. To make it work, the modeler should provide it with some model that assesses how good in terms of the objective that has been set.

In this thesis therefore, the theory, the development and the use of two models of interest are investigated: Gaussian Process Regression (a surrogate model) and the Monte Carlo Method (a method based on random sampling). Great care was given to compile the theoretical basis of these models in order to be a good reference point for the non-experienced reader. The nature of these two models differs quite a bit, but they both can be used by the modeler to yield interesting results. These results will be compared to each other and against a third model's results, a specific wake model. This third model is the Original Model which the Gaussian Process Regression model and the Monte Carlo Method model utilize and compare against. The reliability of the results and computational speed will be the measure of success and ranking for these three models.

Finally, the comparison of the three models continues in how potent they are to propose an optimized layout for a wind farm. Each of the three models is coupled with the binary genetic algorithm that is developed specifically to connect with them. Afterwards, the proposed best layouts are discussed. The results show that the Gaussian Process Regression model performs reliably and very fast in comparison to the Original model. On the other hand, the Monte Carlo model, although also fast when it is used to find an optimized layout, could not be verified that it performs reliably and therefore, its results cannot be trusted without going into further investigation. After the comparison, further discussion follows with some recommendations for future research.