Wind Farm Layout Optimization Research Articles

Machine learning meets mathematical optimization to predict the optimal production of offshore wind parks

In this paper we propose a combination of Mathematical Optimization and Machine Learning to estimate the value of optimized solutions. In particular, we investigate if a machine, trained on a large number of optimized solutions, could accurately estimate the value of the optimized solution for new instances. In this paper we will focus on a specific application: the offshore wind farm layout optimization problem. Mixed Integer Programming models and other state-of-the-art optimization techniques, have been developed to solve this problem. Given the complexity of the problem and the big difference in production between optimized/non optimized solutions, it is not trivial to understand the potential value of a new site without running a complete optimization. This could be too time consuming if a lot of sites need to be evaluated, therefore we propose to use Machine Learning to quickly estimate the potential of new sites (i.e., to estimate the optimized production of a site without explicitly running the optimization). To do so, we trained and tested different Machine Learning models on a dataset of 3000+ optimized layouts found by the optimizer. Thanks to the close collaboration with a leading company in the energy sector, our model was trained on real-world data. Our results show that Machine Learning is able to efficiently estimate the value of optimized instances for the offshore wind farm layout problem.

Constrained multi-objective wind farm layout optimization: Novel constraint handling approach based on constraint programming

Abstract Wind farms are frequently located in proximity to human dwellings, natural habitats, and infrastructure making land use constraints and noise matters of increasing concern for all stakeholders. In this study, we perform a constrained multi-objective wind farm layout optimization considering energy and noise as objective functions, and considering land use constraints arising from landowner participation, environmental setbacks and proximity to existing infrastructure. A multi-objective, continuous variable Genetic Algorithm (NSGA-II) is combined with a novel constraint handling approach to solve the optimization problem. This constraint handling approach uses a combination of penalty functions and Constraint Programming to balance local and global exploration to find feasible solutions. The proposed approach is used to solve the wind farm layout optimization problem with different numbers of turbines and under different levels of land availability (constraint severity). Our results show increasing land availability and/or number of turbines, increases energy generation, noise production, and computational cost. Results also illustrate the potential of the proposed constraint handling approach to outperform existing methods in the context of evolutionary optimization, yielding better solutions at a lower computational cost.

Evolutionary computation for wind farm layout optimization

This paper presents the results of the second edition of the Wind Farm Layout Optimization Competition, which was held at the 22nd Genetic and Evolutionary Computation COnference (GECCO) in 2015. During this competition, competitors were tasked with optimizing the layouts of five generated wind farms based on a simplified cost of energy evaluation function of the wind farm layouts. Online and offline APIs were implemented in C++, Java, Matlab and Python for this competition to offer a common framework for the competitors. The top four approaches out of eight participating teams are presented in this paper and their results are compared. All of the competitors' algorithms use evolutionary computation, the research field of the conference at which the competition was held. Competitors were able to downscale the optimization problem size (number of parameters) by casting the wind farm layout problem as a geometric optimization problem. This strongly reduces the number of evaluations (limited in the scope of this competition) with extremely promising results.

Design of wind farm layout with non-uniform turbines using fitness difference based BBO

Biogeography-based optimization (BBO) is an emerging meta-heuristic algorithm. BBO is inspired from the migration of species from one island to another. This study presents the solution of the wind farm layout optimization problem with wind turbines having non-uniform hub heights and rotor radii using BBO and an improved version of BBO. This study proposes an improved version of BBO, Fitness Difference Based BBO (FD-BBO). FD-BBO is obtained by incorporating the concept of fitness differences in original BBO. First, in order to justify the superiority of FD-BBO over BBO, it is tested over 15 standard test problems of optimization. The numerical results of FD-BBO are compared with the original version of BBO and an advanced version of BBO, Blended BBO (BBBO). Through graphical and statistical analyses, FD-BBO is established to be an efficient and accurate algorithm. The BBO, BBBO and FD-BBO are than applied to solve the wind farm layout optimization problem. In the considered problem, not only the location of the wind turbines but hub heights and rotor radii are also taken as decision variables. Two cases of the problems are dealt: 26 turbines in the farm size of 2000 m ×2000 m and 30 turbines in the farm size of 2000 m ×2000 m. Numerical results are compared with earlier published results and that of original BBO and Blended BBO. It is found that FD-BBO is the better approach to solving the problem under consideration.

