On Learning to Generate Wind Farm Layouts

On Learning to Generate Wind Farm Layouts Dennis Wilson Emmanuel Awa Sylvain Cussat-Blanc CSAIL - MIT Brandeis University University of Toulouse 32 Vassar Street 415 South Street 21 allée de Brienne Cambridge, MA 02139, USA Waltham, MA 02453, USA 31015 Toulouse, France [email protected] [email protected] [email protected] Kalyan Veeramachaneni Una-May O’Reilly CSAIL - MIT CSAIL - MIT 32 Vassar Street 32 Vassar Street Cambridge, MA 02139, USA Cambridge, MA 02139, USA [email protected] [email protected] ABSTRACT such as operation and maintenance costs, turbine costs, or Optimizing a wind farm layout is a very complex problem cable layout. that involves many local and global constraints such as inter- Modern farms cover large areas and boast hundreds, and turbine wind interference or terrain peculiarities. Existing sometimes even thousands, of turbines. The layout design methods are either inefficient or, when efficient, take days process is iterative, computationally expensive, burdened or weeks to execute. Solutions are contextually sensitive to with global and local constraints, and ultimately controlled the specific values of the problem variables; when one value by subjective assessments due to the involvement of a vari- is modified, the algorithm has to be re-run from scratch. ety of stakeholders. During each step, designers must ei- This paper proposes the use of a developmental model to ther refine an incremental layout or propose a new lay- generate farm layouts. Controlled by a gene regulatory net- out which they have generated by incorporating new con- work, virtual cells have to populate a simulated environment straints. Additionally, evaluating a layout requires varied that represents the wind farm. When the cells' behavior is multi-disciplinary models and sub-modules that are extremely learned, this approach has the advantage that it is re-usable computationally expensive. in different contexts; the same initial cell is responsive to a Under these circumstances, we argue that the direct search variety of environments and the layout generation takes few approaches based on global optimization techniques are ex- minutes instead of days. tremely inefficient. In such approaches, the environment is tessellated and an optimization algorithm, generally based on CMA-ES (Covariance Matrix Adaptation Evolution Strat- Categories and Subject Descriptors egy) or on a genetic algorithm, locally optimizes the turbines I.2.8 [Artificial Intelligence]: Problem Solving positions by slightly moving them. When the fundamental constraints or other aspects of the design problem are Keywords changed, the layout optimizer has to be re-run with a new starting point. When the approaches are population-based Layout optimization; Developmental model; Gene regula- they rely on evaluating a population of layouts in each iter- tory network; Machine learning ation causing the algorithm to sometimes run for days at a time. This latency creates a bottleneck in the design pro- 1. INTRODUCTION cess. An algorithm that is efficient and can handle additional Wind farm design is a complex task and the recent trend of constraints during the design process is highly desired. larger farm sizes has greatly increased demands on designers. To start to address weaknesses of the current approaches, Traditionally, a small, well-connected, land area is divided we propose a novel approach that uses a cell-based devel- into smaller cells and turbine placement among cells is de- opmental model to \grow" wind farm layouts. Cells are a cided through a simple search algorithm with a pre-specified metaphor for turbines in a virtual layout. An evolutionary cost function. The cost function is usually limited to mini- algorithm optimizes the cell's behavior with the aim to pop- mizing inter-turbine wake interferences and thus maximizes ulate the environment so that the global network, the farm energy capture. Few approaches consider additional factors layout, maximizes the energy output or the earnings calcu- lated by a cost-benefit (return on investment) simulation of the wind farm. The cells have to respect the local and global constraints and position themselves optimally in the envi- Permission to make digital or hard copies of all or part of this work for ronment. To do so, the cells sense the wind coming from personal or classroom use is granted without fee provided that copies are various directions and decide what to do: divide, reorient not made or distributed for profit or commercial advantage and that copies their division plan, migrate, and more. This bio-inspired bear this notice and the full citation on the first page. To copy otherwise, to approach, commonly named the developmental model or republish, to post on servers or to redistribute to lists, requires prior specific morphogenetic engineering, has been used on complex prob- permission and/or a fee. GECCO’13, July 6-10, 2013, Amsterdam, The Netherlands. lems since the end of the 1990's. Nowadays, developmental Copyright 2013 ACM TBA ...