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Multi-Objective TLBO and GWO-based Optimization for Placement of Renewable
Energy Resources in Distribution System
Bibek KC 1, Hassan Alkhwaildi 2
1 Department of Electrical and Computer Engineering, Southern Illinois University of Carbondale, USA
2 Department of Electrical and Computer Engineering, Southern Illinois University of Carbondale, USA
Keywords
Abstract
Distributed Generation,
Fuzzy Decision,
Hybrid Teaching Learning
-Gray Wolf Algorithm,
Multi-Objective
Optimization,
Renewable Energy
Sources.
The use of renewable solar and wind resources as distributed generation sources in
distribution networks has been welcomed by network operators. In order to exploit the
maximum benefits of using these distributed products, the location of installation and their
capacity should be determined optimally in the distribution network. In this paper, in order
to optimize the placement of solar panels and wind turbines in the distribution network with
the aim of reducing losses and improving reliability based on Energy Not Supplied
subscribers (ENS), a multi-objective evolutionary algorithm based on fuzzy decision
method, called the Multi-Objective Hybrid Training Learning Based Optimization-Grey
Wolf Optimizer (MOHTLBOGWO) proposed that has a High optimization speed and not
trapped at all in the optimal local. At first, the candidate buses are set for the installation of
renewable resources using the Loss Sensitivity Factor (LSF). Then the proposed method is
used to determine the location and optimal capacity of renewable resources through the
candidate bases. Proposed issues have been implemented in a single-objective and multi-
objective manner on a 33 bus IEEE radial distribution network. Also, in this paper, the effect
of distributing renewable resources on the characteristics of the distribution network is
evaluated. The results obtained from the proposed algorithm are compared with the results
of other algorithms to demonstrate the superiority of the proposed method in reducing losses,
improving reliability, and increasing the financial profit of the network. Simulation results
show the better performance of the proposed method in comparison with Teaching–
Learning Based Optimization (TLBO) and Grey Wolf Optimiser (GWO) methods and past
studies to achieve optimal results. Also, the results show that distributing of the capacity and
location of distributed renewable generation leads to a further reduction in losses and a better
improvement of the reliability criterion.
1. Introduction
The growing consumption of electric energy, mainly
produced by burning fossil fuels, leads to various issues,
such as environmental and financial issues. On the other
hand, nearly 15% of active power is produced in large power
plants [1, 2]. This power is lost in transmission lines and
distribution networks. Reducing power losses is one of the
most interesting and most important issues in power system
studies. There are several ways to minimize losses in power
systems at the level of transmission and distribution
networks [3]. DG placement is one of these methods. These
methods have advantages such as improving reliability,
improving the voltage profile, and reducing the power loss
of the active. However, inappropriate placement and
inappropriate DG planning can weaken the distribution
network characteristics [4, 5]. Several studies have been
conducted in the field of exploitation of distribution
networks by optimal utilizing the dispersed generation
sources in the distribution network. Classical, analytical, and
Corresponding Author: Hassan Alkhwaildi
E-mail address: hassan.alkhwaildi@siu.edu
meta-exploratory methods are the methods that have been
proposed in this field. Classical methods are methods that
can determine optimal response over a short period of time,
but with increasing problem dimensions they cannot
determine the optimal response. Analysis methods are
methods that require additional computations and may not be
able to achieve absolute optimal points [6]. Recently; Meta-
heuristic methods have been used to solve the problems of
distribution network utilization. In [7], the Teaching–
learning algorithm has been used and optimization has been
achieved as a single-objective or two-objective. Placement
of wind turbines and solar cells in the distribution network
with the goal of reducing losses and improving the voltage
stability conducted as a two-objective issue using the Particle
Swarm Optimization algorithm [8, 9]. In [10, 11], in order to
reduce the true power losses in distribution networks, the
optimal placement of dispersed generation resources have
been used in a combination and single-objective approach.
In this study, a sensitivity analysis method was used to
determine the best mode for locating dispersed generation
2
sources and capacitors in the network. In [12], the optimal
placement of renewable distributed generation sources is
presented using evolutionary planning and its results are
compared with the genetic method. The results show that,
compared to the proposed method, the genetic algorithm
finds the optimal problem at lower speeds. In [13], the
locating of dispersed generation in distribution networks is
provided by considering the voltage stability criteria. In this
study, the genetic algorithm is used to find the best answer.
In [14, 15], a new and high-efficiency algorithm is proposed
using a firefly algorithm to determine the location and
capacity of dispersed generation sources in an unbalanced
distribution network in a single-objective optimization. The
goal of the problem is to reduce network losses.
The use of Genetic Algorithm (GA) and Simulated
Annealing algorithm for optimal allocation of DG in
distribution network [16, 17] are presented in the form of
single-objective optimization with the aim of reducing of
losses. In [18, 19], the installation location of the DG is
determined by the GA algorithm and its capacity is
determined by the Particle Swarm Optimization (PSO). This
work has been done on the basis of the weight coefficient
method and is presented with the aim of reducing power
losses, decreasing voltage oscillation of the bus and
improving the voltage stability of the distribution network.
In [20, 21], the Ant Colony Optimization (ACO) algorithm
is proposed to determine the best installation location of the
DG in the distribution network. This algorithm is presented
in the form of single-objective optimization for reducing
losses. Harmony Search algorithm (HS) is presented in [22]
as an optimization method for solving this problem with the
goal of reducing losses based on single-objective
optimization. The Artificial Colony Bee (ABC) algorithm
has been introduced in [23, 24] to determine the capacity,
optimal power coefficient and DG installation location. This
algorithm is presented in the form of single-objective
optimization for reducing active losses. In [25], the
Differential Evolution Algorithm (DEA) has been used to
optimize single-objective DGs and achieve minimum losses.
