[Could not find the bibliography file(s)]
– Document in progress –
Introduction
Wind farm layout optimization has been a subject of research for alm
ost 15 years.
Recently, with the increase of focus on
offshore wind energy, where positioning the turbine is based on fewer types of factors, it has raised in interest dramatically.
Optimization Methods
Genetic Algorithm
Genetic algorithm seems to be the most popular approach so far.
It was first introduced by Mosetti et al. in 1994 [?], and followed by many others [?], [?], [?], [?], [?], [?], [?], [?], [?], [?], [?], and [?].
Heuristic Methodology
Aytun Ozturk et al. [?], and Elkinton et al. [?] used a greedy heuristic methodology.
Swarm Optimization
Wan et al. [?] advocate the use of swarm optimization as more efficient than genetic algorithms.
Pattern Search
Du Pont and Cagan [?] use a pattern search algorithm with stochastic injections to avoid converging to local minima.
Cost Functions
Financial Balance
Foundation
Electrical Grid
Wake Models
Test Cases
(1994) Optimization of wind turbine positioning in large windfarms by means of a genetic algorithm, Journal of Wind Engineering and Industrial Aerodynamics 51(1), p. 105-116
In this paper a novel approach to the optimization of large windfarms is presented. The wind turbine distribution at a given site is optimized in order to extract the maximum energy for the minimum installation costs. The optimization is made by associating a windfarm simulation model based on wake superposition with a genetic search code. The purpose of the paper is to prove the feasibility of the method by analyzing the results obtained in some simple applications. As a test case, a square site subdivided into 100 square cells as possible turbine locations has been taken, and the optimization is applied to the number and position of the turbines for three wind cases: single direction, constant intensity with variable direction, and variable intensity with variable direction., url
(2004) Heuristic methods for wind energy conversion system positioning, Electric Power Systems Research 70(3), p. 179-185
This paper considers the problem of determining the locations of wind generators in a wind farm consisting of many generators. The objective is to find a generator placement that maximizes profit, which is the product of the cost efficiency of the generators and the total power output from the wind farm. Generator placement is significant because if generator A is located close to generator B and is located downwind of generatorBthen the power output of generatorAis reduced by an amount that varies with the distance between the generators. The problem can be formulated using mathematical programming but to solve the problem one cannot employ traditional optimization methods. Therefore, a greedy improvement heuristic methodology is developed and described in detail. The effectiveness of the proposed heuristic is demonstrated on a suite of test problems. These results indicate that the proposed method represents an effective solution strategy for this problem., url
(2004) Optimization of energy generation in wind farm through fuzzy control
Wind farms are energy generation systems being autonomous and controllable generating units. At current technological status, each set turbine-generator-power converter should be considered as a unit. These units work as an individual system for variable speed systems. Variable speed wind systems demand for an appropriate control of operating point at different wind regimens as well they can operate at different rotational speed and, consequently, at different system efficiency. Control characteristics of each machine are based on associated power converter that implements control on power flow to the grid. In the paper, authors discuss the design of the controller for the wind farm. The approach is based on the development of a fuzzy controller for the entire farm. So an appropriate structure and rules of inference allow at optimizing the operation characteristics of the farm. The paper demonstrates the demanding for a whole wind farm controller and discusses some results carried out in the development of a fuzzy controller that optimizes total generated power of a wind farm, persecuting the goal of a good quality generated power., url
(2005) Offshore wind farm layout optimization (OWFLO) project: an introduction, Offshore Wind
Optimizing the layout of an offshore wind farm presents a significant engineering challenge. Most of the optimization literature to date has focused on land-based wind farms, rather than on offshore farms. The conventional method used to lay out a wind farm combines a turbine cost model and a wake model in conjunction with an optimization routine. In offshore environments, however, factors such as operation and maintenance (O&M) and availability also play significant roles in the design of a wind farm. To better account for these and the other critical factors that distinguish offshore wind farms from their onshore counterparts, the Offshore Wind Farm Layout Optimization (OWFLO) project was launched in 2004. The objective is to develop an analysis tool that unites offshore turbine micrositing criteria with efficient optimization algorithms. The project combines wake and component cost models, but also includes O&M, availability, and electrical interconnection models. When integrated within an appropriate optimization routine, these “sub-models” will work together to better reflect the real-world conditions and constraints unique to individual offshore sites. The OWFLO project will consider several optimization algorithms—including heuristic and genetic methods—to minimize the cost of energy while maximizing the energy production of the wind farm. This paper summarizes the results from the first year of this on-going project. The development of the component models and analysis software is discussed in detail and some initial results are compared with existing wind farms. A summary of the current and future phases of the project is also presented., pdf
() Offshore Wind Farm Layout Optimization (OWFLO) Project: Preliminary Results, Renewable Energy, p. 1-9
Optimizing the layout of an offshore wind farm presents a significant engineering challenge. Most of the optimization literature to date has focused on land-based wind farms, rather than on offshore farms. Typically, energy production is the metric by which a candidate layout is evaluated. The Offshore Wind Farm Layout Optimization (OWFLO) project instead uses the levelized production cost as the metric in order to account for the significant roles factors such as support structure cost and operation and maintenance (O&M) play in the design of an offshore wind farm. The objective of the project is to pinpoint the major economic hurdles present for offshore wind farm developers by creating an analysis tool that unites offshore turbine micrositing criteria with efficient optimization algorithms. This tool will then be used to evaluate the effects of factors such as distance from shore and water depth on the economic feasibility of offshore wind energy. The project combines an energy production model—taking into account wake effects, electrical line losses, and turbine availability—with offshore wind farm component cost models. The components modeled include the rotor-nacelle assembly, support structure, electrical interconnection, as well as O&M, installation, and decommissioning costs. The models account for the key cost drivers, which include turbine size and rating, water depth, distance from shore, soil type, and wind and wave conditions. When integrated within an appropriate optimization routine, these component models work together to better reflect the real-world conditions and constraints unique to individual offshore sites. The OWFLO project considers several optimization algorithms—including heuristic and genetic methods—to minimize the cost of energy while maximizing the energy production of the wind farm. Particular attention has been paid to the results of recent European studies, including the ENDOW and DOWEC projects. This paper summarizes the initial results from this project. A comparison of model results and data from the Middelgrunden offshore wind farm is presented. The overall energy and cost of energy estimations compare well with the real data, but further improvements to the models are planned. A summary of the on-going and future phases of the project is also presented. Nomenclature
