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This paper defines a new procedure for optimising wind farm turbine placement by means of Monte Carlo simulation method. To verify the algorithm’s accuracy, an experimental wind farm was tested in a wind tunnel. On the basis of experimental measurements, the error on wind farm power output was less than 4%. The optimization maximises the energy production criterion; wind turbines’ ground positions were used as independent variables. Moreover, the mathematical model takes into account annual wind intensities and directions and wind turbine interaction. The optimization of a wind farm on a real site was carried out using measured wind data, dominant wind direction, and intensity data as inputs to run the Monte Carlo simulations. There were 30 turbines in the wind park, each rated at 20 kW. This choice was based on wind farm economics. The site was proportionally divided into 100 square cells, taking into account a minimum windward and crosswind distance between the turbines. The results highlight that the dominant wind intensity factor tends to overestimate the annual energy production by about 8%. Thus, the proposed method leads to a more precise annual energy evaluation and to a more optimal placement of the wind turbines.

The current worldwide energy scenario and the stringent regulations on pollutant emissions in the industrialized countries have led to new strategies concerning energy sources and power generation.

The European Parliament has given its backing to the European Union climate change package which ensures that it will achieve its climate targets by 2020. According to the package, a 20% reduction in greenhouse gas emissions, a 20% improvement in energy efficiency, and a 20% share of renewables in the European Union energy mix should be achieved by 2020 [

During 2009, European Union countries installed 10,163 MW of wind power of the 10,526 MW installed across all of Europe [

As far as investment is concerned, during 2009 wind farms amounted to about €13 billion in the EU. Onshore wind power accounted for €11.5 billion (88.5%), and offshore wind power accounted for approximately €1.5 billion (11.5%) [

Europe’s 2009 installations are characterised by continuing strong development in the mature markets of Spain (2,459 MW) and Germany (1,917 MW), together with Italy (1,114 MW), France (1,088 MW), and the United Kingdom (1,077 MW). Portugal (673 MW), Sweden (512 MW), Denmark (334 MW), and Ireland (233 MW) also performed strongly [

Wind energy will play an important role in achieving the energy targets. Both small and industrial sized wind turbine systems have the maturity to be considered economically effective. The small wind turbine market is still developing and could see major growth in the near future.

Taking into account this scenario, it is important to improve energy production from the wind by means of either more efficient wind turbines or enhanced planning of wind farms in terms of wind turbine placement within wind parks and/or location selection. As is obvious, wind turbines are a mature technology and few margins are possible. For high-power wind farms, energy production needs to be optimised to be financially competitive with conventional forms of energy production.

This paper implements a new mathematical optimization procedure for wind turbine positioning within a wind farm. In this study, multicriteria optimization takes into account maximum energy production and minimum cost. The central factors are wind turbine number and their positioning within the farm based on the criteria above. In this study, a new approach was carried out by using the Monte Carlo simulation. Wind turbine interaction and wind speed intensity, as well as wind direction, were taken into account. A MATLAB [

The topic of the best placement of wind turbines has concerned several authors [

As demonstrated by Ammara et al. in [

The problem of designing wind parks has been addressed by Mosetti et al. [

In particular, first Mosetti et al. [

Kiranoudis et al. [

Marmidis et al. [

In this study, a wake model was implemented according to Jensen [

Wake scheme.

For a linear wake it is possible to link the wake radius, the rotor radius, and the distance from the rotor in the wake using the entrainment constant

The entrainment constant is empirically given by [

Moreover, the axial induction factor “

Considering the momentum conservation equation, the wake air velocity can be calculated taking into account (

In the case of a wind turbine running into multiple wakes, a linear composition of the kinetic energy deficits can be assumed. So the kinetic energy of the mixed wake is the sum of constituent wakes’ kinetic energy deficits. Consequently, (

To analyse systems of large dimensions [

The Monte Carlo class of algorithms is based on repeated random sampling to compute the results [

To validate the mathematical model, a small-scale experimental wind farm was built and tested in a wind tunnel [

Small-scale wind turbine characteristic.

Main small-scale wind turbine dimensions.

For the small-scale wind field, a

Test section: small-scale wind field grid.

Photograph of the wind farm in the wind tunnel test section.

To validate the mathematical model, experimental tests [

Optimal small-scale wind field configuration.

Using the optimal placement, a small-scale wind park power of

To simulate the performance of the wind farm, the wind field area was divided into cells in a grid. A wind turbine was placed in the centre of each cell. A square grid was used, which was divided into 100 possible turbine locations [

To simulate changing wind direction and wind turbine interactions, the following criteria were considered. For each turbine, a relative coordinates system was defined with the

Wind field with relative and global coordinate systems, as well as wakes.

