# An Optimization Framework for Wind Farm Design in Complex Terrain
## 1 Introduction  
In the past two decades, the world has witnessed a remarkable growth of wind energy development. According to the latest statistics from the Global Wind Energy Council (GWEC), the global cumulative installed wind capacity has increased from 23.9 GW in 2001 to 439.1 GW in 2017, representing an average annual increase by 20.4% [1]. Although offshore wind is now attracting a lot of interests and has grown rapidly in recent years, especially in northern Europe, today it represents only 4.3% of the global installed capacity of wind energy [2]. The dominance of onshore wind is mainly due to its longer development history, lower cost, and easier deployment. As a result of the rapid growth of onshore wind, a lot of onshore wind farms have been built worldwide. Since many suitable sites in flat terrain have already been developed with wind farms, more and more wind farms are going to be built in complex terrain, especially for countries featured by a large percentage of topography covered with mountains, such as China. Compared with a wind farm on flat terrain, a wind farm built on complex terrain benefits from the possible richer wind resource at certain locations (brought by the speed-up effect due to the terrain topography change), but it is also more likely to be exposed to more complex flowconditions, higher fatigue loads, more expensive installation, operation and maintenance costs, and other disadvantages [3]. Designing wind farms in complex terrain is not a trivial task, mainly due to the complex interactions of the boundary layer flow with the complex terrain and wind turbine wakes, and also due to the multi-disciplinary nature of the wind farm design problem. This problem typically involves different design and engineering tasks, which may come from technical, logistical, environmental, economical, legal, and/or even social considerations. For most industrial practitioners, the design of wind farms conventionally concerns mainly the micro-siting of wind turbines based on consideration of wind resource, i.e., determining the exact position for each turbine at a selected wind farm site [4]. Typically, a wind farm developer/designer uses a wind resource assessment tool, such as WAsP [5] (the industry-standard PC software for wind resource assessment, siting, and energy yield calculations for wind turbines and wind farms), to assess the wind resource of the wind farm site based on wind measurement data during a period [6]. Then, the final design of the wind farm, mainly the layout of turbines, is determined for maximizing the annual energy production (AEP) while considering certain constraints, such as the proximity of wind turbines. This final layout is usually obtained by either manual adjustments or using some optimization techniques [7]. After finding the turbine layout, other design tasks related to foundations, access roads, electrical system, and other components or systems are handled separately, often by specialized engineering consulting companies. The general problem of modelling the wind flow over complex terrain has been an important research field for a very long time. Seventy years ago, [PERSON] published a review of theoretical models of inviscid flow over hills and mountains [8]. More recently, [PERSON] gave a historical review of studies (until 2000) on wind flow over complex terrain [9]. Similarly, in the wind energy community, the problem of wind resource assessment in complex terrain was investigated by many researchers over a long period [10]. In contrast, wind farm design optimization has only become a hot research area quite recently and the majority of the published studies in this field deal with wind farms in flat terrain or offshore [11]. Few studies investigated the wind farm design optimization problems in complex terrain. [PERSON] et al. [12] proposed a bionic method for optimizing the turbine layout in complex terrain. In this study the objective was to maximize the power output, and the wake flow was simulated by using the virtual particle wake model.