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JMST Advances

, Volume 1, Issue 4, pp 249–257 | Cite as

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

  • Jeong Woo Park
  • Bo Sung An
  • Yoon Seung Lee
  • Hyunsuk Jung
  • Ikjin LeeEmail author
Letters
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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)

The wake effect phenomenon means that inertia and frictional forces do not flow well in the direction in which air circulates. The flowing fluid rubs against stationary fluid around it where air is vortexed at the interface between the stationary and kinetic fluid. It is a frequent phenomenon when there is a dramatic change in the width of the space through which the fluid can flow. In this paper, the wake effect is considered essential because the weakened wind that passed through the wind turbine reduces energy production efficiency of another wind turbine installed behind. Figure 1 shows wind velocity through the rear wind turbine according to the wake effect of the front wind turbine.
Fig. 1

Schematic of analytical wake effect model

This paper proposes to utilize a numerical model considering the wake effect [1, 2, 3] for more accurate wind farm layout optimization. Generally, the amount of energy generated by a wind turbine is determined by the wind speed passing through each wind turbine. To calculate the actual wind speed of passing through each wind turbine by considering the wind wake effect, Jensen’s model is utilized in this study. Considering that, the momentum is preserved in the wake between two wind turbines in Fig. 1, the momentum equilibrium equation can be expressed as
$$ \pi r_{\text{r}}^{2} v + \pi \left( {r_{1}^{2} - r_{\text{r}}^{2} } \right)u_{0} = \pi r_{1}^{2} u_{ij} , $$
(1)
where rr is the rotor radius, v is the wind speed behind the front rotor, r1 is the wake radius, u0 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 u0 [21], the downstream wind speed passing the turbine i under influence of the upstream wind of the turbine j is written as
$$ u_{ij} = u_{0} \left( {1 - \frac{2}{3}\left( {\frac{{r_{\text{r}} }}{{r_{1} }}} \right)^{2} } \right). $$
(2)
To apply the Jensen model, additional assumption about the turbine rotor radius rr and distance x is introduced as
$$ r_{1} = r_{\text{r}} + \alpha x, $$
(3)
where entrainment constraint α is defined by
$$ \alpha = \frac{0.5}{{\ln \left( {z/z_{0} } \right)}}. $$
(4)
In Eq. (4), z is the hub height of the wind turbine and z0 is the surface roughness of ground. In general, the wind speed through the ith wind turbine for n upstream turbines can be written as
$$ u_{i} = u_{0} \left( {1 - \sqrt {\sum\limits_{j = 1}^{n} {\left( {1 - \frac{{u_{ij} }}{{u_{0} }}} \right)^{2} } } } \right). $$
(5)

2.2 Annual energy production calculation

Power generation amount of a wind turbine is determined by wind speed and wind turbine type. The wind turbine installed in the Daegwallyeong farm and its power curve will be explained in detail in Sect. 3.2. Once the power generation of a wind turbine for given wind speed is determined, the total annual energy of the wind farm can be calculated as
$$ \begin{aligned} {\text{AEP}}_{\text{total}} ({\mathbf{X}}) & = \sum\limits_{i = 1}^{{N({\mathbf{X}})}} {{\text{AEP}}_{i} } ({\mathbf{X}}) \\ & = \sum\limits_{i = 1}^{{N({\mathbf{X}})}} {\int_{0}^{{360^{ \circ } }} {\int_{0}^{{u_{\text{max} } }} {P_{i} \left( {u_{i} \left( {u_{0} ,\theta } \right)} \right)} } } \times p\left( {u_{0} ,\theta } \right) \times t{\text{d}}u_{0} {\text{d}}\theta , \\ \end{aligned} $$
(6)
where 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 ith turbine in MWh, \( u_{i} \) is the wind speed for the ith 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 ith turbine denoted as \( P_{i} \left( {u_{i} \left( {u_{0} ,\theta } \right)} \right) \) and the probability density function of u0 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

