Ain Shams Engineering Journal xxx (xxxx) xxxContents lists available at ScienceDirect
Ain Shams Engineering Journal
journal homepage: www.sciencedirect .comElectrical EngineeringAn exact MINLP model for optimal location and sizing of DGs in
distribution networks: A general algebraic modeling system approach⇑ Corresponding author.
E-mail addresses: o.d.montoyagiraldo@ieee.org, omontoya@utb.edu.co (O.D.
Montoya), wjgil@utp.edu.co (W. Gil-González), luisgrisales@itm.edu.co (L.F. Gri-
sales-Noreña).
Peer review under responsibility of Ain Shams University.
Production and hosting by Elsevier
https://doi.org/10.1016/j.asej.2019.08.011
2090-4479/
 2019 Ain Shams University. Production and hosting by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-Noreña, An exact MINLP model for optimal location and sizing of DGs
tribution networks: A general algebraic modeling system approach, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011Oscar Danilo Montoya a,⇑, Walter Gil-González b, L.F. Grisales-Noreña c
a Programa de Ingeniería Eléctrica e Ingeniería Electrónica, Universidad Tecnológica de Bolívar, Km 1 vía Turbaco, Cartagena, Colombia
bUniversidad Tecnológica de Pereira, AA: 97, 660003 Pereira, Colombia
c Instituto Tecnológico Metropolitano, 050012 Medellín, Colombia
a r t i c l e i n f o a b s t r a c tArticle history:
Received 31 December 2017
Revised 6 May 2019
Accepted 19 August 2019
Available online xxxx
Keywords:
Distributed generation
Distribution systems
General algebraic modeling system
Mixed-integer nonlinear programming
Optimal location and sizing of distributed
generationThis paper addresses the classical problem of optimal location and sizing of distributed generators (DGs)
in radial distribution networks by presenting a mixed-integer nonlinear programming (MINLP) model. To
solve such model, we employ the General Algebraic Modeling System (GAMS) in conjunction with the
BONMIN solver, presenting its characteristics in a tutorial style. To operate all the DGs, we assume they
are dispatched with a unity power factor. Test systems with 33 and 69 buses are employed to validate the
proposed solution methodology by comparing its results with multiple approaches previously reported in
the specialized literature. A 27-node test system is also used for locating photovoltaic (PV) sources con-
sidering the power capacity of the Caribbean region in Colombia during a typical sunny day. Numerical
results confirm the efficiency and accuracy of the MINLP model and its solution is validated through the
GAMS package.

 2019 Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under
the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).1. Introduction
1.1. General context
Nowadays, around the world, electricity is mainly produced by
large-scale plants that operate using conventional sources of
energy, such as hydraulic and thermal technologies. Electric plants
are usually located far from final consumers and, therefore, energy
losses associated with transmission lines increase [1,2]. Addition-
ally, the voltage profile can exceed its lower and upper bounds
[3,4]. For that reason, distributed generators (DGs) have become
a local solution for medium- and low-voltage power systems [5–
7]. DGs enable the injection of active and reactive power closer
to consumers, which can produce benefits in terms of quality of
service [8,1,9]. Integrating DGs into the electric system has bothpositive and negative effects because they modify the behavior of
the state variables of the grid, which absolutely depend on their
location and sizing in the power system [10]. Advances in solid-
state electronics and software have boosted the high penetration
of renewable energy into electrical networks, mainly at distribu-
tion levels. Hence, strategies or methods that allow the correct
integration of these emerging technologies are necessary [11,9].
In the last decade, different models, methods, and optimization
techniques for sizing and locating DGs in electric distribution net-
works have been proposed. They have allowed the integration of
renewable energy sources (e.g., wind and photovoltaic (PV) gener-
ation), small-scale hydraulic generation, and biomass generation,
among others, in an appropriated way [12–14]. DGs enable an
improvement of different technical aspects, such as voltage pro-
files, the power capacity of the lines, and the reliability and quality
of service, as well as a reduction of active and reactive power losses
[15]. Said generation technologies also allow utility companies to
diversify their energy matrix and transform electric power grids
into autonomous and smart systems [16].1.2. Motivation
Advances in power electronics transform the possibility of hav-
ing electrical networks with a high penetration of distributed gen-
eration at distribution levels into a reality, mainly with thein dis-
2 O.D. Montoya et al. / Ain Shams Engineering Journal xxx (xxxx) xxxintegration of multiple renewable energy sources. Therefore, math-
ematical models and new solution methodologies should be con-
tinuously developed to address the problem of optimal location
and sizing of such sources in power distribution networks. For that
reason, the motivation behind this study was providing the spe-
cialized literature with a powerful tool (a GAMS optimization pack-
age) for solving large-scale nonlinear discrete problems via
mathematical interpretation. Such tool focuses on the mathemati-
cal modeling itself by concentrating the attention of the researches
in the correct mathematical modeling by using a compact and
structured architecture. For that purpose, this paper presents a
simple implementation of the problem under study in order to
explain all the basic concepts for GAMS usage.
1.3. Brief state-of-the-art
The literature about the optimal location and sizing of DGs in
distribution networks is extensive and rich. This topic has a strong
background in terms of mathematical formulations and solution
techniques. Regarding its mathematical formulation, this problem
corresponds to a nonlinear non-convex optimization model with
discrete and continuous variables [17]; its mathematical structure
is an extension of the classical distribution system power flow
problem with discrete variables [18]. In terms of solution method-
ologies, the approaches most commonly adopted are metaheuristic
optimization techniques [19]. Such optimization approaches allow
the separation of the location problem from the sizing problem by
adopting a master-slave methodologies [19,20].
In the case of master-slave approaches, multiple discrete opti-
mization methods have been proposed: genetic algorithms [21],
ant lion optimizers [22], tabu search algorithms [23], simulated
annealing methods [24], krill herd algorithms [25–27],
population-based incremental learning [28], teaching-based learn-
ing optimizers [29], bat and firefly algorithms [30–33], symbiotic
organism search algorithms [34], harmonic search algorithms
[35], and imperialist competitive algorithms [19].
Regarding the methodology for solving the sizing problem, the
most common approach is particle swarm optimization [6,28],
since it is easy to implement in any computational language and
its results are comparable with interior-point and convex opti-
mization methods [36].