(2005) Placement of wind turbines using genetic algorithms, Renewable Energy 30(2), p. 259-270
A genetic algorithm approach is employed to obtain optimal placement of wind turbines for maximum production capacity while limiting the number of turbines installed and the acreage of land occupied by each wind farm. Specifically, three cases are considered—(a) unidirectional uniform wind, (b) uniform wind with variable direction, and (c) non-uniform wind with variable direction. In Case (a), 600 individuals are initially distributed over 20 subpopulations and evolve over 3000 generations. Case (b) has 600 individuals spread over 20 subpopulations initially and evolves for 3000 generations. Case (c) starts with 600 individuals spread over 20 subpopulations and evolves for 2500 generations. In addition to optimal configurations, results include fitness, total power output, efficiency of power output and number of turbines for each configuration. Disagreement with the results of an earlier study is observed and a possible explanation is provided., url
(2005) Wind farm optimization, University of Auckland, Dept. Engineering Science, Citeseer
This paper will formulate integer programs to determine the optimal positions of wind turbines within a wind farm. The formulations were based on variations of the vertex packing problem. Three formulations are presented, which seek to maximize power generated in accordance with constraints based on the number of turbines, turbine proximity, and turbine interference. These were in the form of budget, clique, and edge constraints. Results were promising, with turbines exhibiting a tendency to concentrate in areas of high elevation and avoid situations where downstream interference would be significant., pdf
(2006) Modeling the Trade-Offs in Offshore Wind Energy Micrositing, Proc. WINDPOWER 2006 Conference and Exhibition
The layout of an offshore wind farm is a complex problem involving many trade-offs. To achieve the most energy at the least cost, these trade-offs must be understood. Energy production increases with turbine spacing, as do electrical costs and losses. Energy production also increases with distance from shore, but so do O&M, foundation, transmission, and installation costs. Determining which of these factors dominate requires a thorough understanding of the physics behind these trade-offs, can lead to the optimal layout, and helps lower the cost of energy from these farms. This paper details the results of ongoing research carried out at the University of Massachusetts. The Offshore Wind Farm Layout Optimization (OWFLO) project investigates these trade-offs in order to better understand the micrositing process for offshore wind energy. A software tool has been developed that estimates the cost of energy for an offshore farm. This tool is comprised of mathematical models of the major cost and energy components of the farm: turbine, support structure, and foundation costs, energy production and losses, availability, etc... These models were used to examine the impacts on the cost and energy trade-offs of modifications in the layout of a theoretical offshore wind farm. The results of an initial examination of these trade-offs are discussed and examples of recent modeling results are compared with data from existing offshore wind farms., url
(2006) Wind Turbine Design Cost and Scaling Model Wind Turbine Design Cost and Scaling Model, Contract(December)
... System (NEMS) runs. The second purpose of this work was to provide a baseline tool for evaluating the impact of machine design and growth on cost for proposed offshore wind turbine systems. 3 Page 8. To prepare this ..., pdf
(2007) An Analytical Framework for Offshore Wind Farm Layout Optimization, Wind Engineering 31(1), p. 17-31
A method is developed for using the levelized cost of energy as the objective function for offshore wind farm layout optimization problems. The method converts the cost of energy into a function of turbine position only. To accomplish this, wind speed data are first characterized by direction sector. Continuous functions are then fitted to the Weibull parameters for each direction sector. The wind direction probability density function and the turbine power curve are also transformed into continuous functions. For each turbine in the farm, the continuous function that describes the Weibull scale parameter can be scaled to reflect wake losses from other turbines. The function may also be adjusted according to the variation in wind speed with fetch. The annual energy production of the farm is thus modeled as a function only of the turbine positions. When combined with wind farm cost estimates, the levelized cost of energy is still only a function of turbine position and can then be used as an objective function within a variety of optimization algorithms, url
(2007) An evolutive algorithm for wind farm optimal design, Neurocomputing 70(16-18), p. 2651-2658
An evolutive algorithm for the optimal design of wind farms is presented. The algorithm objective is to optimize the profits given an investment on a wind farm. Net present value will be used as a figure of the revenue. To work out this figure, several economic factors such as the initial capital investment, the discount rate, the value of the generated energy and the number of the years spanned by the investment are considered. All this factors depends on the preliminary design of the wind park (number, type, tower height and layout situation of wind generators), which are the variables to set., url
(2007) Distributed Genetic Algorithm for Optimization of Wind Farm Annual Profits, 2007 International Conference on Intelligent Systems Applications to Power Systems, p. 1-6, Ieee
In this paper, a distributed genetic algorithm is adopted to search the optimal number and locations of wind turbines in large wind farms. The objective of this optimal process is to find a solution that maximizes the annual profit obtained from a wind farm. It is well known that traditional genetic algorithms are time consuming and the quality of final solution is not very well. For improving the performance of finding the optimal solution in large search space, the distributed genetic algorithm provides a powerful strategy for searching the global optimal by dividing large population into multiple small subpopulations that occasionally exchange some individuals. Test results show that the distributed genetic algorithm well demonstrates its effectiveness on solution quality and execution time., url
(2007) Offshore wind farm layout optimization, url
(2008) Algorithms for Offshore Wind Farm Layout Optimization, Wind Engineering 32(1), p. 67-84
Offshore wind energy is positioned to facilitate substantial growth in wind energy production, but further reductions in the cost of energy will strengthen its ability to compete directly with other energy generating technologies. One simple solution is the optimal use of current technologies. To this end, this study investigates the use of optimization algorithms for offshore wind farm micrositing. First, a discussion is given of five different types of optimization algorithms: gradient search, heuristic, pattern search, simulated annealing, and evolutionary algorithms. The relevance of each algorithm to wind turbine micrositing is then evaluated by considering two separate objectives: minimization of the levelized production cost and maximization of the energy production. The genetic and greedy heuristic algorithms are further evaluated through the use of design simulations. Finally, these algorithms are employed to optimize the layout of a potential, real-world offshore wind farm near Hull, Massachusetts., url
