Wind Farm Layout Optimization Problem Research Articles

Towards a general tool chain integration platform for multi-disciplinary analysis and optimization in wind energy

To enable easier uptake and flexible usage for the wind energy community, a general tool chain integration platform for multi-disciplinary analysis and optimization, TopDesign, is proposed and developed. This work describes its concept and the initial implementation. The platform is written in Python and provided as an open source framework. The design of this platform puts emphasis on flexibility, usability and extensibility. General model classes with standard interfaces, which can wrap custom tools/models in different formats based on different programming languages, will be provided together with examples that are easy to understand and modify. Coupling tools/models into a system thus becomes an easy task of connecting models by inputs and outputs and defining workflow with a directed graph. To demonstrate the usage of the proposed platform, we implement a wind farm evaluation system by coupling the PyWake model, the FLORIS model and self-written constraint models in the platform and apply it in solving wind farm layout optimization problems with two algorithms, as implemented in an in-house optimization Python library. A case study for a wind farm composed of 9 turbines shows the potential of the proposed platform and methodology.

Wind Farm Layout Optimization Subject to Cable Cost, Hub Height, and a Feasible 3D Gaussian Wake Model Implementation

We address the Wind Farm Layout Optimization (WFLO) problem and tackle the optimal placement of several turbines within a specific (wind farm) area by incorporating additional aspects of an economically driven target function. With this, we contribute three refinements for WFLO research: First, while many research contributions optimize the turbines’ locations subject to maximum energy production or energy efficiency, we instead pursue a strategy of maximizing a profit objective. This enables us to incorporate inner-farm wiring costs (underground cable installation). For this, we explore the impact of using MSTs (Minimum Spanning Trees) and adding junction (so-called “Steiner”) points to the terrain plane. Second, while most research focuses on finding optimal x and y coordinates (i.e., address two-dimensional turbine placement), we also optimize the turbines’ hub heights z. Third, we also provide a software implementation of the Gaussian wake model. The latter finds entrance to the open-source WFLO research framework that comes as package <strong>wflo</strong> for statistical software R. We find that taking wiring cost into account may lead to very different turbine placements, however, increasing overall profit significantly. Allowing the optimizer to vary the hub heights may have an ambiguous impact on the wind farm profit.

Gradient-based wind farm layout optimization with inclusion and exclusion zones

Abstract. Wind farm layout optimization is usually subjected to boundary constraints of irregular shapes. The analytical expressions of these shapes are rarely available, and, consequently, it can be challenging to include them in the mathematical formulation of the problem. This paper presents a new methodology to integrate multiple disconnected and irregular domain boundaries in wind farm layout optimization problems. The method relies on the analytical gradients of the distances between wind turbine locations and boundaries, which are represented by polygons. This parameterized representation of boundary locations allows for a continuous optimization formulation. A limitation of the method, if combined with gradient-based solvers, is that wind turbines are placed within the nearest polygons when the optimization is started in order to satisfy the boundary constraints; thus the allocation of wind turbines per polygon is highly dependent on the initial guess. To overcome this and improve the quality of the solutions, two independent strategies are proposed. A case study is presented to demonstrate the applicability of the method and the proposed strategies. In this study, a wind farm layout is optimized in order to maximize the annual energy production (AEP) in a non-uniform wind resource site. The problem is constrained by the minimum distance between wind turbines and five irregular polygon boundaries, defined as inclusion zones. Initial guesses are used to instantiate the optimization problem, which is solved following three independent approaches: (1) a baseline approach that uses a gradient-based solver; (2) approach 1 combined with the relaxation of the boundaries, which allows for a better design space exploration; and (3) the application of a heuristic algorithm, “smart-start”, prior to the gradient-based optimization, improving the allocation of wind turbines within the inclusion polygons based on the potential wind resource and the available area. The results show that the relaxation of boundaries combined with a gradient-based solver achieves on average +10.2 % of AEP over the baseline, whilst the smart-start algorithm, combined with a gradient-based solver, finds on average +20.5 % of AEP with respect to the baseline and +9.4 % of AEP with respect to the relaxation strategy.