The specialized literature has also proposed exact models for
addressing the problem studied in this paper. In [17], a MINLP
model for the problem of optimal location and sizing of DGs in dis-
tribution systems was proposed by implementing a master-slave
approach in the decoupled form. That model combines sequential
quadratic programming methods with a branch and bound
approach, which implies that, so far, a compact formulation has
not been used as proposed in this paper. In [37], a MINLP model
was proposed to address the same problem, and the GAMS soft-
ware was used for its solution. Nevertheless, its implementation
has not yet been extended to daily operation with photovoltaic
(PV) sources, as proposed by us.
1.4. Contribution and scope
Based on the review of the state-of-the-art above, this paper
presents a solution to the problem of optimal location and sizing
of DGs in distribution networks in a tutorial style by taking advan-
tage of the compact modeling available in the GAMS software and
its nonlinear optimization packages. Note that the main contribu-
tion of our research is the possibility of implementing the exact
MINLP model of the problem using compact sets in GAMS without
adopting decoupling methods (e.g., master-slave algorithms),
which allows us to focus on the mathematical formulation itself.
In addition, the scope of our study is mainly defined by electricalPlease cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-No
tribution networks: A general algebraic modeling system approach, Ain Shamsdistribution networks and power losses minimization via the inte-
gration of DGs. This work presents, in a numerical simulation, the
possibility of extending our proposed MINLP model for the optimal
integration of renewable energy resources in a typical electrical
distribution network in Colombia, which is not typically addressed
in metaheuristic or conventional MINLP models. Furthermore, this
paper contains a simple example with the implementation of the
MINLP model, which will help researchers and students to use
the GAMS package for evaluating future studies in this area and
as a powerful comparative approach when emerging optimization
models are tested and validated.
1.5. Document structure
The rest of this document is organized as follows. Section 2 pre-
sents the complete mathematical formulation of the problem by
describing and discussing all the equations along with their vari-
ables and meanings. In Section 3, we provide all the necessary ele-
ments for using GAMS as an optimization package; in addition,
such section reports the complete mathematical implementation
of the MINLP model analyzed in this work as an opportunity to
identify all the concepts that compose the GAMS package. Section 4
presents all the information related to the 33 and 69-node test
feeders. Section 5 details all the numerical results of the proposed
GAMS approach compared with approaches reported in the litera-
ture; in addition, we present the extension of the model for the
daily operation of distribution networks with PV integration in
the context of a Colombian electrical system located in the Carib-
bean region. Section 6 draws the main conclusions derived from
this work as well as some possible future works, followed by the
acknowledgments and the references.
2. Problem description
2.1. Mathematical formulation
The mathematical model of the optimal location and sizing of
DGs in RDN corresponds to a MINLP problem [17]. Here, integer
(binary) variables represent the decision variables associated with
the location or not of a DG in the grid, while continuous variables
are associated to the classical power flow formulation, which is
represented by magnitudes and angles of the voltage per node.
The following is the detailed mathematical model proposed in this
paper [17].
Objective f unctionX X  !
min z ¼ Vi VjYij cos hi  hj  /ij ð1Þ
i2XN j2XN
where z is the value of the objective function, which corresponds to
the power losses in all the branches of the network under a load
peak scenario of demand; XN , the set associated with the nodes of
the network; Vi and Vj, the voltages’ magnitudes at nodes i and j,
respectively; hi and hj, the voltages’ angles at nodes i and j, respec-
tively; Yij, the magnitude of the admittance associated with the line
connected between i and j nodes; and /ij, its angle.
ConstraintsX  
PCG DGi þ Pi ¼ Vi VjYij cos hi  hj  /ij
j2XN ð2Þ
þPDi ; f8i 2 XNg
where PGCi represents the active power generated at node i by a con-
ventional generator; PDGi , the active power generated by a DG
located at node i; and PDi , the total active power demanded at node
i.reña, An exact MINLP model for optimal location and sizing of DGs in dis-
Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011
O.D. Montoya et al. / Ain Shams Engineering Journal xxx (xxxx) xxx 3Eq. (2) represents the active power balance at each node in the
network. X
QCGi  D ¼
 
Qi Vi VjYij sin hi  hj  /ij
j2XN ð3Þ
f8i 2 XNg
where QGCi denotes the reactive power generated at node i by a con-
ventional generator; QDGi , the reactive power generated by a DG
located at node i; and QDi , the total reactive power demanded at
node i.
Eq. (3) represents the reactive power balance at each node in
the network.
Vmini 6 V 6 V
max
i i f8i 2 XNg ð4Þ
where Vmin and Vmaxi i represent the minimum and maximum
allowed voltage values at each node. Note that (4) corresponds to
the voltage regulation constraint.
0 6 PDG 6 x PDG;maxi i i f8i 2 XNg ð5Þ
where PDG;maxi is the maximum allowed active power injection at
node i by a DG and xi represents the decision variable, which takes
a value of 1 if the DG is located at node i and 0 otherwise. Eq. (5)
shows the possibility of locating and sizing a DG at any node in
the RDN. We considered only active power injection in the DGs,
wXhich means that Q
DG
i ¼ 0 in this paper.
x 6 NDGi ava ð6Þ
i2XN
where NDGava is the available number of DGs, which implies that (6)
limits the number of location possibilities for the distributed gener-
ation in the RDN.
xi 2 f0;1g f8i 2 XNg ð7Þ
Finally, (7) expresses the binary nature of the decision variable.Fig. 1. GAMS software environment.
Fig. 2. Electrical configuration of the 7-node test syst
Please cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-No
tribution networks: A general algebraic modeling system approach, Ain Shams2.2. General comments
The MINLP model described from (1) to (7) represents problem
of optimal location and sizing of DGs in a RDN [17]. Such model
only focuses on the technical aspects related to active power losses
in the branches of the network, respecting classical constraints of
the power flow problem [1]. Note that this model corresponds to
an adaptation of the optimal power flow problem reported by
[38], in order to allow the location and sizing of DGs as a function
of the total active power consumption.
An adaptation for obtaining a power flow time-varying formu-
lation can be easily extracted for the model, as mentioned earlier,
by adding some sub-indexes and sums [39]. Here, we used the
demand peak hour to define the optimal location and sizing of each
distributed generator because it represents the worst operating
point in the RDN, with the highest power losses and voltage devi-
ations. In addition, we also extended this model to the daily oper-
ation of an electrical network in order to evaluate the possibility of
sizing PV generators.