(2008) Optimal placement of wind turbines in a wind park using Monte Carlo simulation, Renewable Energy 33(7), p. 1455-1460
In the present study, a novel procedure is introduced for the optimal placement and arrangement of wind turbines in a wind park. In this approach a statistical and mathematical method is used, which is called ‘Monte Carlo simulation method’. The optimization is made by the mean of maximum energy production and minimum cost installation criteria. As a test case, a square site is subdivided into 100 square cells that can be possible turbine locations and as a result, the program presents us the optimal arrangement of the wind turbines in the wind park, based on the Monte Carlo simulation method. The results of this study are compared to the results of previous studies that handle the same issue., url
(2008) Optimization of Offshore Wind Farm Layouts(August)
This study aims to determine the optimal layout of the wind turbines inside an offshore wind farm when taking into account the wake effects. The wake model used is an N.O. Jensen model [12]. For this purpose I use a simulated annealing algorithm adapted to this specific problem, where three types of local search operations, namely remove, move and add, are performed recursively with every turbine until the sys- tem converges. Two different objective functions are considered: the Annual Energy Production and the Profit, which lead to different optimizations. A detailed analysis has been made to help determining the best objective func- tion to choose in each case. Many tests were performed, proving the effectiveness of the program and yielding intuitive results in specially prepared test cases, e.q. in a wind rose with a very strong main wind direction the output layout of the program was a row of turbines facing the wind. The program is also able to increase in a 0.95% the power output of the Danish offshore wind farm Horns Rev, when comparing it with the present layout. A comparison between the installed capacity per km2 and the efficiency of the wind farm was carried out. It was found that for very large wind farms (in the order of a hundred) there is less potential for optimizing the layouts. A sensitivity analysis was performed and the program’s output was seen to be little sensitive to changes in the wind rose. The optimized layout yielded better results than a grid layout if the wind rose was rotated or even changed. The main reason was found to be the tendency of turbines to move towards the perimeter of the wind farm. Using these results, the visual impact was taken into account and a re- arrangement of turbines was proposed for the HR wind farm. A grid-alike layout is adapted following the general trends of the optimized layout, allow- ing a good compromise between visual effects and an optimized layout. The Profit function is also tested, and it is seen that it performs well but that the running times are prohibitive. Some ways around this problem are discussed and compared., pdf
(2008) Optimization of the Regional Spatial Distribution of Wind Power Plants to Minimize the Variability of Wind Energy Input into Power Supply Systems, Journal of Applied Meteorology and Climatology 47(12), p. 3099-3116
In contrast to conventional power generation, wind energy is not a controllable resource because of its stochastic nature, and the cumulative energy input of several wind power plants into the electric grid may cause undesired fluctuations in the power system. To mitigate this effect, the authors propose a procedure to calculate the optimal allocation of wind power plants over an extended territory to obtain a low temporal variability without penalizing too much the overall wind energy input into the power system. The procedure has been tested over Corsica (France), the fourth largest island in the Mediterranean Basin. The regional power supply system of Corsica could be sensitive to large fluctuations in power generation like wind power swings caused by the wind intermittency. The proposed methodology is based on the analysis of wind measurements from 10 anemometric stations located along the shoreline of the island, where most of the population resides, in a reasonably even distribution. First the territory of Corsica has been preliminarily subdivided into three anemological regions through a cluster analysis of the wind data, and the optimal spatial distribution of wind power plants among these regions has been calculated. Subsequently, the 10 areas around each station have been considered independent anemological regions, and the procedure to calculate the optimal distribution of wind power plants has been further refined to evaluate the improvements related to this more resolved spatial scale of analysis. © 2008 American Meteorological Society., url
(2009) A new tool for wind farm optimal design, 2009 IEEE Bucharest PowerTech, p. 1-7, Ieee
An Evolutive Algorithm (EA) for wind farm optimal design is presented. The algorithm objective is to optimize the profits given an investment on a wind farm. Net Present Value (NPV) will be used as a figure of the revenue in the proposed method. To estimate the NPV is necessary to calculate the initial capital investment and net cash flow throughout the wind farm life cycle. The maximization of the NPV means the minimization of the investment and the maximization of the net cash flows (to maximize the generation of energy and minimize the power losses). Both terms depend mainly of the number and type of wind turbines, the tower height and geographical position, electrical layout, among others. Besides, other auxiliary costs must be to keep in mind to calculate the initial investment such as the cost of auxiliary roads or tower foundations. The complexity of the problem is mainly due to the fact that there is not analytic function to model the wind farm costs and most of the main variables are linked., url
(2009) A simple generic wind farm cost model tailored for wind farm optimization
The TOPFARM project addresses optimization of wind farm topology and control strategy based on aeroelastic modeling of loads as well as of power production. Crucial factors in this connection are the overall (ambient) wind climate at the wind farm site, the characteristics, position of the the wind turbine individual wind turbines, the wind turbine control/operation strategy for wind turbines interacting through wakes, and possible a priory defined constraints imposed on the wind farm topology and control. To achieve an optimal economic output from a wind farm during its lifetime, the optimal balance between capital costs, operation and maintenance costs, fatigue lifetime consumption and power production output is to be assessed on a rational background. This is formed by aeroelastic simulations of the loads as well as of the power production for each turbine in a wind farm, taking into account the effects of wind turbine wakes on the individual wind turbine inflow characteristics. In an optimization context, the synthesis of all required sub-models is performed by formulating an object (or penalty) function for the optimization problem. In the framework of TOPFARM this penalty function is formulated in economical terms, whereby the need of cost models for all costs depending on wind farm production and loading arises. The present report deals with a generic wind farm cost model complex with this characteristic. The main components of the cost model complex are wind farm financial costs and wind farm operating costs, each of which in turn consists of a number of separate sub-models
