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 two-stage 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.     

Integrated offshore wind farm design: Optimizing micro‐siting and cable layout simultaneously

Electrical layout and turbine placement are key design decisions in offshore wind farm projects. Increased turbine spacing minimizes the energy losses caused by wake interactions between turbines but requires costlier cables with higher rates of failure. Simultaneous micro‐siting and electrical layout optimization are required to realize all possible savings. The problem is complex, because electrical layout optimization is a combinatorial problem and the computational fluid‐dynamics calculations to approximate wake effects are impossible to integrate into classical optimization. This means that state‐of‐the‐art methods do not generally consider simultaneous optimization and resort to approximations instead. We extend an existing model that successfully optimizes cable design to simultaneously consider micro‐siting. We use Jensen's equations to approximate the wake effect in an efficient manner, calibrating it with years of mast data. The wake effects are precalculated and introduced into the optimization problem. We solve simultaneously for turbine spacing and cable layout, exploiting the tradeoffs between these wind farm features. We use the Barrow Offshore Wind Farm as a case study to demonstrate realizable savings up to 6 MEUR over the lifetime of the plant, although it is possible that unforeseen design constraints have implications for whether the savings seen in our model are fully realizable in the real world. In addition, the model provides insights on the effects of turbine spacing that can be used to simplify the design process or to support negotiations for surface concession at the earlier stages of a project.     

A novel control strategy approach to optimally design a wind farm layout

Recently wind energy has become one of the most important alternative energy sources and is growing at a rapid rate because of its renewability and abundancy. For the clustered wind turbines in a wind farm, significant wind power losses have been observed due to wake interactions of the air flow induced by the upstream turbines to the downstream turbines. One approach to reduce power losses caused by the wake interactions is through the optimization of wind farm layout, which determine the wind turbine positions and control strategy, which determine the wind turbine operations. In this paper, a new approach named simultaneous layout plus control optimization is developed. The effectiveness is studied by comparison to two other approaches (layout optimization and control optimization). The results of different optimizations, using both grid based and unrestricted coordinate wind farm design methods, are compared for both ideal and realistic wind conditions. Even though the simultaneous layout plus control optimization is theoretically superior to the others, it is prone to the local minima. Through the parametric study of crossover and mutation probabilities of the optimization algorithm, the results of the approach are generally satisfactory. For both simple and realistic wind conditions, the wind farm with the optimized control strategy yield 1–3 kW more power per turbine than that with the self-optimum control strategy, and the unrestricted coordinate method yield 1–2 kW more power per turbine than the grid based method.     

基于网格-坐标化遗传算法的风电场布局优化

采用Jensen尾流模型来描述风电机组间尾流的干扰效应。首先基于网格化的改进遗传算法获得风电机组的数量和布局初始位置,再通过坐标化遗传算法对风电机组位置进行进一步调整优化,从而提高单位成本的发电量。根据所提出的方法,在3种不同的风场（定风向定风速、定风速变风向和变风速变风向）下,针对2 km×2 km的标准风场区域进行风电机组布局优化,再将其应用到不规则的实际案例,对比分析表明所提出的方法能有效提高发电量。     

Technoeconomic study for the optimization of turbine size and wind farm layouts

A technoeconomic analysis and optimization of wind turbine size and layout are performed using WAsP software. A case study of a 100‐MW wind farm located in Egypt is considered. Wind atlas for Egypt was used as the input data of the WAsP software. Two turbine models of powers 52 and 80 MW are considered for this project. The wind turbine size and distributions are selected based on the technoeconomic optimization, namely minimum wake effect, maximum annual energy production (AEP) rate, optimum cash flow, and payback period. The future worth method is adopted in economic comparison between the two alternatives, and the cash flow diagram provided the payback period and future worth after the lifetime of the plant. The results showed that (1) the AEP dramatically decreases for a wind farm area less than 15 km²; (2) the turbine spacing, spacing‐to‐diameter ratio, and the setback distances decrease and the wind turbine density and wake losses increase with decreasing the wind turbines size; (3) the total net AEP using G52 is lower than that of using G80 by about 16%; (4) the technoeconomic analysis recommended using G80 as it has higher profit than those of G52 by about $20 million.     

