Wind Farm Layout Optimization Research Articles

Modelling Wind for Wind Farm Layout Optimization Using Joint Distribution of Wind Speed and Wind Direction

Reliable wind modelling is of crucial importance for wind farm development. The common practice of using sector-wise Weibull distributions has been found inappropriate for wind farm layout optimization. In this study, we propose a simple and easily implementable method to construct joint distributions of wind speed and wind direction, which is based on the parameters of sector-wise Weibull distributions and interpolations between direction sectors. It is applied to the wind measurement data at Horns Rev and three different joint distributions are obtained, which all fit the measurement data quite well in terms of the coefficient of determination . Then, the best of these joint distributions is used in the layout optimization of the Horns Rev 1 wind farm and the choice of bin sizes for wind speed and wind direction is also investigated. It is found that the choice of bin size for wind direction is especially critical for layout optimization and the recommended choice of bin sizes for wind speed and wind direction is finally presented.

Solving the wind farm layout optimization problem using random search algorithm

Wind farm (WF) layout optimization is to find the optimal positions of wind turbines (WTs) inside a WF, so as to maximize and/or minimize a single objective or multiple objectives, while satisfying certain constraints. In this work, a random search (RS) algorithm based on continuous formulation is presented, which starts from an initial feasible layout and then improves the layout iteratively in the feasible solution space. It was first proposed in our previous study and improved in this study by adding some adaptive mechanisms. It can serve both as a refinement tool to improve an initial design by expert guesses or other optimization methods, and as an optimization tool to find the optimal layout of WF with a certain number of WTs. A new strategy to evaluate layouts is also used, which can largely save the computation cost. This method is first applied to a widely studied ideal test problem, in which better results than the genetic algorithm (GA) and the old version of the RS algorithm are obtained. Second it is applied to the Horns Rev 1 WF, and the optimized layouts obtain a higher power production than its original layout, both for the real scenario and for two constructed scenarios. In this application, it is also found that in order to get consistent and reliable optimization results, up to 360 or more sectors for wind direction have to be used. Finally, considering the inevitable inter-annual variations in the wind conditions, the robustness of the optimized layouts against wind condition changes is analyzed, and the optimized layouts consistently show better performance in power production than the original layout, despite of considerable variations in wind direction and speed.

A semi-analytical model for velocity profile at wind turbine wake using blade element momentum

The shape of wake behind a wind turbine is normally assumed to have a hat shape for the models used in wind farm layout optimization purposes; however, it is know from experimental tests and numerical simulations that this is not a real assumption. In reality, the results of actual measurements and detailed numerical simulation show that the velocity in wake region has a S-shape profile. The present study calculated a semi-analytical profile for the shape of the wake behind a wind turbine using blade element momentum method. It is shown that the wake shape differs in different operational conditions and geometrical characteristics of the wind turbine.

Optimal wind farm sitting using high-resolution digital elevation models and randomized optimization

We investigate the problem of wind farm design in isolated mountainous areas. We first describe a remote sensing approach for the terrain reconstruction of complex terrains. We then employ a well--known evolutionary optimization algorithm to find the optimal wind farm layout. Although the algorithm has been efficiently used for off--shore or smooth on--shore areas, we show that its performance is significantly affected by the complex topography. Moreover, we illustrate how a priori information can be exploited to improve both the computational time and efficiency of the optimization algorithm.