MORSA: Multi-objective reptile search algorithm based on elite non-dominated sorting and grid indexing mechanism for wind farm layout optimization problem

The proposal of the wind farm layout optimization (WFLO) problem aims to better utilize wind energy. A multi-objective reptile search algorithm (MORSA) based on elite non-dominated sorting and grid indexing mechanism was proposed to solve the multi-objective optimization problem of wind farm layout under the Jansen wake model to maximize power generation while minimizing costs. Firstly, the elite non-dominated sorting method was used to sort the population, and then the crowding distance method was used to maintain the diversity between the optimal sets. By calculating the crowding distance, the same level of non-dominated populations are sorted. Then, the grid index mechanism is added to the archive for selection and deletion. Leaders can use the roulette wheel to select and delete some solutions in high-density grids. By obtaining the optimal Pareto solution set while maintaining the diversity of the population, the effectiveness of solving multi-objective optimization problems is improved. The improved algorithm solves the WFLO problem based on the Jansen wake model by using two different initial self-flow winds for performance testing while considering the effects of single wake and multiple wake with or without partial wake occlusion. The performance of the WFLO (output power and cost) was compared without considering wake obstruction, MORSA can obtain the minimum turbine cost of 26.3601 and the maximum power generation of 2.3078E-08 with a single wake flow of 16 m/s. The experimental results show that the proposed MORSA has better convergence and applicability, and has shown good results in multi-objective layout optimization of wind farms.

Optimal placement of fixed hub height wind turbines in a wind farm using twin archive guided decomposition based multi-objective evolutionary algorithm

Harnessing maximum wind energy's power output and efficiency is vital to combat environmental challenges tied to conventional fossil fuels. Wind power's cost-effectiveness and emission reduction potential underscore its significance. Efficient wind farm layout plays a pivotal role, both technically and commercially. Evolutionary algorithms show their potential while solving multi-objective wind farm layout optimization problems. However, due to the large-scale nature of the problems, existing algorithms are getting trapped into local optima and fail to explore the search space. To address this, the TAG-DMOEA algorithm is upgraded with an adaptive offspring strategy (AOG) for better exploration. The proposed algorithm is employed on a wind farm layout problem with real-time data of wind speed and direction from two different locations. Unlike mixed hub heights, fixed hub heights such as 60, 67, and 78 m are adopted to conduct the case studies at two potential locations with real-time statistical data for the investigation of improved results. The results obtained by TAG-DMOEA-AOG on six cases are compared with 10 state-of-the-art algorithms. Statistical tests such as Friedman test and Wilcoxon signed rank test along with post hoc analysis (Nemenyi test) confirmed the superiority of the TAG-DMOEA-AOG on all cases of the considered multi-objective wind farm layout optimization problem.

A teaching-learning-based optimization algorithm with reinforcement learning to address wind farm layout optimization problem

As the global demand for renewable energy continues to rise, wind energy has received widespread attention as an eco-friendly energy source. Wind power generation is regarded as one of the key means to reduce carbon emissions and achieve sustainable development. Usually, a mass of turbines works together to produce electricity in a wind farm. However, downstream turbines will inevitably be influenced by the wake generated by upstream turbines, resulting in unused wind energy being lost. To reduce the negative effects of the wake, maximization of wind farm output power, and minimization of wind farm cost, a teaching-learning-based optimization algorithm with reinforcement learning is proposed in this paper. The improvements of the proposed algorithm mainly include the following three points: i) the original serial structure of the algorithm is changed to a parallel structure to accelerate the convergence and improve the efficiency of the algorithm. ii) the parameter F, which is adjusted by RL, is proposed to adjust the selection of the updating phase due to the design of a parallel structure. iii) in the modified learner phase, an individual is added to participate in the update, and a selection probability is proposed to improve the ability of the algorithm to retain the information of superior individuals. To study the performance of the modified algorithm, it was first tested against 10 other advanced algorithms on a benchmark testing suite. They then ran numerical experiments on four hypothetical wind farm cases under two simulated wind conditions. Finally, the superiority of improved algorithm over others and the effectiveness of addressing wind farm layout problem are demonstrated by experimental results.

