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www.etasr.com Ton et al.: Optimal Location and Size of Distributed Generators in an Elecric Distribution System ….
Optimal Location and Size of Distributed Generators
in an Electric Distribution System based on a Novel
Metaheuristic Algorithm
Trieu Ngoc Ton
Faculty of Electrical and Electronics Engineering
HCMC University of Technology and Education
Ho Chi Minh City, Vietnam
trieutn.ncs@hcmute.edu.vn
Viet Anh Truong
Faculty of Electrical and Electronics Engineering
HCMC University of Technology and Education
Ho Chi Minh City, Vietnam
anhtv@hcmute.edu.vn
Thuan Thanh Nguyen
Faculty of Electrical Engineering Technology
Industrial University of Ho Chi Minh City
Ho Chi Minh City, Vietnam
nguyenthanhthuan@iuh.edu.vn
Tu Phan Vu
Postgraduate Training Committee
Vietnam National University-HCMC
Ho Chi Minh City, Vietnam
vptu@vnuhcm.edu.vn
Abstract—This paper proposes a method for optimizing the
location and size of Distributed Generators (DGs) based on the
Coyote Algorithm (COA), in order to minimize the power loss in
an Electric Distribution System (EDS). Compared to other
algorithms, COA does not need control parameters during its
execution. The effectiveness of COA was evaluated in an EDS
with 33 nodes for two scenarios: the optimization of location and
capacity of DGs in an initial radial configuration, and the best
radial configuration for power loss reduction. Results were
compared with other methods, showing that the proposed COA is
a reliable tool for optimizing the location and size of DGs in an
EDS.
Keywords-distributed generators; coyote algorithm; electric
distribution system; power loss; radial configuration
I. INTRODUCTION
Distributed Generators (DGs) are connected to an Electric
Distribution System (EDS) offering economic benefits and
energy security, and their appearance has increased rapidly. An
EDS performs the task of supplying electric energy to
consumers, ensuring power quality, reliability, and safety
requirements within the permitted limits. Meanwhile, it also
brings many other benefits, such as reducing the load on the
grid, improving voltage, reducing losses, and supporting the
grid. Some of the problems related to connecting DGs in an
EDS consist of the increasing penetration of renewable DGs,
the maximization of emitted power and reliability, the
minimization of investment, operating costs and total
payments, the reduction of system losses, and the improvement
of voltage configuration, maximizing social welfare and profit
margin. Depending on the goals, it is possible to combine DGs
appropriately to reduce the line overload and increase the
operating range of the system, in order to operate more
flexibly. Exploiting the maximum potential benefits of DGs
with minimum cost must be satisfied with technical constraints
and the optimization of economic objectives [1, 2]. When
considering connecting DGs to an EDS, it is necessary to
consider their location and their allowable amount, in order to
get their maximum size pumped into the grid, minimizing loss
to attract investment, ensuring the reliability of electric supply,
and gaining economic benefits. Therefore, the problem of
determining the location and capacity of DGs for power loss
reduction is important [3, 4].
Various methods have been employed in order to determine
the location and capacity of DGs in an EDSs. Some classical
methods are linear and non-linear programming (NLP) [5],
mixed integer NLP [6], dynamic programming [7], ordinal
optimization [8], and optimal power flow (OPF) [9]. The
disadvantages of these methods are the slow convergence to
optimal results, or the fall into local extremes. Metaheuristic
methods have been applied for solving this problem, such as
Genetic Algorithm (GA) [10, 11], Particle Swarm Optimization
(PSO) [11-13], symbiotic organisms search [14], Artificial Bee
Colony algorithm (ABC) [15], invasive weed optimization
[16], Cuckoo Search (CSA) [17], Fireworks Algorithm (FWA)
[18], Stochastic Fractal Search (SFS) [19], Harmony Search
Algorithm (HSA) [20], and Salp Swarm Algorithm (SSA) [21].
These methods have the advantage of handling conveniently
problem’s constrains. In addition, the solutions obtained are
usually better than these obtained by the classical methods.
However, finding suitable, stable, and reliable methods for
each specific problem is a complicated task. Therefore, finding
new methods to solve the problem of optimizing location and
capacity of DGs in an EDS is a desired task. The Coyote
Algorithm (COA) is based on the social life of coyotes, and
[22] validated its efficiency using forty benchmark functions.