This mathematical formulation can be directly implemented in
the GAMS platform [40], which allowed us to obtain an adequate
solution with a low computational effort. Such solution can be
local or global, depending on the characteristics of the problem
under analysis.
The next section presents a possible GAMS implementation for
a small radial distribution network. Such implementation uses sets
and a compact formulation [41].3. General algebraic modeling system: GAMS
The GAMS software is a powerful optimization package devel-
oped for interpreting and solving nonlinear large-scale optimiza-
tion problems based on a compact formulation [40,42]. Said
software works with a simple plain text structure, where the opti-
mization model is written using five essential components [43]:
i. The sets where the variables make sense, e.g., set of nodes:
i 2 XN .
ii. All the scalars, parameters, and matrices involved in the
model, i.e., number of generators, matrices, and vectors.
iii. All the variables in the model, e.g., voltages, powers, angles,
etc.
iv. The equations’ names and their mathematical structures,
e.g., expressions (2) and (3) associated with the power bal-
ance constraints.
v. The nature of the model (i.e., MINLP) and displaying options.
Fig. 1 presents the GAMS interface and the words reserved for
implementing an optimization model.
Note that, at the bottom of Fig. 1, each reserved word is needed
to define all the particular components of the model under study.
In that sense, we present a simple example that can illustrate the
complete structure of an optimization model implemented in the
GAMS software [41]. Such example aims at guiding readers on
the easy utilization of this optimization toolbox for addressing
optimization problems in engineering. For that purpose, let us con-
sider the grid depicted in Fig. 2, an electrical network composed of
7 nodes and 6 lines operated at 23 kV as voltage output at the sub-em used in the GAMS implementation example.
reña, An exact MINLP model for optimal location and sizing of DGs in dis-
Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011
4 O.D. Montoya et al. / Ain Shams Engineering Journal xxx (xxxx) xxxstation (slack node). Its line parameters, as well as power con-
sumption, are reported in Table 1.
The 7-node test system was implemented as an example in
GAMS considering 23 kV and 1 MVA as voltage and base power,
respectively. We also considered the possibility of installing one
distributed generator with unlimited capability.
Algorithm 1. GAMS implementation of the model in (1)–(7) for
the 7-node examplePlease cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-No
tribution networks: A general algebraic modeling system approach, Ain ShamsFrom Algorithm 1, it can be seen that all the components in the
optimization model (1)–(7) were included. Hence, the following
are the most important features of this implementation:
i. The command ALIAS(N,NP), in line 5, allows the duplica-
tion of the set of nodes N in the set NP to evaluate the power
balance equations and the objective function.
ii. All the parametric information of the model was defined
between lines 6 and 39.
iii. The set of variables was classified into continuous variables
(voltage, angles, and powers) and binary variables (optimal
location of the DG), as can be seen from lines 40 to 48.
iv. Lines 49 and 50 define the voltage constraint (4) and the typ-
ical behavior of the slack node in a radial distribution net-
work, i.e., plane voltage.
v. Lines 51 to 57 define the name of the equations, while lines
58, 59, and 61 are the objective function and the active and
reactive power balance constraints (i.e., the compact repre-
sentation of (1)–(3)).
v. Lines 63 to 65 represent the maximum number of DGs avail-
able as well as their minimum and maximum power outputs
(i.e., constraints (5) and (6)).
v. Lines 66 to 69 define the characteristics of the model and its
type (minimization), as well as its displaying features.
Note that, if we solve this model in GAMS by fixing the number
of available DGs at zero, then the base case of the network is
achieved. Figs. 3 and 4 present the GAMS outputs when zero and
one distributed generator are considered.
Note that, in Fig. 3, the total power losses without distributed
generation reach 128:058 kW, while in Fig. 4 the final losses
decrease to 56:9563 kW when one DG is installed. To reduce such
losses, GAMS determined that the distributed generator must be
located at node 3 with a total capacity of 6:3610 MVA.
It is important to mention that the model implemented in
GAMS is general for the problem analyzed in this paper, which
implies that, based on the parametric information of the test sys-
tem, it can find an optimal solution to the proposed MINLP model,
as will be confirmed in the next section. For detailed information
about GAMS and a complete description of its functionalities, refer
to [40,43,41].
4. Test systems and simulation cases
This section presents the electrical configuration, as well as the
test system information, of the radial distribution systems
employed in this work for validating the MINLP formulation and
its solution in the GAMS package. Two test system were used: a
33-node test system and a 69-node test feeder. The complete infor-
mation of these test systems is presented below.
4.1. 33-node test feeder
This test system is composed of 33 nodes and 32 branches with
12:66 kV of operating voltage. The slack node is located at node 1,
and its configuration is presented in Fig. 5. This feeder has
3715 kW and 2300 kVAr of total active and reactive power
demand. The initial active power losses of this system equal
210:9876 kW. For this test system, the possibility of installing 3
distributed generators was considered since that is the most com-
monly reported solution in the specialized literature [28]. Each dis-
tributed generator is limited from 0 kW to 2500 kW.1 In addition,
we considered voltage and power base values of 12:66 kV and
1000 kW, respectively.reña, An exact MINLP model for optimal location and sizing of DGs in dis-
Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011
O.D. Montoya et al. / Ain Shams Engineering Journal xxx (xxxx) xxx 5
Table 1
Electrical parameters of the 7-node test feeder used in the GAMS implementation example
Node i Node j Rij [X] Xij [X] Pj [kW] Qj [kW]
1 2 0.5025 0.3025 1000 600
2 3 0.4020 0.2510 900 500
3 4 0.3660 0.1864 2500 1200
2 5 0.3840 0.1965 1200 950
5 6 0.8190 0.7050 1050 780
2 7 0.2872 0.4088 2000 1150
Fig. 3. GAMS output with zero DGs.
Fig. 4. GAMS output with a unique DG.
