## 1 INTRODUCTION

During recent years, wind energy has moved from an emerging technology to become a nearly competitive technology with conventional energy sources. An increased proportion of the turbines to be installed in the future, are foreseen to be sited in large wind farms. Establishment of large wind farms requires enormous investments, putting steadily greater emphasis on optimal topology layout. Today, the design of a wind farm is typically based on an optimization of the power output only, whereas the load aspect is treated in a rudimentary manner only, in the sense that the wind turbines are required only to comply with the design codes.

Wind farm layout optimization is a relatively new research topic, with some of the first articles on the subject includes Mosetti *et al*. in 1994 [1] and Beyer *et al*. in 1996. [2] Since then, the topic has become gradually more popular to reach around 10 journal and conference articles produced every year (see [3] and [4] for a more exhaustive review). The vast majority of the research work on this topic has been focused on the types of optimization algorithm used to solve the problem, keeping the various cost functions as simple as possible. A notable exception to this observation is the work of Elkinton [5], which presents a rather sophisticated modeling of different costs function, in particular the electrical grid and foundation costs. While most consider the power losses because of wake effect, to the authors knowledge, none consider the costs associated with the wake induced fatigue loads on the wind turbine components. However, a complete optimization of layout and control of wind farms requires, in addition to the power production, a detailed knowledge of the loading of the individual turbines. This is not a trivial problem. The power production and loading, related to turbines placed in a wind farm, deviate significantly from the production and loading pattern of a similar stand-alone wind turbine subjected to the same (external) wind climate.

To achieve the optimal economic output from a wind farm, an optimal balance between capital costs, operation and maintenance (O&M) costs, fatigue lifetime consumption of turbine components, and power production output is to be determined on a rational background. The overall objective of the TOPFARM project [6] is to establish this background in terms of advanced flow models that include instationary wake effects, advanced (and fast) aero-elastic models for load and production prediction as well as dedicated cost and control strategy models, and subsequently to synthesize these models into an optimization problem subjected to various kinds of constraints, as, for example, area constraints and turbine interspacing constraints. The design variables in the optimization problem are the relative position of the wind farm wind turbines (including the possibility for positioning a given number of turbines in one or more wind farms).

When considering a computationally demanding iterative process, it is of crucial importance, that the resulting models of the complex wind field within a wind farm can be condensed into fast, though accurate, flow simulation tools. The basic strategy for achieving this goal goes through a chain of flow models of various complexities, where the advanced and very demanding computational fluid dynamic (CFD) based models, together with available experimental evidence, are used to formulate, calibrate, and validate simpler models ranging from simplified CFD models to more engineering stochastic type of models.

Aero-elastic modeling is needed to calculate production as well as structural loads for each of the turbines in the wind farm. It is a challenge on one hand to keep computational costs limited, while on the other hand to have accurate prediction of the loads of each turbine. Complete aero-elastic calculations for each turbine are clearly not feasible due to the very large number of cases that need to be considered when taking into account wind direction and wind speed variations. In this work, a simplified approach is taken, where the fatigue load calculations are based on a database of precalculated generic load cases for turbines in wake operation. Aggregated lifetime equivalent loads can then be found by summing up contributions from the individual load cases.

When aiming at an economic optimization of wind farm topology, cost models are essential, encompassing both financial costs, and operating costs. Only costs that depend on the wind farm topology (including wind farm infra structure, wind turbine foundations, production, and loading) are relevant. [7] In the context of this work, these costs are denoted variable costs, contrary to fixed costs that are, for example, cost of planning and projecting of the wind farm, cost of the land available for the intended wind farm project, price of turbines (assuming a fixed number of turbines), and external civil engineering costs. The variable costs need to be evaluated only on a relative basis, whereas the knowledge of the absolute costs are not necessary for the optimization.

A proper optimization approach is essential for successfully carrying out the optimization. One aspect is the choice of the type of optimization algorithm among global methods and local gradient-based methods, where the likelihood of being captured in a local minimum needs to be traded off against rate of convergence and total computational costs. Another aspect is a clever mapping of the wind farm layout design variables by using as few variables as possible, thus limiting the feasible set, and how to include constraints on layout and on the wind farm performance characteristics (e.g., power fluctuations and space used). In order to speed up the optimization time, a multi-fidelity approach is proposed. Different types of multi-fidelity methods exist (see Robinson *et al*. [8] for a short review). The basic idea in this work is first to use a global optimization approach on the basis of simplified cost functions over a coarse discretization of the domain as well as the wind direction and wind speed distribution considered; and subsequently to refine the resulting layout by increasing gradually the complexity of the cost functions and the resolution of the discretization by using a gradient based optimization algorithm. The approach presented in this work is sequential, with the higher fidelity model being used to refine the result found by the lower fidelity model.

This paper presents a summary of activities leading to the implementation of the optimization methodology of the TOPFARM project. Further details and information can be found in a previous conference article [9] and in a technical report by the same authors of this article. [10]

The paper is structured as follows. The method section introduces the different optimization algorithms used in this work, the way they are constrained, and how they are setup using a multi-fidelity approach. The different cost functions are then presented followed by a description of the wind turbine aero-elastic and wake models they rely upon. Three test cases are presented in the result section: (i) a hypothetical six-turbine offshore wind farm, (ii) the existing Stags Holt–Coldham (UK) onshore wind farm consisting of 17 turbines, and (iii) the existing offshore wind farm of Middelgrunden (DK) consisting of 20 turbines. All cases give satisfying results and demonstrate the range of applications of the TOPFARM optimization platform. The discussion section presents different issues related to the implementation of the methods and running the test cases. Finally, in conclusion, it some future work ideas for improving the optimization framework is proposed.