(2009) Efficient hybrid distributed genetic algorithms for wind turbine positioning in large wind farms, 2009 IEEE International Symposium on Industrial Electronics(ISlE), p. 2196-2201, Ieee
An efficient hybrid distributed genetic algorithm is proposed to determine the proper number and locations of wind turbines in large wind farms. The objective of this optimal process is to find a solution that maximizes the annual profit obtained from a wind farm. It is well-known that genetic algorithms are good for global searches, but are weak for local searches. To improve the performance of finding the optimal solution in a large search space, the hybrid methodology combines a distributed genetic algorithm and steepest ascent hill-climbing local search algorithms. The hill-climbing algorithm provides a powerful strategy for searching the local optimal solution by exploring the neighborhood of the current state. In this paper, the hill-climbing algorithm is further enhanced by a heuristic method to reduce the execution time for finding the optimal value. Test results show that this proposed hybrid distributed genetic algorithm adequately demonstrates its effectiveness in solution quality and execution time., url
(2009) Modeling and simulation of optimal wind turbine configurations in wind farms, 2009 World Non-Grid-Connected Wind Power and Energy Conference, p. 1-5, Ieee
Wake effect is a key factor leading to the efficiency decrease of the whole wind farm. For different configurations of wind turbines, the accurate prediction of wake effect between wind turbines is vital to the calculation of wind farm cost and benefit. To describe the wake effect better in the wind turbine optimization, a new non-linear wake expansion of the wake model was introduced into the calculation of flat or slightly undulating topography and offshore wind farms. Combining the cost-benefit model of wind farm projects and considering multiple factors and the benefit evaluation model of increasing the number of wind turbines in a wind farm, and then a more complete and effective mathematical model was developed to decide the optimal configuration of wind turbines. Finally, a program using a genetic algorithm was made based on the above models. According to the economical efficiency analysis and comparison of the different wind turbine placement schemes for some wind farm projects to the earlier studies, the optimal number of the wind turbines and the corresponding placement scheme were determined and shows some differences from the earlier study. ©2009 IEEE., url
(2009) Optimal micro-siting of wind turbines by genetic algorithms based on improved wind and turbine models, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference(3), p. 5092-5096, Ieee
Micro-siting of wind turbines is a key technology for wind farm configuration. In this paper, Weibull function is used to describe the probability of wind speed distribution and turbine speed-power curve is employed to estimate turbine power generation. The improved wind and turbine models are formulated into an optimal control framework in terms of minimizing the cost per unit energy of the wind farm, which is solved by a binary-encoded genetic algorithm. Simulation results indicate that the proposed method could provide better performance and represents a more realistic and effective strategy for optimal micro-siting of the wind farm., url
(2009) Optimal Siting of Wind Turbines Using Real-Coded Genetic Algorithms, EWEC 2009(010)
In this paper, a real-coded genetic algorithm is utilized to optimize wind turbine placement in a wind farm. The location of each wind turbine could be freely adjusted within a predefined cell in order to maximize the generated energy. Simulations are carried out to demonstrate that the present study could improve wind farm efficiency and extract more energy., url, pdf
(2009) Simulated Annealing for Optimization of Wind Farm Annual Profit, Logistics and Industrial Informatics, 2009. LINDI 2009. 2nd International 0(2), p. 1–5, IEEE
In this paper, a simulated annealing is designed and applied to compute the optimal placement of wind turbines in a wind farm. The objetive of this process is to find a combination of aero-generators that maximizes the annual profit obtained from a wind farm, measured as the generated power in one year. Simulated annealing (SA) is a metaheuristic for global optimization that we will use here to search in the large landscape of possible solutions. Maximizing the generated power depends on the distribution of the aero-generators and the geometry of the wind farm. In this article we analyze several case studies according to different wind conditions. We will show optimal solutions and prove that they are better concerning the present best result in the literature., url
(2009) Solving the Turbine Positioning Problem for Large Offshore Wind Farms by Simulated Annealing, Wind Engineering 33(3), p. 287-297
The current paper is concerned with determining the optimal layout of the turbines inside large offshore wind farms by means of an optimization algorithm. We call this the Turbine Positioning Problem. To achieve this goal a simulated annealing algorithm has been devised, where three types of local search operations are performed recursively until the system converges. The effectiveness of the proposed algorithm is demonstrated on a suite of real life test cases, including Horns Rev offshore wind farm. The results are verified using a commercial wind resource software indicating that this method represents an effective strategy for the wind turbine positioning problem. The findings enable the comparison of the optimized and the grid layouts and the study of the wake differences between these configurations. It is seen that for very large offshore wind farms the difference in wake losses is negligible while, as the wind farm’s size reduces, the differences start becoming significant. A sensitivity analysis is also performed showing that greater density of turbines in the perimeter of the optimized wind farm reduces the wake losses even if the wind climate changes., url
(2009) Study on computational grids in placement of wind turbines using genetic algorithm, 2009 World Non-Grid-Connected Wind Power and Energy Conference 2, p. 1-4, IEEE
To optimize the placement of wind turbines using a genetic algorithm for the fixed size of wind farm, the appropriate computational grids are the basis of the succeeding work. The optimized scheme was tightly restricted by the rationality and accuracy of computational grids. In this paper, based on the consideration of actual wind and wake characteristics of wind turbines, the (a) shape of the grids, (b) arranging the direction of the grids, and (c) the density of the grids were introduced to study the effect of computation grids on the optimization results. Furthermore, the grids' division method in the scheme's optimization of wind turbines placement under different conditions was discussed to increase the power capacity of the wind farm to obtain the maximum benefit of the investment., url
(2009) Wind Farm Optimal Design Including Risk, Renewable Energy
(2010) An extended pattern search approach to wind farm layout optimization, ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2010, p. 1-10
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 established simplified wake model, which accounts the farm is estimated using an 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 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 functions. In addition, the same evaluation models and objective the algorithm’s layouts motivate a heuristic that yields the best layouts found to date.