A neighborhood search integer programming approach for wind farm layout optimization

Abstract. Two models and a heuristic algorithm to address the wind farm layout optimization problem are presented. The models are linear integer programming formulations where candidate locations of wind turbines are described by binary variables. One formulation considers an approximation of the power curve by means of a stepwise constant function. The other model is based on a power-curve-free model where minimization of a measure closely related to total wind speed deficit is optimized. A special-purpose neighborhood search heuristic wraps these formulations with increasing tractability and effectiveness compared to the full model that is not contained in the heuristic. The heuristic iteratively searches for neighborhoods around the incumbent using a branch-and-cut algorithm. The number of candidate locations and neighborhood sizes are adjusted adaptively. Numerical results on a set of publicly available benchmark problems indicate that a proxy for total wind speed deficit as an objective is a functional approach, since high-quality solutions of the metric of annual energy production are obtained when using the latter function as an substitute objective. Furthermore, the proposed heuristic is able to provide good results compared to a large set of distinctive approaches that consider the turbine positions as continuous variables.

A comparison of eight optimization methods applied to a wind farm layout optimization problem

Abstract. Selecting a wind farm layout optimization method is difficult. Comparisons between optimization methods in different papers can be uncertain due to the difficulty of exactly reproducing the objective function. Comparisons by just a few authors in one paper can be uncertain if the authors do not have experience using each algorithm. In this work we provide an algorithm comparison for a wind farm layout optimization case study between eight optimization methods applied, or directed, by researchers who developed those algorithms or who had other experience using them. We provided the objective function to each researcher to avoid ambiguity about relative performance due to a difference in objective function. While these comparisons are not perfect, we try to treat each algorithm more fairly by having researchers with experience using each algorithm apply each algorithm and by having a common objective function provided for analysis. The case study is from the International Energy Association (IEA) Wind Task 37, based on the Borssele III and IV wind farms with 81 turbines. Of particular interest in this case study is the presence of disconnected boundary regions and concave boundary features. The optimization methods studied represent a wide range of approaches, including gradient-free, gradient-based, and hybrid methods; discrete and continuous problem formulations; single-run and multi-start approaches; and mathematical and heuristic algorithms. We provide descriptions and references (where applicable) for each optimization method, as well as lists of pros and cons, to help readers determine an appropriate method for their use case. All the optimization methods perform similarly, with optimized wake loss values between 15.48 % and 15.70 % as compared to 17.28 % for the unoptimized provided layout. Each of the layouts found were different, but all layouts exhibited similar characteristics. Strong similarities across all the layouts include tightly packing wind turbines along the outer borders, loosely spacing turbines in the internal regions, and allocating similar numbers of turbines to each discrete boundary region. The best layout by annual energy production (AEP) was found using a new sequential allocation method, discrete exploration-based optimization (DEBO). Based on the results in this study, it appears that using an optimization algorithm can significantly improve wind farm performance, but there are many optimization methods that can perform well on the wind farm layout optimization problem, given that they are applied correctly.

Combined layout and cable optimization of offshore wind farms

Reducing wind energy costs is a crucial goal to promote renewable energy and reduce dependencies on fossil fuels, both to fight climate change and to increase energy independence. Two main optimization problems arise during the design of offshore wind farms: the Wind Farm Layout Optimization (WFLO) problem and the Wind Farm Cable Routing (WFCR) problem. The goal of WFLO is to find the optimal turbine locations within a given area to maximize revenues from energy production minus construction costs. The goal of WFCR is to minimize the costs of subsea cables that transfer the electricity produced by turbines. Traditionally, the two NP-hard problems have been studied separately and are solved sequentially, despite being strongly related. The output of WFLO defines the input to WFCR, and their goals are opposing: while larger distances between turbines have a positive effect on WFLO due to reduced wake losses, they negatively impact the cable costs in WFCR. Hence, we study the combined optimization problem, unifying the two problems. We propose a novel heuristic that uses a combined local search to modify solutions of WFLO and WFCR simultaneously. While the combined approach is more computationally demanding than the sequential approach, the proposed method solves industry-scale problems and improves up to 12 million Euro the Net Present Value (NPV) of wind parks, particularly when the energy density is low. Furthermore, the combined approach reduces the up-front investment costs by up to 10%, significantly reducing investment risks, and enabling a faster expansion of wind energy.