In [26], the Bacterial Foraging Optimization (BFO) Search
Algorithm was used to optimize the planning of DG units in
the distribution system with the goal of reducing losses,
reducing operating costs, and improving voltage stability.
This work is based on the weighting coefficient method and
the multi-objective optimization form. The Imperialistic
Competitive Algorithm (ICA) is used in [27] as a single-
objective optimization to minimize losses in the system. The
Plant Growth Simulation Algorithm (PGSA) has been used
in [28-30] to determine the unit capacity and the loss
sensitivity factor in choosing optimal DG location. Firefly
Algorithm (FA) is used in [21, 31] to optimize single-
objective DGs with the goal of reducing power losses. In [32,
33], Ant Lion Optimizer (ALO) algorithm is used to
determine optimal location of installation and DG size based
on renewable resources with the goal of reducing losses and
improving the profiles and voltage stability in a multi-
objective optimization based on weight coefficient method.
In [34], the optimal placement of wind turbines in the
distribution network is proposed using Cuckoo Search
Algorithm (CSA) in a single-objective optimization with the
goal of reducing power losses. In [35, 36], the locating of
wind turbines and solar panels is proposed to reduce power
losses and improve voltage stability using PSO algorithm
based on multi-objective optimization and weight coefficient
method.
As mentioned in most of the previous studies, the
problem of positioning is presented as single or two-
objective optimization with the goal of reducing losses and
improving the voltage profile, based on the weight
coefficients method. In order to achieve a more accurate and
realistic exploitation of the distribution network, the problem
of the location of distributed generation should be considered
as a multi-objective. One of the best ways for solving multi-
objective problems is the use of Pareto levels to determine
the optimal answer, which in this paper focuses on it and
presents a multi-objective hybrid algorithm. On the other
hand, the placement of renewable resources from the
perspective of reliability, and considering the network failure
rate and energy not-supplied network, has been less
investigated. In this paper, these concepts are considered. In
this paper, the proposed method is based on the combination
of Teaching–learning and gray wolfs algorithms The
Teaching–learning algorithm was presented in 2012 [37] and
the high convergence rate and the lack of control parameters
were the features of this method. The gray wolf method is
presented in 2014 [38] and has been greatly welcomed to
solve the power engineering optimization problems. This
method has features such as high convergence speed, high
computational power, fast and large searches and Avoid
Local Optimal. Therefore, in this paper, in order to locating
solar panels and wind turbines in a 33-buses radial standard
distribution network and reducing losses and improving
reliability, Utilizing the benefits of both methods, a multi-
objective hybrid algorithm based on a fuzzy decision method
called MOTLBOGWO is proposed. The main contribution
of this article are following:
• Use of a new cumulative smart method called the
HTLBOGWO method
• Solve multi-objective problem of locating
renewable resources based on fuzzy decision
method in MOHTLBOGWO algorithm
• Study of the location of renewable energy sources
from the perspective of reliability
• Assess the dispersal of location and capacity of
renewable energy sources over network
characteristics
The rest of this paper is organized as follows:
In Section 2, Loss Sensitivity Factor Formulation is
described for determining the candidate buses for the
installation of renewable energy sources. In Section 3, the
problem formulation including optimization target function
and problem constraints is presented. In Section 4, the
proposed algorithm, the fuzzy decision method and
implementation of the proposed method in problem solving
described. In Section 5, the simulation results are presented
and the conclusions are presented in Section 6.
2. Loss Sensitivity Factor
In this study, the Loss-Sensitivity Factor (LSF) is
presented to show buses that are sensitive to losses [39, 40].
Also, using this factor can reduce the search area and the time
of the optimization process. In other words, the buses that are
3
in trouble for losses are identified by this factor, and thus
instead of searching all the network buses for the installation
of dispersed generation by the optimization method, the
search area is limited to these buses, thereby the time of the
calculations is reduced. For a transmission line 'L' connected
between the buses "i" and "k", as shown in Figure 1, the
active power losses on this line are defined by RI2, defined
as Eq. (1) [32, 39].
Figure 1. Distribution Network Equivalent Circuit [32]
22
k k ik
ik loss 2
k
(P Q )R
P(V )
−
+
=
(1)
The LSF can be calculated as follows [41]:
ik loss k ik
2
kk
P2Q R
Q (V )
−
=
(2)
The normalized voltage is obtained by dividing the
voltage in the base conditions by 0.95 [32, 39]. Buses whose
their voltages are less than 1.01 can be considered as the
candidate bass for DG installation. It's worth noting that
LSFs introduce a sequence of buses for the installation of
DG.
3. Problem Formulation
In this study, multi-objective optimization of location and
capacity of solar panels and wind turbines in the distribution
network using the MOHTLBOGWO hybrid algorithm is
proposed to reduce losses and improve reliability. In order to
achieve Pareto set levels, Problem optimization variables,
the optimal location and capacity of dispersed wind and solar
generation sources are determined using intelligent single-
objective optimization (using the HTLBOGWO method) as
well as multi-objective based on decision-making fuzzy-
based approach.
3.1. Objective Function
In this study, the minimization of power losses and
improvement of Reliability is considered as an objective
function and is described below.
• Line loss
Total network losses are equal to the losses of all network
lines. To calculate network losses, you must first get the
current of lines. To calculate the current of lines, it is also
necessary to solve the load distribution problem and obtain
the voltage of the buses [42]. By calculating the buses
voltages, the line currents and network losses are calculated
as follows:
(3)
(4)
where k is between the buses i and j. Rk and Xk are the
resistance and reactance of the k-th line, and Nb is the
number of grid lines.