(2010) Design of wind farm layout for maximum wind energy capture, Renewable Energy 35(3), p. 685-694, Elsevier Ltd
Wind is one of the most promising sources of alternative energy. The construction of wind farms is destined to grow in the U.S., possibly twenty-fold by the year 2030. To maximize the wind energy capture, this paper presents a model for wind turbine placement based on the wind distribution. The model considerswake loss, which can be calculated based on wind turbine locations, and wind direction. Since the turbine layout design is a constrained optimization problem, for ease of solving it, the constraints are transformed into a second objective function. Then a multi-objective evolutionary strategy algorithm is developed to solve the transformed bi-criteria optimization problem, which maximizes the expected energy output, as well as minimizes the constraint violations. The presented model is illustrated with examples as well as an industrial application., url
(2010) New approach on optimization in placement of wind turbines within wind farm by genetic algorithms, Renewable Energy 35(7), p. 1559-1564, Elsevier Ltd
In the present study, the placement of wind turbines in wind farm has been resolved with a new coding and also a novel objective function in Genetic algorithm approach. In comparison to previous works, the results have been noticeably improved. The presented objective function, with its adjustable coefficients, provides more control on the cost, power, and efficiency of wind farm in comparison with earlier objective functions. Furthermore, in earlier jobs it was required to consider some subpopulations as well as individuals. However, there is no need to use the subpopulations in recent research by applying new coding approach in solving this problem. Therefore, running genetic algorithm only once for each case is sufficient. In this approach, three cases are considered (a) unidirectional uniform wind, (b) uniformwind with variable direction, and (c) non-uniform wind with variable direction. In Case (a), 10 individuals evolve over 150 generations. Case (b) has 20 individuals evolve for 150 generations. Case (c) starts with 20 individuals evolve for 100 generations. In addition to optimal configurations, results include fitness, total power output, efficiency of output power, number of turbines and objective function coefficients for each configuration., url
(2010) Offshore windfarm layout optimization, 2010 9th International Conference on Environment and Electrical Engineering, p. 542-545, Ieee
The paper investigates the appliance of an optimization routine to establish best offshore windfarm layout, in terms of chosen cost function. An introduction to windfarm layout problem is given. Wake effect, turbine spacing and in- farm wind distribution are covered. Sample Matlab program results are provided and commented on., url
(2010) On Aerodynamic Optimization of Wind Farm Layout, Pamm 10(1), p. 539-540
This paper presents a method for determination of optimum positions of single wind turbines within the wind farms installed on arbitrary configured terrains, in order to achieve their maximum production effectiveness., url
(2010) Optimal Micro-siting of Wind Farms by Particle Swarm Optimization, Advances in Swarm Intelligence 6145, Ying Tan, Yuhui Shi, Kay Chen Tan (ed.), p. 198-205, Berlin, Heidelberg: Springer Berlin Heidelberg
This paper proposes a novel approach to optimal placement of wind turbines in the continuous space of a wind farm. The control objective is to maximize the power produced by a farm with a fixed number of turbines while guaranteeing the distance between turbines no less than the allowed minimal distance for turbine operation safety. The problem of wind farm micro-siting with space constraints is formulated to a constrained optimization problem and solved by a particle swarm optimization (PSO) algorithm based on penalty functions. Simulation results demonstrate that the PSO approach is more suitable and effec- tive for micro-siting than the classical binary-coded genetic algorithms., url
(2010) Optimal positioning of wind turbines on Gökçeada using multi-objective genetic algorithm, Wind Energy 13(4), p. 297-306
This paper addresses the problem of optimal placement of wind turbines in a farm on Gokçeada Island located at the north-east of Aegean Sea bearing full potential of wind energy generation. A multi-objective genetic algorithm approach is employed to obtain optimal placement of wind turbines by maximizing the power production capacity while constraining the budget of installed turbines. Considering the speed and direction history, wind with constant intensity from a single direction is used during optimization. This study is based on wake deficit model mainly because of its simplicity, accuracy and fast calculation time. The individuals of the Pareto optimal solution set are evaluated with respect to various criteria, and the best configurations are presented. In addition to best placement layouts, results include objective function values, total power output, cost and number of turbines for each configuration., url
(2010) Optimization of the Layout of Large Wind Farms using a Genetic Algorithm
In this study, a code ‘Wind Farm Optimization using a Genetic Algorithm’ (referred as WFOG) is developed in MATLAB for optimizing the placement of wind turbines in large wind farms to minimize the cost per unit power produced from the wind farm. A genetic algorithm is employed for the optimization. WFOG is validated using the results from previous studies. The grid spacing (distance between two nodes where a wind turbine can be placed) is reduced to 140 wind turbine rotor diameter as compared to 5 rotor diameter in previous studies. Results are obtained for three different wind regimes: Constant wind speed and fixed wind direction, constant wind speed and variable wind direction, and variable wind speed and variable wind direction. Cost per unit power is reduced by 11.7 % for Case 1, 11.8 % for Case 2, and 15.9 % for Case 3 for results obtained using WFOG. The advantages/benefits of a refined grid spacing of 140 rotor diameter (1 m) are evident and are discussed., url
(2010) Optimization of Wind Farm Layout, FME Transactions 38, p. 107-114
This paper presents a method for determination of optimum positions of single wind turbines within the wind farms installed on arbitrary configured terrains, in order to achieve their maximum production effectiveness. This method is based on use of the genetic algorithm as optimization technique. The wind turbine aerodynamic calculation is unsteady, based on the blade modeled as a vortex lattice and a free-wake type airflow behind the blade. Optimization method is developed for two different fitness functions. Both functions use the total energy obtained from the farm as one of the key variables. The second also involves the total investments in a single wind turbine, so the optimization process can also include the total number of turbines as an additional variable. The method has been tested on several different terrain configurations, with special attention paid to the overall algorithm performance improvements by selecting certain genetic algorithm parameters., pdf
(2010) Optimization of wind farm turbines layout using an evolutive algorithm, Renewable Energy 35(8), p. 1671-1681
The optimum wind farm configuration problem is discussed in this paper and an evolutive algorithm to optimize the wind farm layout is proposed. The algorithm’s optimization process is based on a global wind farm cost model using the initial investment and the present value of the yearly net cash flow during the entire wind-farm life span. The proposed algorithm calculates the yearly income due to the sale of the net generated energy taking into account the individual wind turbine loss of production due to wake decay effects and it can deal with areas or terrains with non-uniform load-bearing capacity soil and different roughness length for every wind direction or restrictions such as forbidden areas or limitations in the number of wind turbines or the investment. The results are first favorably compared with those previously published and a second collection of test cases is used to proof the performance and suitability of the proposed evolutive algorithm to find the optimum wind farm configuration., url
(2010) The Wind Farm Layout Optimization Problem
An important phase of a wind farm design is solving the Wind Farm Layout Optimization Problem (WFLOP), which consists in optimally positioning the turbines within the wind farm so that the wake effects are minimized and therefore the expected power production maximized. Although this problem has been receiving increasing attention from the scientific community, the existing approaches do not completely respond to the needs of a wind farm developer, mainly because they do not address construction and logistical issues. This paper describes the WFLOP, gives an overview on the existing work, and discusses the challenges that may be overcome by future research., pdf
