Optimization of Wind Farm Layout and Wind Turbine Geometry Using a Multi-Level Extended Pattern Search Algorithm That Accounts for Variation in Wind Shear Profile Shape

2012 ◽  
Author(s):  
Bryony L. DuPont ◽  
Jonathan Cagan ◽  
Patrick Moriarty
Keyword(s):  
Wind Speed ◽  
Wind Shear ◽  
Wind Farm ◽  
Search Algorithm ◽  
Atmospheric Stability ◽  
Pattern Search ◽  
Power Development ◽  
Profile Shape ◽  
Multi Level ◽  
Extended Pattern Search

This paper presents a multi-level Extended Pattern Search algorithm (EPS) to optimize both the local positioning and geometry of wind turbines on a wind farm. Additionally, this work begins to draw attention to the effects of atmospheric stability on wind farm power development. The wind farm layout optimization problem involves optimizing the local position and size of wind turbines such that the aerodynamic effects of upstream turbines are reduced, thereby increasing the effective wind speed at each turbine, allowing it to develop more power. The extended pattern search, employed within a multi-agent system architecture, uses a deterministic approach with stochastic extensions to avoid local minima and converge on superior solutions compared to other algorithms. The EPS presented herein is used in an iterative, hierarchical scheme — an overarching pattern search determines individual turbine positioning, then a sub-level EPS determines the optimal hub height and rotor for each turbine, and the entire search is iterated. This work also explores the wind shear profile shape to better estimate the effects of changes in the atmosphere, specifically the changes in wind speed with respect to height on the total power development of the farm. This consideration shows how even slight changes in time of day, hub height, and farm location can impact the resulting power. The objective function used in this work is the maximization of profit. The farm installation cost is estimated using a data surface derived from the National Renewable Energy Laboratory (NREL) JEDI wind model. Two wind cases are considered: a test case utilizing constant wind speed and unidirectional wind, and a more realistic wind case that considers three discrete wind speeds and varying wind directions, each of which is represented by a fraction of occurrence. Resulting layouts indicate the effects of more accurate cost and power modeling, partial wake interaction, as well as the differences attributed to including and neglecting the effects of atmospheric stability on the wind shear profile shape.

An Extended Pattern Search Approach to Wind Farm Layout Optimization

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Bryony L. Du Pont ◽  
Jonathan Cagan
Keyword(s):  
Wind Speed ◽  
Wind Farm ◽  
Search Algorithm ◽  
Pattern Search ◽  
Global Evaluation ◽  
Layout Problem ◽  
Pattern Search Algorithm ◽  
Wind Farm Layout ◽  
Search Approach ◽  
Extended Pattern Search

An extended pattern search approach is presented for the optimization of the placement of wind turbines on a wind farm. Problem-specific extensions infuse stochastic characteristics into the deterministic pattern search, inhibiting convergence on local optima and yielding better results than pattern search alone. The optimal layout for a wind farm is considered here to be one that maximizes the power generation of the farm while minimizing the farm cost. To estimate the power output, an established wake model is used to account for the aerodynamic effects of turbine blades on downstream wind speed, as the oncoming wind speed for any turbine is proportional to the amount of power the turbine can produce. As turbines on a wind farm are in close proximity, the interaction of turbulent wakes developed by the turbines can have a significant effect on the power development capability of the farm. The farm cost is estimated using an accepted simplified model that is a function of the number of turbines. The algorithm develops a two-dimensional layout for a given number of turbines, performing local turbine movement while applying global evaluation. Three test cases are presented: (a) constant, unidirectional wind, (b) constant, multidirectional wind, and (c) varying, multidirectional wind. The purpose of this work is to explore the ability of an extended pattern search (EPS) algorithm to solve the wind farm layout problem, as EPS has been shown to be particularly effective in solving multimodal layout problems. It is also intended to show that the inclusion of extensions into the algorithm can better inform the search than algorithms that have been previously presented in the literature. Resulting layouts created by this extended pattern search algorithm develop more power than previously explored algorithms using the same evaluation models and objective functions. In addition, the algorithm’s resulting layouts motivate a heuristic that aids in the manual development of the best layout found to date. The results of this work validate the application of an extended pattern search algorithm to the wind farm layout problem, and that its performance is enhanced by the use of problem-specific extensions that aid in developing results that are superior to those developed by previous algorithms.