• Reliability
Reliability indicators are distribution system reliability
assessment factors that were first introduced by the IEEE in
1998 to evaluate the distribution system. Basic reliability
indicators are three load point indicators, a) The average rate
of breakdown, b) the average withdrawal, and (c) the annual
withdrawal period. A radial distribution system includes a set
of series equipment including lines, brackets, fuses, and
disconnected switches, and so on. A subsystem connected to
the load point of a system requires that all equipment
between it and the supply point be in operation. Therefore,
the principle of serial systems can be considered directly for
these systems as follows.
1
n
pi
i
=
=
(5)
1
n
p i i
i
ur
=
=
(6)
1
1
n
ii
pi
pn
pi
i
r
u
r
=
=
==
(7)
In the above equation, n is represent the number of outage
events affecting load point p,
i
denotes Equipment failure
rate I (failure/year) and ri is repair time equip I (hours).
Based on the basic indices of the load point and energy
consumption at load points, energy not-supplied (ENS)
(kWh/year) is calculated as follows [43].
()
1
nl
a j j
j
ENS L u
=
=
(8)
where, nl represents the total number of load points, the
unavailability of the load point j (hours/year), and the
average load connected at the load point j (kW).
3.2. Constraints
In solving this optimization problem, a series of equal
and unequal constraints is considered, which is expressed in
sequence.
• Equilibrium power equations
The sum of the algebraic input and output power in the
distribution system should be equal to:
ij
k
kk
VV
IR jX
−
=+
2
1
b
N
loss k k
k
P R I
=
=
4
DG
DG
NLN
Swing DG Lineloss
i 1 i 1 q 1
NLN
Swing DG Lineloss
i 1 i 1 q 1
P P (i) P (i) Pd(q)
Q Q (i) Q (i) Qd(q)
= = =
= = =
+ = +
+ = +
(9)
• Voltage constraint
The value of the voltage in each bus should be between a
minimum and a maximum value as follows:
min i max
V V V
(10)
In the above relation, Vmin and Vmax are considered to
be 0.95 and 1.05 p.u respectively [32].
• Constraints on the production of DG
To prevent reverse power flow, the installed DG capacity
in the network is limited as follows, which should not exceed
the power supplied by the post [32].
DG
NLN
DG Lineloss
i 1 i 1 q 1
3
P (i) P (i) Pd(q)
4
= = =
+
(11)
DG
NLN
DG Lineloss
i 1 i 1 q 1
3
Q (i) Q (i) Qd(q)
4
= = =
+
(12)
On the other hand, DGs themselves have the minimum
and the maximum production capacity is as follows [43].
min max
DG DG DG
P P (i) P
(13)
min max
DG DG DG
Q Q (i) Q
(14)
• Line capacity constraints
The Complex power transmission of each line should be
less than the nominal value given in the following equation.
Li Li(rated)
SS
(15)
4. Overview of Proposed Algorithm
4.1. TLBO
The TLBO algorithm is a smart optimization method that
was introduced by Rao [15] based on the influence of teacher
to students to increase scientific level of class. This method
is based on this principle that the teacher tries to close class
level to himself and students, in addition to exploit the
teacher's knowledge with regard to other classmates, use
their knowledge to increase level of them. Because of the
teacher can't bring level of individual students to himself, so
tries to increase the average level of whole class and
evaluates the class level based on the exams and students’
scores. The mathematical expression of this approach is that
first the population of problem variables (teacher and
students) are defined randomly. All of these populations are
compared together by the objective function and set of
variables with best solution are considered as the teacher.
This approach is divided into two phases: teacher phase and
student phase.
• Teacher phase
In this step teacher tries to bring class average to himself.
But since it is very difficult, teacher tries to increase class
average from Mi to M_new. Each set of problem variables
are updated based on the difference of these two values.
Difference of these two values can be saved by the parameter
Diff_Mean as follows:
_ ( _ )
i i f i
Diff Mean r M new T M=−
(16)
Where Tf is the teacher parameter that is selected
randomly between 1 and 2. The ri is a random number
between 0 and 1. Using the follow equation each set of
variables are updated.
,,_
new i old i i
X X Diff Mean=+
(17)
• Student phase
Students in addition to teacher’s knowledge, benefit from
each other’s knowledge. The mathematical expression of this
approach is that in each step and in each repetition each set
of variable (student) selects one of students randomly. For
example student i selects student j and this i is opposite of j.
If the student j has more knowledge respects to student i then
the student i updates his status based on the following
equation:
,,
()
new i old i i i j
X X r X X= + −
(18)
The student status is varied as follows:
,,
()
new i old i i j i
X X r X X= + −
(19)
After the all students changed their status, their level is
evaluated by the objective function. Under these conditions
the best student is compared with the teacher of previous step
and if a better result has, is replaced with previous iteration
teacher. This process is continued to obtain convergence
conditions.
4.2. GWO
One of the population-based intelligent and evolutionary
algorithms is the Gray Wolf algorithm (GWO) which was
first announced by Mir-Jalili in 2014 [38]. In this algorithm,
the performance and behaviour of gray wolfs for hunting is
simulated. Figure 2 shows that parameters such as α, β, δ,
and ω represent the leaders of the group so that α directs the
group as leader of the group and has important decisions
about hunting, resting place and so on. The second group of
leadership belongs to β. In addition to being able to help α
due to having a good decision, β members are also the best
substitutes for the α wolfs when they are old or dead; ω but
is at the bottom of this group. They are the last wolves that
are allowed to eat. The other group members that are not α,
β and ω are called δ [38].
5
Figure 2. Leader hierarchy in gray wolves group
The principles of GWO function are as follows:
• Investigating, pursuing and following the hunt;
• Pursuing, sieging and harassing the hunt until it
stops; and
• Attacking to the hunt.
