# Wind farm layout optimization using genetic algorithm and its application to Daegwallyeong wind farm

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## Abstract

This paper proposes a new wind farm layout optimization methodology based on a genetic algorithm by implementing a simulation model considering wake effect. This method consists of (1) batch optimization to efficiently obtain a rough wind farm layout for the maximum energy production in a large scale, and (2) post-optimization to obtain a refined layout to further improve the energy production in a small scale. The proposed two-step optimization enables to efficiently optimize wind farm layout and thus can be applicable to layout optimization of large-scale wind farms. A case study with the actual Daegwallyeong wind farm shows that wake loss is improved by 2.3% point after the proposed layout optimization which means about 2.5% more energy production compared with the existing layout.

## Keywords

Wind farms Optimization Genetic algorithm Jensen’s model Daegwallyeong wind farm## 1 Introduction

Recently due to the environmental problems caused by existing energy sources and nuclear plant accidents, environmentally friendly energy sources such as wind power, biogas, solar energy, and renewable energy have attracted people’s attention, and various optimization studies on wind power [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] and solar energy [11, 12] have been proposed to maximize energy generation efficiency at the minimum cost. Among them, a major advantage of the wind power generation is that it does not require any extra cost except repair and maintenance cost. However, since it is very expensive to relocate installed wind turbines, various demonstration tests and optimization studies of wind farm layout have been proposed to maximize its energy generation efficiency. Especially genetic algorithms with various objective functions [13, 14, 15, 16, 17, 18] have been widely and successfully used for wind farm layout optimization for energy generation maximization. On the other hand, studies on economic evaluation of relocation of existing batches [19, 20] have been proposed to suggest relocation decision because already installed wind turbines are not easy to relocate until the design life is reached.

Among the wind farms installed in Korea, the Daegwallyeong wind farm produces the largest amount of wind power, and thus many studies on the farm have been performed [5, 6, 7, 8, 9]. Some studies have improved accuracy of the wind analysis model by calibrating weather data using a Weibull distribution [5, 6, 7], and there have been researches to find the optimum layout by relocating the existing wind farm layout in a trial and error manner [9]. However, a systematic wind farm layout optimization method has not been yet proposed, and accurate and realistic wind farm analysis models are not considered for the layout optimization.

Consequently, this paper proposes to use the wind farm analysis model considering wake loss implemented in MATLAB for wind farm layout optimization. In addition, two-step layout optimization using a genetic algorithm is proposed for more computationally efficient optimization and is applied to the Daegwallyeong wind farm for a case study. Korea Meteorological Agency’s wind data measured in 2017 are utilized in this study.

The remainder of the paper is organized as follows. Section 2 explains the numerical model for wind wake effect considered in the proposed method. Section 3 presents the Daegwallyeong wind farm model to be optimized in this study. Section 4 compares optimized wind farm layout results of the Daegwallyeong wind farm with those from the actual layout. Finally, Sect. 5 concludes the paper.

## 2 Theoretical background

When designing a wind farm, it is important to maximize its economic efficiency or annual production energy by considering various factors such as characteristic of a wind turbine, initial investment, and maintenance cost of the wind turbine as design variables. In the proposed study, all costs including investment and maintenance cost will not be considered during optimization since the number of wind turbines in the Daegwallyeong wind farm will be fixed. Section 2.1 explains the numerical model for wind wake effect and a typical factor for wind turbine installation, Sects. 2.2 and 2.3 describe how to calculate annual energy production and wind speed calibration using the numerical model, respectively, which will be used in the layout optimization explained in Sect. 3.

### 2.1 Wake effect (vortex phenomenon)

*r*

_{r}is the rotor radius,

*v*is the wind speed behind the front rotor,

*r*

_{1}is the wake radius,

*u*

_{0}is the oncoming wind speed, and

*u*is the downstream wind speed at a distance

*x*. Then, assuming that the wind speed right behind the rotor is 1/3 of

*u*

_{0}[21], the downstream wind speed passing the turbine

*i*under influence of the upstream wind of the turbine

*j*is written as

*r*

_{r}and distance

*x*is introduced as

*α*is defined by

*z*is the hub height of the wind turbine and

*z*

_{0}is the surface roughness of ground. In general, the wind speed through the

*i*th wind turbine for

*n*upstream turbines can be written as

### 2.2 Annual energy production calculation

**X**is a binary design variable vector in grid area, \( {\text{AEP}}_{\text{total}} ({\mathbf{X}}) \) is the total annual energy of the farm in MWh,

*N*(

**X**) is the number of the installed wind turbines, \( {\text{AEP}}_{i} ({\mathbf{X}}) \) is the annual energy for the

*i*th turbine in MWh, \( u_{i} \) is the wind speed for the

*i*th turbine considering the wake effect described in Sect. 2.1,

*θ*is the wind direction, and

*t*is the total hours in 1 year, that is, 24 × 365. Eq. (6) shows that the multiplication of the power of the

*i*th turbine denoted as \( P_{i} \left( {u_{i} \left( {u_{0} ,\theta } \right)} \right) \) and the probability density function of

*u*

_{0}and

*θ*denoted as \( p\left( {u_{0} ,\theta } \right) \) is integrated to calculate \( {\text{AEP}}_{i} ({\mathbf{X}}) \).