Optimization of Floating Offshore Wind Energy Systems Using an Extended Pattern Search Method

2016 ◽  
Author(s):  
Caitlin Forinash ◽  
Bryony DuPont
Keyword(s):  
Wind Farm ◽  
Wind Farms ◽  
Power Production ◽  
Pattern Search ◽  
Offshore Wind ◽  
Offshore Wind Farm ◽  
Power Development ◽  
Offshore Wind Farms ◽  
Onshore Wind ◽  
Extended Pattern Search

An Extended Pattern Search (EPS) approach is developed for offshore floating wind farm layout optimization while considering challenges such as high cost and harsh ocean environments. This multi-level optimization method minimizes the costs of installation and operations and maintenance, and maximizes power development in a unidirectional wind case by selecting the size and position of turbines. The EPS combines a deterministic pattern search algorithm with three stochastic extensions to avoid local optima. The EPS has been successfully applied to onshore wind farm optimization and enables the inclusion of advanced modeling as new technologies for floating offshore wind farms emerge. Three advanced models are incorporated into this work: (1) a cost model developed specifically for this work, (2) a power development model that selects hub height and rotor radius to optimize power production, and (3) a wake propagation and interaction model that determines aerodynamic effects. Preliminary results indicate the differences between proposed optimal offshore wind farm layouts and those developed by similar methods for onshore wind farms. The objective of this work is to maximize profit; given similar parameters, offshore wind farms are suggested to have approximately 24% more turbines than onshore farms of the same area. EPS layouts are also compared to those of an Adapted GA; 100% efficiency is found for layouts containing twice as many turbines as the layout presented by the Adapted GA. Best practices are derived that can be employed by offshore wind farm developers to improve the layout of platforms, and may contribute to reducing barriers to implementation, enabling developers and policy makers to have a clearer understanding of the resulting cost and power production of computationally optimized farms; however, the unidirectional wind case used in this work limits the representation of optimized layouts at real wind sites. Since there are currently no multi-turbine floating offshore wind farm projects operational in the United States, it is anticipated that this work will be used by developers when planning array layouts for future offshore floating wind farms.

An Extended Pattern Search Approach to Wind Farm Layout Optimization

2010 ◽  
Author(s):  
Bryony L. Du Pont ◽  
Jonathan Cagan
Keyword(s):  
Wind Farm ◽  
Search Algorithm ◽  
Turbine Blades ◽  
Pattern Search ◽  
Total Power ◽  
Local Optima ◽  
Wake Model ◽  
Power Capability ◽  
Search Approach ◽  
Extended Pattern Search

An extended pattern search approach is presented for optimizing the placement of wind turbines on a wind farm. The algorithm will develop a two-dimensional layout for a given number of turbines, employing an objective function that minimizes costs while maximizing the total power production of the farm. The farm cost is developed using an established simplified model that is a function of the number of turbines. The power development of the farm is estimated using an established simplified wake model, which accounts for the aerodynamic effects of turbine blades on downstream wind speed, to which the power output is directly proportional. The interaction of the turbulent wakes developed by turbines in close proximity largely determines the power capability of the farm. As pattern search algorithms are deterministic, multiple extensions are presented to aid escaping local optima by infusing stochastic characteristics into the algorithm. This stochasticity improves the algorithm’s performance, yielding better results than purely deterministic search methods. Three test cases are presented: a) constant, unidirectional wind, b) constant, multidirectional wind, and c) varying, multidirectional wind. Resulting layouts developed by this extended pattern search algorithm develop more power than previously explored algorithms with the same evaluation models and objective functions. In addition, the algorithm’s layouts motivate a heuristic that yields the best layouts found to date.

scholarly journals Experimental Study on Wake Evolution of a 1.5 MW Wind Turbine in a Complex Terrain Wind Farm Based on LiDAR Measurements

