This paper presents a heuristic building block for wind farm layout optimization algorithms. For each pair of wake-interacting turbines, a vector is defined. Its magnitude is proportional to the wind speed deficit of the waked turbine due to the waking turbine. Its direction is chosen from the inter-turbine, downwind, or crosswind directions. These vectors can be combined for all waking or waked turbines and averaged over the wind resource to obtain a vector, a "pseudo-gradient", that can take the role of gradient in classical gradient-following optimization algorithms. A proof-of-concept optimization algorithm demonstrates how such vectors can be used for computationally efficient wind farm layout optimization. Results for various sites, both idealized and realistic, illustrate the types of layout generated by the proof-of-concept algorithm. These results provide a basis for a discussion of the heuristic's strong points-speed, competitive reduction in wake losses, and flexibility-and weak points-partial blindness to the objective and dependence on the starting layout. The computational speed of pseudo-gradient-based optimization is an enabler for analyses that would otherwise be computationally impractical. Pseudo-gradient-based optimization has already been used by industry in the design of large-scale (offshore) wind farms. ... Read more

We present an analysis of three datasets of 10min metocean measurement statistics and our resulting recommendations to both producers and users of such datasets. Many of our recommendations are more generally of interest to all numerical measurement data producers. The datasets analyzed originate from offshore meteorological masts installed to support offshore wind farm planning and design: the Dutch OWEZ and MMIJ and the German FINO1. Our analysis shows that such datasets contain issues that users should look out for and whose prevalence can be reduced by producers. We also present expressions to derive uncertainty and bias values for the statistics from information typically available about sample uncertainty. We also observe that the format in which the data are disseminated is sub-optimal from the users' perspective and discuss how producers can create more immediately useful dataset files. Effectively, we advocate using an established binary format (HDF5 or netCDF4) instead of the typical text-based one (comma-separated values), as this allows for the inclusion of relevant metadata and the creation of significantly smaller directly accessible dataset files. Next to informing producers of the advantages of these formats, we also provide concrete pointers to their effective use. Our conclusion is that datasets such as the ones we analyzed can be improved substantially in usefulness and convenience with limited effort. ... Read more

The construction and management of a wind farm involve many disciplines. It is hard for a single designer or developer to keep an overview of all the relevant concepts, models, and tools. Nevertheless, this is needed when performing integrated modeling or analysis. To help researchers keep this overview, we have created WESgraph (the Wind Energy System graph), a knowledge base for the wind farm domain, implemented as a graph database. It currently contains 1222 concepts and 1725 relations between them. This paper presents the structure of this graph database – content stored in nodes and the relationships between them – as a foundational ontology, which classifies the domain's concepts. This foundational ontology partitions the domain in two: a part describing physical aspects and a part describing mathematical and computational aspects. This paper also discusses a number of generally difficult cases that exist when adding content to such a knowledge base. This paper furthermore discusses the potential applications of WESgraph and illustrates its use for computation pathway discovery – the application that triggered its creation. It also contains a description of our practical experience with its design and use as well as our thoughts about the community use and management of this tool. ... Read more