On the spread and decay of wind turbine wakes in ambient turbulence

The decay of the downstream wake of a wind turbine plays an important role in the performance of wind farms. The spread and decay of a wake depend both on wake meandering (advection of the wake as a whole) and wake diffusion (widening of the wake within its meandering frame of reference). Both of these effects depend strongly on the intensity of the ambient turbulence relative to the velocity deficit in the wake, and on the integral length scale of the turbulence relative to the wake width. Recent theory, which we review here, shows how intense large-scale turbulence can lead to a rapid x−2 decay in the time-averaged centreline velocity deficit, as compared to a x−1 decay for smaller scale turbulence, where x is distance downstream. We emphasise in this paper that common wind farm models do not predict this rapid decay. We present new experimental measurements of the velocity deficit downstream of a porous disc in relatively large-scale ambient turbulence which corroborate predictions of a x−2 decay, and we show theoretically that the commonly used k-ϵ model does not capture this effect. We further show that a commercial CFD package, configured to match our experiments and employing the k-ϵ model, fails to predict such rapid decay. We conclude that steady simulations of wind turbine wake dynamics are insufficient for informing wind farm layout optimisation.

Solving wind farm layout optimization with mixed integer programs and constraint programs

The wind farm layout optimization problem is concerned with the optimal location of turbines within a fixed geographical area to maximize profit under stochastic wind conditions. Previously, it has been modeled as a maximum diversity (or $$p$$ -dispersion-sum) problem, but such a formulation cannot capture the nonlinearity of aerodynamic interactions among multiple wind turbines. We present the first constraint programming (CP) and mixed integer linear programming (MIP) models that incorporate such nonlinearity. Our empirical results indicate that the relative performance between these two models reverses when the wind scenario changes from a simple to a more complex one. We then extend these models to include landowner participation and noise constraints. With the additional constraints, the MIP-based decomposition outperforms CP in almost all cases. We also propose an improvement to the previous maximum diversity model and demonstrate that the improved model solves more problem instances.

Multi-Objective Wind Farm Layout Optimization Considering Energy Generation and Noise Propagation With NSGA-II

Recently, the environmental impact of wind farms has been receiving increasing attention. As land is more extensively exploited for onshore wind farms, they are more likely to be in proximity with human dwellings, increasing the likelihood of a negative health impact. Noise generation and propagation remain an important concern for wind farm's stakeholders, as compliance with mandatory noise limits is an integral part of the permitting process. In contrast to previous work that included noise only as a design constraint, this work presents continuous-location models for layout optimization that take noise and energy as objective functions, in order to fully characterize the design and performance spaces of the wind farm layout optimization (WFLOP) problem. Based on Jensen's wake model and ISO-9613-2 noise calculations, single- and multi-objective genetic algorithms (GAs) are used to solve the optimization problem. Results from this bi-objective optimization model illustrate the trade-off between energy generation and noise production by identifying several key parts of Pareto frontiers. In particular, it was observed that different regions of a Pareto front correspond to markedly different turbine layouts. The implications of noise regulation policy—in terms of the actual noise limit—on the design of wind farms are discussed, particularly in relation to the entire spectrum of design options.

Wind farm layout optimization using imperialist competitive algorithm

In this work, the wind farm layout optimization problem is dealt with using a new approach. The aim of wind farm layout optimization is to maximize the output power of a wind farm considering the wake losses. Layout optimization minimizes the wake losses regarding the location of the turbines. Three different wind scenarios with different wind direction angles, wind direction blowing probabilities, and Weibull distribution parameters are assumed. Since, the problem is nonlinear and constrained, imperialist competitive algorithm is used as a modern and powerful algorithm for continuous optimization problems. The optimization outcomes indicate that imperialist competitive algorithm yields promising results.

Wind farm layout optimization in complex terrain: A preliminary study on a Gaussian hill

One of the crucial problems for wind farm (WF) development is wind farm layout optimization. It seeks to find the optimal positions of wind turbines (WTs) inside a WF, so as to maximize and/or minimize a single objective or multiple objectives, while satisfying certain constraints. Although this problem for WFs in flat terrain or offshore has been investigated in many studies, it is still a challenging problem for WFs in complex terrain. In this preliminary study, the wind flow conditions of complex terrain without WTs are first obtained from computational fluid dynamics (CFD) simulation, then an adapted Jensen wake model is developed by considering the terrain features and taking the inflow conditions as input. Using this combined method, the wake effects of WF in complex terrain are properly modelled. Besides, a random search (RS) algorithm proposed in previous study is improved by adding some adaptive mechanisms and applied to solve the layout optimization problem of a WF on a Gaussian shape hill. The layout of the WF with a certain number of WTs is optimized to maximize the total power output, which obtained steady improvements over expert guess layouts.

