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

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.

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

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.

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

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

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.

An Extended Pattern Search Approach to Wind Farm Layout Optimization

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

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.

Exploring the Effectiveness of Various Patterns in an Extended Pattern Search Layout Algorithm

Automated synthesis of product layout has the potential of substantially reducing design cycle time while allowing for quick check of interference, clearance, scale and fit prior to the building of physical prototypes. The search for optimal positions and orientations of parts in the layout typically requires a huge number of iterations. An extended pattern search layout algorithm based on coordinate search was introduced in an earlier paper and shown quite effective over the previous state-of-the-art. Coordinate search is a simple and straightforward way of implementing the extended pattern search method in the layout problem. However, it is not taking advantage of the wide variety of heuristics admissible in pattern search methods for identifying promising search directions. By introducing various search patterns and exploring their effectiveness in the layout problem, the question of whether complex tactics can do better than the basic coordinate pattern search is addressed. This paper presents four different heuristics for generating pattern directions in the extended pattern search layout algorithm: the conjugate direction method, the modified gradient method, the rank ordering method, and the simplex method. These heuristics are utilized to identify promising search directions and update the set of pattern directions used in the algorithm over iterations. The performance of the different heuristics is compared to that of the basic coordinate extended pattern search layout approach.