Wind Farm Layout Design using Cuckoo Search Algorithm
Shafiqur Rehman
, Syed S. Ali
and Syed H. Adil
Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Universiti Teknologi PETRONAS, Bandar Seri Iskandar, Tronoh 31750, Malaysia
Faculty of Engineering, Sciences, and Technology, Iqra University, Karachi, Pakistan
Keywords: Wind Farm Layout Design, Wind Energy, Optimization, Cuckoo Search Algorithm, Genetic Algorithm.
Abstract: Wind energy has emerged as a strong alternative to fossil fuels for power generation. To generate this
energy, wind turbines are placed in a wind farm. The extraction of maximum energy from these wind farms
demands an efficient layout of the wind farms. This layout determines the location of each turbine in the
wind farm. Due to its sheer complexity, the wind farm layout design problem is considered a complex
optimization problem. In recent years, several attempts have been made to develop techniques and
algorithms for optimization of wind farms. This paper proposes yet another optimization algorithm based on
the cuckoo search (CS), which is a recent optimization method. The proposed cuckoo search algorithm is
compared with genetic algorithm which is by far the highest utilized algorithm for wind farm layout design.
Empirical results indicate that the proposed cuckoo search algorithm outperformed the genetic algorithm for
the given test scenarios in terms of yearly power output and efficiency.
Wind power is emerging as an effective source of
cleaner and affordable energy compared to
traditional fossil fuels. These features of wind
energy advocate its use at a massive level, thus
prompting the researchers and energy producers to
give serious attention to wind power generation
during the past many years. This has resulted in
notable developments in various areas of
investigation related to wind energy. These areas
include sensors and instrumentation, assessment of
wind energy potential, design and characterization of
wind turbines, and the development of wind farms
(Ettoumi, 2008) and (Muskaterov and Borissova,
2010). This paper deals with efficient design of wind
farms. More specifically, the aim is optimal
placement of wind turbines in a wind farm, while
considering various design objectives and
Although there are various commercially
available software packages for wind farm layout
design, many researchers have developed interest in
utilizing computational intelligence techniques for
the purpose. It is due to the fact that, despite their
sophistication, these software packages merely serve
as assistant to human designers, and the
responsibility of an efficient design mainly lies on
the experience and intelligence of the designer. This
may lead to less efficient designs. On the other hand,
computational intelligence techniques have been
very effectual for a huge variety of complex
optimization problems, since these techniques are
least dependent on human intervention and are
capable of generating efficient solutions due to their
built-in intelligence.
For many years, computational intelligence
algorithms have been used for optimal design of
wind farms, with genetic algorithm (Goldberg,
1989) being the first and the highest utilized
algorithm (Khan and Rehman, 2013) thus far. Many
initial researchers in the domain, such as Mosetti et
al., 1994 and Grady et al., 2005 adapted genetic
algorithm for wind farm design. The algorithm has
also received significant attention by many other
researchers (Khan and Rehman, 2013) for the same
problem. Apart from genetic algorithms, particle
swarm optimization algorithms have also been
utilized for wind farm design (Chwodhury and
Zhang, 2010) (Chowdhury, 2012), (Rahmani et al.
2010) and (Wan et al., 2010). However, application
of other various other intelligent algorithms, such as
ant colony optimization, honey bee colony
optimization, tabu search, and cuckoo search is
Rehman, S., Ali, S. and Adil, S.
Wind Farm Layout Design using Cuckoo Search Algorithm.
In Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2016), pages 257-262
ISBN: 978-989-758-184-7
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
either very limited or non-existent. This paper is,
therefore, motivated by the above observation and
proposes a cuckoo search based algorithm for
efficient wind farm layout design, which will be the
first such attempt to the best of our knowledge.
The rest of the paper is organized as follows. In
Section 2, the wake and cost models used in this
study are described. This is followed by discussion
on the cuckoo search algorithm in Section 3. Section
4 provides the results and discussion, followed a by
a conclusion in Section 5.
The assumptions made in this paper are the same as
proposed in the initial studies (Mosetti et al., 1994)
and (Grady et al., 2005) in the domain. These
assumptions are still in use in recent studies.
Accordingly, a simplified version of Jensen model
(proposed in (Mosetti et al., 1994)) is used in this
paper to find the optimal layout design of a wind
farm. Following notations have been used.
A : Axial induction factor
α : Entrainment factor
: Surface roughness
Z : Hub height
: Thrust coefficient
: Distance downstream from turbine j to
turbine i (i.e., distance between the
current turbine and the turbine creating
wake effect on it)
: Wind speed downstream under multiple
N : Total number of turbines
: Set of all turbines creating wake effect
on turbine i
: Wake radius immediately downstream of
the wind turbine
Wake radius at x distance downstream of
the wind turbine
Number of rows and columns that exist
in the solution space
The schematic of the wake model is shown in Fig. 1.