Differential Evolution With a New Encoding Mechanism for Optimizing Wind Farm Layout

This paper presents a differential evolution algorithm with a new encoding mechanism for efficiently solving the optimal layout of the wind farm, with the aim of maximizing the power output. In the modeling of the wind farm, the wake effects among different wind turbines are considered and the Weibull distribution is employed to estimate the wind speed distribution. In the process of evolution, a new encoding mechanism for the locations of wind turbines is designed based on the characteristics of the wind farm layout. This encoding mechanism is the first attempt to treat the location of each wind turbine as an individual. As a result, the whole population represents a layout. Compared with the traditional encoding, the advantages of this encoding mechanism are twofold: 1) the dimension of the search space is reduced to two, and 2) a crucial parameter (i.e., the population size) is eliminated. In addition, differential evolution serves as the search engine and the caching technique is adopted to enhance the computational efficiency. The comparative analysis between the proposed method and seven other state-of-the-art methods is conducted based on two wind scenarios. The experimental results indicate that the proposed method is able to obtain the best overall performance, in terms of the power output and execution time.

Offshore wind farm layout optimization using particle swarm optimization

This article explores the application of a wind farm layout optimization framework using a particle swarm optimizer to three benchmark test cases. The developed framework introduces an increased level of detail characterizing the impact that the wind farm layout can have on the levelized cost of energy by modelling the wind farm’s electrical infrastructure, annual energy production, and cost as functions of the wind farm layout. Using this framework, this paper explores the application of a particle swarm optimizer to the wind farm layout optimization problem considering three different levels of wind farm constraint faced by modern wind farm developers. The particle swarm optimizer is found to yield improvements in the layout with respect to the levelized cost of energy for the three benchmark cases when compared to two past studies. This highlights both applicability of the particle swarm optimizer to the problem and the ways in which a wind farm developer could make use of the present framework in the development and design of future wind farms.

Wind farm layout optimization to maximize total power production

With the rapid increase in energy demand, renewable energy has been considered as an alternative energy resource around the world. A new nonlinear mathematical model is developed in the presented study and a comparison is obtained with a mathematical modelling study from the literature. The results superior according to power generation under a single wind direction. Jensen’s wake decay model is used to state multiple wake effect among the turbines. The power production is maximized in terms of the minimization of wake effects. Mathematical formulations are represented and compared with the model from the literature. The generated layouts are presented and expected power among the Introduction turbines are significantly improved.

Optimal placement of wind turbines within a wind farm considering multi-directional wind speed using two-stage genetic algorithm

Most wind turbines within wind farms are set up to face a pre-determined wind direction. However, wind directions are intermittent in nature, leading to less electricity production capacity. This paper proposes an algorithm to solve the wind farm layout optimization problem considering multi-angular (MA) wind direction with the aim of maximizing the total power generated on wind farms and minimizing the cost of installation. A twostage genetic algorithm (GA) equipped with complementary sampling and uniform crossover is used to evolve a MA layout that will yield optimal output regardless of the wind direction. In the first stage, the optimal wind turbine layouts for 8 different major wind directions were determined while the second stage allows each of the previously determined layouts to compete and inter-breed so as to evolve an optimal MA wind farm layout. The proposed MA wind farm layout is thereafter compared to other layouts whose turbines have focused site specific wind turbine orientation. The results reveal that the proposed wind farm layout improves wind power production capacity with minimum cost of installation compared to the layouts with site specific wind turbine layouts. This paper will find application at the planning stage of wind farm.

Optimization of wind farm layout on a limited area

Optimization of wind farm layout on a limited area

Study on offshore wind farm layout optimization based on decommissioning strategy

In recent years, along with the first generation of wind power reaching retirement age, the high decommissioning cost arises with more and more attention all around the word. To reduce this huge cost, an innovative offshore wind farm layout optimization method based on decommissioning strategy is presented in this paper. In the optimization method, the decommissioning strategy means that the foundations can be reused after the retirement of the first generation of wind turbines, and then smaller second-generation wind turbines will be installed on the original foundations. The optimization process is based on the Multi-Population Genetic Algorithm (MPGA). A conceptual two-dimensional (2D) wake model is adopted to calculate wind losses caused by wake effect. The Cost of Energy (COE) is regarded as the criteria to judge the effectiveness of this new method. The way to estimate costs will also be introduced in this study. Finally, a case study in Waglan sea area in Hong Kong is analyzed and discussed. From the case results, Hong Kong is an ideal region to develop the offshore wind industry, and the proposed optimization method can reduce the COE down to 1.02 HK$/kWh.

Economics- and Reliability-Based Design for an Offshore Wind Farm

This study examines the optimal layout of an offshore wind farm for a fixed number of wind turbines (WTs) and a fixed area of coverage. After the optimal layout of the turbines is determined, the topology of the cable connections is optimized. The wind decay that is associated with the wake effect is considered and the charged system search algorithm is utilized to obtain the optimal WT layout that maximizes the power output of the wind farm. The Wind Atlas Analysis and Application Program software is utilized to verify the optimality of the layout. Mixed integer linear programming is utilized to optimize the topology of radial cable connections. The system reliabilities of the proposed layout and the traditional regular layout are considered. Finally, the optimal wind-farm layout that maximizes wind power output, minimizes cable cost, and maximizes reliability is obtained.