In the simulation of the GWO, α is considered as a top
answer. After that, the next two responses after α are
considered β and δ. Finally, the rest answers are regarded ω.
To model a suitable situation that gray wolves encircle their
hunt during hunting are shown as follows [38].
(20)
(21)
where t represents the repetition,
A
,
C
, and
P
X
indicate the
coefficients vectors, the position of the bait and the gray wolf
respectively. The coefficients vector is obtained from the
following equation [38].
1
2A ar a=−
(22)
2
2Cr=
(23)
where vectors of random numbers at a distance are shown by
and that are selected from [0, 1] area and vector
a
decreases from 2 to 0 during repetitions.
According to the wolf ability due to finding and
surrounding the hunt and in order to having a mathematical
simulation of this kind of behaviour, it is assumed that the
three top wolves in the group have more knowledge about
the hunting place. By storing the position of the three above
mentioned wolves, ω wolves have to change their location
based on the position of the three top members of the group
which can be expressed as follows [38]:
1 2 3
,,D C X X D C X X D C X X
= − = − = −
(24)
1 2 3
1 2 3
,,X X a D X X a D X X a D
= − = − = −
(25)
1 2 3
( 1) 3
X X X
Xt ++
+=
(26)
4.3. HTLBOGWO (TLRBO)
The TLBO algorithm is a robust algorithm capable of
solving engineering problems. However, a new phase has
been added to this algorithm to increase the global and local
search capability as well as track the optimal answer. This
phase is due to the choice of first, second and third students
as the best answers after the student phase. After selecting
the top three students, the remaining students will learn from
these three students. The process of selection students and
their ranking is considered to be the ranking phase, which is
called the TLRBO algorithm.
Since the ranking phase and follow up of the students and
their learning from the top three students are very similar to
the behaviour of the gray wolf algorithm, So in the
formulation of TLRBO, method of selection the wolf-alpha,
beta, and delta and the method of updating the location of the
wolfs of Omega to follow up the top three wolves have been
used. Therefore, the proposed algorithm will be a
combination of the TLBO and GWO algorithms.
4.4. HTLBOGWO (TLRBO) Multi-Objective Algorithm
Multi-objective issues have multiple goals, which are
mostly contradictory. The answer to these problems is a set
of solutions called Pareto optimal solutions [44]. This set
includes Pareto optimal solutions that represent the best
balance between the objectives. Multi-objective
optimization is considered as a minimization problem and
formulated as follows [43]:
1 2 0
min : F(x)= ( x), ( x),..., ( x),imize f f f
(27)
to: g (x) 0, i 1,2,...,
i
subject m=
(28)
h (x) 0, i 1,2,...,
ip==
(29)
i i i
L x U
(30)
where 0 represents the number of targets, m denotes the
number of inequality constraints and p is the number of
equality constraints. [Li, Ui] are the boundaries variable i.
Given the nature of the multi-objective problems, various
solutions cannot be compared through mathematical
relations operators. In this case, Pareto optimal parental
concepts allow us to compare two solutions in a multi-
objective search space [43].
Two key points in finding a suitable set of optimal Pareto
solutions for the given problem are convergence and
coverage. Convergence refers to the ability of a multi-
objective algorithm to determine the exact approximation of
Pareto's optimal solution. The coverage reflects the
distribution of Pareto's optimal response along the
objectives. Since many of the current multi-objective
algorithms are deductive, coverage and the number of
answers for decision-making after the optimization process
are very important. The ultimate goal for a multi-objective
optimizer is to find the exact approximation of the optimal
Pareto correct solution (convergence) with uniform
distribution (coverage) for all purposes.
To solve multi-objective problems using the
MOHTLBOGWO algorithm, it first equipped to an archive
to store and restores the best approximation of the optimal
Pareto solution. The position updating of the search factors
for MOHTLBOGWO is the same, but the student's position
is selected from the archive. In order to find a suitable
6
expansion for the Pareto optimal frontier, a place from the
low-density Pareto optimal frontier, similarly for multi-
objective particle swarm optimization algorithm (MOPSO)
[45] is selected. To find the low-density area of Pareto
optimal frontier, the search space should be divided. This is
accomplished by finding the best and worst objectives of
Pareto's optimal solution, the definition of the hyper-sphere
to cover all the solution, and the division of the hyper-sphere
into sub-hyper-sphere in each repetition. After the creation
of the section, the choice is made by a roulette wheel
mechanism with the following probability for each section
proposed by Coello Coello [2].
i
i
c
PN
=
(31)
where c is a constant number greater than one, and Ni is the
number of obtained Pareto's optimal response in the i-th
section. This allows MOHTLBOGWO algorithm equations
with higher probability to choose positions from low
population sections.
4.5. Fuzzy Decision Making
The ultimate goal of a multi-objective optimization
algorithm is to identify solving in the Pareto optimal set.
However, identifying the entire Pareto optimal set is not
possible due to its wide dimensions to prove the optimality,
and therefore not recommended. Therefore, to investigate the
feasibility of having Pareto optimal sets in multiple
optimization problems, there is a practical approach. In the
present study, a fuzzy approach is applied to select the best
solution of the Pareto set. The j-objective function of a
solution in Pareto set fj is defined by a membership function
j as follows [46]:
max
max
max
1
0
min
jj
jj min
jj
min
jj
j
j
j
ff
ff ff
ff
ff
=
−
−
(32)
where
min
j
f
and
max
j
f
are the minimum and maximum
values of the objective function j. For each i solution, the
membership function is calculated as follows [19]:
1
11
ni
j
j
jmn
i
j
ij
=
==
=
(33)
where n is the number of objective functions and m is the
number of solutions. The answers have the maximum value
of μi for the best compromise answer.