基于Park-Gauss模型考虑大气稳定性对布局优化的影响

基于Park模型尾流区线性膨胀假设和径向风速呈高斯分布假设,提出一种新的修正型的工程尾流模型Park-Gauss模型,采用小生境遗传算法,并考虑大气稳定性对风电场布局优化的影响。结果表明:对常风速单风向风电场微观选址布局优化结果是风力机组主要布置在垂直风向的第1排和最后1排;大气边界层稳定性对风电场微观选址布局优化影响显著,在大气边界层不稳定状态下,风电场安装机组总数最多、发电总量及风电场利用效率最高,中性状态和稳定状态依次次之。     

Overall Optimization for Offshore Wind Farm Electrical System

Based on particle swarm optimization (PSO), an optimization platform for offshore wind farm electrical system (OWFES) is proposed in this paper, where the main components of an offshore wind farm and key technical constraints are considered as input parameters. The offshore wind farm electrical system is optimized in accordance with initial investment by considering three aspects: the number and siting of offshore substations (OS), the cable connection layout of both collection system (CS) and transmission system (TS) as well as the selection of electrical components in terms of voltage level and capacity. Because hundreds of optimization variables, continuous or discrete, are involved in the problem, a mix integer PSO (MIPSO) is required to obtain the solution. The fuzzy C‐means clustering (FCM) algorithm is used to partition the wind farm into several sub regions. The collection system layout in each sub region as well as the connection scheme between offshore substations are optimized by an adaptive PSO‐minimum spanning tree algorithm (APSO‐MST) which has been proposed in a previous work. The simulation results show that the proposed optimization platform can find an optimized layout that save 3.01% total cost compared with the industrial layout, and can be a useful tool for OWFES design and evaluation. Copyright © 2016 John Wiley & Sons, Ltd.     

考虑时间窗约束的海上风电机组运维方案优化

降低运维成本是保障海上风电经济效益的关键,运维方案优化对降低海上风电机组运维成本和提高发电量起着双重作用。根据风电机组零部件的可靠度模型,计算出每台风电机组最佳维修时机对应的时间窗,考虑提前维修和故障后维修的经济损失,建立包含时间窗约束的海上风电机组运维方案优化模型,然后设计基于参数优化的改进遗传算法计算出最优运维方案。最后采用某海上风电场内风电机组运维案例验证模型和算法,结果表明考虑时间窗约束的运维方案可大幅度提高海上风电的经济效益,改进遗传算法比传统遗传算法具有更强的寻优能力。     

几何约束条件下海上风电场布局优化方法研究

考虑实际工程需求,开发一种几何约束条件下海上风电场智能布局优化方法。该方法使用Gaussian模型计算风力机尾流区的速度亏损,并以最大化风电场年发电量为目标采用差分进化算法进行优化,可满足海上风电场布局时的各类几何约束。利用该方法分别在3行、4行、7行几何约束下对中国某海上风电场的风力机排布方式进行优化。结果显示,相比于原始布局方案,在考虑海缆铺设成本增加的情况下布局优化方案可提升风电场年发电量2.13%～2.64%。进一步分析表明,布局优化过程中可行解数量的设置需综合考虑智能算法寻优难度的影响。     

Optimization of wind farm turbines layout using an evolutive algorithm

The optimum wind farm configuration problem is discussed in this paper and an evolutive algorithm to optimize the wind farm layout is proposed. The algorithm's optimization process is based on a global wind farm cost model using the initial investment and the present value of the yearly net cash flow during the entire wind-farm life span. The proposed algorithm calculates the yearly income due to the sale of the net generated energy taking into account the individual wind turbine loss of production due to wake decay effects and it can deal with areas or terrains with non-uniform load-bearing capacity soil and different roughness length for every wind direction or restrictions such as forbidden areas or limitations in the number of wind turbines or the investment. The results are first favorably compared with those previously published and a second collection of test cases is used to proof the performance and suitability of the proposed evolutive algorithm to find the optimum wind farm configuration.     