Volumetric scans of wind turbine wakes performed with three simultaneous wind LiDARs under different atmospheric stability regimes

Aerodynamic optimization of wind farm layout is a crucial task to reduce wake effects on downstream wind turbines, thus to maximize wind power harvesting. However, downstream evolution and recovery of wind turbine wakes are strongly affected by the characteristics of the incoming atmospheric boundary layer (ABL) flow, such as wind shear and turbulence intensity, which are in turn affected by the ABL thermal stability. In order to characterize the downstream evolution of wakes produced by full-scale wind turbines under different atmospheric conditions, wind velocity measurements were performed with three wind LiDARs. The volumetric scans are performed by continuously sweeping azimuthal and elevation angles of the LiDARs in order to cover a 3D volume that includes the wind turbine wake. The minimum wake velocity deficit is then evaluated as a function of the downstream location for different atmospheric conditions. It is observed that the ABL thermal stability has a significant effect on the wake evolution, and the wake recovers faster under convective conditions.

Modelling complex terrain effects for wind farm layout optimization

The flow over four analytical hill geometries was calculated by CFD RANS simulations. For each hill, the results were converted into numerical models that transform arbitrary undisturbed inflow profiles by rescaling the effect of the obstacle. The predictions of such models are compared to full CFD results, first for atmospheric boundary layer flow, and then for a single turbine wake in the presence of an isolated hill. The implementation of the models into the wind farm modelling software flapFOAM is reported, advancing their inclusion into a fully modular wind farm layout optimization routine.

A comprehensive measure of the energy resource: Wind power potential (WPP)

Currently, the quality of available wind energy at a site is assessed using wind power density (WPD). This paper proposes to use a more comprehensive metric: the wind power potential (WPP). While the former accounts for only wind speed information, the latter exploits the joint distribution of wind speed and wind direction and yields more credible estimates. The WPP investigates the effect of wind velocity distribution on the optimal net power generation of a farm. A joint distribution of wind speed and direction is used to characterize the stochastic variation of wind conditions. Two joint distribution methods are adopted in this paper: bivariate normal distribution and anisotropic lognormal method. The net power generation for a particular farmland size and installed capacity is maximized for different distributions of wind speed and wind direction, using the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. A response surface is constructed to represent the computed maximum wind farm capacity factor as a function of the parameters of the wind distribution. Two different response surface methods are adopted in this paper: (i) the adaptive hybrid functions (AHF), and (ii) the quadratic response surface method (QRSM). Toward this end, for any farm site, we can (i) estimate the parameters of the joint distribution using recorded wind data (for bivariate normal or anisotropic lognormal distributions) and (ii) predict the maximum capacity factor for a specified farm size and capacity using this response surface. The WPP metric is illustrated using recorded wind data at four differing stations in the state of North Dakota. The results illustrate the variation of wind conditions and, subsequently, its influence on the quality of wind resources. A comparison of four sites in North Dakota shows that WPD and WPP follow different trends, and the ranking of candidate sites in terms of a realistic resource potential measure is not captured by WPD.

Double-stage genetic algorithm for wind farm layout optimization on complex terrains

This paper deals with the problem of optimal wind turbine micro siting on complex terrains. A realistic wind farm terrain can be very complex not only for the topography of the terrain but also for other factors. Such factors are the environmental impact of the wind farm, the costs of land, the costs of access roads, wind turbine installation and maintenance costs, the costs of electrical infrastructure, etc. A grid-based wind farm model that takes all of these factors into consideration is proposed. For the purpose of an optimization algorithm, a double-stage genetic algorithm is proposed. In the first stage, the optimal micro-areas for wind turbine positioning are determined, whereas the second stage defines precise optimal positions of wind turbine foundations. The double-stage genetic algorithm increases the accuracy of wind turbine positioning and decreases the dimensionality of the problem. The algorithm has been tested on a realistic wind farm terrain in Serbia.