4.6. Implementation of MOHTLBOGWO
The steps to implement the proposed method in problem
solving are as follows:
• Step 1: Random generation of the initial population
from the set of variables including the location of
the installation and the capacity of solar and wind
units as well as the power factor of wind turbines.
• Step 2: the value of the target function is calculated
for each set of variables and the best set is selected
in terms of the value of the objective function as the
representative of the entire population.
• Step 3: Each set of variables is updated by the
proposed algorithm, and if the new variables have
better results, they will be replaced with the
previous set.
• Step 4: if the condition for convergence does not
exist, go to step 1. Otherwise, go to step 5.
• Step 5: Stop the algorithm.
5. Simulation Results and Discussion
5.1. Testing System
As shown in Figure 3, in this paper, the proposed method
is implemented on the IEEE standard 33-buses radial
network. In the 33-buses network, the total consumption of
this network is 3720 kW and 2300 kVAR. The 33-buses
Network has 37 branches. System information is presented
in [47].
Figure 3. IEEE Standard Radial 33-buses Distribution Network
5.2. Simulation Strategies
In this paper, the optimal placement of solar panels and
wind turbines for the purpose of reducing losses and
improving reliability indicators are presented using the
proposed method HTLBOGWO. First, simulations were
performed in a single-objective optimization. Then, multi-
objective optimization was proposed based on fuzzy decision
method and the results were compared and analyzed. In
single-objective optimization, simulation results obtained
from TLBO, GWO, and HTLBOGWO methods are
evaluated based on indicators of loss reduction and energy
not-supplied subscriber reduction (reliability improvement).
In multi-objective optimization, the results of multi-
objective methods MOGWO, MOTLBO and
MOTLBOGWO are presented. In Figure 4, the LSF curve of
the 33-buses network is presented. In this figure, the buses 6,
28, 29, 30, 9, 10, 13, 8, 27, 31 and 26 are based on the LSF
curve considered as the candidate buses for installing wind
turbines and solar panels Which are similar to Candida buses
in reference [32].
7
Figure 4. LSF curve of the 33-buses network
5.3. Single-Objective Optimization Results
In this section, the results of single-objective positioning
of solar panels and wind turbines are presented for the
purpose of reducing losses and reducing ENS for 1, 2 and 3
DGs 1 megawatts. In Table 1, the results are presented with
the objective of reducing losses. In the positioning of 3 solar
panels, the buses 13, 24 and 30 were selected for installation
with a capacity of 996, 938 and 852 kW respectively. The
network losses before positioning were 202.68 kilowatts.
After locating one, two, and three panels, this value has
dropped to 127.28, 86.55 and 72.11 kW, respectively. In
locating of 3 wind turbines, the buses 30, 13 and 24 were
selected for installation with a capacity of 997, 1000 and 789
kW and with power factors 0.8659, 0.8122 and 0.8726
respectively. With locating 1, 2 and 3 wind turbines, the
network losses dropped from 202.68 to 81.43, 32.17 and
13.68 kilowatts, respectively. With 1, 2 and 3 wind turbines,
the network losses dropped from 202.68 to 81.43, 32.17 and
13.68 kilowatts, respectively.
Also, the minimum voltage is also improved by the use
of panels and turbines. The results also show that the ENS
value before the locating of solar panels and wind turbines
was 6.695 MW, and after locating 3 panels it reached 0.628
MW, and after locating 3 turbines reached 0.671 MWh. The
results show that the cost of network losses with the optimal
locating of solar panels and wind turbines has decreased and
financial benefits from loss reduction have increased. In
addition, the results have shown that increasing the number
of DGs has led to a further reduction in losses, reduction cost
of losses, and ENS, as well as further increase in the
minimum voltage and net profit of the network. The results
show that the performance of wind turbines was better than
solar panels in improving the distribution network
characteristics. In other words, in terms of reduction of losses
and ENS, as well as the improvement of minimum voltage,
it achieves better results due to the injection of reactive
power in addition to the active power to the distribution
network.
Table 1. Optimal sizing DG’s for 33 bus IEEE system (active power loss objective function)
The convergence curve of the combined HTLBOGWO
combination method, along with TLBO and GWO methods
for single-objective optimization of solar panels and wind
turbines with the goal of reducing losses for 3 DGs, is shown
in Figure 5 and Figure 6, respectively. As can be seen, in
locating solar panels and wind turbines, the HTLBOGWO
method has less convergence fluctuations, and achieved a
lower loss rate than the TLBO and GWO with a higher
convergence rate and less repetition.
Single-objective optimization results with the goal of
reducing losses using TLBO, GWO and HTLBOGWO
methods for 3DG are presented in Table 2. As can be seen,
the proposed method is better than other methods in terms of
reducing losses, reducing cost of losses, reducing ENS,
improving the minimum voltage and increasing the financial
profit of the network.