Investigating the possibility of using different hub height wind turbines in a wind farm

Many researchers have focused on the layout design of a wind farm using the computational methods. Most of previous researches focused on relevant large cell size and using same hub height wind turbines. In this paper, the authors investigate the possibility of using different hub height wind turbines in a wind farm. A limited area (2?km?×?2?km) with constant wind speed and direction is considered as the potential wind farm area, and a nested genetic algorithm is used as optimisation algorithm. Two different hub height wind turbines are introduced with two different cell sizes. Power output, cost, payback period, and total profit are selected as evaluation criteria when comparing the layouts with same hub height wind turbines with the layouts with different hub height wind turbines. The results demonstrate that it is feasible and possible to use different hub height wind turbines in a wind farm.     

An experimental investigation on the wake interferences among wind turbines sited in aligned and staggered wind farms

An experimental investigation was conducted for a better understanding of the wake interferences among wind turbines sited in wind farms with different turbine layout designs. Two different types of inflows were generated in an atmospheric boundary layer wind tunnel to simulate the different incoming surface winds over typical onshore and offshore wind farms. In addition to quantifying the power outputs and dynamic wind loads acting on the model turbines, the characteristics of the wake flows inside the wind farms were also examined quantitatively. After adding turbines staggered between the first 2 rows of an aligned wind farm to increase the turbine number density in the wind farm, the added staggered turbines did not show a significant effect on the aeromechanical performance of the downstream turbines for the offshore case. However, for the onshore case, while the upstream staggered turbines have a beneficial effect on the power outputs of the downstream turbines, the fatigue loads acting on the downstream turbines were also found to increase considerably due to the wake effects induced by the upstream turbines. With the same turbine number density and same inflow characteristics, the wind turbines were found to be able to generate much more power when they are arranged in a staggered layout than those in an aligned layout. In addition, the characteristics of the dynamic wind loads acting on the wind turbines sited in the aligned layout, including the fluctuation amplitudes and power spectrum, were found to be significantly different from those with staggered layout.     

Experimental verification of computational predictions in power generation variation with layout of offshore wind farms

The optimization of wind farms with respect to spatial layout is addressed experimentally. Wake effects within wind turbine farms are well known to be deleterious in terms of power generation and structural loading, which is corroborated in this study. Computational models are the predominant tools in the prediction of turbine‐induced flow fields. However, for wind farms comprising hundreds of turbines, reliability of the obtained numerical data becomes a growing concern with potentially costly consequences. This study pursues a systematic complementary theoretical, experimental and numerical study of variations in generated power with turbine layout of an 80 turbine large wind farm. Wake effects within offshore wind turbine arrays are emulated using porous discs mounted on a flat plate in a wind tunnel. The adopted approach to reproduce experimentally individual turbine wake characteristics is presented, and drag measurements are argued to correctly capture the variation in power generation with turbine layout. Experimental data are juxtaposed with power predictions using ANSYS WindModeller simulation suite. Although comparison with available wind farm power output data has been limited, it is demonstrated nonetheless that this approach has potential for the validation of numerical models of power loss due to wake effects or even to make a direct physical prediction. The approach has even indicated useful data for the improvement of the physics within numerical models. Copyright © 2014 John Wiley & Sons, Ltd.     