Since anemometers to measure wind speed are installed in general at lower positions than wind turbines, it is necessary to calibrate the measured wind speed passing through wind turbines. The Deacon equation [22, 23] is utilized for the calibration and expressed as
$$ U(z_{2} ) = U(z_{1} )\left( {\frac{{z_{2} }}{{z_{1} }}} \right)^{p} , $$
(7)
where \( U(z_{1} ) \) is the wind speed at height of z1, and p is the wind rate coefficient defined as
$$ p = a + b\ln \left( {U_{2} } \right), $$
(8)
where
$$ a = \frac{1}{{\ln \left( {\frac{{z_{\text{g}} }}{{z_{0} }}} \right)}} + \frac{0.088}{{1 - 0.088\ln \left( {\frac{{z_{\text{a}} }}{10}} \right)}}, $$
(9)
and
$$ b = \frac{ - 0.088}{{1 - 0.088\ln \left( {\frac{{z_{\text{a}} }}{10}} \right)}}. $$
(10)
In Eqs. (9) and (10), zg is the geometric altitude mean and za 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
$$ p = \frac{{\ln \left( {\frac{{U(z_{2} )}}{{U(z_{1} )}}} \right)}}{{\ln \left( {\frac{{z_{2} }}{{z_{1} }}} \right)}}. $$
(11)

3 Layout optimization of Daegwallyeong wind farm

3.1 Wind farm model

Currently, 53 wind turbines are installed in the Daegwallyeong wind farm among which 49 wind turbines have been recently installed within a range of 7 km both in horizontal and vertical directions as shown in Fig. 2. However, due to environmental problems such as roads and mountainous terrain, areas where wind turbines are installable in the above range are limited as marked in red in Fig. 3.
Fig. 2

Wind turbine layout installed in Daegwallyeong wind farm

Fig. 3

Limited installable areas in Daegwallyeong wind farm

In addition, since the layout optimization of the wind turbines requires a large amount of computations, grids are utilized in the area where the wind turbines are to be installed as in the previous researches. Figure 4 shows the grids created for the limited installable area in Fig. 3. Firstly, 28 × 28 grids are created in the entire 7 km × 7 km area which means each grid has a size of 250 m × 250 m. Later, these coarse grids become finer for more accurate layout optimization. Since there are a total of 285 grids in the installable area, layout optimization of the wind farm is performed with 285 binary inputs. Details of the optimization process are discussed in Sect. 3.4.
Fig. 4

Grids created for optimization

3.2 Specification of wind turbines

The wind turbines currently installed in the Daegwallyeong wind farm are VESTAS V80 2 MW and generate up to 2 MW energy depending on wind speed passing the wind turbines. Key information of the wind turbines in this study is presented in Table 1. Figure 5 shows the power curve of the wind turbine according to the wind speed. When the wind speed is less than 3 m/s, no energy is generated. On the other hand, when the wind speed is more than 15 m/s, the maximum power is generated as shown in Fig. 5. However, the wind speed higher than 25 m/s is not considered in this study since the wind turbine does not operate at the wind speed due to equipment maintenance problems.
Table 1

Specifications of wind turbines

Number of blades

3

Diameter

80 m

Height

80 m

Swept area

5000 m2

Fig. 5

Power curve of VESTAS V80

3.3 Calibration of wind speed data

In this study, the wind data in the Daegwallyeong area measured every minute from January to December 2017 by Korea Meteorological Agency is utilized [24, 25]. Figure 6 shows the wind speeds measured in an anemometer at a height of 10 m excluding wind speeds less than 3 m/s. As can be seen in Fig. 6, most of wind directions are about 270° which means most of winds blow westward, and most of wind speeds are less than 10 m/s.
Fig. 6

Characteristics of wind data measured in 2017

Since the height of the wind turbine installed in the Daegwallyeong farm is 80 m, it is necessary to calibrate the measured wind speed according to the height as explained in Sect. 2.3. For the calibration, mean values of the wind speeds measured at specific heights from 2005 to 2009 listed in Table 2 are used. Then, the wind rate coefficient can be estimated as
$$ p = \frac{{\ln \left( {\frac{{U(z_{2} )}}{{U(z_{1} )}}} \right)}}{{\ln \left( {\frac{{z_{2} }}{{z_{1} }}} \right)}} = \frac{{\ln \left( {\frac{5.5}{3.6}} \right)}}{{\ln \left( {\frac{80}{10}} \right)}} = 0.2038. $$
(12)
Table 2