Fig. 5. Electrical configuration of the 33-node test system.The information of all the branches, as well as the load con-
sumption of the 33-node test feeder, is listed in Table 2.4.2. 69-node test feeder
This test system consists of 69 nodes and 68 branches with
12:66 kV of operating voltage. The slack node is located at node
1, and its configuration is depicted in Fig. 6. This feeder has
3890:7 kW and 2693:6 kVAr of total active and reactive power
demand. The initial active power losses of this system equal
225:0718 kW. For this test system, we also considered the possibil-
ity of installing 3 distributed generators, and each of them limited
from 0 kW to 2000 kW. In addition, we also considered 12:66 kV
and 1000 kW as voltage and power base values, respectively.
The information of all the branches, as well as the load con-
sumption of the 69-node test feeder, is presented in Table 3.5. Computational validation
To solve the general MINLP model that represents the problem
of optimal location and sizing of DGs in radial distribution systems,
we employed the GAMS optimization package with the solver
BONMIM in a desktop computer with an INTEL(R) Core(TM)
i5 3550 3:5-GHz processor and 8 GB of RAM running a 64-bitPlease cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-No
tribution networks: A general algebraic modeling system approach, Ain Shamsversion of Windows 7 Professional. The implemented mathemati-
cal model is the same as the one presented in Section 3, except that
the information of each test feeder was modified.
To demonstrate the robustness and efficiency of the GAMS
package for locating and sizing DGs in distribution networks, we
compared our results with the solutions previously reported in
[34,24]. In addition, we considered that all the DGs were operated
with a unity power factor, as recommend in [28].5.1. 33-node test feeder
Table 4 presents a list of solutions provided by [34] for the 33-
node test feeder with the corresponding location, size, and power
losses when 3 DGs are considered.
Note that the power losses results reported in Table 4 show that
the GAMS optimization package in conjunction with the BONMIN
solver finds the best solution with respect to the all comparative
methods, i.e., 72:79 kW, followed by the REPSO method with
76:91 kW and the LSFSA approach with 82:03 kW, in the first three
positions. It is also important to highlight that the MINLP model we
proposed, solved through a GAMS implementation, finds an alter-
native set of nodes for locating all the distributed generators
(e.g., nodes 6, 18, and 30) with a total power injection of 2:9336
MW, while the REPSO and LSFSA approaches reach 2:5212 MW
and 2:4677 MW, respectively. Such values imply that the solutions
provided by REPSO and LSFSA can be stuck in local optima, while
our approach allows the improvement of those solutions by
increasing the total power injection. In order to find the best
solution.
Fig. 7 presents a comparison of the power losses reduction per-
centages of all the approaches reported in Table 4, along with the
initial power losses. This figure confirms that the GAMS approach
allows the highest power losses reduction, 65:50 %, followed by
the REPSO and LSFSA approaches with 63:55 % and 61:12 %,
respectively.5.2. 69-node test feeder
Table 5 presents a list of solutions provided by [34] for the 69-
node test feeder with the corresponding location, size, and result-
ing power losses, when 3 DGs were considered.
The behavior of the power losses presented in Table 5 proves
that the GAMS approach effectively converges to the best solution,
in contrast with the other methodologies. In this system, our
MINLP model, solved through the BONMIN solver, reaches final
power losses of 72:09 kW, followed by the LSFSA and TLBO meth-
ods with 77:10 kW and 81:00 kW, respectively.
Fig. 8 shows the power losses reduction achieved by the pro-
posed GAMS approach as well as the other methods. Note that
the GAMS approach achieves the highest reduction in power losses,
with 67:97 %, which confirms the efficiency and accuracy of the
proposed MINLP model and its solution by GAMS.reña, An exact MINLP model for optimal location and sizing of DGs in dis-
Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011
6 O.D. Montoya et al. / Ain Shams Engineering Journal xxx (xxxx) xxx
Table 2
Electrical parameters of the 33-node test feeder.
Node i Node j Rij [X] Xij [X] Pj [kW] Qj [kW]
1 2 0.0922 0.0477 100 60
2 3 0.4930 0.2511 90 40
3 4 0.3660 0.1864 120 80
4 5 0.3811 0.1941 60 30
5 6 0.8190 0.7070 60 20
6 7 0.1872 0.6188 200 100
7 8 1.7114 1.2351 200 100
8 9 1.0300 0.7400 60 20
9 10 1.0400 0.7400 60 20
10 11 0.1966 0.0650 45 30
11 12 0.3744 0.1238 60 35
12 13 1.4680 1.1550 60 35
13 14 0.5416 0.7129 120 80
14 15 0.5910 0.5260 60 10
15 16 0.7463 0.5450 60 20
16 17 1.2890 1.7210 60 20
17 18 0.7320 0.5740 90 40
2 19 0.1640 0.1565 90 40
19 20 1.5042 1.3554 90 40
20 21 0.4095 0.4784 90 40
21 22 0.7089 0.9373 90 40
3 23 0.4512 0.3083 90 50
23 24 0.8980 0.7091 420 200
24 25 0.8960 0.7011 420 200
6 26 0.2030 0.1034 60 25
26 27 0.2842 0.1447 60 25
27 28 1.0590 0.9337 60 20
28 29 0.8042 0.7006 120 70
29 30 0.5075 0.2585 200 600
30 31 0.9744 0.9630 150 70
31 32 0.3105 0.3619 210 100
32 33 0.3410 0.5302 60 40
Fig. 6. Electrical configuration of the 69-node test system.
2 To determine the total power output of each generator, the maximum capacities5.3. Optimal location of renewable generators in a daily operational
environment
Here, we explore the possibility of using GAMS for locating
renewable generators (PV systems) in radial distribution systems
by considering the typical solar radiation performance in a Colom-
bian system in the Caribbean region. For that purpose, we employ
the 27-node test feeder reported in [42] with the branch and peak
load information reported in Table 6. The grid configuration of this
test feeder is illustrated in Fig. 9. To evaluate the daily operation of
this system including PV systems, we employ the demand varia-
tion and the PV generation capacity in Fig. 10. In addition, we
use 13:8 kV and 1000 kW as voltage and power bases, respectively;
during GAMS implementation.