2020 ◽  
Vol 12 (6) ◽  
pp. 2467 ◽  
Author(s):  
Fei Zhao ◽  
Yihan Gao ◽  
Tengyuan Wang ◽  
Jinsha Yuan ◽  
Xiaoxia Gao
Keyword(s):  
Wind Speed ◽  
Wind Shear ◽  
Wind Farm ◽  
Wind Farms ◽  
Field Measurements ◽  
Development Trend ◽  
Asymmetric Distribution ◽  
Lidar Measurements ◽  
Wind Characteristics ◽  
The Development Trend

To study the wake development characteristics of wind farms in complex terrains, two different types of Light Detection and Ranging (LiDAR) were used to conduct the field measurements in a mountain wind farm in Hebei Province, China. Under two different incoming wake conditions, the influence of wind shear, terrain and incoming wind characteristics on the development trend of wake was analyzed. The results showed that the existence of wind shear effect causes asymmetric distribution of wind speed in the wake region. The relief of the terrain behind the turbine indicated a subsidence of the wake centerline, which had a linear relationship with the topography altitudes. The wake recovery rates were calculated, which comprehensively validated the conclusion that the wake recovery rate is determined by both the incoming wind turbulence intensity in the wake and the magnitude of the wind speed.

An Extended Pattern Search Method for Offshore Floating Wind Layout and Turbine Geometry Optimization

2016 ◽  
Author(s):  
Caitlin Forinash ◽  
Bryony DuPont
Keyword(s):  
Wind Farm ◽  
Cost Model ◽  
Geometry Optimization ◽  
Interaction Model ◽  
Solution Space ◽  
Wind Farms ◽  
Power Production ◽  
Pattern Search ◽  
Offshore Wind ◽  
Extended Pattern Search

An Extended Pattern Search (EPS) method is developed to optimize the layout and turbine geometry for offshore floating wind power systems. The EPS combines a deterministic pattern search with stochastic extensions. Three advanced models are incorporated: (1) a cost model considering investment and lifetime costs of a floating offshore wind farm comprised of WindFloat platforms; (2) a wake propagation and interaction model able to determine the reduced wind speeds downstream of rotating blades; and (3) a power model to determine power produced at each rotor, and includes a semi-continuous, discrete turbine geometry selection to optimize the rotor radius and hub height of individual turbines. The objective function maximizes profit by minimizing cost, minimizing wake interactions, and maximizing power production. A multidirectional, multiple wind speed case is modeled which is representative of real wind site conditions. Layouts are optimized within a square solution space for optimal positioning and turbine geometry for farms containing a varying number of turbines. Resulting layouts are presented; optimized layouts are biased towards dominant wind directions. Preliminary results will inform developers of best practices to include in the design and installation of offshore floating wind farms, and of the resulting cost and power production of wind farms that are computationally optimized for realistic wind conditions.

The atmospheric turbulence characteristics in a diurnal cycle

2020 ◽  
Vol 34 (14n16) ◽  
pp. 2040109
Author(s):  
Yi-Lei Song ◽  
Lin-Lin Tian ◽  
Ning Zhao
Keyword(s):  
Wind Speed ◽  
Diurnal Cycle ◽  
Wind Shear ◽  
Atmospheric Stability ◽  
Atmospheric Flow ◽  
Eddy Simulation ◽  
Mean Wind Speed ◽  
Engineering Models ◽  
Wind Characteristics ◽  
Stability Classification

During a whole-day period, profiles of mean wind speed, wind shear and turbulence level shows great variability due to continuously varying atmospheric stability. Clearly understanding the spatial and temporal behaviors of the atmospheric wind flow is of great importance for science purposes. Large-eddy simulation (LES) technique is employed here to reproduce the evolution of atmospheric flow during a diurnal cycle. With the obtained LES results, wind characteristics in terms of wind speed, wind shear, turbulence intensity and turbulent kinetic energy can be examined referring to the stability classification. Besides, wind profiles obtained using currently available engineering models are also included for comparison. Disparities between the model predictions and the LES results illustrate that the standard engineering models cannot well capture the wind characteristics driven by the varying atmospheric stability solely, and a further improvement in models is highly needed.