Wind speed measured at each height

Height (m)

10

50

80

Wind speed (m/s)

3.6

4.9

5.5

Calibrated wind speeds using Eqs. (7) and (12) are shown in Fig. 7 which shows that the portion of wind speeds above 10 m/s increases significantly after calibration.
Fig. 7

Calibrated wind speed data

3.4 Details for wind farm layout optimization

In this study, a genetic algorithm is used for the wind farm layout optimization since it is good at finding a global optimum with discrete or binary inputs. In the proposed study, a batch optimization that yields the maximum energy generation on the grid set shown in Fig. 4 is first performed. Details on the batch optimization are listed in Table 3 which shows that the length of X is 285, the number of grids in the installable area, and the ith component of X becomes 1 when a wind turbine is installed in the ith 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.
Table 3

Information used in the batch optimization

Input variables

Binary input X of length = 285

Objective function

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

Constraint

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

After the batch optimization, post-optimization is performed to further increase the energy generation. Schematic of the post-optimization is shown in Fig. 8 which shows that the position of a wind turbine is further calibrated within the grid by moving it by half of the grid length. For example, if a wind turbine is installed in the grid 123 as a result of the batch optimization, the wind turbine can be relocated in four positions during the post-optimization. The post-optimization is also performed using the genetic algorithm. Information for the post-optimization is shown in Table 4. The length of 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.
Fig. 8

Schematic of post-optimization

Table 4

Input variables and objective function in the post-optimization

Input variables

Binary input X of length = 98

Objective function

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

4 Optimization results of wind farm model

To verify the optimized wind farm layout of Daegwallyeong area using the layout optimization and the post-optimization described in Sect. 3.4, we compared annual energy productions obtained from the actual and optimized layouts as shown in Table 5. To see the wake loss effect, annual energy production obtained from the actual layout using no wake model is compared in Table 5 as well. As can be seen in Table 5, annual energy production of the actual wind farm estimated using no wake model is 1.75 × 108 MWh. However, it is 1.55 × 108 MWh using the wake effect model. After the batch optimization, the annual energy production becomes 1.56 × 108 MWh and wake loss is 10.9%. Furthermore, after the post-optimization, the annual energy production is further improved to 1.59 × 108 MWh and the wake loss is 9.1% which is about 2% point less than the batch optimization result.
Table 5

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 × 108

 Wake model (56 × 56 grids)

1.55 × 108

11.4

Optimized layout (wake model)

 Batch optimization (28 × 28 grids)

1.56 × 108

10.9

 Post-optimization (56 × 56 grids)

1.59 × 108

9.1

Figure 9 compares the actual and optimized wind farm layouts, and shows that the number of wind turbines blocking the wind has decreased in the optimized wind farm layout. Figure 10 compares relative wind powers of the actual and optimized wind farms which are the power generated by each turbine divided by the maximum generated power. As can be seen from Fig. 10, the wind power production of the actual wind farm decreases compared with the optimized wind farm. Figure 9 also shows the 39th–49th wind turbines of the actual wind farm, which show poor energy generation due to the wake loss caused by nearby wind turbines. On the other hand, difference between the maximum and minimum energy generation of wind turbines in the optimized wind farm is relatively small since the wake loss is considered during the optimization.
Fig. 9

Comparison of actual and optimized wind farm layouts

Fig. 10

Comparison of wind power generation between actual and optimized layouts

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 × 107 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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Copyright information

© The Korean Society of Mechanical Engineers 2019

Authors and Affiliations

  1. 1.Korea Advanced Institute of Science and TechnologyDaejeonSouth Korea
  2. 2.Daejeon Science High SchoolDaejeonSouth Korea

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