Corresponding author: Thuan Thanh Nguyen
Engineering, Technology & Applied Science Research Vol. 10, No. 1, 2020, 5325-5329 5326
www.etasr.com Ton et al.: Optimal Location and Size of Distributed Generators in an Elecric Distribution System ….
However, the application of COA on engineering problems,
such as DGs placement in order to examine its effectiveness, is
a worthy consideration. This paper describes the application of
COA in optimizing the location and size of DGs for power loss
reduction in an EDS with 33 nodes, and the comparison of the
obtained results with other metaheuristic methods.
II. PROBLEM OF OPTIMAL PLACEMENT OF DGS
The objective function of the DGs’ location and size
optimization in an EDS is the reduction of the active power
loss, formulated as: � = ���(∑�
��) (1)
where ∑�
�� is the total power loss in the EDS. The
placement of DGs in the EDS should satisfy the following
constraints:
• Power balance: The sum of output power from the slack
bus and the DGs must be equal to the sum of loads and
power loss in the EDS.
• The limits of nodes’ voltage and branches’ current are:
V��� �� ≤ �� ≤ V��� �� , � = 1,2,⋯,���� �� � ≤ �� ���,� �� , � = 1,2,⋯, ��!��"# (2)
where LCF is the load carrying factor of the i
th
branch.
• The power limits of DGs are:
�$%,�,��� ≤ �$%,� ≤ �$%,�,��� , � = 1,2,⋯,�$% (3)
III. APPLICATION OF COYOTE ALGORITHM
A. The Coyote Algorithm (COA)
Unlike other metaheuristic methods, COA does not need
control parameters, enhancing its performance stability on the
DGs optimization procedure. In order to search the solution in
the search space, COA uses a population of coyotes divided
into groups, and the social condition of each coyote in its group
is considered as a candidate solution. Candidate solutions are
generated based on the interaction among coyotes in each
group and the interaction among groups of the population. The
interactions are described as follows:
1) Renewal of the Social Condition of Coyotes in Each Group
The behavior of each coyote depends on the leader of its
group, while each group usually has its own characteristics.
The process of finding new solutions is as follows: In the g
th
group, the coyote having the best adaptive function value is
chosen as alpha (&'(). Subsequently, the culture tendency ()*()
of the group is determined by the median social condition of
the group’s coyotes, and a new social condition of each coyote
is generated as: �_,)"( = ,)"( + ./.1&'( − ,)/(3 + .4. 1)*( − ,)4(3 (4)
where �_,)"( and ,)"( are new and current social conditions of
the c
th
coyote in the g
th
group, sc/( and sc4( are the social
conditions of two coyotes selected randomly in the g
th
group,
and finally ./ and .4 are random numbers in the range of [0, 1].
2) Birth of a New Coyote to Replace an Old One in Each
Group
The coyote having the worst social condition, in the group,
will die, and a newborn puppy will replace it, as:
78�889,:( = ;
7/,:( , .<,: < >/ 74,:( , .<,: < >/ + >47!,:( , ?*ℎA.B�,A (5)
where 78�889,:( (j=1, 2, …, D) is the jth variable of the puppy’s
social condition vector solution, D is the dimension of the
problem, 7/,:( and 74,:( are the variables of two solutions chosen
randomly in the group, .<,: is a random number in the range of
[0, 1], and 7!,:( is a random variable, and >/ and >4 are the
probabilities of scatter and association, which guide the cultural
diversity of the coyotes from the group, determined as:
C>/ = 1/E >4 = (1 − >/)/2 (6)
3) Interchange of Coyotes Between Groups
Although coyotes are living in groups, sometimes some
individuals leave their group in order to live alone or join
another group. Based on this feature, to expand the process of
creating new solutions, coyotes are exchanged among groups
of the population. The probability (� ) of a coyote leaving one
group to join another and vice versa is determined as: � = 0.005 × �"4 (7)
where �I is the number of coyotes in the group.
B. COA in Optimizing Location and Size of DGs
This section presents the application of the COA in
optimizing the location and size of DGs, in order to minimize
the active power loss in an EDS. The following steps describe
the overall procedure:
• Step 1: Select the parameters of COA, including group
number (�J), group size (�I), and the maximum number of
generations (KLMN).