RANS-AD based ANN surrogate model for wind turbine wake deficits

Inside wind farms, wake effects are the primary source of turbine interactions, and as such, they constitute one of the most important aspects of wind farm operations. The two most widespread methods for calculating the wind farm wake flow are computational fluid dynamics (CFD) methods and engineering models. Both methods have drawbacks; CFD methods can be very accurate but are computationally expensive. Vice versa, engineering models sacrifice accuracy by simplifying the physics, thereby improving computational efficiency.In cases where many evaluations of the flow are needed, this trade-off is a hindrance. One such case is wind farm layout optimization problems. It has been shown that the estimation of wake flows can be improved by surrogate modeling. Recently, Artificial Neural Networks (ANN) have been demonstrated to predict accurate wakes over a mesh. In this work, a new mesh-free ANN-based wake model is proposed. This new model can predict the flow everywhere in the domain, and as it employs smooth activation functions, it is suitable for gradient-based optimization.Two ANNs were trained with data generated by Reynolds-Averaged Navier-Stokes with Actuator Disc simulations for several yaw angles. The first ANN predicts streamwise wake velocity induction/deficit, the second ANN predicts added wake turbulence intensity. Both ANNs predict with a low error.

A chaotic local search-based LSHADE with enhanced memory storage mechanism for wind farm layout optimization

The search for clean energy alternatives to fossil fuels has been a major effort by researchers all over the world. Wind energy is one of the most optimal choices because of its cleanliness and renewability. However, the existence of the wake effect leads to a decrease in conversion efficiency. Finding the best wind turbine layout has become an important factor in the wind power generation system. Inspired by the excellent optimization capability of meta-heuristic algorithms, they are increasingly applied to solve complex constraints and design objectives in the wind farm layout optimization problems. It is reported that LSHADE, which is an advanced variant of differential evolution, provides a more efficient configuration of wind turbines than other meta-heuristic algorithms. This motivates us to conduct research in this direction and design an effective meta-heuristic algorithm with a chaotic local search strategy and an enhanced memory storage mechanism, which contributes to the reduction of global carbon emissions. The proposed new algorithm is called CLSHADE. The validity of the proposed algorithm is verified by the simulation of different constraints and wind field distribution profiles. Compared to four state-of-the-art meta-heuristic algorithms, the average conversion rate of the proposed algorithm is 92.87%, 89.13%, and 96.86% for three wind distribution profiles, respectively. The results show that the proposed algorithm has superiorities and effectiveness in wind farm layout optimization.

An improved spherical evolution with enhanced exploration capabilities to address wind farm layout optimization problem

The utilization of metaheuristics for optimizing wind farm layouts (WFLOP) has emerged as a popular research area in recent years. However, effectively screening and improving metaheuristics to obtain optimal layouts remain a challenging task. Traditional metaheuristic screening methods require testing numerous algorithms, resulting in high computational resource consumption and trial-and-error costs due to the lack of theoretical guidance. To overcome this challenge, this study proposes a complex network-based metaheuristic screening method. Population interaction networks are utilized to classify metaheuristics into two categories: biased exploitation and biased exploration. The results of several metaheuristics on WFLOP suggest that exploration-biased algorithms generally outperform exploitation-biased ones. This discovery holds great significance as it has the potential to predict the performance of various algorithms on WFLOP to a certain degree. Additionally, it provides valuable suggestions for algorithm selection and improvement. Building upon this new methodology, we screen and improve the spherical evolution algorithm to enhance its exploration capabilities. Experimental results demonstrate that the improved spherical evolution algorithm significantly outperforms its competitors on WFLOP.