Design optimization of a wind farm layout for maximum wind energy capture: A new constructive approach

Wind energy is becoming an attractive source of clean energy. However, this type of power source is subject to power reductions due to losses in wind energy conversion system and to frequent changes in wind velocity. For that reason, the important phase of a wind farm design is solving the wind farm layout optimization problem, which consists in optimally positioning the turbines within the wind farm so that the wake effects are minimized and therefore the expected power production is maximized. This problem has been receiving increasing attention from the scientific community. In this article, a mathematical optimization scheme is employed to optimize the locations of wind turbines with respect to maximizing the wind farm power production. To formulate the mathematical optimization problem, we used Jensen’s wake model. We calculate the wake loss and express the expected wind farm power as a differentiable function in terms of the locations of the wind turbines. Furthermore, we develop a new constructive approach to find the best solution to the wind turbines placement problem. Finally, our results are compared with those in some other ealier studies.

Decomposition based multi-objective evolutionary algorithm for windfarm layout optimization

An efficient windfarm layout to harness maximum power out of the wind is highly desirable from technical and commercial perspectives. A bit of flexibility on layout gives leeway to the designer of windfarm in planning facilities for erection, installation and future maintenance. This paper proposes an approach where several options of optimized usable windfarm layouts can be obtained in a single run of decomposition based multi-objective evolutionary algorithm (MOEA/D). A set of Pareto optimal vectors is obtained with objective as maximum output power at minimum wake loss i.e. at maximum efficiency. Maximization of both output power and windfarm efficiency are set as two objectives for optimization. The objectives thus formulated ensure that in any single Pareto optimal solution the number of turbines used are placed at most optimum locations in the windfarm to extract maximum power available in the wind. Case studies with actual manufacturer data for wind turbines of same as well as different hub heights and with realistic wind data are performed under the scope of this research study.

Three-dimensional structure of wind turbine wakes as measured by scanning lidar

Abstract. The lower wind speeds and increased turbulence that are characteristic of turbine wakes have considerable consequences on large wind farms: turbines located downwind generate less power and experience increased turbulent loads. The structures of wakes and their downwind impacts are sensitive to wind speed and atmospheric variability. Wake characterization can provide important insights for turbine layout optimization in view of decreasing the cost of wind energy. The CWEX-13 field campaign, which took place between June and September 2013 in a wind farm in Iowa, was designed to explore the interaction of multiple wakes in a range of atmospheric stability conditions. Based on lidar wind measurements, we extend, present, and apply a quantitative algorithm to assess wake parameters such as the velocity deficits, the size of the wake boundaries, and the location of the wake centerlines. We focus on wakes from a row of four turbines at the leading edge of the wind farm to explore variations between wakes from the edge of the row (outer wakes) and those from turbines in the center of the row (inner wakes). Using multiple horizontal scans at different elevations, a three-dimensional structure of wakes from the row of turbines can be created. Wakes erode very quickly during unstable conditions and can in fact be detected primarily in stable conditions in the conditions measured here. During stable conditions, important differences emerge between the wakes of inner turbines and the wakes of outer turbines. Further, the strong wind veer associated with stable conditions results in a stretching of the wake structures, and this stretching manifests differently for inner and outer wakes. These insights can be incorporated into low-order wake models for wind farm layout optimization or for wind power forecasting.

Trading off sound pressure level and average power production for wind farm layout optimization

This research explores the trade-offs between a wind farm's average power production and noise impact on nearby observers. Two specific wind farm designs were studied and optimized using the FLORIS wake model and an acoustic model based on semi-empirical turbine noise calculations. It was found in the two wind farms that the average power production could be increased, up to 8.01% in one and 3.63% in the other, ignoring sound level considerations. Including a noise restriction in the optimization had a minimal impact on the optimal average power production within about a five-decibel range. Past this range, sound limitations decreased the wind farm's power production significantly. By analyzing average power production and sound pressure level together, we can take advantage of the multi-modality of the optimization to find solutions were noise impact can be improved with an insignificant effect on power production.

Decomposition based multi-objective optimization to simultaneously determine the number and the optimum locations of wind turbines in a wind farm

Wind energy is one of the most progressive types of renewable energies deployed using wind turbines, which convert wind power into electrical energy. Various methodologies and layouts have been proposed to determine the optimal layout (numbers and locations) of wind turbines inside a wind farm to extract maximum energy. However, limited availability of land area has resulted in the construction of these wind farms near to human habitats causing a negative impact on human health. Compared to other factors, noise has become an immense concern for wind farm designers, as it needs to be constrained within the mandatory limits. Using a well-established wake model and ISO-9613-2 noise calculation, this study performs a wind farm layout optimization (WFLO) based on a multi-objective trade-off between minimization of noise propagation and maximization of energy generation. A novel hybrid methodology is proposed as a combination of proposed probabilistic variable decomposed multi-objective evolutionary algorithm (VdRBNSGA-II) and a newly developed gradient-based non-dominated normalized normal constraint (nD-NNC) method. As opposed to previous works, generated non-dominated front provides various alternative energy-noise solutions along with an additional information on turbine layouts, which allows a decision maker to select among different competing solutions based on the existing noise and other regulations.