• Step 2: The initial population of coyotes is represented as sc"( = O �/,"( , …,�QRS,"( ,�/,"( , …,�QRS,"( T with U = 1,2,…,�(
and ) = 1,2,…, �" . Variables �V,"( and �V,"( represent
location and power of the k
th
DG, initialized as: �V,"( = .?W�XY2 + rand(0,1).(���� − 2)^ (8) �V,"( = rand(0,1)× 1�V,���( − �V,���( 3 + �V,���( (9)
where �V,���( and �V,���( are the maximum and minimum
power of the k
th
DG.
• Step 3: The initialized population is evaluated based on a
fitness function, determined as: ��* = � + _ × O�&71���� �� − ����,03 + �&7(���� −���� �� ,0) + �&7(�� ��� − �� ��� �� ,0)T (10)
Engineering, Technology & Applied Science Research Vol. 10, No. 1, 2020, 5325-5329 5327
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where K is a penalty factor set to 1000, ���� and ���� are
the minimum and maximum voltages in the EDS, and �� ��� is the maximum load carrying factor in the EDS.
• Step 4: The main loop begins from this step until Step 8,
and it is repeated until the preset generation value is
reached. The inner loop in Steps 5-6 is repeated until the
last group of the population is reached.
• Step 5: The social condition of the coyotes in each group is
renewed. For each group, the alpha coyote is selected, and
the median of all coyotes is determined. A new social
condition is generated for each coyote using (4). The fitness
value is calculated for the new social condition. If the social
condition is better than the previous one, it will replace it.
• Step 6: A puppy coyote, generated by (5), replaces an old
one. The fitness value of the puppy’s social condition is
calculated. If the puppy’s social condition is better than the
worst social condition in the group, it will replace it. If the
current group is not the last group of the population, Step 5
is repeated, otherwise, this inner loop ends, and Step 7 is
executed.
• Step 7: A coyote is interchanged between the groups. If .&�X (0,1� = � , two groups are randomly selected for
exchanging coyotes. In the selected groups, two coyotes
are randomly chosen, and they are interchanged between
the two chosen groups.
• Step 8: In the proposed COA method, the stopping
criterion is based on a maximum number of generations.
The algorithm terminates when the generation reaches a
maximum value. Otherwise, a new generation starts from
Step 4. As the maximum number of generations is reached,
the best social condition of all coyotes in the population is
considered as the optimal solution for the DGs’ location
and size optimization.
IV. NUMERICAL RESULTS
In order to demonstrate the efficiency of the COA on the
DGs’ location and size optimization, the algorithm was
implemented in Matlab 2016a. Its performance was evaluated
in an EDS with 33 nodes [23], considering two scenarios:
• Scenario 1: Location and size of DGs are optimized in the
EDS with the initial radial configuration with open switches
{33-34-35-36-37}.
• Scenario 2: Location and size of DGs are optimized in the
EDS with the optimal radial configuration for power loss
reduction with open switches {7-9-14-28-32}.
COA, for both scenarios, employed 5 groups, with 6
coyotes in each group, and the number of maximum
generations was set to 300. The obtained results were
compared with other methods in the literature, such as GA [11],
PSO [11], CSA [17], FWA [18], SFS [19], HSA [20], and SSA
[21]. In order to obtain optimal results, COA was executed in
independent runs, and the best result was considered as the
optimal solution. The results of the DGs’ location and size
optimization in scenario 1 are shown in Table I. After placing
DGs in the nodes 30, 14 and 24 with corresponding power
1.07144, 0.75396 and 1.09944MW, power loss reduced from
202.6863 to 71.4599kW, corresponding to 64.74% power loss
reduction. The minimum voltage amplitude in the EDS
enhanced from 0.9131 to 0.9687p.u.. In comparison with other
methods, the obtained results are better than the ones obtained
by GA, PSO, CSA, FWA and HSA. Power loss reduction from
COA was 64.74%, being 17.19, 16.69, 1.38, 8.49 and 12.48%
higher than GA, PSO, CSA, FWA and HSA. Compared to SFS
and SSA, power loss obtained from COA is nearly the same.