$15.00. models are commonly used to grow shapes or solve simple providing a way to generate layouts with a variable number combinatorial functions [9, 2, 13, 21, 8, 5]. However, their of turbines. For algorithms that search for locations in the applications to real-world problems are still to be explored. continuous domain, the number of turbines is fixed giving Producing modular robot morphologies [6] or the topology limited flexibility for the cost function to affect turbine num- of optical fibers [16] are two examples of existing applica- ber. Additionally, proximity constraints are often violated, tions. After a learning process, usually based on a genetic requiring sophisticated repair approaches. algorithm that optimizes an encoding of the cell behavior, Problem dimensionality: When the problem is solved they have been shown to solve highly locally constrained via the discrete version, an x km by x km farm is divided problems and to scale up easily to harder problems without into m2 km cells giving the problem a binary dimensionality additional learning [4]. x2 of m2 . On the other hand if the problem is solved via a This paper is organized as follows. In x2, we present the continuous version the number of dimensions is 2×N where background in wind farm layout optimization and the lim- N is the number of turbines. itations of existing methods. Then, in x3, we present the Reusability: One fundamental drawback of direct search wind farm evaluation function, the developmental approach approaches is that the algorithm has to be run every time that generates the layouts, and the gene regulatory network there are changes in the problem space, or when additional that controls the cells. x4 presents experiments that denote constraints are added. Fully realistic layout evaluation tools the properties of the evodevo model such as its scalability such as OpenWind by AWS Truepower take so long that and its adaptativity to the environment. In x5 we conclude they are not practical to use in an iterative algorithm; an and consider what further aspects of the layout optimization example optimization using this software to evaluate fitness problem can be addressed by out approach. would take approximately one week. 2. BACKGROUND AND LIMITATIONS The objective of this work is to address the problems men- tioned above by means of a developmental approach. A 2.1 Background developmental model works differently in that, rather than Approaches to solving the wind turbine layout problem generating a solution, it learns a parameterized function can be broadly sorted into three categories. In the first which, when executed a certain number of times, produces category, the approaches divide the site into a number of an entire solution. At each iteration, the function is sensitive cells and use a discrete optimization algorithm that decides to conditions affecting energy capture and cost of energy. As whether or not to place a turbine in the cell. A genetic algo- long as the evaluation model is the same, the function can be rithm optimizes the corresponding boolean matrix [17, 11, executed for a new farm, with different conditions, without 12, 26, 10, 19, 27]. having to re-learn. In the second approach, a continuous space search algorithm is used to move each turbine locally to identify the 3. LAYOUT EMBRYOGENESIS optimal placement. For example, a particle swarm optimization algorithm is used in [25, 3, 22]. A particle represents a 3.1 Developmental model turbine layout by a vector of N(x, y) Cartesian coordinates, The developmental model is based on the replication of where N is the theoretical maximum number of turbines to virtual cells of size X meters by X meters that occupy a place in the farm. A constraint-repairing algorithm keeps virtual environment. The developmental process starts with the layout coherent in regard to a secure area constraint. a single cell positioned in the middle of the environment. As Finally, a third set of approaches start with a grid lay- shown on Figure 1, each cell senses the amount of energy it out and generate slight modifications on an existing layout receives from eight different directions. These amounts are by the use of CMA-ES to introduce a stochastic component computed based on the wind speed distribution described as [24]. Each decision variable, i.e. one of the coordinates of part of the farm specifications with the energy lost to wake the turbines, is perturbed by adding a normally distributed effects, i.e. the interference of other turbines, subtracted. random value. The standard deviation is also evolved using The inter-turbine interference model is described in x3.3. the members of the population that have survived a selec- tion process based on their fitness. The algorithm learns the stochastic perturbations that will optimize the solution by learning the correlation among variables. This learning is performed by maintaining a matrix of covariances among the distributions controlling the perturbations of decision variables for every layout.

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