(2010) TOPFARM-next generation design tool for optimization of wind farm topology and operation... background, vision and challenges, Torque 2010
This paper describes the background and vision of the TOPFARM project, which aims at rational economical optimization of wind farm layout and control strategy, in the sense that the optimal between capital balance maintenance costs, costs, operation and fatigue lifetime consumption and power production output is pursued. Consequently, and contrary to common practice, both production and load aspects are thus included in the optimization procedure. A key factor in the successful achievement of the project goal is computational speed, which is a challenge that inevitable has to be meet on all levels ranging from the wind farm flow field modelling over aeroelastic simulation to the optimization procedure. Examples of specific derived challenges, following from this request, are identified and described, and solutions to overcome qualitatively sketched., url
(2010) TOPFARM-next generation design tool for optimization of wind farm topology and operation... background, vision and challenges, Torque 2010
This paper describes the background and vision of the TOPFARM project, which aims at rational economical optimization of wind farm layout and control strategy, in the sense that the optimal between capital balance maintenance costs, costs, operation and fatigue lifetime consumption and power production output is pursued. Consequently, and contrary to common practice, both production and load aspects are thus included in the optimization procedure. A key factor in the successful achievement of the project goal is computational speed, which is a challenge that inevitable has to be meet on all levels ranging from the wind farm flow field modelling over aeroelastic simulation to the optimization procedure. Examples of specific derived challenges, following from this request, are identified and described, and solutions to overcome qualitatively sketched., url
(2010) TOPFARM-next generation design tool for optimization of wind farm topology and operation... background, vision and challenges, Torque 2010
This paper describes the background and vision of the TOPFARM project, which aims at rational economical optimization of wind farm layout and control strategy, in the sense that the optimal between capital balance maintenance costs, costs, operation and fatigue lifetime consumption and power production output is pursued. Consequently, and contrary to common practice, both production and load aspects are thus included in the optimization procedure. A key factor in the successful achievement of the project goal is computational speed, which is a challenge that inevitable has to be meet on all levels ranging from the wind farm flow field modelling over aeroelastic simulation to the optimization procedure. Examples of specific derived challenges, following from this request, are identified and described, and solutions to overcome qualitatively sketched., url
(2010) Wind farm topology optimization including costs associated with structural loading, (TORQUE) The Science of Making Torque from the Wind, 3rd Conference, url
(2010) Wind farm topology optimization including costs associated with structural loading, Torque 2010, url
(2010) Wind turbines type and number choice using combinatorial optimization, Renewable Energy 35(9), p. 1887-1894, Elsevier Ltd
The paper addresses the problem associated with the optimal wind park design. A combinatorial opti- mization model for wind turbines type and number choice and placement considering the given wind conditions and wind park area is developed. The wind park investment costs and the total power relation as function of wind turbines number and type are used as optimization criteria. The optimization problem is formulated as a single criterion mixed-integer nonlinear discrete combinatorial task. The different wind park conditions are introduced into optimization tasks formulation as variables relations and restrictions. Two basic wind directions cases are taken into consideration – uniform and predomi- nant wind directions for two wind park area shapes – square and rectangular. The developed wind park design approach was tested numerically by solving of different optimization tasks formulations based on wind turbines real parameters data. The numerical testing shows the applicability of the developed optimization approach. Using it will help to find mathematically reasoned wind turbines choice as contradiction to the heuristic approaches., url
(2011) A fast algorithm based on the submodular property for optimization of wind turbine positioning, Renewable Energy 36(11), p. 2951-2958
In the design of a wind farm, the placement of turbines is an important factor that affects the efficiency and profit, but automatic placement of turbines is still a challenging problem. This study reveals the “submodular” property of the wind turbine positioning problem based on Jensenwake model. Based on this property, a “lazy greedy” algorithm is used to optimize the placement. This method can obtain solutions with theoretical guarantee of quality. It can also estimate the lower bound of the optimal value of the objective function. This method is tested on three types of wind scenarios. Compared to previous research, this algorithm takes much less time, and always gains a better solution. To enlarge the application scope, the wake model is extended to the large scale complex terrain in this study. The present algorithm and some other algorithms are tested in the simulation of the complex terrain. The experimental results demonstrate the present method’s superior performance., url
(2011) An Improved Evolutive Algorithm for Large Offshore Wind Farm Optimum Turbines Layout, IEEE Trondheim PowerTech, p. 1-6
A tool for optimal wind turbines location in large offshore wind farms is proposed. The algorithm objective is to optimize the profits given an investment on an offshore wind farm. Net Present Value (NPV) is used as a figure of the revenue in the proposed method. To estimate the NPV is necessary to calculate the initial capital investment and net cash flow during the offshore wind farm life cycle. The problem is an integer- mixed type problem, exhibits manifold optimal solutions (convexity) and some variables have a range of non allowed values (solutions space not simply connected). This fact makes the problem non-derivable, preventing the use of classical analytical optimization techniques. The proposed optimization algorithm is an improved evolutionary algorithm, for which crossover and mutation operations, specifics to the problem of micro positioning, have been developed.
(2011) Application of Powell's optimisation method for the optimal number of wind turbines in a wind farm, IET Science, Measurement & Technology 5(3), p. 77
The goal of every wind farm designer is the production of the maximum possible power and minimising the installation cost. The cost can be significantly reduced using the minimum required number of wind turbines for specific power production, occupying at the same time the least possible acreage of land. In this work, Powell’s optimisation method has been used for the estimation of the optimal number of wind turbines and the total produced power in a wind farm. The method’s results are compared with those of earlier studies that have followed other approaches, presenting its effectiveness. The proposed method can be useful in the studies of wind farm designers as a supportive tool for the estimation of the optimal number of wind turbines in a wind farm., url
(2011) Genetic Optimal Micrositing of Wind Farms by Equilateral-Triangle Mesh(1994)