Tidal farm analysis using an analytical model for the flow velocity prediction in the wake of a tidal turbine with small diameter to depth ratio

A tidal turbine is a device converting hydrodynamic power into electrical power. Lately, more and more projects have been developed in order to optimize the productivity of this kind of energy. In such research with industrial interest, under the impact of the wake effect on the output power, the analysis of a tidal farm layout is regarded as the first priority. Simple approaches such as those developed for wind farms could be used in tidal turbine arrangement optimization. These methodologies can be improved by taking into account the turbulence in tidal farms and tidal turbines' mechanical characteristics. The goal of this work is to propose a predictive analytical model to estimate the tidal speed in the far wake of tidal turbines with small diameter to depth ratio (20% here). It is a first step prior to integrate the wake model in a tidal farm layout optimization algorithm. The wake model development is achieved reanalyzing the far wake's equations used in wind farm applications. A turbine represented by an Actuator Disc (AD) in conjunction with a Computational Fluid Dynamics (CFD) numerical model is used as a reference for this purpose. The CFD-AD model has been validated with experimental results from literature. The novelty of the present work consists in expressing the far wake's radius expansion as a function of the ambient turbulence and the thrust coefficient. The proposed equation is used in conjunction with the Jensen's model in a manner that the velocities downstream a tidal turbine can be estimated. The velocity distribution in the far wake of a single turbine obtained by the proposed model is in good agreement with the CFD numerical model. As a matter of fact, the model provides satisfactory accuracy in the cases of two parks: one with five aligned turbines and one with ten staggered turbines.     

A passively self-adjusting floating wind farm layout to increase the annual energy production

Wake losses inside a wind farm occur due to the aerodynamic interactions when a downwind turbine is in the wake of upwind turbines. The ability of floating offshore wind turbines (FOWTs) to relocate their positions in the horizontal plane introduces an opportunity to decrease the wake losses in a floating wind farm (FWF). Our goal is to use this ability to passively move the downwind FOWT out of the wake of upwind ones. Since the mooring system (MS) attached to a FOWT is responsible for its station keeping, the horizontal motions of the FOWT depend on the MS design. Hence, if we can design the MS to passively move the FOWT out of the wake, we can increase the FWF annual energy production (AEP). In this paper, we investigate if we can benefit from relocating FOWTs in a FWF and increase its AEP. In addition, we present a novel approach that considers the ability of a FOWT to relocate its position as a new degree of freedom (DoF) in the FWF layout design. This means we will have a self-adjusting wind farm layout where the FOWTs passively re-arrange themselves depending on the wind direction and the wind speed. Consequently, we will have a slightly different wind farm layout for every wind direction and every wind speed. To achieve this layout, we include the MS design as part of the FWF's layout design. In a self-adjusting FWF layout, each FOWT is attached to a customized MS design allowing it to relocate its position in the best way possible according to the wind direction, to increase the overall AEP of the wind farm. The results of one case study show that the novel approach can increase the FWF's AEP by 1.6% when compared with a current state of the art optimized floating wind farm layout. Finally, we implemented our method as an open-source python tool to be used and enhanced further within the wind energy community.     

水平轴风力机组风场全局优化策略研究

为优化风场布置,减小上游风力机尾迹影响,以实现风场全局优化,基于致动线方法,利用OpenFOAM(多物理场运行与操作开源软件)对风力机组风场进行了15种风轮俯仰工况及9种错排布置的数值模拟,比较各优化策略下的风场总输出功率,并结合流场细微结构参数分布,分析不同优化方法对风场全局影响的流动机理。结果表明:尾迹对风场下游风力机影响严重。两种数值模拟优化方法均可实现风场全局优化,其中风轮俯仰优化策略可使风场总输出功率最大提高34.5%;风力机组错排布置可提高68.5%。此外,风场上游风力机功率在风轮俯仰时下降明显,风力机组错排时几乎无变化。     