### 2.3 Site calibration for wind turbine

*z*

_{1}, and

*p*is the wind rate coefficient defined as

*z*

_{g}is the geometric altitude mean and

*z*

_{a}is the height of the wind speed measurement. However, since it is difficult to calculate the wind rate coefficient

*p*, data measured at two different heights are substituted into Eq. (7) which yields

## 3 Layout optimization of Daegwallyeong wind farm

### 3.1 Wind farm model

### 3.2 Specification of wind turbines

Specifications of wind turbines

Number of blades | 3 |

Diameter | 80 m |

Height | 80 m |

Swept area | 5000 m |

### 3.3 Calibration of wind speed data

Wind speed measured at each height

Height (m) | 10 | 50 | 80 |

Wind speed (m/s) | 3.6 | 4.9 | 5.5 |

### 3.4 Details for wind farm layout optimization

**X**is 285, the number of grids in the installable area, and the

*i*th component of

**X**becomes 1 when a wind turbine is installed in the

*i*th grid otherwise 0. In addition, the objective function is to maximize AEP described in Sect. 2.2, and since the number of wind turbines installed in the Daegwallyeong farm is 49, the sum of

**X**’s components is constrained to be 49.

Information used in the batch optimization

Input variables | Binary input |

Objective function | \( \hbox{max} \,{\text{AEP}}_{\text{total}} ({\mathbf{X}}) \) |

Constraint | \( {\text{sum}}({\mathbf{X}}) = 49 \) |

**X**during the post-optimization is 98 as shown in Table 4 since there are 49 wind turbines and each turbine has two binary coordinate inputs as shown in Fig. 8.

Input variables and objective function in the post-optimization

Input variables | Binary input |

Objective function | \( \hbox{max} \,{\text{AEP}}_{\text{total}} ({\mathbf{X}}) \) |

## 4 Optimization results of wind farm model

^{8}MWh. However, it is 1.55 × 10

^{8}MWh using the wake effect model. After the batch optimization, the annual energy production becomes 1.56 × 10

^{8}MWh and wake loss is 10.9%. Furthermore, after the post-optimization, the annual energy production is further improved to 1.59 × 10

^{8}MWh and the wake loss is 9.1% which is about 2% point less than the batch optimization result.

Comparison of annual energy production using wind data measured in 2017

Annual energy production (MWh) | Wake loss (%) | |
---|---|---|

Actual Daegwallyeong wind farm layout | ||

No wake model | 1.75 × 10 | – |

Wake model (56 × 56 grids) | 1.55 × 10 | 11.4 |

Optimized layout (wake model) | ||

Batch optimization (28 × 28 grids) | 1.56 × 10 | 10.9 |

Post-optimization (56 × 56 grids) | 1.59 × 10 | 9.1 |

## 5 Conclusion

In this study, the wind farm analysis model considering wake loss is applied for layout optimization using a genetic algorithm of the Daegwallyeong wind farm. The actual wind data measured in 2017 in the Daegwallyeong area are used for the layout optimization. For more computationally efficient optimization, two-step layout optimization is proposed where the first step is batch optimization in a large scale and the second step is post-optimization in a small scale. As a result of the Daegwallyeong wind farm layout optimization, the wake loss is reduced by 2.3% point compared with the actual wind farm layout which leads to an additional 0.4 × 10^{7} MWh production per year, that is, about 2.5% more energy production compared with the actual wind farm. This conclusion does not mean that the current layout has to be changed to the layout obtained from the proposed optimization since the Daegwallyeong wind farm is used for verification purpose. However, the proposed method can be applied in the future to the following cases: (1) when economical benefit from relocating wind turbines is higher than relocating cost; (2) when wind turbines in the Daegwallyeong area reach their design life and need to be replaced; (3) when constructing new wind farms not only on land, but also in offshore areas.

## Notes

### Acknowledgements

This research was supported by Energy Cloud R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT (No. 2016006843).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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