Influence of Atmospheric Stability on Wind Turbine Power Performance Curves

2006 ◽  
Vol 128 (4) ◽  
pp. 531-538 ◽  
Author(s):  
Jonathon Sumner ◽  
Christian Masson
Keyword(s):  
Wind Speed ◽  
Wind Farm ◽  
Similarity Theory ◽  
Atmospheric Stability ◽  
Performance Testing ◽  
System Of Nonlinear Equations ◽  
Power Performance ◽  
Turbine Efficiency ◽  
The Impact ◽  
Power Curves

The impact of atmospheric stability on vertical wind profiles is reviewed and the implications for power performance testing and site evaluation are investigated. Velocity, temperature, and turbulence intensity profiles are generated using the model presented by Sumner and Masson. This technique couples Monin-Obukhov similarity theory with an algebraic turbulence equation derived from the k-ϵ turbulence model to resolve atmospheric parameters u*, L, T*, and z0. The resulting system of nonlinear equations is solved with a Newton-Raphson algorithm. The disk-averaged wind speed u¯disk is then evaluated by numerically integrating the resulting velocity profile over the swept area of the rotor. Power performance and annual energy production (AEP) calculations for a Vestas Windane-34 turbine from a wind farm in Delabole, England, are carried out using both disk-averaged and hub height wind speeds. Although the power curves generated with each wind speed definition show only slight differences, there is an appreciable impact on the measured maximum turbine efficiency. Furthermore, when the Weibull parameters for the site are recalculated using u¯disk, the AEP prediction using the modified parameters falls by nearly 5% compared to current methods. The IEC assumption that the hub height wind speed can be considered representative tends to underestimate maximum turbine efficiency. When this assumption is further applied to energy predictions, it appears that the tendency is to overestimate the site potential.

scholarly journals How wind speed shear and directional veer affect the power production of a megawatt-scale operational wind turbine

2020 ◽  
Vol 5 (3) ◽  
pp. 1169-1190
Author(s):  
Patrick Murphy ◽  
Julie K. Lundquist ◽  
Paul Fleming
Keyword(s):  
Wind Speed ◽  
Wind Farm ◽  
Turbine Blades ◽  
Atmospheric Stability ◽  
Power Production ◽  
High Plains ◽  
Power Curve ◽  
Mean Power ◽  
Rotor Disk ◽  
Utility Scale

Abstract. Most megawatt-scale wind turbines align themselves into the wind as defined by the wind speed at or near the center of the rotor (hub height). However, both wind speed and wind direction can change with height across the area swept by the turbine blades. A turbine aligned to hub-height winds might experience suboptimal or superoptimal power production, depending on the changes in the vertical profile of wind, also known as shear. Using observed winds and power production over 6 months at a site in the high plains of North America, we quantify the sensitivity of a wind turbine's power production to wind speed shear and directional veer as well as atmospheric stability. We measure shear using metrics such as α (the log-law wind shear exponent), βbulk (a measure of bulk rotor-disk-layer veer), βtotal (a measure of total rotor-disk-layer veer), and rotor-equivalent wind speed (REWS; a measure of actual momentum encountered by the turbine by accounting for shear). We also consider the REWS with the inclusion of directional veer, REWSθ, although statistically significant differences in power production do not occur between REWS and REWSθ at our site. When REWS differs from the hub-height wind speed (as measured by either the lidar or a transfer function-corrected nacelle anemometer), the turbine power generation also differs from the mean power curve in a statistically significant way. This change in power can be more than 70 kW or up to 5 % of the rated power for a single 1.5 MW utility-scale turbine. Over a theoretical 100-turbine wind farm, these changes could lead to instantaneous power prediction gains or losses equivalent to the addition or loss of multiple utility-scale turbines. At this site, REWS is the most useful metric for segregating the turbine's power curve into high and low cases of power production when compared to the other shear or stability metrics. Therefore, REWS enables improved forecasts of power production.

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