Fig. 1. The EDS with 33 nodes
TABLE I. OPTIMAL DG PLACEMENT FOR SCENARIO 1
Method DG size in MW
(node)
Power loss
(kW)
Loss reduction
(%)
Vmin (node)
Initial - 202.6863 - 0.9131 (18)
COA
1.07144 (30)
0.75396 (14)
1.09944 (24)
71.4599 64.74 0.9687 (33)
GA [11]
1.5 (11)
0.4228 (29)
1.0714 (30)
106.3 47.55 -
PSO [11]
0.9816 (13)
0.8297 (32)
1.1768 (8)
105.3 48.05 -
CSA [17]
0.7798 (14)
1.1251 (24)
1.3496 (30)
74.26 63.36 0.9778
FWA [18]
0.5897 (14)
0.1895 (18)
1.0146 (32)
88.68 56.25 0.9680
SFS [19]
0.7540/(14)
1.0994/(24)
1.0714/(30)
71.47 64.74 0.9687
HSA [20]
0.1070 (18)
0.5724 (17)
1.0462 (33)
96.76 52.26 0.9670
SSA [21]
0.7536 (33)
1.1004 (23)
1.0706 (29)
71.45 64.75 0.9686 (32)
The results of the DGs’ location and size optimization in
the system with scenario 2 are shown in Table II. Using the
radial configuration of {7-9-14-28-32} after placing DGs in
nodes 16, 12 and 25 with corresponding power 0.50263,
0.53576 and 1.61605MW, power loss reduced to 56.2782kW,
corresponding to 72.23% power loss reduction. The minimum
voltage amplitude in the EDS was enhanced to 0.9722p.u. at
node 32. The obtained results from COA are better than these
obtained from CSA, SFS and SSA. Power loss reduction from
Engineering, Technology & Applied Science Research Vol. 10, No. 1, 2020, 5325-5329 5328
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COA was 72.23%, being 1.24%, 1.28% and 1.27% higher than
CSA, SFS and SSA. Comparing scenarios 1 and 2, power loss
obtained in the former was 71.4599kW (64.74%), and
56.2782kW, (72.23%) in scenario 2. In addition, the minimum
voltage amplitude in scenario 2 improved more than in scenario
1. The voltage profile of the system after optimizing the
location and size of DGs using COA is shown in Figure 2. The
voltage of the nodes improved after installing DGs, while the
installation of DGs according to scenario 2 gained better
voltage profile than scenario 1. Moreover the load carrying
factor of the system, shown in Figure 3, reduced after
optimizing the location and size of DGs using COA, as its
maximum, being 0.8250 in the initial configuration, reduced to
0.4475 and 0.4640 for scenarios 1 and 2, respectively.
TABLE II. OPTIMAL DG PLACEMENT FOR SCENARIO 2
Method
DG size in MW
(node)
Power loss
(kW)
Loss reduction
(%)
Vmin (node)
COA
0.50263 (16)
0.53576 (12)
1.61605 (25)
56.2782 72.23 0.9722 (32)
CSA [17]
1.7536 (29)
0.5397 (12)
0.5045 (16)
58.79 70.99 0.9802
SFS [19]
1.0682/(24)
0.9503/(30)
0.9317/(8)
58.88 70.95 0.9741
SSA [21]
0.932 (8)
1.068 (24)
0.950 (30)
58.87 70.96 0.9741 (33)
Fig. 2. The voltage profile of the 33-node EDS
Fig. 3. The load carrying factor of the 33-node EDS
The mean and minimum convergence curves in 50
independent runs for both scenarios are shown in Figures 4 and
5. The figures show that the mean and minimum curves
converge to nearly equal values. This shows the stability and
reliability of the COA in each run for the DGs’ location and
size optimization in the EDS.
Fig. 4. The convergence curves of COA in scenario 1
Fig. 5. The convergence curves of COA in scenario 2
V. CONCLUSION
This paper presented a method based on COA for
optimizing the DGs location and size in an EDS, in order to
reduce power loss. The effectiveness of the COA was
evaluated in an EDS with 33 nodes. Two scenarios of DGs’
radial configuration were considered: the initial radial
configuration, and placement in the optimal radial
configuration with minimum power loss. Numerical results
showed that COA is better than methods such as GA, PSO,
CSA, FWA, HAS, SFS and SSA. In addition, there is no need
for control parameters in the process of applying COA to the
optimization problem. Moreover, the numerical results in 50
independent runs showed that COA is a reliable method for the
problem of optimizing the location and capacity of DGs in an
EDS to satisfy other goals.
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