Considering induction factor using BEM method in wind farm layout optimization

For wind farm layout optimization process, a simple linear model has been mostly used for considering the wake effect of a wind turbine on its downstream turbines. In this model, the wind velocity in the wake behind a turbine is obtained as a function of turbine induction factor which was considered to be 0.324 almost in all the previous studies. However, it is obviously evident that this factor is a strong function of turbine blade geometry and operational conditions. In the present study, a new method is introduced by which the induction factor for wind turbines can be calculated based on the method of Blade Element Momentum theory. By this method, the effect of blade profile, wind speed and angular velocity of wind turbine on the induction factor can be easily taken into account. The results show that for different blade profiles and operational conditions, the induction factor differs from the single value used so far. Also it is shown that this difference has a very significant effect in calculated gained power from a wind farm. It is clearly seen that considering the new method for calculating an appropriate induction factor affects the total calculated power generation of a wind farm and consequently influences the farm layout in optimization process.

Explicit Solutions for Simple Models of Wind Turbine Interference

Wind turbine interference - the reduction in output power of a turbine downwind of any others - is a major problem for wind farm optimization and control. With interference, it is well-known for specific cases that co-operative optimization of power output yields more power than does the selfish optimization of individual turbines. This paper develops explicit solutions for simple models of interference for the general case of any number of turbines in line with the wind. For the simplest case of no wake recovery, analytical solutions for co-operative and selfish optimization are derived. They show that co-operative optimization nearly always yields more power and never yields less. Adding a simple form of wake recovery for equally spaced turbines precludes analytical solutions, but numerical solutions are developed to find the power to any required level of accuracy. Again, co-operative optimization is superior in nearly all cases. These simple solutions should be useful for demonstrating the importance of interference and for testing methods for optimizing wind farm layout and operation. It is shown that the maximum benefit from co-operative operation occurs at turbine spacing comparable to that commonly used in wind farms. The analysis is then extended to include topographical effects modeled as changes in wind speed along the line. Explicit solutions are obtained for two turbines in line. Co-operative optimization remains the best strategy. In particular, when the wind speed increases, it quickly becomes optimal to shut down the first turbine.

Combined optimization of a wind farm and a well field for wind-enabled groundwater production

Energy requirements constitute a significant cost in groundwater production and can also add to a large carbon footprint when fossil fuels are used for power. Wind-enabled water production is advantageous as it minimizes air pollution impacts associated with groundwater production and relies on a renewable resource. Also, as groundwater extraction represents a deferrable load (i.e., it can be carried out when energy demands within an area are low), it provides a convenient way to overcome the intermittency issue associated with wind power production. Multiple turbine wind farms are needed to generate large quantities of power needed for large-scale groundwater production. Turbines must be optimally located in these farms to ensure proper propagation of kinetic energy throughout the system. By the same token, well placement must reconcile the competing objectives of minimizing interferences between production wells while ensuring the drawdowns at the property boundary are within acceptable limits. A combined simulation–optimization based model is developed in this study to optimize the combined wind energy and water production systems. The wind farm layout optimization model is solved using a re-sampling strategy, while the well field configuration is obtained using the simulated annealing technique. The utility of the developed model is to study wind-enabled water production in San Patricio County, TX. Sensitivity analysis indicated that identifying optimal placement of turbines is vital to extract maximum wind power. The variability of the wind speeds has a critical impact on the amount of water that can be produced. Innovative technologies such as variable flow pumping devices and aquifer storage recovery must be used to smooth out wind variability. While total groundwater extraction is less sensitive to uncertainty in hydrogeological parameters, improper estimation of aquifer transmissivity and storage characteristics can affect the feasibility of wind-driven groundwater production.

