A Comparison of Eight Optimization Methods Applied to a Wind Farm Layout Optimization Problem

Selecting a wind farm layout optimization method is difficult. Comparisons between optimization methods in different papers can be uncertain due to the difficulty of exactly reproducing the objective function. Comparisons by just a few authors in one paper can be uncertain if the authors do not have experience using each algorithm. In this work we provide an algorithm comparison for a wind farm layout optimization case study between eight optimization methods applied, or directed, by researchers who developed those algorithms or who had other experience using them. We provided the objective function to each researcher to avoid ambiguity about relative performance due to a difference in objective function. While these comparisons are not perfect, we try to treat each algorithm more fairly by having researchers with experience using each algorithm apply each algorithm and by having a common objective function provided for analysis. The case study is from the IEA Wind Task 37, based on the Borssele III and IV wind farms with 81 turbines. Of particular interest in this case study is the presence of disconnected boundary regions and concave boundary features. The optimization methods studied represent a wide range of approaches, including gradient-free, gradient-based, and hybrid methods; discrete and continuous problem formulations; single-run and multi-start approaches; and mathematical and heuristic algorithms. We provide descriptions and references (where applicable) for each optimization method as well as lists of pros and cons to help readers determine an appropriate method for their use case. All the optimization methods perform similarly, with optimized wake loss values between 15.48 % and 15.70 % as compared to 17.28 % for the unoptimized provided layout. Each of the layouts found were different, but all layouts exhibited similar characteristics. Strong similarities across all the layouts include tightly packing wind turbines along the outer borders, loosely spacing turbines in the internal regions, and allocating similar numbers of turbines to each discrete boundary region. The best layout by AEP was found using a new sequential allocation method, discreet exploration-based optimization (DEBO). Based on the results in this study, it appears that using an optimization algorithm can significantly improve wind farm performance, but there are many optimization methods that can perform well on the wind farm layout optimization problem given that they are applied correctly.</p

Multi-objective constrained optimization for energy applications via tree ensembles

Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable types, e.g. continuous and categorical, are challenges commonly present in real-world applications. In some cases, proposed optimal solutions need to obey explicit input constraints related to physical properties or safety-critical operating conditions. This paper proposes a novel data-driven strategy using tree ensembles for constrained multi-objective optimization of black-box problems with heterogeneous variable spaces for which underlying system dynamics are either too complex to model or unknown. In an extensive case study comprised of synthetic benchmarks and relevant energy applications we demonstrate the competitive performance and sampling efficiency of the proposed algorithm compared to other state-of-the-art tools, making it a useful all-in-one solution for real-world applications with limited evaluation budgets

Airfoil Optimization Through Differential Evolution

This thesis presents the development of a numerical optimization algorithm for airfoils, and how it can be used in design of wind turbine blades. It was found that the developed algorithm successfully improves the goal parameters under given conditions and constraints. This research was conducted on behalf of Winfoor AB who has developed a conceptually new blade design, in which every single blade is made up of three individual blades, kept together by rods in a truss like manner. Their wish was to develop a new airfoil for their turbine, with higher performance and a more docile stall, and yet remaining a high airfoil thickness in order to not alter structural stability. The task was conducted by describing the airfoils with B-splines and writing an optimization algorithm in MATLAB in which the flow characteristics of the airfoils were determined by the external software XFOIL. This thesis shows how to characterize numerical optimization problems, what differential evolution is and how it can be implemented in a MATLAB-code, how airfoils can be described with B-splines, the usage of XFOIL and how penalty functions can be imposed for constrained optimization problems, to mention some of the wisdoms this work has brought. This research is important as numerical optimization of airfoils is not yet the standard method for airfoil design, and thus it can possibly contribute with valuable insights and results to further development of airfoil optimization

Intelligent power system operation in an uncertain environment

This dissertation presents some challenging problems in power system operations. The efficacy of a heuristic method, namely, modified discrete particle swarm optimization (MDPSO) algorithm is illustrated and compared with other methods by solving the reliability based generator maintenance scheduling (GMS) optimization problem of a practical hydrothermal power system. The concept of multiple swarms is incorporated into the MDPSO algorithm to form a robust multiple swarms-modified particle swarm optimization (MS-MDPSO) algorithm and applied to solving the GMS problem on two power systems. Heuristic methods are proposed to circumvent the problems of imposed non-smooth assumptions common with the classical approaches in solving the challenging dynamic economic dispatch problem. The multi-objective combined economic and emission dispatch (MO-CEED) optimization problem for a wind-hydrothermal power system is formulated and solved in this dissertation. This MO-CEED problem formulation becomes a challenging problem because of the presence of uncertainty in wind power. A family of distributed optimal Pareto fronts for the MO-CEED problem has been generated for different scenarios of capacity credit of wind power. A real-time (RT) network stability index is formulated for determining a power system\u27s ability to continue to provide service (electric energy) in a RT manner in case of an unforeseen catastrophic contingency. Cascading stages of fuzzy inference system is applied to combine non real-time (NRT) and RT power system assessments. NRT analysis involves eigenvalue and transient energy analysis. RT analysis involves angle, voltage and frequency stability indices. RT Network status index is implemented in real-time on a practical power system --Abstract, page iv