In this test system, we evaluate the possibility of installing from
1 to 3 PV generators with the curve of power generation reported
in Fig. 10. Note that, in this test system, the total power losses per
day are 2094:01 kWh/day when renewable power generation has
not yet been installed, while such losses are lower when different
numbers of PV generators are installed, as reported in Table 7. In
addition, said Table shows the size of each PV generator, e.g., in
the case of 2 PV generators, the GAMS package suggests locatingPlease cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-No
tribution networks: A general algebraic modeling system approach, Ain Shamsthem at nodes 10 and 16 with maximum capacities of 1:321 p.u
and 1:008 p.u, respectively2
Note that the GAMS package solves the problem for all the dif-
ferent options; in the case of 1 PV generator, it achieves a reduction
of 7:54 % in the total power losses per day, while with 2 and 3 gen-
erators, the reductions are 12:53 % and 17:32 %, respectively. These
results imply that, as the number of PV generators increases, power
losses decrease. Notwithstanding, these reductions tend to the sat-
uration due to the impossibility of generating power at night, as
depicted in Fig. 11, where the energy reduction in the system exhi-
bits an exponential decreasing asymptotic behavior approaching
1600 kWh/day.
5.4. General comments
The numerical validation presented in the section above shows
that:
U The MINLP model and its implementation in GAMS can produce
excellent solutions in terms of power losses reduction for the
33-node test feeder and the 69-node test feeder.
U The 27-node test feeder, with a daily operation, revealed the
possibility of using the MINLP model with time-varying vari-
ables for solving the problem of optimal location and sizing of
renewable generators (e.g., PV systems) through its GAMS
implementation.
U The integration of multiple PV modules for generating renew-
able power in distribution grids allows the reduction of their
total daily power losses. However, a massive integration of such
modules does not cause important reductions in said losses.reported in Table 7 should be multiplied by the typical generation provided in Fig. 10.
reña, An exact MINLP model for optimal location and sizing of DGs in dis-
Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011
O.D. Montoya et al. / Ain Shams Engineering Journal xxx (xxxx) xxx 7
Table 3
Electrical parameters of the 69-node test feeder.
Node i Node j Rij [X] Xij [X] Pj [kW] Qj [kW]
1 2 0.0005 0.0012 0 0
2 3 0.0005 0.0012 0 0
3 4 0.0015 0.0036 0 0
4 5 0.0251 0.0294 0 0
5 6 0.3660 0.1864 2.6 2.2
6 7 0.3811 0.1941 40.4 30
7 8 0.0922 0.0470 75 54
8 9 0.0493 0.0251 30 22
9 10 0.8190 0.2707 28 19
10 11 0.1872 0.0619 145 104
11 12 0.7114 0.2351 145 104
12 13 1.0300 0.3400 8 5
13 14 1.0440 0.3450 8 5
14 15 1.0580 0.3496 0 0
15 16 0.1966 0.0650 45 30
16 17 0.3744 0.1238 60 35
17 18 0.0047 0.0016 60 35
18 19 0.3276 0.1083 0 0
19 20 0.2106 0.0690 1 0.6
20 21 0.3416 0.1129 114 81
21 22 0.0140 0.0046 5 3.5
22 23 0.1591 0.0526 0 0
23 24 0.3463 0.1145 28 20
24 25 0.7488 0.2475 0 0
25 26 0.3089 0.1021 14 10
26 27 0.1732 0.0572 14 10
3 28 0.0044 0.0108 26 18.6
28 29 0.0640 0.1565 26 18.6
29 30 0.3978 0.1315 0 0
30 31 0.0702 0.0232 0 0
31 32 0.3510 0.1160 0 0
32 33 0.8390 0.2816 10 10
33 34 1.7080 0.5646 14 14
34 35 1.4740 0.4873 4 4
3 36 0.0044 0.0108 26 18.55
36 37 0.0640 0.1565 26 18.55
37 38 0.1053 0.1230 0 0
38 39 0.0304 0.0355 24 17
39 40 0.0018 0.0021 24 17
40 41 0.7283 0.8509 102 1
41 42 0.3100 0.3623 0 0
42 43 0.0410 0.0478 6 4.3
43 44 0.0092 0.0116 0 0
44 45 0.1089 0.1373 39.22 26.3
45 46 0.0009 0.0012 39.22 26.3
4 47 0.0034 0.0084 0 0
47 48 0.0851 0.2083 79 56.4
48 49 0.2898 0.7091 384.7 274.5
49 50 0.0822 0.2011 384.7 274.5
8 51 0.0928 0.0473 40.5 28.3
51 52 0.3319 0.1140 3.6 2.7
9 53 0.1740 0.0886 4.35 3.5
53 54 0.2030 0.1034 26.4 19
54 55 0.2842 0.1447 24 17.2
55 56 0.2813 0.1433 0 0
56 57 1.5900 0.5337 0 0
57 58 0.7837 0.2630 0 0
58 59 0.3042 0.1006 100 72
59 60 0.3861 0.1172 0 0
60 61 0.5075 0.2585 1244 888
61 62 0.0974 0.0496 32 23
62 63 0.1450 0.0738 0 0
63 64 0.7105 0.3619 227 162
64 65 1.0410 0.5302 59 42
11 66 0.2012 0.0611 18 13
66 67 0.0047 0.0014 18 13
12 68 0.7394 0.2444 28 20
68 69 0.0047 0.0016 28 20
Please cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-Noreña, An exact MINLP model for optimal location and sizing of DGs in dis-
tribution networks: A general algebraic modeling system approach, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011
8 O.D. Montoya et al. / Ain Shams Engineering Journal xxx (xxxx) xxx
Table 4
Location and dispatch of the generators in the 33-node test feeder.
Method Power generation [p.u] (Node) Losses [kW]
GA [21] 1.5000 (11) 0.4228 (29) 1.0714 (30) 106.30
PSO [21] 1.1768 (8) 0.9816 (13) 0.9297 (32) 105.35
TLBO [29] 0.8847 (9) 0.8953 (18) 1.1958 (31) 104.00
REPSO [44] 1.2274 (6) 0.6068 (14) 0.6870 (31) 76.91
HSA [45] 0.5927 (16) 0.2133 (17) 0.1913 (18) 135.69
SOS [34] 2.2066 (6) 0.2000 (28) 0.7167 (29) 104.19
LSFSA [24] 1.1124(6) 0.4874 (18) 0.8679 (30) 82.03
GAMS 0.7709 (14) 1.0969 (24) 1.0658 (30) 72.79
Table 6
Electrical parameters of the 27-node test feeder.