The micrositing problem designs the layout, i.e. the number of turbines and specific location of each one, for a given farm based on the information of the weather, terrain and landscape of the farm. It aims to capture the wind energy of a farm more effectively while satisfying the constrains on economical, social and environmental issues. The micrositing process, a challenging subject involving fluid dynamics and decision making, plays a crucial role in wind farmplanning (Conover & Davis, 1994). In engineering practice, designers usually calculate the wind flow of a given wind farm by commercial software, and empirically determine the installation positions of turbines based on the flow field. The flow field usually does not include the influence of turbines on the deflexion of the original air flow, i.e. wake effects. However, as the wake effects are complicated and strongly coupled, they play a crucial role in wind farm micrositing. In academia, the micrositing problem with the consideration of turbine wake effects were studied for relative flat terrains. Patel (1999) suggested that wind turbines should be placed in rows 8 ∼ 12 rotor diameters apart in the windward direction, and 1.5 ∼ 3 rotor diameters apart in the crosswind direction. As wind profiles were not considered, the solution was still an “empirical” one. Mosetti et al. (1994), for the first time, applied genetic algorithms (GA) to solve the problem of wind farm micrositing in a systematical manner. Grady et al. (2005) improved Mosetti’s work in terms of programming and computing, and obtained more reasonable results. Wan et al. (2009) introduced the Weibull function to describe the probability ofwind speed distributions and employed turbine speed-power curves to estimate turbine power generation. In Mosetti et al. (1994) and Grady et al. (2005), a square wind farm of 2km × 2km was partitioned into 10 × 10 squares and the turbines could only be installed in the center of suitable small squares. The square mesh (SM) simplified and reformulated the micrositing problem into a discrete-time optimization one, which could be tackled by a binary-coded GA. Although SM is the most simple and instinctive choice, it is worthwhile investigating alternative, and probably better meshing methods. In this paper, a novel equilateral-triangle mesh (ETM) is presented, which proves to be a more suitable method in terms of wind farm production and energy efficiency. The remainder of this paper is organized as follows. Section 2 introduces the methodology of the optimal micrositing problem. Section 3 carries out computational simulations and analyzes the results. Section 4makes concluding remarks., pdf
(2011) Optimization of Wind Farm Micro Sitting Based on Genetic Algorithm, Advanced Materials Research 347-353, p. 3545-3550
In order to increase wind energy utilization efficiency by the optimization of the wind farm micro sitting, a method which could calculate the wind farm velocity is proposed by consideration of multi turbines wake loss and superposition. Based on the given velocity data of a wind farm, the maximal annual energy production is set as the optimal objective and the ordinates of wind turbines would be the optimal variables, micro sittings of the wind farm turbines are optimized by genetic algorithm. Layout calculation result of the optimal method is quite similar to that of other successful search method, but higher efficiency is reached, and the micro sitting layout is agreement with the regular plum-type layout. Annual energy productions are also calculated under the condition of different wind turbine number. Results show annual energy production increases with the wind turbine number increased, but the increasing trend is lower and lower. The research could provide a reference to wind farm micro-sitting., url
(2011) Optimization of wind turbine placement using a viral based optimization algorithm, Procedia Computer Science 6, p. 469-474
In the present research, a new viral based optimization algorithm is used to find the optimal solution to wind turbine placement problems considering constant wind speed and unidirectional uniform wind. In this study, a MATLAB based program is developed to search the optimal number and position of wind turbines in large wind farms with the objective of minimizing the total cost per unit of power produced from the wind park. The results obtained by the proposed algorithm are compared with results from previous studies., url
(2011) Overall design optimization of wind farms, Renewable Energy 36(7), p. 1973-1982
An Evolutive Algorithm (EA) for wind farm optimal overall design is presented. The algorithm objective is to optimize the profits given an investment on a wind farm. Net Present Value (NPV) will be used as a figure of the revenue in the proposed method. To estimate the NPV is necessary to calculate the initial capital investment and net cash flow throughout the wind farm life cycle. The maximization of the NPV means the minimization of the investment and the maximization of the net cash flows (to maximise the generation of energy and minimise the power losses). Both terms depend mainly on the number and type of wind turbines, the tower height and geographical position, electrical layout, among others. Besides, other auxiliary costs must be to keep in mind to calculate the initial investment such as the cost of auxiliary roads or tower foundations. The difficulty of the problem is mainly due to the fact that there is neither analytic function to model the wind farm costs nor analytic function to model net generation. The complexity of this problem arises not only from a technical point of view, due to strong links between its variables, but also from a purely mathematical point of view. The problem consists of both discrete and continuous variables, being therefore an integer-mixed type problem. The problem exhibits manifold optimal solutions (convexity), some variables have a range of non allowed values (solutions space not simply connected) and others are integers. This fact makes the problem non-derivable, pre- venting the use of classical analytical optimization techniques., url
(2011) Seeding evolutionary algorithms with heuristics for optimal wind turbines positioning in wind farms, Renewable Energy 36(11), p. 2838-2844, Elsevier Ltd, url
(2011) TOPFARM - NEXT GENERATION DESIGN TOOL FOR OPTIMISATION OF WIND FARM TOPOLOGY AND OPERATION(January 2011)
() TOPFARM : Multi-fidelity Optimization of Wind Farms, p. 2-36
(2011) Topfarm wind farm optimization tool
(2011) Topfarm wind farm optimization tool
An offshore wind farm optimization framework was presented in detail and validated on two test cases: 1) Middelgrunden and 2) Stags Holt/Coldham. A detailed flow model for the mean flow in a wind farm was used together with a fatigue load calculation approach taking into account dynamic wake meandering and using pre-calculated short term fatigue loads in a database for rapid calculation of lifetime equivalent loads and energy production. A cost function was defined for the financial balance composed by energy production, turbine degradation, O&M, electrical grid costs and foundation costs. The cost function was coupled to an optimizer for optimization of the financial balance by adjusting the locations of individual turbines in a wind farm. The results are over all satisfying and are giving some interesting insights on the pros and cons of the design choices. They show in particular that the inclusion of the fatigue loads costs gives some additional details in comparison with pure power based optimization. The Middelgrunden test case resulted in an improvement of the financial balance of 2.1 M€ originating from a very large increase in the energy production value of 9.3 M€ counterbalanced by mainly electrical grid costs. The Stags Holt/Coldham test case resulted in an improvement of the financial balance of 3.1 M€.
(2011) TopFarm: Multi-fidelity Optimization of Offshore Wind Farm, ISOPE 2011(2007)
A wind farm layout optimization framework based on a multi-fidelity model approach is applied to the offshore test case of Middelgrunden, Denmark. While aesthetic considerations have heavily influenced the famous curved design of Middelgrunden wind farm, this work focuses on testing a method that optimizes the profit of offshore wind farms based on a balance of the energy production, the electrical grid costs, the foundations cost, and the wake induced lifetime fatigue of different wind turbine components. The multi-fidelity concept uses cost function models of increasing complexity (and decreasing speed) to accelerate the convergence to an optimum solution. In the EU TopFarm project, three levels of complexity are considered. The first level uses a simple stationary wind farm wake model to estimate the Annual Energy Production AEP, a foundations cost function based on the water depth, and an electrical grid cost function. The second level calculates the AEP and adds a wake induced fatigue cost function based on the interpolation of a database of simulations done for various wind speed and wake setups with the aero-elastic code HAWC2 and the Dynamic Wake Meandering (DWM) model. The third level includes directly the HAWC2 and DWM models in the optimization loop in order to estimate both the fatigue costs and the AEP. The novelty of this work is the implementation of the multi-fidelity, the inclusion of the fatigue costs in the optimization framework, and its application on an existing offshore wind farm test case.