A SPATIAL PLANNING SUPPORT SYSTEM FOR WIND FARM CONSTRUCTION WITH MACRO AND MICRO PERSPECTIVES

Abstract. Wind energy is well-known Renewable energy that contributes to countries achieving their sustainable development goals, so governments have planned to increase electricity generation from wind energy in recent years. Selecting suitable places for installing wind farms is one of the most challenging parts of wind energy projects because of the necessity of identifying various parameters, which is considered a site selection problem and needs spatial planning to solve. Furthermore, in constructing a wind farm, finding the optimum placement of wind turbines, known as the wind farm layout optimization (WFLO) problem, is crucial for obtaining maximum total power capacity while minimizing the number of turbines installed. In this research, the analysis is divided into two macro and micro levels to find an efficient and comprehensive approach. In the first level, after removing the restricted area, the MCDM method is used to find the most suitable sites, considering economic, social, and environmental criteria. After selecting one of the most suitable areas located in the middle of Alborz province, the GA algorithm as a meta-heuristic method is employed to solve the WFLO problem at the micro level. The essential criterion in this level is the wake effect among turbines which is simulated according to the Jensen model. As a test case, the selected area was subdivided into 144 cells that, after micro siting, 28 V47-660-45 turbines were placed, which could have a total power of 8732.283 kW capacity.

Progressive global best artificial bee colony algorithm for wind farm layout optimisation problem

Progressive global best artificial bee colony algorithm for wind farm layout optimisation problem

Progressive Global Best Artificial Bee Colony Algorithm For Wind Farm Layout Optimization Problem

Progressive Global Best Artificial Bee Colony Algorithm For Wind Farm Layout Optimization Problem

Discrete complex-valued code pathfinder algorithm for wind farm layout optimization problem

• A discrete complex-valued code pathfinder algorithm (DCPFA) has been proposed. • The DCPFA algorithm’s exploration and exploitation abilities were improved. • The DCPFA is applied to solve wind farm layout optimization (WFLO) problem. • The experimental results show that DCPFA found solutions have lower cost values per unit of power. In wind farm planning, it is necessary to optimize the location of turbines to reduce the influence of eddy currents between each other and generate more energy. This problem is also transformed into a discrete optimization problem, it is named wind farm layout optimization (WFLO) problem, to solve this optimization problem we can obtain the optimal turbine placement scheme. With the complexity of wind condition in WFLO problem increases, it becomes very difficult to solve, so more and more researchers use metaheuristic algorithms to solve this problem. Improve the solution accuracy of the WFLO problem, it will increase renewable energy use and lowering carbon emissions. In order to improve the solution accuracy of WFLO problem, a discrete complex-valued code pathfinder algorithm (DCPFA) has been proposed in this paper, and used to solve the WFLO problem. In DCPFA, the algorithm’s exploration ability was improved, and the algorithm achieves a balance between exploration and exploitation. To test the performance of DCPFA in solving the WFLO problem, two complex wind conditions in wind farms are simulated. Comparing the results with other famous metaheuristic optimization algorithms and recently published literature, the DCPFA found a solution that will have lower cost values per unit of power, such as DCPFA’s solution in wind condition (1) can output 34120(KW), it is bigger than RSA’s 32498(KW) and GA’s 32038(KW), DCPFA’s solution in wind condition (2) can output 19375(KW), it is bigger than SSA’s 17781(KW) and BPSO-TVAV’s 15796 (KW). More importantly, in the objective function (Cost/KW), DCPFA is also ranked first in two wind condition. According to the experimental results, it can be explained that DCPFA’s effectiveness and robustness in solving WFLO problems.

An adaptive replacement strategy-incorporated particle swarm optimizer for wind farm layout optimization

The wind farm layout optimization (WFLO) aims to maximize power generation of a wind farm by optimizing the location of wind turbines. Traditional mathematical methods cannot provide a satisfactory solution for a wind farm due to the high complexity of the problem. Meta-heuristic algorithms have been used to optimize it. Particularly, genetic algorithms (GA) have been widely used and obtained success in WFLO problems. However, GA still suffers from the issues of insufficient optimization efficiency. In this study, a genetic learning particle swarm optimization with an adaptive strategy, termed AGPSO, is proposed to optimize WFLO problems. The strategy adaptively adjusts the location of the worst turbine to improve the conversion efficiency of a wind farm. Four wind scenarios, including single wind speed with single wind direction, single wind speed with uniform multiple wind directions, single wind speed with nonuniform multiple directions, and multiple wind speeds with multiple wind directions scenarios ones, are utilized to verify the effectiveness of AGPSO and the effect of different wind scenarios for it. Twelve constraints and three different scales are used to further verify the robustness of AGPSO and the effect of wind turbine location on WFLO problems. Extensive numerical experiment results demonstrate that AGPSO performs significantly better than other twelve state-of-the-art competitors in terms of conversion efficiency under different wind farms, wind scenarios, and constraints. AGPSO obtains the best average of 89.92%, 92.90%, 95.39%, and 90.75% conversion efficiency in a wind farm with 25 wind turbines under four wind scenarios, respectively.