Table 3 presents the results of single-objective
positioning of solar panels and wind turbines with the goal
of reducing ENS for 1, 2 and 3 DG 1 megawatts. As can be
seen, with the locating of 1 and 2 solar panels, the network
losses are decreasing, but in the positioning of the three
panels, the losses compared to the positioning of the two
turbines increased from 87.17 to 97.04 kilowatt, but in
Maximum Size 3MW (kW/pf/@Bus)
No PV
1PV
2PV
3PV
Power Losses (kW)
210.98
127.28
86.55
72.11
ENS (MWh/yr)
6.695
4.158
1.923
0.628
Minimum Voltage (pu)
0.91308
0.9285
0.9629
0.9667
Size and Location
--
1000/1@30
893/1@ 10,
1000/1@ 30
996/1@ 13,
938/1@ 24,
852/1@ 30
Total Size (kW)
--
1000
1893
Losses Cost ($/yr)
110891
66899.8
45491.3
37903.5
Net Saving ($/yr)
--
43991.2
65399.7
72987.5
No WT
1WT
2WT
3WT
Power Losses (kW)
210.98
81.43
32.17
13.68
ENS (MWh/yr)
6.695
4.158
2.233
0.640
Minimum Voltage (pu)
0.91308
0.9360
0.9796
0.9892
Size and Location
--
1000/0.8011@30
861/ 0.8742 @10,
1000/0.8091@30
997/0.8659 @30,
1000/0.8122 @13,
789/ 0.8726@24
Total Size (kW)
--
Losses Cost ($/yr)
110891
42801
16913.5
7191.6
Net Saving ($/yr)
--
68090
93977.5
103699.4
8
contrast to the positioning of the three panels, the ENS value
was strongly Dropped to 0.0025 MWh. In the positioning of
wind turbines, with increasing its number, the amount of
losses decreased, the minimum network voltage increased
and the amount of ENS decreased, so that it reached 0.002
MW in the positioning of 3 turbines. Also, with the optimal
locating of turbines, the cost of losses is reduced and the
amount of financial gain in the locating of the three turbines
has a maximum value. This table also shows that wind
turbines have a better effect on the characteristics of the
distribution network than solar panels.
Figure 5. Convergence curve of different methods with the aim of
reducing the losses in the 3 PV positioning
Single-objective optimization results with the aim of
reducing the ENS obtained from the HTLBOGWO method
are presented in Table 4 and compared with the TLBO and
GWO methods. The amount of losses by the proposed
method was 97.04 kilowatts and the losses obtained from the
TLBO and GWO methods were 101.25 and 103.17 kW
respectively. Also, the amount of ENS by the proposed
method, 0.025 MWh and by TLBO and GWO methods were
0.048 and 0.044 MW, respectively, which indicates the
superiority of the proposed method in solving the problem of
positioning solar panels. Also, according to
Table 4, in the locating of solar panels and wind turbines,
the HTLBOGWO method performed better than other
methods in terms of reducing losses, reducing ENS,
improving the minimum voltage and financial profit of the
network.
Figure 6. Convergence curve of different methods with the aim of
reducing losses in the 3 WT positioning
5.3. Assessment of the Renewable Resource Dispersion
Effect
In this section, the effect of dispersing the capacity of
solar panels and wind turbines has been evaluated in problem
solving. In other words, the effect of using a 3 MW DG with
the use of three DGs with a capacity of 1 MW on the power
loss, reliability index, minimum network voltage, cost of
losses and financial profit of the network has been evaluated.
The results obtained in Table 5 and Table 6 are presented for
the purpose of decreasing losses and decreasing the ENS in
a single-objective optimization, respectively. As can be seen,
when using three DGs with a capacity of 1 MW instead of
using a 3 MW DG The amount of network losses and ENS
will be lower and the network obtaining the higher minimum
voltage , more financial gain and reduce cost of losses. For
example, according to Table 5, in dispersal conditions, the
network losses decreased from 103.96 to 72.11 kV and ENS
values decreased from 4.379 to 0.628 megawatts / h.
According to Table 6, under dispersal conditions, the amount
of network losses decreased from 161.26 to 97.04 kilowatts
and ENS values from decreased 0.11 to 0.025 MWh. The
voltage profile curve of 33-buses network before locating
and under dispersion conditions for solar panels and wind
turbines is plotted in Figure 7. Also Figure 7 shows the
voltage profile curve of 33-buses network before locating
and under conditions where there is no dispersion condition.
Figure 7 and Figure 8 showed that the distribution and
distribution of power in the network buses leads to
improvement of the network voltage profile.
Table 2. Optimal sizing DG’s for 33-bus IEEE system (active power loss objective function-algorithms comparison)
Maximum Size 3MW (kW/pf/@Bus)
No PV
TLBO
GWO
HTLBOGWO
Power Losses (kW)
210.98
74.10
73.29
72.11
ENS (MWh/yr)
6.695
0.734
0.659
0.628
Minimum Voltage (pu)
0.9130
0.9621
0.9648
0.9667
Size and Location
--
872 (29), 858 (13), 946
(24)