(2011) TopFarm: Multi-fidelity Optimization of Offshore Wind Farm, ISOPE(2007)
A wind farm layout optimization framework based on a multi-fidelity model approach is applied to the offshore test case of Middelgrunden, Denmark. While aesthetic considerations have heavily influenced the famous curved design of Middelgrunden wind farm, this work focuses on testing a method that optimizes the profit of offshore wind farms based on a balance of the energy production, the electrical grid costs, the foundations cost, and the wake induced lifetime fatigue of different wind turbine components. The multi-fidelity concept uses cost function models of increasing complexity (and decreasing speed) to accelerate the convergence to an optimum solution. In the EU TopFarm project, three levels of complexity are considered. The first level uses a simple stationary wind farm wake model to estimate the Annual Energy Production AEP, a foundations cost function based on the water depth, and an electrical grid cost function. The second level calculates the AEP and adds a wake induced fatigue cost function based on the interpolation of a database of simulations done for various wind speed and wake setups with the aero-elastic code HAWC2 and the Dynamic Wake Meandering (DWM) model. The third level includes directly the HAWC2 and DWM models in the optimization loop in order to estimate both the fatigue costs and the AEP. The novelty of this work is the implementation of the multi-fidelity, the inclusion of the fatigue costs in the optimization framework, and its application on an existing offshore wind farm test case.
(2011) Wind Park Layout Design Using Combinatorial Optimization
The energy sector has essential influence on climate change and atmospheric pollution. Wind energy, being a clean and renewable energy, can greatly contribute to decreasing of the air pollution negative impacts. Generally speaking, the production of renewable energy from wind can have a positive socioeconomic benefit – it not only help to reduce the climate changing but also support meeting of the long-term world economical goals. Taking that into account, many countries are encouraging the building of industrial wind parks. The building of a wind park is an expensive and complex task involving a wide range of engineering and scientific knowledge. The design of a wind park can have profound implications for its future profitability. Sustainable wind park development has to be done in an ecological way which means evaluating of the all possible positive and negative influences on the environment. The development of new wind energy projects requires also a significant consideration of land use issues. One of the most important factors in selecting a wind energy site is the availability of proper wind resources. The wind itself is a variable source of energy. The ability of a wind turbine to extract power from varying wind is a function of three main factors – the wind power availability, the power curve of the generator, and the ability of the turbine to respond to wind fluctuations (Üstüntaşa & Şahin, 2008). Wind turbines are available in various sizes and power output. They are designed to operate over a range of wind speeds (3-25 m/s) and can be erected singly by an individual property owner or grouped together to form a wind farm (wind park) connected to a public grid (Rodman & Meentemeyer, 2006). The common challenge for the wind park designer is to maximize the energy capture within the given restrictions (White et al., 1997; Kusiak & Song, 2010). As there is pressure to build more compact wind farms to optimize land utilization, an determination of array losses for very close turbine spacing is required (Smith et al., 2006). The investigations on wind energy using essentially cover four principal topics (Ettoumi et al., 2008). The first one deals with the sensors and instrumentation used for wind measurements. The second one examines the evaluation of wind energy potential for a given region using various statistical approaches. The third is focused on the design and characterization of wind energy turbines. The fourth is the design and development of wind parks. The results of investigations in those areas are used by wind park planners to develop cost-effective wind parks. The investigations discussed here concern the problems associated with the forth topic – design of the wind park layout, including choice of the turbines type, number and their placement in the wind park area. How to choose the number and the type of the turbines to install depends on a variety of factors – wind conditions, terrain, investments costs, power output, environmental influence, etc. More powerful turbine is usually preferred to the less powerful one since both the cost of a turbine and the energy it generates is usually proportional to its nominal power. The placement of wind turbines on the wind park site (i.e. wind park layout) is affected by several factors which have to be taken into account – the number of turbines, wind direction, wake interactions between wind turbines, land availability (area and shape), etc. For the goal a combinatorial design model for defining wind turbines type, number and placement is proposed. It is used for formulation of mixed- integer nonlinear discrete combinatorial optimization tasks satisfying different design requirements and restrictions. The tasks solutions results define different optimal wind park layout designs. The solutions results can be used also to evaluate the impact of alternative wind park layout schemes on the investment costs and wind park power output.
(2012) Design of wind farm layout using ant colony algorithm, Renewable Energy 44, p. 53-62, url
(2012) DETC2012-71478 WIND FARM LAYOUT OPTIMIZATION CONSIDERING ENERGY GENERATION AND NOISE PROPAGATION, p. 1-10
(2012) Optimization Models for Turbine Location in Wind Farms
(2012) Unrestricted wind farm layout optimization (UWFLO): Investigating key factors influencing the maximum power generation, Renewable Energy 38(1), p. 16-30
A new methodology, the Unrestricted Wind Farm Layout Optimization (UWFLO), that addresses critical aspects of optimal wind farm planning is presented in this paper. This methodology simultaneously determines the optimum farm layout and the appropriate selection of turbines (in terms of their rotor diameters) that maximizes the net power generation. The farm layout model obviates traditional restrictions imposed on the location of turbines. A standard analytical wake model has been used to account for the velocity deficits in the wakes created by individual turbines. The wind farm power generation model is validated against data from a wind tunnel experiment on a scaled down wind farm. Reasonable agreement between the model and experimental results is obtained. The complex nonlinear optimization problem presented by the wind farm model is effectively solved using constrained Particle Swarm Optimization (PSO). It is found that an optimal combination of wind turbines with differing rotor diameters can appreciably improve the farm efficiency. A preliminary wind farm cost analysis is per- formed to express the cost in terms of the turbine rotor diameters and the number of turbines in the farm. Subsequent exploration of the influences of (i) the number of turbines, and (ii) the farm land size, on the cost per Kilowatt of power produced, yields important observations., url
(2013) A fast and effective local search algorithm for optimizing the placement of wind turbines, Renewable Energy 51, p. 64-70, Elsevier Ltd, url
(2013) Bionic optimization for micro-siting of wind farm on complex terrain, Renewable Energy 50, p. 551-557, url
() Computing the Optimal Layout of a Wind Farm, p. 93-104
(2013) Offshore wind farm layout optimization using mathematical programming techniques, Renewable Energy 53, p. 389-399, Elsevier Ltd, url
(2013) Optimal placement of wind turbines within wind farm using binary particle swarm optimization with time-varying acceleration coefficients, Renewable Energy 55, p. 266-276, Elsevier Ltd, url
(2013) The investigation of tower height matching optimization for wind turbine positioning in the wind farm, Journal of Wind Engineering and Industrial Aerodynamics 114, p. 83-95, Elsevier, url
[Could not find the bibliography file(s)]