Wind farm power production in the changing wind: Robustness quantification and layout optimization

Wind farms operate often in the changing wind. The wind condition variations in a wide range of time scales lead to the variability of wind farms’ power production. This imposes a major challenge to the power system operators who are facing a higher and higher penetration level of wind power. Thus, wind farm developers/owners need to take the variability into consideration in the designing/planning stage, in addition to the conventional main objective of maximizing the expected power output under a fixed wind distribution. In this study, we first propose a new metric to evaluate the variability of wind power based on the characteristics of the wind farm and its local wind conditions. Then a series of robustness metrics are proposed to quantify wind farm’s ability to produce power with high mean value and low variability under changing wind, considering both short-term and long-term wind condition variations. Based on these metrics, wind farm layout optimization is performed to maximize the robustness of a real offshore wind farm in Denmark. The results demonstrate that the robustness metrics are more flexible and complete than the conventional metrics for characterizing wind farm power production, such as mean power output or wind power variability alone, and it is feasible to design wind farms to produce power with high mean value and low variability.

Application of an offshore wind farm layout optimization methodology at Middelgrunden wind farm

This article explores the application of a wind farm layout evaluation function and layout optimization framework to Middelgrunden wind farm in Denmark. This framework has been built considering the interests of wind farm developers in order to aid in the planning of future offshore wind farms using the UK Round 3 wind farms as a point of reference to calibrate the model. The present work applies the developed evaluation tool to estimate the cost, energy production, and the levelized cost of energy for the existing as-built layout at Middelgrunden wind farm; comparing these against the cost and energy production reported by the wind farm operator. From here, new layouts have then been designed using either a genetic algorithm or a particle swarm optimizer. This study has found that both optimization algorithms are capable of identifying layouts with reduced levelized cost of energy compared to the existing layout while still considering the specific conditions and constraints at this site and those typical of future projects. Reductions in levelized cost of energy such as this can result in significant savings over the lifetime of the project thereby highlighting the need for including new advanced methods to wind farm layout design.

A tight upper bound for quadratic knapsack problems in grid-based wind farm layout optimization

ABSTRACTThe 0-1 quadratic knapsack problem (QKP) in wind farm layout optimization models possible turbine locations as nodes, and power loss due to wake effects between pairs of turbines as edges in a complete graph. The goal is to select up to a certain number of turbine locations such that the sum of selected node and edge coefficients is maximized. Finding the optimal solution to the QKP is difficult in general, but it is possible to obtain a tight upper bound on the QKP's optimal value which facilitates the use of heuristics to solve QKPs by giving a good estimate of the optimality gap of any feasible solution. This article applies an upper bound method that is especially well-suited to QKPs in wind farm layout optimization due to certain features of the formulation that reduce the computational complexity of calculating the upper bound. The usefulness of the upper bound was demonstrated by assessing the performance of the greedy algorithm for solving QKPs in wind farm layout optimization. The results show that the greedy algorithm produces good solutions within 4% of the optimal value for small to medium sized problems considered in this article.

A novel geometric pattern-based approach to maximize power output of a wind farm

The placement of wind turbines is crucial for a wind farm because the power generation of wind turbine is greatly affected by the wake effect produced by the upstream turbines. The optimum placement of wind turbines in a wind farm will give the maximum total power output. The effective methodology is imperative to place turbines in such a way that effect of the wake is minimum on a performance of turbines and has a proper utilization of the wind farm area. The present study proposes a novel approach based on the geometrical pattern-inspired placement methodology to locate wind turbines and maximize the power output of a wind farm. In the proposed approach, various geometrical patterns made from circle, hexagon, pentagon and triangle are considered for the numerical investigation. Further, wind behavior is modeled for uniform and variable wind speed from all directions. The present approach is also experimented numerically with and without land availability constraints. Heat transfer search algorithm is used to solve the wind farm layout optimization problem with the proposed approach and the results are compared with other approaches available in the literature. Results show that the proposed geometrical pattern-based approach produces the higher power generation (~4–8%) compared to other approaches for the variable wind speed scenario. In the case of land availability constraints, about 4% higher power generation compared to the grid-based approach is achieved. In order to place turbines with an optimum performance of a wind farm, the present approach can be helpful to wind farm developers.