Node i Node j Rij [X] Xij [X] Pj [kW] Qj [kW]
1 2 0.15208 0.19855 0 0
2 3 0.65805 0.59745 0 0
3 4 0.19742 0.17924 297.5 184.4
4 5 0.43848 0.26038 0 0
5 6 0.48720 0.28931 255 158
6 7 0.48197 0.22732 0 0
7 8 0.87630 0.41330 212.5 131.7
8 9 1.09540 0.51663 0 0
9 10 0.87630 0.41330 266.1 164.9
2 11 0.87630 0.41330 85 52.7
Fig. 7. Power losses reduction of different methods in the 33-node test feeder. 11 12 1.07780 0.50836 340 210.7
12 13 0.65722 0.30998 297.5 184.4
13 14 0.49073 0.23145 191.3 118.5
14 15 0.87630 0.41330 106.3 65.8
Table 5 15 16 0.87630 0.41330 255 158
Location and dispatch of generators in the 69-node test feeder. 3 17 0.87630 0.41330 255 158
Method Power generation [p.u] (Node) Losses [kW] 17 18 0.52578 0.24798 127.5 79
18 19 0.78867 0.37197 297.5 184.4
GA [21] 0.9297 (21) 1.0752 (62) 0.9925 (64) 89.00 19 20 0.83248 0.39263 340 210.7
PSO [21] 0.9925 (17) 1.1998 (61) 0.7956 (63) 83.20 20 21 0.87630 0.41330 85 52.7
TLBO [29] 0.7574 (25) 1.0188 (60) 1.1784 (63) 81.00 4 22 0.87630 0.41330 106.3 65.8
HSA [45] 1.6283 (63) 0.1416 (64) 0.0149 (65) 86.66 5 23 0.87630 0.41330 55.3 34.2
SOS [34] 0.2588 (57) 0.2000 (58) 1.5247 (61) 82.08 6 24 0.35052 0.16532 69.7 43.2
LSFSA [24] 0.4962 (18) 0.3113 (60) 1.7354 (65) 77.10 8 25 0.52578 0.24798 255 158
GAMS 0.8131 (12) 1.4447 (61) 0.2896 (64) 72.09 8 26 0.52578 0.24798 63.8 39.5
26 27 0.70104 0.33064 170 105.4
Fig. 9. Electrical configuration of the 27-node test system.
Fig. 8. Power losses reduction of different methods in the 69-node test feeder.
Fig. 10. Percentage of power consumption and availability on a typical sunny day in
the Caribbean region of Colombia.This situation occurs because PV generators only inject power
during sunny hours, which makes them unusable during the
night period.
6. Conclusions
An exact mathematical model to represent the optimal location
and sizing of DGs in radial distribution networks, using a MINLP
representation, was presented in this paper. Such mathematical
model was solved by the GAMS optimization package, via compact
formulation through the BONMIM nonlinear large-scale discretePlease cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-Noreña, An exact MINLP model for optimal location and sizing of DGs in dis-
tribution networks: A general algebraic modeling system approach, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011
O.D. Montoya et al. / Ain Shams Engineering Journal xxx (xxxx) xxx 9
Table 7
Power losses per day in the 27-node test feeder when different numbers of PV
generators are installed.
Number of PV DGs Losses [kWh/day] Location
1 1936.20 1.520 (20)
2 1831.58 1.321 (10) - 1.008 (16)
3 1731.30 1.128 (10) - 0.975 (16) - 1.234 (20)
Fig. 11. Analysis of power losses reduction by increasing the number of the PV
systems.solver, and compared with multiple methodologies reported in the
specialized literature, which confirmed its efficiency and accuracy
in terms of power losses reduction. Additionally, an illustrative
example of the GAMS implementation in a small test feeder was
presented to show its ease of use for solving nonlinear optimiza-
tion models.
Furthermore, an extension of the static MINLP model for opti-
mal location and sizing of distributed generators in radial dis-
tributed networks was simulated to assess the possibility of
addressing, through GAMS implementations, daily operation prob-
lems with renewable energy resources, as in the case of PV gener-
ators. This extension allowed an evaluation of the impact of PV
location and sizing on total energy losses during a typical sunny
day in an electrical system in the Caribbean region in Colombia.
In the future, the proposed MINLP model and its solution in
GAMS can be used to size renewable generators (e.g., PV and wind
generators) with variable power factor capacities in radial test
feeders. In addition, such model will be modified to include capac-
itors and battery energy storage systems for islanded microgrid
applications.7. Financial support
This work was funded in part by the Administrative Department
of Science, Technology, and Innovation of Colombia (COLCIENCIAS)
through its National Scholarship Program, under Grant 727-2015;
in part by Instituto Tecnológico Metropolitano de Medellín, under
Project P17211; in part by Universidad Tecnológica de Bolívar,
under Projects C2018P020 and C2019P011; and in part by Univer-
sidad Nacional de Colombia, under Proyect ”Estrategia de transfor-
mación del sector energético Colombiano en el horizonte de 2030 -
Energética 2030” - ”Generación distribuida de energía eléctrica en
Colombia a partir de energía solar y eólica” (Code: 58838, Hermes:
38945).References
[1] Prakash P, Khatod DK. Optimal sizing and siting techniques for distributed
generation in distribution systems: a review. Renew Sustain Energy Rev
2016;57:111–30. doi: https://doi.org/10.1016/j.rser.2015.12.099.
[2] Bawan EK. Distributed generation impact on power system case study: losses
and voltage profile. In: Power engineering society summer meeting, 2000.
IEEE, vol. 3; 2000. p. 1645–56.Please cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-No
tribution networks: A general algebraic modeling system approach, Ain Shams[3] Rezaee Jordehi A. Allocation of distributed generation units in electric power
systems: a review. Renew Sustain Energy Rev 2016;56:893–905. doi: https://
doi.org/10.1016/j.rser.2015.11.086.
[4] Abdelaziz A, Ali E, Elazim SA. Optimal sizing and locations of capacitors in
radial distribution systems via flower pollination optimization algorithm and
power loss index. Eng Sci Technol, Int J 2016;19(1):610–8. doi: https://doi.org/
10.1016/j.jestch.2015.09.002.
[5] Iqbal F, Khan MT, Siddiqui AS. Optimal placement of DG and DSTATCOM for
loss reduction and voltage profile improvement. Alexandr Eng J. https://doi.
org/10.1016/j.aej.2017.03.002.