Wind farms form an ever increasing share of the world’s electricity production capacity. But now that wind energy subsidy schemes are coming to an end, the cost per unit of electricity produced must become structurally lower than the fossil fuel-based power plants society wants replaced. Optimization of the farms’ design [1] is essential to achieving this. So the objective is to minimize the expected cost per unit of electricity. This objective depends on the expectation for the amount of electricity produced and for the farm’s cradle-to-grave costs. We here assume those costs to be fixed, so that the objective becomes maximization of expected electricity production. So we ignore aspects such as cable layout and their impact on the design. Effectively, we consider a fixed number of turbines whose positions can be chosen; this set of positions is called the wind farm layout. However, we must consider the period over which the electricity is produced: The farm lifetime production is important, but so is yearly production, as large inter-year variation poses financial risks. Therefore, we are studying the effect of inter-year variation of the wind resource. A site’s wind resource is represented by the joint probability distribution of wind directions and wind speeds encountered there over time. Specifically, we wish to create optimized layouts that are robust against this inter-year variation. For us—comparing layouts whose profiles of yearly expected production are undominated—, this means that we prefer layouts with a more constant relative performance. We have not fixed a formalization of this robustness concept, but would like to explore imprecise probabilistic options. Calculating the expected power production of a wind farm given a layout and wind resource is computationally expensive, because for each of the many required pairs of wind speed and wind direction a complex wake pattern must be computed. Also, when optimizing, the layout changes each iteration and computationally non-trivial constraints must be satisfied. Of course, considering yearly variation in wind resources yet again multiplies the computational effort required. Even when using simplified wake models runs, our robustness study would be practically infeasible using the classical optimization algorithms [2]. Therefore, we have designed a more efficient optimization approach. It (i) takes downwind, crosswind, and inter-turbine unit vectors, (ii) multiplies these by the power deficits caused by the wakes, and (iii) takes the expectation over the wind resource to create pseudo-gradients, to be used instead of real gradients. It has been shown to be competitive with other approaches in terms of optimal objective value, but substantially faster. We have used pseudo-gradient-based optimization to perform layout optimizations for a realistic site and for a set of wind resources that consists of 35 yearly ones, their average, one with a uniform wind resource, and one with just a single wind direction. Moreover, because wind resource normalization is not needed for the derivation of pseudo-gradients, we also considered the lower and upper envelopes of the 35 yearly wind resources as optimizer inputs. Some conclusions: (i) Inter-year wind resource variation is substantial, i.e., about half the probability mass shifts around. (ii) For the different layouts generated by our algorithm, the inter-year production differences for one layout are larger than differences between different layouts for one single year. (iii) The set of layouts with undominated production profiles is relatively small, mainly due to the fact that relative performance of layouts is mostly stable over the years. (iii) Among these, there exist robust layouts as we defined them, but in a trivial sense, as they are more optimal in general over all yearly wind resources considered. (iv) Therefore, there is no real trade-off achieved yet between robustness and optimality. Further investigation is warranted to determine (i) the impact of the optimization algorithm and its parameter settings, as the results appear to depend chaotically on these settings and (ii) the relevance of optimizing for a specific wind resource. ... Read more

Wind farm sites can have complex, disconnected shapes and may encompass exclusion zones. Even offshore this is the case, due to sea lanes, underwater pipelines and cables, wrecks, and unidentified buried objects. An example is Borssele Wind Farm Site IV1 (BWFS IV), which is pictured in Figure 11 as the collection of greencolored parcels. Within BWFS IV, as shown in Figure 21, there is an archaeologically significant wreck—red boat—and multiple magnetic anomalies— green dots—that indicate buried objects. Furthermore, regulations require turbines to be placed a certain safety distance—one rotor radius— inside the parcels. ... Read more

We investigate how to model indifference with choice functions. We take the coherence axioms for choice functions proposed by Seidenfeld, Schervisch and Kadane as a source of inspiration, but modify them to strengthen the connection with desirability. We discuss the properties of choice functions that are coherent under our modified set of axioms and the connection with desirability. Once this is in place, we present an axiomatisation of indifference in terms of desirability. On this we build our definition of indifference in terms of choice functions, which we discuss in some detail. ... Read more

We describe a probabilistic approach to design airfoils for wind energy applications. An analytical expression is derived for the probability of perturbations to the operational blade-section angle of attack. It includes the combined influence of wind shear, yaw-misalignment, and turbulence intensity. The theoretical fluctuations in angle of attack are validated against an aero-structural simulation of a 10 MW horizontal axis wind turbine, operating under different inflow conditions. Finally we incorporate the probabilistic approach into a multi-objective airfoil optimization problem, which is solved with a genetic algorithm. The results illustrate the compromise between airfoil performance for a specific angle of attack and robustness of airfoil performance over a large range of angle of attack fluctuations ... Read more

We present an interface for eliciting sets of acceptable gambles on a three-outcome possibility space, discuss an experiment conducted for testing this interface, and present the results of this experiment. Sets of acceptable gambles form a representation for imprecise probabilities that is close to human behavior and eliciting them directly may improve the quality of the resulting uncertainty
model. The experiment consisted of a betting competition for the 2014 FIFA World Cup: For each match bets were assigned based on the sets of acceptable gambles elicited from the participants. A new algorithm was designed for generating fair bets for assignment. Participant feedback indicated that improving the usability and transparency of the interface would ease the elicitation procedure. The experiment’s results underlined that imprecision is an essential aspect of real-life uncertainty modeling. ... Read more

The construction and management of an offshore wind farm involves many disciplines, e.g. meteorology and economics. It is hard for a single researcher to keep an overview of all the relevant concepts, models, and tools from these disciplines. Nevertheless, this is needed when performing integrated modeling or analysis in the offshore wind farm domain. To help researchers keep this overview, we present OWFgraph, a knowledge base for the offshore wind farm domain, implemented as a graph database that is meant to be open and ever-improving.
A graph database stores content in nodes and relationships. A relationship is a directed edge between two nodes. In our implementation, each of the nodes and relationships can have multiple properties, i.e., key-value pairs; moreover, nodes can have multiple labels, whereas relationships have only a single type. ... Read more