Furthermore, Figure 2 illustrates a typical wind farm
grid. For fair comparison of the proposed cuckoo
search algorithm with other techniques, the gird size
and other properties are adopted from the
fundamental studies (Mosetti et al., 1994) and
(Grady et al., 2005). Following these properties, the
grid is divided into 100 possible turbine locations. A
turbine can be placed at the center of a cell. The size
of each cell is taken as five times the rotor diameter
(D). More precisely, since a rotor diameter of 40 m
is assumed, a cell size is 200 m. A hub directly
facing the wind direction is not under effect of any
wake. Therefore, the wind speed remains unaffected
as visible in Figure 2. The equations to calculate the
wake generated power, and optimization objectives
(Eqs. (1) to (12)) have been adopted from Mosetti et
al., 1994 (since the same model was followed by
various other studies) and presented below for the
sake of clarity and completion. Interested reader
may find more details in (Mosetti et al., 1994) on the
wake and power efficiency model. According to this
model, we have
If the hub is subjected to only one wake, then the
wind speed is affected according to:
However, if any hub is subjected to multiple wakes,
then the wind speed is determined by
The radius r
of the wake downstream immediately
after a turbine is calculated using:
Furthermore, the radius r
of the wake at a distance
downstream of any wind turbine is calculated
using following equation,
The relationship between thrust coefficient and axial
induction factor is given by
SMARTGREENS 2016 - 5th International Conference on Smart Cities and Green ICT Systems
Figure 1: Schematic of the Wake Model.
Figure 2: A 10 x 10 Wind Farm Grid.
The thrust coefficient is normally known for the
system. Therefore, we can calculate axial induction
factor a instead of CT. (The solution of Eq. 6 gives
two values of a. We select one which gives a real
value for r
in Eq. 4). Finally, the entrainment factor
α is found out using the following equation.
Total cost of placing N turbines in the grid is
calculated using following equation.
Total power generated by N turbines under
multiples wakes is calculated using following
Total power generated by N turbines without any
wake is calculated using following equation.
The efficiency of the wind power generation is
calculated using following equation.
Wind Farm Layout Design using Cuckoo Search Algorithm
With the above equations, the wind farm layout
design problem is fundamentally the wind turbine
placement problem where the objective is to
minimize the total cost versus total power generated
for N number of turbines. Therefore, the objective of
this optimization problem can be stated as:
Cuckoo search is a search algorithm originally
proposed by Yang and Deb in 2009 (Yang and Deb,
2009) as an optimization tool for numerical
functions and continuous problems. The algorithm is
based on the brooding parasitism of cuckoo species
in natural habitat. Some cuckoo species by laying
their eggs in the nests of other host birds (of other
species). Some host birds can engage in direct
conflict with the intruding cuckoos.
The CS algorithm evolves from the following
three behavioral patterns of real cuckoos (Yang and
Deb, 2009):
(1) Each cuckoo lays one egg at a time. The egg
is dumped in a nest randomly chosen by the cuckoo.
(2) The best nests with high quality of eggs
(solutions) will carry over to the next generations.
(3) The number of available host nests is fixed,
and a host can discover an alien egg with probability
(0,1). Thus, the host bird can either throw the
egg out of its nest or abandon the nest in order to
build a completely new nest in a new location.
Each nest represents a potential solution in
search space. The CS algorithm also determines
how to update the position of cuckoo laid egg. Each
cuckoo updates its position of laying egg based on
current step size via Lévy flights. Lévy flight is a
natural phenomenon noticed in some birds and fruit
flies. It is a combination of short and very long
steps, with sudden turns (typically around 90
These sudden turns are of essential importance for
the CS algorithm, and determine the next position of
the bird/fly using the following equation:
> 0 represents a step size. This step size
should be closely related to the scale of the test
function that the algorithm is applied on. In most
can be set to the value of 1 (Yang and Deb,
2009). It has been shown that the use of Levy flight
is much more efficient in exploring the search space
as its step length is significantly longer when a large
number of steps are performed compared to a simple
random walk. The random step length is drawn from
a Levy distribution which has an infinite variance
with an infinite mean:
The consecutive positions generated through
steps/iterations of a cuckoo, create a random walk
process which obeys a power-law step length
distribution with a heavy tail.