[6] Mahdad B, Srairi K. Adaptive differential search algorithm for optimal location
of distributed generation in the presence of SVC for power loss reduction in
distribution system. Eng Sci Technol, Int J 2016;19(3):1266–82. doi: https://
doi.org/10.1016/j.jestch.2016.03.002.
[7] Galiveeti HR, Goswami AK, Choudhury NBD. Impact of plug-in electric vehicles
and distributed generation on reliability of distribution systems. Eng Sci
Technol, Int J 2018;21(1):50–9. doi: https://doi.org/10.1016/
j.jestch.2018.01.005.
[8] Elmitwally A. A new algorithm for allocating multiple distributed generation
units based on load centroid concept. Alexandr Eng J 2013;52(4):655–63. doi:
https://doi.org/10.1016/j.aej.2013.08.011.
[9] Sadiq A, Adamu S, Buhari M. Optimal distributed generation planning in
distribution networks: a comparison of transmission network models with
FACTS. Eng Sci Technol, Int J. https://doi.org/10.1016/j.jestch.2018.09.013.
[10] Grisales Noreña LF, Restrepo Cuestas BJ, Jaramillo Ramirez FE. Location and
sizing of distribted generation: a review. Ciencia e Ingeniería Neogranadina
2017;27(2):157–76. doi: https://doi.org/10.18359/rcin.2344.
[11] Keane A, Ochoa LF, Borges CLT, Ault GW, Alarcon-Rodriguez AD, Currie RAF,
et al. State-of-the-art techniques and challenges ahead for distributed
generation planning and optimization. IEEE Trans Power Syst 2013;28
(2):1493–502. doi: https://doi.org/10.1109/TPWRS.2012.2214406.
[12] Theo WL, Lim JS, Ho WS, Hashim H, Lee CT. Review of distributed generation
(DG) system planning and optimisation techniques: comparison of numerical
and mathematical modelling methods. Renew Sustain Energy Rev
2017;67:531–73. doi: https://doi.org/10.1016/j.rser.2016.09.063.
[13] Pesaran M, A H, Huy PD, Ramachandaramurthy VK. A review of the optimal
allocation of distributed generation: objectives, constraints, methods, and
algorithms. Renew Sustain Energy Rev 2017;75(October):293–312. doi:
https://doi.org/10.1016/j.rser.2016.10.071.
[14] Dixit M, Kundu P, Jariwala HR. Incorporation of distributed generation and
shunt capacitor in radial distribution system for techno-economic benefits.
Eng Sci Technol, Int J 2017;20(2):482–93. doi: https://doi.org/10.1016/
j.jestch.2017.01.003.
[15] Ellabban O, Abu-Rub H, Blaabjerg F. Renewable energy resources: current
status, future prospects and their enabling technology. Renew Sustain Energy
Rev 2014;39:748–64. doi: https://doi.org/10.1016/j.rser.2014.07.113.
[16] Parhizi S, Lotfi H, Khodaei A, Bahramirad S. State of the art in research on
microgrids: a review. IEEE Access 2015;3:890–925. doi: https://doi.org/
10.1109/ACCESS.2015.2443119.
[17] Kaur S, Kumbhar G, Sharma J. A MINLP technique for optimal placement of
multiple DG units in distribution systems. Int J Electr Power Energy Syst
2014;63(Supplement C):609–17. doi: https://doi.org/10.1016/j.
ijepes.2014.06.023.
[18] Abido MA. Optimal power flow using tabu search algorithm. Electr Power
Comp Syst 2002;30(5):469–83. doi: https://doi.org/10.1080/
15325000252888425.
[19] HassanzadehFard H, Jalilian A. A novel objective function for optimal DG
allocation in distribution systems using meta-heuristic algorithms. Int J Green
Energy 2016;13(15):1615–25. doi: https://doi.org/10.1080/
15435075.2016.1212355.
[20] Bohre AK, Agnihotri G, Dubey M. Optimal sizing and sitting of DG with load
models using soft computing techniques in practical distribution system. IET
Gener Transm Distrib 2016;10(11):2606–21. doi: https://doi.org/10.1049/iet-
gtd.2015.1034.
[21] Moradi M, Abedini M. A combination of genetic algorithm and particle swarm
optimization for optimal DG location and sizing in distribution systems. Int J
Electr Power Energy Syst 2012;34(1):66–74. doi: https://doi.org/10.1016/j.
ijepes.2011.08.023.
[22] D.P.R.P., V.R.V.C., G.M.T., Ant Lion optimization algorithm for optimal sizing of
renewable energy resources for loss reduction in distribution systems. J Electr
Syst Inf Technol 2018;5(3): 663–80. https://doi.org/10.1016/j.jesit.2017.06.
001.
[23] Gandomkar M, Vakilian M, Ehsan M. A genetic based tabu search algorithm for
optimal dg allocation in distribution networks. Electr Power Comp Syst
2005;33(12):1351–62. doi: https://doi.org/10.1080/15325000590964254.
[24] Injeti SK, Kumar NP. A novel approach to identify optimal access point and
capacity of multiple DGs in a small, medium and large scale radial distribution
systems. Int J Electr Power Energy Syst 2013;45(1):142–51. doi: https://doi.
org/10.1016/j.ijepes.2012.08.043.
[25] Sultana S, Roy PK. Krill herd algorithm for optimal location of distributed
generator in radial distribution system. Appl Soft Comput 2016;40:391–404.
doi: https://doi.org/10.1016/j.asoc.2015.11.036.
[26] Sultana S, Roy PK. Oppositional krill herd algorithm for optimal location of
distributed generator in radial distribution system. Int J Electr Power Energy
Syst 2015;73:182–91. doi: https://doi.org/10.1016/j.ijepes.2015.04.021.reña, An exact MINLP model for optimal location and sizing of DGs in dis-
Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011
10 O.D. Montoya et al. / Ain Shams Engineering Journal xxx (xxxx) xxx[27] ChithraDevi S, Lakshminarasimman L, Balamurugan R. Stud Krill herd
Algorithm for multiple DG placement and sizing in a radial distribution
system. Eng Sci Technol, Int J 2017;20(2):748–59. doi: https://doi.org/10.1016/
j.jestch.2016.11.009.