Using the

Therefore, the two conditions in (

As far as the Monte Carlo Method simulation is concerned, the method is used to randomly place a certain number of wind turbines on a certain terrain. Several sets of Monte Carlo simulations were carried out to verify if the algorithm is sensitive to the number of attempts. In this work, 10,000 attempts are the best trade-off between accuracy and CPU time.

In this work, a small size wind turbine was used: JIMP20 manufactured by Jonica Impianti. The wind turbine power output versus wind velocity is shown in Figure

Main wind turbine characteristics.

Description | Value |
---|---|

Manufacturer | Jonica Impianti |

Model | JIMP20 |

Power | 20 kW |

Rotor diameter | 8 m |

Blade number | 3 |

Blade air foil | SG6040-6041 |

Hub height | 15 m |

Rotational speed | 100–200 r/min |

Cut in wind velocity | 3.5 m/s |

Cut out wind velocity | 37.5 m/s |

Over speed control | Active |

Yaw control | Passive |

Generator | Synchronous permanent magnet |

Electric tension | 380 V AC |

Wind turbine characteristic.

Wind direction variation was taken into account in the optimization procedure. Thus, velocity and direction data (measurements every 10 min) for a specific site (as an example) were used [

Test case site wind probability density function.

Test case site wind direction frequency.

Case study site and positioning grid.

Two different studies were carried out to verify algorithm performance. Firstly, 10,000 Monte Carlo simulations were run taking into account all the wind intensity and wind direction data in one year (case 1). Secondly, another 10,000 Monte Carlo simulations were run taking into account dominant wind direction and intensity only (case 2). In both cases, 30 wind turbines were considered.

Research into optimal wind turbine placement highlighted that most authors only considered dominant wind direction and magnitude. This is a restrictive approximation considering how high the wind varies in specific sites. Thus, results obtained by neglecting wind direction and magnitude variability tend to be less precise in annual energy production estimation. Therefore, investors in the wind energy sector would not have had the correct cash flow using that economic analysis. The technique in this paper can estimate annual energy production more precisely.

Figure

Optimal placement after 10,000 Monte Carlo simulation runs (case 1).

Optimal placement after 10,000 Monte Carlo simulation runs (case 2).

Figure

The results also show that optimization using the dominant wind direction and intensity tends to overestimate annual energy production by 8.79% compared to those calculated using all the wind direction and intensity data.

This study presents a new optimization technique for wind turbine placement based on the Monte Carlo method. The annual energy output of the wind park was used as a fitness parameter, while wind turbine position was considered an independent variable. The mathematical model takes into account wind turbine interaction, as well as wind direction and intensity, as a function of time. By considering wind variability in the optimization method, instead of a fixed wind, a new and more precise way to set up a wind park is revealed. This led to a more realistic estimation of annual energy production.

To verify model accuracy, an experimental test in a wind tunnel was carried out using a small-scale wind field with correspondingly small-scale wind turbines. Moreover, a simulation of the experimental model was run using the implemented algorithm. By comparing the experimental and simulated results, it is possible to notice how the model is able to predict wind park power output with a low error (less than 4%). Thus, the model is capable of taking into account turbine interactions correctly.

In this paper, two main studies were carried out and presented. The first study is based on the use of wind data in terms of direction and intensity per year. In the second, only dominant wind direction and intensity were used.

The results suggest that optimal wind turbine placement should take into account changing wind direction and intensity which can lead to a scattered wind turbine distribution on the ground, while placement using only the dominant wind data prevalently aligned with the dominant wind direction. In both cases, all the available terrain surface is taken up. Moreover, using dominant wind intensity tends to overestimate the annual energy production by about 9%. Thus, using all the wind data leads to a more precise annual energy evaluation and a more optimal placement of wind turbines.

Axial induction factor

Entrainment constant

Number of wind turbines in the field

Wind turbine rotor radius

Wind turbine rotor diameter

Small-scale wind turbine rotor diameter

Hydraulic diameter of wind tunnel test section

Wind tunnel test section length

Wake radius at distance

Wind velocity of undisturbed wind

Air velocity at distance

Air velocity just behind the wind turbine rotor

Air velocity downstream of

Distance from the rotor

Surface roughness of the installation site

Wind turbine hub height.

The authors declare that there is no conflict of interests regarding the publication of this paper.