Solving Wind Farm Layout Optimization with Mixed Integer Programming and Constraint Programming

2013 ◽  
pp. 284-299 ◽  
Author(s):  
Peter Y. Zhang ◽  
David A. Romero ◽  
J. Christopher Beck ◽  
Cristina H. Amon
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Constraint Programming ◽  
Wind Farm ◽  
Layout Optimization ◽  
Mixed Integer ◽  
Wind Farm Layout ◽  
Wind Farm Layout Optimization

A Tight Upper Bound for Grid-Based Wind Farm Layout Optimization

2016 ◽  
Author(s):  
Ning Quan ◽  
Harrison Kim
Keyword(s):  
Upper Bound ◽  
Numerical Experiments ◽  
Wind Farm ◽  
Optimization Problems ◽  
Layout Optimization ◽  
Mixed Integer ◽  
Wind Farm Layout ◽  
Wind Farm Layout Optimization ◽  
Quadratic Knapsack ◽  
Grid Based

This paper uses the method developed by Billionnet et al. (1999) to obtain tight upper bounds on the optimal values of mixed integer linear programming (MILP) formulations in grid-based wind farm layout optimization. The MILP formulations in grid-based wind farm layout optimization can be seen as linearized versions of the 0-1 quadratic knapsack problem (QKP) in combinatorial optimization. The QKP is NP-hard, which means the MILP formulations remain difficult problems to solve, especially for large problems with grid sizes of more than 500 points. The upper bound method proposed by Billionnet et al. is particularly well-suited for grid-based wind farm layout optimization problems, and was able to provide tight optimality gaps for a range of numerical experiments with up to 1296 grid points. The results of the numerical experiments also suggest that the greedy algorithm is a promising solution method for large MILP formulations in grid-based layout optimization that cannot be solved using standard branch and bound solvers.

Wind Farm Layout Optimization in Complex Terrains Using Computational Fluid Dynamics

2015 ◽  
Author(s):  
Jim Y. J. Kuo ◽  
I. Amy Wong ◽  
David A. Romero ◽  
J. Christopher Beck ◽  
Cristina H. Amon
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Energy Production ◽  
Wind Farm ◽  
Layout Optimization ◽  
Mixed Integer ◽  
Cfd Simulations ◽  
Wind Farm Layout ◽  
Wind Farm Layout Optimization ◽  
Wake Effects

The aim of wind farm design is to maximize energy production and minimize cost. In particular, optimizing the placement of turbines in a wind farm is crucial to minimize the wake effects that impact energy production. Most work on wind farm layout optimization has focused on flat terrains and spatially uniform wind regimes. In complex terrains, however, the lack of accurate analytical wake models makes it difficult to evaluate the performance of layouts quickly and accurately as needed for optimization purposes. This paper proposes an algorithm that couples computational fluid dynamics (CFD) with mixed-integer programming (MIP) to optimize layouts in complex terrains. High-fidelity CFD simulations of wake propagation are utilized in the proposed algorithm to constantly improve the accuracy of the predicted wake effects from upstream turbines in complex terrains. By exploiting the deterministic nature of MIP layout solutions, the number of expensive CFD simulations can be reduced significantly. The proposed algorithm is demonstrated on the layout design of a wind farm domain in Carleton-sur-Mer, Quebec, Canada. Results show that the algorithm is capable of producing good wind farm layouts in complex terrains while minimizing the number of computationally expensive wake simulations.

Constrained Multi-Objective Wind Farm Layout Optimization: Introducing a Novel Constraint Handling Approach Based on Constraint Programming

2015 ◽  
Author(s):  
Sami Yamani Douzi Sorkhabi ◽  
David A. Romero ◽  
J. Christopher Beck ◽  
Cristina H. Amon
Keyword(s):  
Land Use ◽  
Constraint Programming ◽  
Wind Farm ◽  
Layout Optimization ◽  
Constraint Handling ◽  
Objective Functions ◽  
Nsga Ii ◽  
Wind Farm Layout ◽  
Multi Objective ◽  
Wind Farm Layout Optimization

Recently, land has been exploited extensively for onshore wind farms and turbines are frequently located in proximity to human dwellings, natural habitats, and infrastructure. This proximity has made land use constraints and noise generation and propagation matters of increasing concern for all stakeholders. Hence, wind farm layout optimization approaches should be able to consider and address these concerns. In this study, we perform a constrained multi-objective wind farm layout optimization considering energy and noise as objective functions, and considering land use constraints arising from landowner participation, environmental setbacks and proximity to existing infrastructure. The optimization problem is solved with the NSGA-II algorithm, a multi-objective, continuous variable Genetic Algorithm. A novel hybrid constraint handling tool that uses penalty functions together with Constraint Programming algorithms is introduced. This constraint handling tool performs a combination of local and global searches to find feasible solutions. After verifying the performance of the proposed constraint handling approach with a suite of test functions, it is used together with NSGA-II to optimize a set of wind farm layout optimization test cases with different number of turbines and under different levels of land availability (constraint severity). The optimization results illustrate the potential of the new constraint handling approach to outperform existing constraint handling approaches, leading to better solutions with fewer evaluations of the objective functions and constraints.

A Comparative Study of the Influence of Different Wake Models on Wind Farm Layout Optimization

2021 ◽  
Author(s):  
Puyi Yang ◽  
Hamidreza Najafi
Keyword(s):  
Wind Farm ◽  
Wind Farms ◽  
Vital Role ◽  
Layout Optimization ◽  
Zone Model ◽  
Wind Farm Layout ◽  
Yaw Control ◽  
Wind Farm Layout Optimization ◽  
Wake Model ◽  
Large Wind

Abstract The accuracy of analytical wake models applied in wind farm layout optimization (WFLO) problems plays a vital role in the present era that the high-fidelity methods such as LES and RANS are still not able to handle an optimization problem for large wind farms. Based on a verity of analytical wake models developed in the past decades, FLOw Redirection and Induction in Steady State (FLORIS) has been published as a tool integrated several widely used wake models and the expansions for them. This paper compares four wake models selected from FLORIS by applying three classical WFLO scenarios. The results illustrate that the Jensen wake model is the fastest one but the defect of underestimation of velocity deficit is obvious. The Multi Zone model needs to be applied additional tunning on the parameters inside the model to fit specific wind turbines. The Gaussian-Curl wake model as an advanced expansion of the Gaussian wake model does not perform an observable improvement in the current study that the yaw control is not included. The default Gaussian wake model is recommended to be used in the WFLO projects which implemented under the FLROIS framework and has similar wind conditions with the present work.

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