The performance of the proposed cuckoo search
algorithm was evaluated empirically through
simulations. A software simulator was exclusively
developed in C++ programming language for this
purpose. Thirty independent runs were done for each
test scenario and results were subjected to statistical
testing as per the standard practice. Two test
scenarios were used depicting different wind
conditions and directions. These scenarios have been
used in several earlier studies (Mosetti et al., 1994),
(Grady et al., 2005), (Emami and Noghreh, 2010),
(Gonzalez et al., 2010), (Huang, 2007), (Huang,
2009), (Mittal, 2010), (Wang et al., 2009a), and
(Wang et al, 2009b). These scenarios are briefly
discussed below for the sake of completeness. The
proposed CS algorithm was benchmarked with
genetic algorithms. The reason for selecting genetic
algorithm for comparison is that the genetic
algorithm has been used in most studies related to
wind farm layout design (Khan and Rehman, 2013).
4.1 Case A
This scenario assumes the wind is coming from all
the directions with equal probability, while
considering mean wind speed of 12 m/s. For
simplified calculations, wind directions were divided
the in 36 equal intervals with 10 degree difference
(i.e., 0
, 10
, 20
, …, 350
). It is also implicitly
assumed that each turbine in the grid rotates along
with the prevailing wind direction, while it is
installed at the center of the cell in the grid. Thus,
each turbine is facing the prevailing wind direction.
The turbines affected by wake from preceding
turbines will receive downstream wind speeds as per
Eqs. (2) and (3) for single and multiple wakes,
SMARTGREENS 2016 - 5th International Conference on Smart Cities and Green ICT Systems
respectively. It is important to mention that since the
wind directions may be approaching from all
directions, it is required to determine the wake
effects geometrically on the turbines downstream.
Table 1 shows the results for the proposed CS
algorithm and GA, while considering 19 and 39
turbines. The results indicate that CS was able to
achieve better results than GA for both turbine
configurations. For example, the total yearly power
output and the efficiency achieved by CS were
higher than that of GA, for both 19 and 39 turbines.
For GA, the yearly output and efficiency with 19
turbines was 9245 KW and 93.859 %, respectively,
while for CS, the corresponding values were
9385.35 KW and 95.287 %. A similar pattern can be
observed for 39 turbines.
4.2 Case B
In this scenario, wind is coming from all possible
directions with equal probability but with varying
mean wind speeds of 8, 12, and 17 m/s. This case is
similar to Case A except for the wind speeds.
Therefore, as in case A, wind direction was divided
in 36 equal intervals with angle difference of 10
degrees (i.e., 0
, 10
, 20
,…, 350
). Furthermore,
turbine installation and calculations of wake effect
remain similar to case A. The complexity of case B
is intensified by the fact that the probability of
having wind direction may be different for different
mean wind speeds. In particular, previous studies
(Mosetti et al.,1994) and (Grady et al., 2005) have
used the probability distribution shown in Fig. 3,
where it is observed that wind distributions from,
to 350
are higher than the remaining angles,
with the peak at around 310
. The same distribution
was used to evaluate the performance of the CS
algorithm and comparison with GA.
Figure 3: Varying wind speeds for different directions
(developed from (Mosetti et al.,1994)).
Table 2 shows a comparison between the proposed
CS algorithm and GA. Two configurations
consisting of 15 and 39 turbines were used in the
analysis. Similar to the results of ase A, CS also
outperformed GA for both 15 and 39 turbines. This
is evident from the yearly output and efficiency
which are higher for CS compared with GA, as
depicted in the table.
This paper presented a novel approach for
optimization of a wind farm layout. A recent
optimization technique, namely, the cuckoo search
algorithm, was engineered to optimize the layout
design. The proposed approach was compared with
the infamous genetic algorithm which has been
Table 1: Comparison of solution features for Case A.
Attribute GA CS GA CS
Fitness Value 0.00174 0.00171 0.00157 0.00151
Total kw/ year 9245 9385.35 17220 17860.73
Efficiency (%) 93.859 95.287 85.174 88.343
No. of turbines 19 19 39 39
Table 2: Comparison of solution features for Case B.
Attribute GA CS GA CS
Fitness Value
0.000994 0.000906 0.000803 0.000779
Total kw/ year
13460 14769.38 32038 34563.01
Efficiency (%)
94.620 97.613 86.619 87.857
No. of turbines
15 15 39 39
Wind Farm Layout Design using Cuckoo Search Algorithm
extensively used to solve different variations of the
wind turbine layout design problem in many
previous studies. The resulted revealed that the
proposed cuckoo search algorithm produced higher
yearly energy output and better efficiency for all the
considered test scenarios and different number of
wind turbines. This signifies that the cuckoo search
algorithm was more efficient than genetic algorithm
in traversing the search space, which resulted in
better solutions by cuckoo search.
This work was supported by Deanship of Research
at King Fahd University of Petroleum & Minerals
under project number IN131012.
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