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 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

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.

Layout Optimization of Shapeable Components With Extended Pattern Search Applied to Transmission Design

2004 ◽  
Vol 126 (1) ◽  
pp. 188-191 ◽  
Author(s):  
Su Yin ◽  
Jonathan Cagan ◽  
Peter Hodges
Keyword(s):  
Cross Section ◽  
Search Algorithm ◽  
Automatic Transmission ◽  
Layout Optimization ◽  
Pattern Search ◽  
Fixed Size ◽  
Pattern Search Algorithm ◽  
Transmission Design ◽  
Product Layout ◽  
Extended Pattern Search

An extended pattern search algorithm is presented for the placement of shapeable components within a product layout. Shapeable octrees are used to evaluate the amount of overlap between pairs of components, extending previous technology that requires fixed-size components. The method is used to conceptualize the layout of the cross-section of an automatic transmission.

A Sensitivity-Based Pattern Search Algorithm for 3D Component Layout

2002 ◽  
Author(s):  
Chandankumar Aladahalli ◽  
Jonathan Cagan ◽  
Kenji Shimada
Keyword(s):  
Objective Function ◽  
Search Algorithm ◽  
Search Space ◽  
Pattern Search ◽  
Step Size ◽  
Simple Method ◽  
Pattern Search Algorithm ◽  
Component Layout ◽  
Extended Pattern Search ◽  
Better Than

This paper introduces the Sensitivity-based Pattern Search (SPS) algorithm for 3D component layout. Although based on the pattern search algorithm, SPS differs in that at any given step size the algorithm does not necessarily perturb the search space along all possible search dimensions. Instead all possible perturbations, or moves are ranked in decreasing order of their effect on the objective function and are applied in that order. The philosophy behind this algorithm is that moves that affect the objective function more must be applied before the moves that affect the objective function less. We call this effect on the objective function the sensitivity of the objective function to a particular move and present a simple method to quantify it. This algorithm performs better than the previous Extended Pattern Search algorithm with decrease in run time of up to 28%.

Minimum Height Packing for Layered Manufacturing Using an Extended Pattern Search Algorithm

2003 ◽  
Author(s):  
Chandankumar Aladahalli ◽  
Jonathan Cagan ◽  
Kenji Shimada
Keyword(s):  
Search Algorithm ◽  
3D Models ◽  
Layered Manufacturing ◽  
Pattern Search ◽  
Maximum Height ◽  
Pattern Search Algorithm ◽  
Time To Build ◽  
Component Layout ◽  
Minimum Height ◽  
Extended Pattern Search

This paper introduces an approach to solve the minimum height layout problem for layered manufacturing using a pattern search based algorithm called Extended Pattern Search. In the batch processing of several components in a typical layered manufacturing run, it is efficient in terms of cost and time to build the components after packing their 3D models such that the maximum height of the components is minimized. 3D component layout based on a pattern search algorithm provides a framework to accomplish such minimum height packing. A method to determine the objective function weights for a class of problems is also provided. Finally error minimizing build directions are incorporated in the 3D layout framework by imposing suitable spatial orientation constraints on individual components.

Layout of an Automobile Transmission Using Three-Dimensional Shapeable Components

1999 ◽  
Author(s):  
Su Yin ◽  
Jonathan Cagan ◽  
Peter Hodges ◽  
Xianren Li
Keyword(s):  
Search Algorithm ◽  
Three Dimensional ◽  
Pattern Search ◽  
Optimization Process ◽  
Functional Requirements ◽  
Pattern Search Algorithm ◽  
Torque Capacity ◽  
Product Layout ◽  
Extended Pattern Search ◽  
Connection Cost

Abstract An extended pattern search algorithm is presented for the placement of shapeable components within a product layout. The algorithm is applied to an automobile transmission layout taking into account the shapeability of the components. Overlap between components is allowed and penalized during the optimization process. Shapeable octrees are used to evaluate the amount of overlap between pairs of components. The algorithm minimizes the connection cost in addition to optimizing the position and size of the components. A shapeable component has a defined geometry, but its size may vary within limits. The size of clutches in a transmission is determined by the torque capacity requirement, thermal requirement, and gain requirement. Under a given load, the size of a clutch satisfying a set of functional requirements is related to its location in the transmission assembly, making it necessary to design the clutches on the fly while laying out the components.

An Extended Pattern Search Algorithm for Three-Dimensional Component Layout

2000 ◽  
Vol 122 (1) ◽  
pp. 102-108 ◽  
Author(s):  
Su Yin ◽  
Jonathan Cagan
Keyword(s):  
Search Algorithm ◽  
Three Dimensional ◽  
Pattern Search ◽  
Test Problems ◽  
Spatial Constraint ◽  
Routing Problem ◽  
Pattern Search Algorithm ◽  
Component Layout ◽  
Different Types ◽  
Extended Pattern Search

An extended pattern search algorithm is introduced for efficient component layout optimization. The algorithm is applicable to general layout problems, where component geometry can be arbitrary, design goals can be multiple and spatial constraint satisfactions can be of different types. Extensions to pattern search are introduced to help the algorithm to converge to optimal solutions by escaping inferior local minima. The performance on all of the test problems shows that the algorithm runs one-to-two orders of magnitude faster than a robust simulated annealing-based algorithm for results with the same quality. The algorithm is further extended to solve a concurrent layout and routing problem, which demonstrates the ability of the algorithm to apply new pattern strategies in search and to include different objective functions in optimization. [S1050-0472(00)01901-2]

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