889 (24), 903 (30), 994
(10)
996/1@ 13, 938/1@ 24,
852/1@ 30
Total Size (kW)
--
Losses Cost ($/yr)
110891
38949.0
38525.7
37903.5
Net Saving ($/yr)
--
71942
72365.3
72987.5
No WT
TLBO
GWO
HTLBOGWO
10
Power Losses (kW)
210.98
14.02
13.82
13.68
ENS (kWh/yr)
6.695
0.787
0.657
0.640
Minimum Voltage (pu)
0.9130
0.9892
0.9891
0.9892
Size and Location
--
972 (24) 0.8636, 1000 (30)
0.8011, 760 (13) 0.8299
962 (24) 0.8659, 804 (13)
0.8122, 1000 (30) 0.8726
997/0.8659 @30,
1000/0.8122 @13, 789/
0.8726@24
Total Size (kW)
--
--
--
Losses Cost ($/yr)
110891
7370.5
7267.1
7191.6
Net Saving ($/yr)
--
103520.5
103623.9
103699.4
Table 3. Optimal sizing DG’s for 33 bus IEEE system (ENS objective function)
Maximum Size 3MW (kW/pf/@Bus)
No PV
1PV
2PV
3PV
Power Losses (kW)
210.98
129.47
87.17
97.04
ENS (kWh/yr)
6.695
3.502
0.965
0.035
Minimum Voltage (pu)
0.9130
0.9319
0.9655
0.9705
Size and Location
--
1000/1@13
1000/1@30, 1000/1@ 13
709/1@30, 810/1@10,
957/1@13
Total Size (kW)
--
1000
Losses Cost ($/yr)
110891
68053.5
45819.5
51008.3
Net Saving ($/yr)
--
42837.5
65071.5
59882.7
No WT
1WT
2WT
3WT
Power Losses (kW)
210.98
103.21
62.16
55.43
ENS (kWh/yr)
6.695
3.412
0.9630
0.011
Minimum Voltage (pu)
0.9130
0.9385
0.9576
0.98248
Size and Location
--
1000 (10) 0.8237
1000 (30) 0.9480,
1000 (10) 0.9981
993 (13) 0.8579, 802 (29)
0.8427, 762 (30) 0.8209
Total Size (kW)
--
Losses Cost ($/yr)
110891
54251.4
32671.6
29136.6
Net Saving ($/yr)
--
56639.6
78219.4
81754.4
Table 4. Optimal sizing DG’s for 33 bus IEEE system (ENS objective function-Algorithms comparison)
Maximum Size 3MW (kW/pf/@Bus)
No PV
TLBO
GWO
HTLBOGWO
Power Losses (kW)
210.98
101.25
103.17
97.04
ENS (kWh/yr)
6.695
0.048
0.044
0.035
Minimum Voltage (pu)
0.9130
0.9694
0.9677
0.9705
Size and Location
--
986 (9),
789 (29),
1000 (13)
807 (29),
830 (13),
1000 (10)
709 (30),
810 (10),
957 (13)
Total Size (kW)
--
Losses Cost ($/yr)
110891
53217.5
54228.8
51008.3
Net Saving ($/yr)
--
57673.5
56662.2
59882.7
No WT
TLBO
GWO
HTLBOGWO
Power Losses (kW)
210.98
58.17
59.61
55.43
ENS (kWh/yr)
6.695
0.018
0.016
0.011
Minimum Voltage (pu)
0.9130
0.9808
0.9800
0.98248
Size and Location
--
893
(9) 0.8760, 762
(30) 0.982,
1000
(13) 0.9519
652
(29) 0.9660, 978
(13) 0.9465, 920
(30) 0.9824
993
(13) 0.8579, 802
(29) 0.8427, 762
(30) 0.8209
Total Size (kW)
--
Losses Cost ($/yr)
110891
30577.0
31334.6
29136.6
Net Saving ($/yr)
--
80314
79556.4
81754.4
Table 5. Results of DGs distribufication (SOO-Loss minimization)
Maximum Size 3MW (kW/pf/@Bus)
PV
1DG (3000)
(kVA/P.F)
1DG (3000)
(kVA/P.F) ALO [32]
1DG (3000)
(kVA/P.F) [47]
3DG (1000)
(kVA/P.F)
Power Losses (kW)
101.96
103.053
118.96
72.11
ENS (kWh/yr)
4.379
--
--
0.628
Minimum Voltage (pu)
0.9510
0.9503
0.9441
0.9667
Size and Location
2585/1@29
2450/1@6
1857.5/1@8
996/1@ 13,
938/1@ 24,
852/1@ 30
Total Size (kW)
Losses Cost ($/yr)
53590.1
54164.6
62525.3
37903.5
11
Net Saving ($/yr)
57300.9
56726.4
44002.6
68624.7
WT
1DG (3000)
(kVA/P.F)
1DG (3000)
(kVA/P.F) ALO [32]
1DG (3000)
(kVA/P.F) [47]
3DG (1000)
(kVA/P.F)
Power Losses (kW)
61.36
71.75
82.78
13.68
ENS (kWh/yr)
4.406
--
--
0.671
Minimum Voltage (pu)
0.9667
0.9528
0.9549
0.9892
Size and Location
2544(6)0.8236
2238.8 (18) 0.87
2265.2 (8) 0.82
997/0.8659 @30,
1000/0.8122
@13,
789/ 0.8726 @24
Total Size (kW)
Losses Cost ($/yr)
32253.1
37711.8
43509.1
7191.6
Net Saving ($/yr)
78637.9
73179.3
63018.8
99336.6
Figure 7. Network voltage profile of 33 buses before placing solar
panels and under dispersion conditions
Figure 8. Network voltage profile of 33 buses before placing wind
turbines and under dispersion conditions
5.4. Multi-Objective Optimization Results
In this section, multi-objective optimization of the
locating of solar panels and wind turbines is presented based
on the fuzzy decision approach using the HTLBOGWO
method and the results are compared with the TLBO and
GWO multi-objective methods. The Pareto optimal set of
solutions for placement of 1 panel and 1 wind turbine with a
capacity of 1 MW is shown in Figure 9 and Figure 10,
respectively. As shown in Figure 9, the MOHTLBOGWO
method, in comparison with the MOTLBO and MOGWO
response scattering, offers better results in terms of achieving
an optimal response. Also, in the terms of achieving to lower
losses, lower ENS, minimum voltage, lower cost of losses
and higher financial profit, the proposed method
performance was better than the other two methods. Also,
according to Table 7 and Table 8, in the multi-objective
optimization, items such as the losses, ENS, the minimum
voltage, the cost of losses, and the amount of financial gain
are located between the single-objective values that aimed at
reducing losses and reducing ENS. In other words, in the
multi-objective optimization, there is a Compromise
between the losses and ENS.
