1. Introduction
One of the key aspects of wind farm design is to determine the position of the wind turbines within a given area, and one of the main objectives of this wind turbines layout is to minimize the wake effect between wind turbines. The wake generated by upstream wind turbines causes wind speed reduction resulting in power losses in the downstream wind turbines. In addition, the unstable turbulent flow caused by the wake increases the fatigue load of those wind turbines affected by the wake. The wind speed deficit by the wake effect can be estimated using a wake model. However, it is difficult to optimize the wind turbine layout by considering the range of effects of the wake that changes according to the wind direction. To solve the complex wind farm layout optimization (WFLO) problem, various layout optimization methods have been introduced, and many related studies addressed this [
1,
2]. The first study was published in 1994 by Mosetti et al. [
3], where they introduced the genetic algorithm (GA), now considered one of the most typical optimization methods to address the WFLO problem. Although the wind farm model applied by Mosetti’s study is not a practical model, their proposed model and the wind scenario have been used as a comparative benchmark to examine the performance of various algorithms.
In general, the optimization methodology for the WFLO problem can be divided into heuristic and mathematical programming methods. A heuristic is a method of searching for an optimal solution based on probabilistic theory, and mathematical programming is a method of formulating and optimizing the variables and boundary conditions of a problem. Algorithms that use heuristic methods for the WFLO problem include the GA [
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19], evolutionary strategy [
20,
21,
22], particle swarm optimization [
23,
24,
25], and greedy heuristic [
26,
27]. Moreover, other works on the development of various algorithms have been conducted [
28,
29,
30,
31,
32,
33]. Among these methods, GA is the most widely used. GA is a representative optimization algorithm of heuristic methodology based on the concept of the evolution of nature. Although it considers a cooperative system of the population, the optimal solution may vary depending on the number of populations and generations, and it is difficult to exactly determine these factors. However, GA is still actively used in various fields owing to its versatility. The mathematical programming method includes mixed-integer programming [
34,
35,
36,
37] and gradient-based optimization [
38,
39,
40,
41]. Unlike heuristics methods, it has the advantage of ensuring global optimization. However, it works appropriately only in the cases when a given problem can be expressed as a complete function mathematically. The WFLO problem falls into the class of problems called combinatorial optimization, and due to its computational complexity and discrete constraints, it is difficult to express it as a complete mathematical function to find an optimal solution [
29]. Therefore, mathematical programming methods are not suitable for wind farm design because of the properties (non-linear, multi-modal, discontinuous) of the WFLO problem [
1,
2].
The optimization methodology for the WFLO problem developed in this study is a method using the simulated annealing (SA) algorithm. The SA algorithm simulates the annealing process in metallurgy which increases the rigidity of metal materials. Similar to the GA, the SA algorithm is one of the representative heuristic approaches that was developed based on the natural law [
42]. Although the GA is the most widely used algorithm for the WFLO problem, SA is also one of the most popular methods among heuristic methodologies in the optimization field. In particular, in the SA algorithm, the process of simulating the annealing process of crystal structures inside the metal under temperature conditions is similar to the situation in which the turbines are placed at promising locations in the wind farm. Furthermore, unlike GA, in which various structures may exist depending on the design purpose, the SA algorithm structure is consistent. The SA algorithm is also a representative optimization algorithm, but despite its usefulness, it has not been widely applied to wind farm layout optimization. Therefore, in this study, we developed an SA algorithm for the wind farm layout optimization problem. Subsequently, we compared and evaluated the SA algorithm to those presented in previous studies.
To compare and evaluate the performance of an algorithm, a reference target in which the algorithm is applied is needed. Mosetti’s study mentioned above has been used in numerous studies to evaluate the performance of various algorithms for wind farm layout optimization. Grady et al. [
4] developed a GA with a subpopulation and compared the results to Mosetti’s findings which yielded more efficient layout results than Mosetti’s. They mentioned that although GA was an effective global optimization method, it was necessary for a sufficient number of populations and generations and that large computational costs could be incurred due to the large number of independent variables. González et al. [
8] also used a GA and compared their results to Grady’s study. They resulted in improved energy efficiency and shortened calculations compared to Grady. Zhang et al. [
9] adopted the greedy algorithm and compared it to Mosetti and Grady, and derived enhanced layout results using more wind turbines than previous studies. Parada et al. [
19] compared their results to Grady’s study and demonstrated that there was an optimized layout of the regular pattern in the same wind farm model as previous studies. Most studies compared their results to Mosetti and Grady’s studies to evaluate their developed algorithms. Mosetti’s case studies are considered to be the basis for evaluating algorithms in the development of the wind farm layout optimization algorithm.
In this study, we propose a new methodology for wind farm layout optimization using the SA algorithm. Various optimization methodologies have been developed in the past, but the SA algorithm has not been widely applied, despite its advantages. Therefore, this study aims to secure a variety of optimization methodologies for more efficient wind farm design. To evaluate the performance of the developed algorithm, a comparison was made under the same conditions as the previous studies, and the applicability of the developed algorithm was examined. In the actual wind farm design phase, various conditions (power cables, access road, prohibited area, geographical characteristics, etc.) must be reflected, but this study compared and evaluated the basic performance of the optimal placement algorithm, limited to wind farm efficiency and cost, which were the focusses of previous studies.
4. Conclusions
In this study, an optimization method using the SA algorithm for the wind farm layout optimization problem was proposed and was applied to three scenarios considered in previous studies to evaluate the performance of the optimization algorithm. The performed case studies were as follows: (a) constant wind speed and single wind direction, (b) constant wind speed and multiple wind directions, and (c) variable wind speed and multiple wind directions. The same layout results as in the previous studies were obtained in case study (a) due to the simple wind scenario. In case study (b), a symmetrical layout, which was not observed in previous studies, was obtained and the resulting layout demonstrated the best fitness results. Finally, in case study (c), the SA algorithm demonstrated the optimal number of wind turbines and the layout results that were not observed in previous studies. Most of the compared previous studies use the GA, whereas the SA algorithm in this study demonstrated the best performance. It should be noted that it is hard to evaluate the performance in terms of the absolute difference. This is due to the fact that optimization algorithms may be applied differently depending on the characteristics of the problem. However, the results indicate that the SA algorithm can be successfully applied to the wind farm layout optimization problem.
In addition, the cost model and the objective function, which were suggested by Mosetti et al. to obtain the optimal layout, have a tradeoff between efficiency and cost, and this problem should be addressed in future works. Finally, to demonstrate the practical applicability of the optimal layout algorithms, more practical wind scenarios need to be examined.