This work is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 4.0 International License.
43
D. Schumanski, D.de Oliveira Macedo, J. Almansa Malagoli and C. Schimith Silva Coelho,
“Single-Phase Variable Reluctance Motor Design using Particle Swarm Optimization”,
Latin-American Journal of Computing (LAJC), vol. 11, no. 1, 2024
Single Phase Variable
Reluctance Motor Design
Using Particle Swarm
Optimization
ARTICLE HISTORY
Received 16 March 2023
Accepted 12 May 2023
Published 08 January 2024
Danyelle Schumanski
Federal University of Paraná
Curitiba-PR, Brazil
schumanski@ufpr.br
ORCID: 0009-0008-3165-4150
Dullian Carly de Oliveira Macedo
University of Paraná
Pontal do Paraná-PR, Brazil
dullianmacedo@ufpr.br
ORCID: 0009-0004-5813-616X
Juliana Almansa Malagoli
Federal University of Paraná
Curitiba-PR, Brazil
juliana.malagoli@ufpr.br
ORCID: 0000-0002-8723-033X
Cinthia Schimith Silva Coelho
Pontifical Catholic University of Paraná
Curitiba-PR, Brazil
cinthia.coelho@pucpr.br
ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024
This work is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 4.0 International License.
ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024
44
DOI:
LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 1, January 2024
10.5281/zenodo.10402205
LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 1, January - June 2024
Single-Phase Variable Reluctance Motor Design
using Particle Swarm Optimization
Danyelle Schumanski
Federal University of Paraná
Electrical Engineering Post-
Graduation Program
Curitiba-PR, Brazil
schumanski@ufpr.br
Dullian Carly de Oliveira Macedo
Federal University of Paraná
Civil Engineering Undergraduate
Pontal do Paraná-PR, Brazil
dullianmacedo@ufpr.br
Cinthia Schimith Silva Coelho
Pontifical Catholic University of
Paraná
Electrical Engineering Department
Curitiba-PR, Brazil
cinthia.coelho@pucpr.br
Juliana Almansa Malagoli
Federal University of Paraná
Electrical Engineering Post-
Graduation Program
Curitiba-PR, Brazil
juliana.malagoli@ufpr.br
Abstract— Electrical engines are built under electromagnetism
concepts to create mechanical power, those can be seen as simple
machines, as it depends on reluctance, even being called as
“reluctance motor”, what gives this engine the possibility of being
widely used for many purposes. The main objective of this research
is to minimize copper losses of a single-phase 6x6 variable
reluctance synchronous motor. For that, a Particle Swarm
Optimization (PSO) algorithm will be used to obtain the optimum
configuration through the Finite Elements Method (FEM). In this
context, electric motor design equations were dimensioned based on
similar machines. The next procedure was to use FEMM (Finite
Element Method Magnetics) software, that allows the magnetic flow
density analysis inside the motor air gap. Finally, it is noteworthy
that the copper losses results were analyzed before and after the
variable reluctance motor optimization with computational tools.
Keywords—single-phase reluctance motor, finite element
method, particle swarm optimization
I. I
NTRODUCTION
Variable reluctance synchronous motors (VRSMs) are
common engines with simple building aspects low
computational and financial costs, but with a wide range of
applications. These are the main reasons why reference [1]
considered these motors competitive. The VRSMs dual
capacity of acting like a motor and a generator, which avoids
high inrush currents, reduce costs and operates under constant
rotation, that are aspects of engines without windings and
magnets and with a single source of incitation applied to the
stator windings, what intends to minimize all the resistive
losses of machinery winding that occur in the stator current
flow.
Therefore, it is possible to estimate an optimal motor,
based on specifications of power and size of a previous model
[2]. In this context, the research objective is to minimize the
copper losses, of a variable reluctance motor (VRM), by using
the particle swarm method (PSO algorithm). This way,
dimension parameters were used to design the original motor
and the optimum motor was designed after applying the finite
elements method. Finally, after the optimization process,
copper losses and magnetic flow densities were evaluated and
the results of both original and optimum motors were
compared
II. L
ITERATURE
R
EVIEW
This section will be divided in three parts: Particle Swarm
Optimization, Finite Elements Method and Variable
Reluctance Motor Design.
A. Swarm Particle Optimization
The PSO algorithm is a computational method that aims to
optimize a problem through a proceeding that generates a
sequence of approximate solutions that at each interaction,
tend to converge to an optimum solution [3]. Comparative
studies about the PSO (Particle Swarm Optimization) aspects
were inspired on animal behavior, where each individual, of
an equally dispersed population inside the problem area,
efficiencies were compared. At each executed interaction, the
individuals tend to group in smaller spaces around the best
solution, therefore, an inertia constant can be estimated, based
on the group tendency to find the best solution and considering
each individual's best solution.
After a sequence of interactions performed by each
individual, the optimum solution for the problem is found [4].
Next the algorithm implementation steps:
• Initially, each swarm particle has a position
inside
the search space and the speed
, where the positions
are automatically generated;
• For each swarm particle executed interaction, the
particle position and the group position
are updated, in case they are better than the previous.
During the interaction, the speeds and positions of each swarm
particle are updated by the Equations 1 and 2, respectively, to
obtain the new position:
;
(
+ 1
)
+ ωv
+
1
1
(
−
)
+. . .