An innovative method of investigating the wind turbine’s inflow speed in a wind farm due to the multiple wake effect issue

In order to produce more power, several turbines are grouped in a wind farm, resulting in the wake interaction. Therefore, in a complex wind farm layout with multiple wakes affecting, determining the turbine’s velocity is essential. It is especially critical in solving wind farm layout optimization problems since it takes plenty of testing layouts to find the optimal one. This article presents an innovative method that calculates the turbine’s inflow speed through the wake interactions in a wind farm. As its main feature, the proposed method generates mesh on every turbine and calculates each cell’s speed based on the upstream wake, which affects it. Then the mass conservation applies to all cells, and an equivalent velocity for the turbine is obtained. This procedure is implemented for a hypothetical wind farm to calculate the wind farm’s output power for three different wind directions. Moreover, the gained energy is optimized through the PSO algorithm to discover the optimal wind farm layout. The proposed method is also tested on the Horns Rev offshore wind farm as the validation case, showing that it is compatible with the experimental and numerical results.

Topology optimization of wind farm layouts

A novel approach for the solution of the wind farm layout optimization problem is presented. The annual energy production is maximized with constraints on the minimum and maximum number of wind turbines placed, and on the minimum spacing between the wind turbines. The proposed approach relies on a density-based topology optimization method, where continuous density variables varying between zero and one are assigned to each potential wind turbine location. A wind turbine exists if its associated variable equals one, otherwise it does not exist if the associated variable is zero. Intermediate values of the density variables are penalized with interpolation schemes traditionally used in the context of multi-material structural topology optimization. The penalized intermediate values of the design variables become uneconomical and the optimization algorithm is implicitly pushed towards a preference of crisp 0–1 final values. The optimization problem is solved with a gradient-based algorithm based on first-order information. Because of the proposed problem formulation, the functions involved are formulated explicitly in terms of the design variables and their analytical gradients can be calculated directly. The numerical results highlight the capability of the proposed approach in finding optimized wind farm layouts with small computational resources and time.

A Comparative Study of Multi-Stage Approaches for Wind Farm Layout Optimization

Abstract The wind farm layout optimization (WFLO) problem is a complex and nonconvex optimization problem. Even though many different heuristic algorithms and mathematical programming methods have been tested and discussed, there is no consensus about which algorithm is the most suitable approach for solving WFLO problems. Every algorithm presents its own advantages and disadvantages in solving different optimization problems; thus, multi-stage approaches may combine the advantages of multiple algorithms and offer superior performance. One multi-stage approach used for solving WFLO problems is to apply an algorithm in the first stage to produce an optimized layout which serves as the initial condition for a second-stage algorithm to perform further refinement. This paper presents a comparison between two types of multi-stage methods: the Heuristic-Gradient-based (H-G) model which consists of a heuristic algorithm in stage 1 and a gradient-based algorithm in stage 2 and the Discrete-Continuous (D-C) model which consists of a heuristic algorithm in the discrete scheme in stage 1 and an algorithm in the continuous scheme in stage 2. Annual energy production (AEP) is used as the objective function while the computational time associated with each approach is documented. Three scenarios are investigated in this paper with different complexity in the wind conditions. It was observed that the D-C models provide the optimal solutions with an average of 0.67% higher AEP and an average of 6.2% lower computational time in comparison with the H-G models. The results from this study provide a basis for selecting a proper optimization algorithm for solving WFLO problems which can lead to a significant increase in the overall annual energy production and a large reduction in computational time.