Optimization of cable layout designs for large offshore wind farms

Installation of a wind farm exposes several problems such as site selection, placement of wind turbines in the site, and designing of cable infrastructure within the farm. The latter problem, called cable layout design, is the determination of cable connections among turbines and one or more transmitters such that energies generated by turbines will be sent through the cable routes, and eventually gathered at the transmitter(s). This problem is especially important for offshore wind farms where the featured and expensive cables are used. The main objective of the present study is to address the cable layout design problem of offshore wind farms to reduce cable costs in the design using optimization-based approaches. The problem, firstly, is modelled as a mixed integer linear program (MIP) under a set of real-life constraints such as different cable and transmitter types and non-crossing connections between the turbines. Then, a novel mathematical model, which is a modification of the MIP model by imposing several heuristic rules, is proposed to solve the layout problem of large offshore wind farms. Experiments on a set of small- and moderate-sized test instances reveal that the heuristic model, MIP_H, reduces the computer time nearly 55% compared to that of MIP model while the average cable costs generated by the models are close to each other. MIP_H, besides its efficiency, provides more cost-effective layouts compared to MIP model for large-sized real-life examples. Additionally, a comparative study on MIP_H and existing methods in the literature shows that MIP_H is able to solve all instances of the real-life examples providing less cable costs in average.     

Characteristics of turbine spacing in a wind farm using an optimal design process

The characteristics of turbine spacing for optimal wind farm efficiency were investigated using combined numerical models. The effects of wakes from upstream turbines were predicted by a model capable of determining velocity distributions on a rotor plane, based on Ainslie's approach. The performance results of a wind farm showed good agreement with measurements. The blade element momentum theory, in combination with a dynamic wake model, was applied. Wake model used the results of aerodynamic analysis as input properties. The optimal distance between wind turbines was predicted using a genetic algorithm to maximize efficiency in a wind farm. The results showed that the spacing between the first and the second turbines had the importance to the entire farm's efficiency.     

Optimization of turbine design in wind farms with multiple hub heights,using exact analytic gradients and structural constraints

Wind farms are generally designed with turbines of all the same hub height. If wind farms were designed with turbines of different hub heights, wake interference between turbines could be reduced, lowering the cost of energy (COE). This paper demonstrates a method to optimize onshore wind farms with two different hub heights using exact, analytic gradients. Gradient‐based optimization with exact gradients scales well with large problems and is preferable in this application over gradient‐free methods. Our model consisted of the following: a version of the FLOw Redirection and Induction in Steady‐State wake model that accommodated three‐dimensional wakes and calculated annual energy production, a wind farm cost model, and a tower structural model, which provided constraints during optimization. Structural constraints were important to keep tower heights realistic and account for additional mass required from taller towers and higher wind speeds. We optimized several wind farms with tower height, diameter, and shell thickness as coupled design variables. Our results indicate that wind farms with small rotors, low wind shear, and closely spaced turbines can benefit from having two different hub heights. A nine‐by‐nine grid wind farm with 70‐meter rotor diameters and a wind shear exponent of 0.08 realized a 4.9% reduction in COE by using two different tower sizes. If the turbine spacing was reduced to 3 diameters, the reduction in COE decreased further to 11.2%. Allowing for more than two different turbine heights is only slightly more beneficial than two heights and is likely not worth the added complexity.     

Large eddy simulations of the effect of vertical staggering in large wind farms

In order to study the effect of vertical staggering in large wind farms, large eddy simulations (LES) of large wind farms with a regular turbine layout aligned with the given wind direction were conducted. In the simulations, we varied the hub heights of consecutive downstream rows to create vertically staggered wind farms. We analysed the effect of streamwise and spanwise turbine spacing, the wind farm layout, the turbine rotor diameter, and hub height difference between consecutive downstream turbine rows on the average power output. We find that vertical staggering significantly increases the power production in the entrance region of large wind farms and is more effective when the streamwise turbine spacing and turbine diameter are smaller. Surprisingly, vertical staggering does not significantly improve the power production in the fully developed regime of the wind farm. The reason is that the downward vertical kinetic energy flux, which brings high velocity fluid from above the wind farm towards the hub height plane, does not increase due to vertical staggering. Thus, the shorter wind turbines are effectively sheltered from the atmospheric flow above the wind farm that supplies the energy, which limits the benefit of vertical staggering. In some cases, a vertically staggered wind farm even produced less power than the corresponding non vertically staggered reference wind farm. In such cases, the production of shorter turbines is significantly negatively impacted while the production of the taller turbine is only increased marginally.