[28] Grisales-Noreña LF, Gonzalez-Montoya D, Ramos-Paja CA. Optimal sizing and
location of distributed generators based on PBIL and PSO Techniques. Energies
2018;11(1018):1–27.
[29] Mohanty B, Tripathy S. A teaching learning based optimization technique for
optimal location and size of DG in distribution network. J Electr Syst Inf
Technol 2016;3(1):33–44. doi: https://doi.org/10.1016/j.jesit.2015.11.007.
[30] Sudabattula SK, M K. Optimal allocation of solar based distributed generators
in distribution system using Bat algorithm. Perspect Sci 2016;8:270–2. doi:
https://doi.org/10.1016/j.pisc.2016.04.048. recent Trends in Engineering and
Material Sciences.
[31] Yammani C, Maheswarapu S, Matam SK. A Multi-objective Shuffled Bat
algorithm for optimal placement and sizing of multi distributed generations
with different load models. Int J Electr Power Energy Syst 2016;79:120–31.
doi: https://doi.org/10.1016/j.ijepes.2016.01.003.
[32] Othman M, El-Khattam W, Hegazy Y, Abdelaziz AY. Optimal placement and
sizing of voltage controlled distributed generators in unbalanced distribution
networks using supervised firefly algorithm. Int J Electr Power Energy Syst
2016;82:105–13. doi: https://doi.org/10.1016/j.ijepes.2016.03.010.
[33] Behera SR, Dash SP, Panigrahi BK. Optimal placement and sizing of DGs in
radial distribution system (RDS) using Bat algorithm. In: 2015 International
conference on circuits, power and computing technologies [ICCPCT-2015]. p.
1–8. doi: https://doi.org/10.1109/ICCPCT.2015.7159295.
[34] Nguyen TP, Dieu VN, Vasant P. Symbiotic organism search algorithm for
optimal size and siting of distributed generators in distribution systems. Int J
Energy Optim Eng 2017;6(3):1–28. doi: https://doi.org/10.4018/
IJEOE.2017070101.
[35] Nekooei K, Farsangi MM, Nezamabadi-Pour H, Lee KY. An improved multi-
objective harmony search for optimal placement of DGs in distribution
systems. IEEE Trans Smart Grid 2013;4(1):557–67. doi: https://doi.org/
10.1109/TSG.2012.2237420.
[36] S.C., A.T., Optimal power flow using Moth Swarm Algorithm with Gravitational
Search Algorithm considering wind power. Future Gener Comput Syst.
https://doi.org/10.1016/j.future.2018.12.046.
[37] Nojavan S, Jalali M, Zare K. An MINLP approach for optimal dg unit’s allocation
in radial/mesh distribution systems take into account voltage stability index.
Trans Electr Eng 2015;39(E2):155–65. doi: https://doi.org/10.22099/
ijste.2015.3488.
[38] Engelmann A, Muhlpfordt T, Jiang Y, Houska B, Faulwasser T. Distributed AC
optimal power flow using ALADIN, IFAC-PapersOnLine 2017;50(1):5536–41.
In: 20th IFAC World Congress.https://doi.org/10.1016/j.ifacol.2017.08.1095.
[39] Montoya OD, Grajales A, Garces A, Castro CA. Distribution systems operation
considering energy storage devices and distributed generation. IEEE Latin Am
Trans 2017;15(5):890–900. doi: https://doi.org/10.1109/TLA.2017.7910203.
[40] GAMS Development Corp., General Algebraic Modeling System. <https://www.
gams.com/download/>.
[41] Castillo E, Conejo A, Pedregal P, García R, Alguacil N. Building and solving
mathematical programming models in engineering and science, pure and
applied mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley;
2001.
[42] Montoya OD, Garces A, Castro CA. Optimal conductor size selection in radial
distribution networks using a mixed-integer non-linear programming
formulation. IEEE Latin Am Trans 2018;16(8):2213–20. doi: https://doi.org/
10.1109/TLA.2018.8528237.
[43] Montoya OD. Solving a classical optimization problem using GAMS optimizer
package: economic dispatch problem implementation. Ingenieria y ciencia
2017;13(26):39–63. doi: https://doi.org/10.17230/ingciencia.13.26.2.Please cite this article as: O. D. Montoya, W. Gil-González and L. F. Grisales-No
tribution networks: A general algebraic modeling system approach, Ain Shams[44] Jamian J, Mustafa M, Mokhlis H. Optimal multiple distributed generation
output through rank evolutionary particle swarm optimization.
Neurocomputing 2015;152:190–8. doi: https://doi.org/10.1016/j.
neucom.2014.11.001.
[45] Kollu R, Rayapudi SR, Sadhu VLN. A novel method for optimal placement of
distributed generation in distribution systems using HSDO. Int Trans Electr
Energy Syst 2014;24(4):547–61. doi: https://doi.org/10.1002/etep.1710.
Oscar D. Montoya received his BEE, M.Sc. and Ph.D
degrees in Electrical Engineering from Universidad
Tecnológica de Pereira, Colombia, in 2012 and 2014
respectively. His research interests include mathemati-
cal optimization, planning and control of power sys-
tems, renewable energies, energy storage, protective
devices and smartgrids.Walter Gil-González received his BEE and M.Sc. degrees
in Electrical Engineering from Universidad Tecnológica
de Pereira, Colombia, in 2011 and 2013 respectively. He
is currently studying a Ph.D in Electrical Engineering at
Universidad Tecnológica de Pereira, Colombia. His
research interests include mathematical optimization,
planning and control of power systems, renewable
energies, energy storage, protective devices and smart-
grids.Luis F. Grisales received his BEE and M.Sc. degrees in
Electrical Engineering from Universidad Tecnológica de
Pereira, Colombia, in 2013 and 2015 respectively. He is
currently studying a Ph.D in Engineering at Universidad
Nacional de Colombia. Actually, is professor in the
Instituto TecnolÓgico Metropolitano de Medellín,
attached to the Department of Electromechanics and
mechatronics, member of the research group MATyER.
His research interests include mathematical modelling,
optimization techniques, planning and control of power
systems, renewable energies, energy storage, power
electronic and smartgrids.reña, An exact MINLP model for optimal location and sizing of DGs in dis-
Engineering Journal, https://doi.org/10.1016/j.asej.2019.08.011