TOPFARM: Multi‐fidelity optimization of wind farms

A wind farm layout optimization framework based on a multi-fidelity optimization approach is applied to the offshore test case of Middelgrunden, Denmark as well as to the onshore test case of Stag Holt – Coldham wind farm, UK. While aesthetic considerations have heavily influenced the famous curved design of the Middelgrunden wind farm, this work focuses on demonstrating a method that optimizes the profit of wind farms over their lifetime based on a balance of the energy production income, the electrical grid costs, the foundations cost, and the cost of wake turbulence induced fatigue degradation of different wind turbine components. A multi-fidelity concept is adapted, which uses cost function models of increasing complexity (and decreasing speed) to accelerate the convergence to an optimum solution. In the EU-FP6 TOPFARM project, three levels of complexity are considered. The first level uses a simple stationary wind farm wake model to estimate the Annual Energy Production (AEP), a foundations cost model depending on the water depth and an electrical grid cost function dictated by cable length. The second level calculates the AEP and adds a wake-induced fatigue degradation cost function on the basis of the interpolation in a database of simulations performed for various wind speeds and wake setups with the aero-elastic code HAWC2 and the dynamic wake meandering model. The third level, not considered in this present paper, includes directly the HAWC2 and the dynamic wake meandering model in the optimization loop in order to estimate both the fatigue costs and the AEP. The novelty of this work is the implementation of the multi-fidelity approach in the context of wind farm optimization, the inclusion of the fatigue degradation costs in the optimization framework, and its application on the optimal performance as seen through an economical perspective. Copyright © 2013 John Wiley & Sons, Ltd.

A new mathematical programming approach to optimize wind farm layouts

The optimal placement of turbines in a wind farm is critical to the maximization of power production. In this paper, we develop a new mathematical programming approach for wind farm layout optimization. We use Jensen's wake decay model to represent multi-turbine wake effects. We develop mixed integer linear and quadratic optimization formulations and apply them to several example layout cases in the literature. Compared to previous approaches, our models produce layouts that tend to be more symmetric and that generate slightly more power. Our formulations solve quickly, allowing a decision maker to efficiently explore the impact of different turbine densities in a wind farm.

A system-level cost-of-energy wind farm layout optimization with landowner modeling

This work applies an enhanced levelized wind farm cost model, including landowner remittance fees, to determine optimal turbine placements under three landowner participation scenarios and two land-plot shapes. Instead of assuming a continuous piece of land is available for the wind farm construction, as in most layout optimizations, the problem formulation represents landowner participation scenarios as a binary string variable, along with the number of turbines. The cost parameters and model are a combination of models from the National Renewable Energy Laboratory (NREL), Lawrence Berkeley National Laboratory, and Windustry. The system-level cost-of-energy (COE) optimization model is also tested under two land-plot shapes: equally-sized square land plots and unequal rectangle land plots. The optimal COEs results are compared to actual COE data and found to be realistic. The results show that landowner remittances account for approximately 10% of farm operating costs across all cases. Irregular land-plot shapes are easily handled by the model. We find that larger land plots do not necessarily receive higher remittance fees. The model can help site developers identify the most crucial land plots for project success and the optimal positions of turbines, with realistic estimates of costs and profitability.

Wind Farm Layout Optimization Using a Viral Systems Algorithm

In the present research a new viral systems optimization algorithm is developed to find the optimal number and position of wind turbines in large wind farms with the main objective of minimizing the cost per unit power produced from the wind park. The developed algorithm is applied to three well known problems in literature which are: 1) constant wind speed and unidirectional uniform wind, 2) constant wind speed with variable direction, and 3) non-uniform variable wind speed with variable direction. In the final results, the distance between two wind turbines is reduced to one meter, compared to 5 rotor diameters in previous studies.