Figure 9. Pareto optimal answers set curve in the placement of the
solar panels by various methods
Figure 10. Pareto optimal answers set curve in the placement of
the wind turbines by various methods
In Figure 11, the multi-objective positioning of both
panels and turbines simultaneously is presented using
various methods. The numerical results are also given in
Table 9. The results show that the proposed MOTLBOGWO
100 110 120 130 140 150 160 170
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Power Loss (KW)
ENS (KWh/yr)
MOGWO
MOTLBO
MOhTLBO-GWO
Fuzzy Best Solution
60 65 70 75 80 85 90 95 100 105 110
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Power Loss (KW)
ENS (KWh/yr)
MOGWO
MOTLBO
MOhTLBO-GWO
Fuzzy Best Solution
11
method offers better Pareto-optimal solution than other
methods and has obtained the optimal solution with less
dispersion. Also, according to Table 9, can be seen that the
simultaneous use of 1 panel and 1 turbine instead of use one
panel or one turbine, has led to a further reduction of losses
and ENS, a further increase in the minimum voltage and net
profit of the network.
Figure 11. Pareto optimal answers set curve (PV + WT only with
maximum capacity of 3 megawatts)
Table 6. Results of DGs distribufication (SOO-ENS minimization)
Maximum Size 3MW (kW/pf/@Bus)
1DG (3000)
(kVA/P.F)
3DG (1000)
(kVA/P.F)
Power Losses (KW)
161.26
97.04
ENS (kWh/yr)
1.337
0.035
Minimum Voltage (pu)
0.9466
0.9705
Size and Location
2097 (10)
709 (30),
810 (10),
957 (13)
Total Size (kW)
Losses Cost ($/yr)
84761.3
51008.3
Net Saving ($/yr)
26129.7
59882.7
1DG (3000)
(kVA/P.F)
3DG (1000)
(kVA/P.F)
Power Losses (kW)
100.09
55.43
ENS (kWh/yr)
0.481
0.011
Minimum Voltage (pu)
0.9564
0.98248
Size and Location
2639 (13) 0.8729
993 (13) 0.8579, 802 (29) 0.8427, 762
(30) 0.8209
Total Size (kW)
Losses Cost ($/yr)
52611.4
29136.6
Net Saving ($/yr)
58279.6
81754.4
Table 7. Fuzzy multi-objective results for 1 PV placement
Maximum Size 3MW (kW/pf/@Bus)
No DG
1PV
(Loss objective)
1PV
(ENS objective)
1PV
(Loss+ENS bjective)
Power Losses (kW)
210.98
101.96
161.26
124.62
ENS (kWh/yr)
6.695
4.379
1.337
1.602
Minimum Voltage (pu)
0.9130
0.9510
0.9466
0.9486
Size and Location
--
2585/1@29
2097/1@10
2007/1@30
Total Size (kW)
--
2585
2097
2007
Losses Cost ($/yr)
110891
53590.1
84761.3
65505.4
Net Saving ($/yr)
--
57300.9
26129.7
45385.6
Table 8. Fuzzy multi-objective results for 1 WT placement
Maximum Size 3MW (kW/pf/@Bus)
No DG
1WT
(Loss objective)
1WT
(ENS objective)
1WT
(Loss+ENS objective)
Power Losses (kW)
210.98
61.36
100.09
73.3816
ENS (kWh/yr)
6.695
4.406
0
1422.4586
Minimum Voltage (pu)
0.9130
0.9667
0.9564
0.95677
37.5 38 38.5 39 39.5 40 40.5 41
0
100
200
300
400
500
600
700
800
900
Power Loss (KW)
ENS (KWh/yr)
MOGWO
MOTLBO
MOhTLBO-GWO
Fuzzy Best Solution
12
Size and Location
--
2544/0.8236@6
2639/0.8729@7
2078/0.833@30
Total Size (kW)
--
2544
2639
2078
Losses Cost ($/yr)
110891
32253.1
52611.4
38569.3
Net Saving ($/yr)
--
78637.9
58279.6
72321.7
Table 9. Fuzzy multi-objective results for 1 PV and 1 WT placement simultaneously
Maximum Size 3MW (kW/pf/@Bus)
No DG
1 PV
1 WT
1PV+1WT
Power Losses (kW)
210.98
124.6299
73.3816
38.3211
ENS (kWh/yr)
6.695
1.602
1.422
0.342
Minimum Voltage (pu)
0.9130
0.9486
0.9567
0.9805
Size and Location
--
2007/1@30
2078/0.833@30
873/1@13 1405/0.8@30
Total Size (kW)
--
2007
2078
2278
Losses Cost ($/yr)
110891
65505.4
38569.3
20141.5
Net Saving ($/yr)
--
45385.6
72321.7
90749.5
6. Conclusions
In this paper, the new MOHTLBOGWO method was
used to determine the location and capacity of solar panels
and wind turbines for the purpose of reducing losses and
improving reliability in the distribution network. The
proposed problem was evaluated based on single-objective
and multi-objective optimization based on fuzzy decision
making in optimizing the use of renewable resources in the
33 Buses distribution network. The effectiveness of the
proposed method in various optimizations was presented
and compared with the MOTLBO and MOGWO results.
The results showed that in the optimal placement of the
solar panels and wind turbines, unlike their single-objective
optimization, there is a compromised between the reduction
of losses and improved reliability, and the optimal solution
was determined from the set of answers of the Pareto levels.
In comparison with the MOTLBO and MOGWO methods,
the MOHTLBOGWO method has a better convergence in
Pareto levels and achieves optimal solutions. Also, the
ability of the proposed method in single-objective
optimization In comparison with previous studies in
reducing losses, improving the minimum voltage and
increasing network profits was confirmed. The results also
showed that the dispersal of renewable resources in the
distribution network would result in more reduction of
losses, greater improvement on reliability, and more
financial gain on the network.
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