. . . +
2
2
(
−
)
(1)
(
+ 1
)
=
+
(
+ 1
)
(2)
where
(
+ 1
)
is the updated term for particle speed,
+ 1 is the actual instant, is the previous instant, ω is the
algorithm inertia constant,
1
is the individual acceleration
coefficient responsible for controlling the particle movement
distance in one interaction,
2
is the group acceleration
ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024
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DOI:
LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 1, January 2024
10.5281/zenodo.10402205
D. Schumanski, D.de Oliveira Macedo, J. Almansa Malagoli and C. Schimith Silva Coelho,
“Single-Phase Variable Reluctance Motor Design using Particle Swarm Optimization”,
Latin-American Journal of Computing (LAJC), vol. 11, no. 1, 2024.
coefficient, responsible for controlling a particle movement
distance in one interaction, is the best particle position,
is the most visited position by the particles,
and
are aleatory numbers inside the research space [0,1],
(
+ 1
)
is the new particle position,
is the previous
particle position. So, if the stop criterion is not verified, the
algorithm returns to Step 2, to start the next interaction,
otherwise, will be used as the intended solution.
It is possible to understand that the particle swarm
optimization has 3 (three) main steps, knowing the number of
interactions is the factor that determines the number of times
where the system was evaluated and updated. The main steps,
for that, are the following:
• Start: set the parameters and the population (initialize
and
randomly for each particle/individual);
• Evaluate: analyze the actual position of each particle:
and ;
• Update: update speed and position of each particle (
,
+ 1 and
, + 1).
Fig. 1. PSO algorithm flowchart
Figure 1 represents the flowchart with the description of
the adopted method. This way, it can be considered that the
particle swarm optimization comes partially from concepts
and mathematical operators for implementation. During the
computational process becomes fast and of low cost in terms
of speed and memory.
B. Finite Elements Method
The Finite Elements Method (FEM) is a set of different
numerical methods that approximate problem solutions with
Partial or Ordinary Differential Equations (PDE and ODE,
respectively) through a geometry subdivision in smaller
elements, known as finite elements. Knowing that the exact
solution for this problem is very similar to the result of the
approximate solution found through this method [5], [6], [7].
The magnetostatic design equations for magnetic circuits
operation are based on Ampère and Gauss generalized laws,
and they can be described as:
= +
(3)
= 0 (4)
Where: H is the magnetic field (A/m), J is the current
superficial density
(
/²
)
, D is the electrical induction
(
/²
)
, and B is the magnetic flow density (T).
A magnetic field can be formed by a current in conductive
materials, and due to the local form of the building relations,
it is known that the flow and the magnetic field H are related,
because the final magnetic permeability μ product with the
field is, by definition, the magnetic flow density B:
= (5)
The magnetic permeability describes the degree of
opposition of a material to the passage of a flow [6]. In
general, the relative permeability of a substance, related to the
air permeability, is given by:
=
(6)
C. Single-Phase Variable Reluctance Synchronous Motor
Design
Design equations are an essential part of the optimization
processes, once the motor size affects the current flow and its
distribution along the engine parts. Figure 2 shows the main
engine dimensions that must be determined in order to obtain
the rotor and stator projects.
Fig. 2. Dimensions: (a) stator e (b) rotor, of the single-phase variable
reluctance 6x6 motor
The rotor diameter can be calculated through the input
power.
=
4
1
(7)
where P is the input power; k1 is a format constant; TRV is
the engine volume set; w is a conversion unit from RPM to
rad/s [8]. And then, the pile length (L) can be considered a
multiple of the rotor diameter (Dr):
= 1 (8)
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LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 1, January 2024
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LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 1, January - June 2024
Later, the number of poles inside the stator (Nps), will
define the poles angles (Bs):
=
180º
(9)
An important consideration is that the smaller the engine
air gap, the highest the current flow. With this information,
reference [9] considers that the engine air gap size must be
close to 0,50% of the rotor diameter. Another possible
consideration is to work under the percentage of 0,25%:
= 0,0026 (10)
The engine breech can be considered as the difference
between the rotor diameter and the poles, and it can stand half
the current that goes through the poles. Its size is defined by:
= 1,1 +
2
2
(11)
Relations between the rotor diameter (Dr) and the
external stator diameter (Ds) must be inside an interval of
0.40 to 0.70. The following relation adopted a standard of
0.55 for the relation previously defined [1]:
=
0,55
(12)
The poles width (ts) are another important information,
that happens because the flow passes intensely through this
material. This measure can be calculated using:
= 2 +
2
2
(13)
By adding the stator pole width to twice the size of the
engine air gap length, the rotor pole width can be found, as
can be seen:
= +
(
2
)
(14)
Besides that, the rotor polar arc (Br) is given by:
= 2
(15)
A crucial information to the motor proportions is the rotor
pole height (dr), that can be obtained by:
=
2
(16)
And another important measure is the engine breech
height (Ys), that can be calculated by using the width of the
rotor pole (tr) with an addition of 20 to 40%. In this case, the
chosen addition was of 20% [9].
= 1,2
2
(17)
After calculating the rotor diameter, its height and breech,
the axis diameter (Deix) can be calculated:
= 2
(
+
)
(18)
And the stator pole height (ds) can be found with:
=
2
(19)
However, the number of turns, per phase (Ne), is a result
of the interaction between the saturated magnetic flow
density (Bsat), the peak current (Ip) and the engine air gap
width, as can be seen in the equation:
=
2
(20)
Given that the wire that must be used to form the turns has
its transversal section (ac) calculated after the peak current
divided by the maximum current flow (Jc) and the square root
of the number of phases (q):
=
(21)
This calculus can provide the copper loss results. The first
step to understand the losses is to calculate the coil resistance:
=
2
(
22
)
where
is the copper resistivity and ac the wire
transversal section, what allows finding the losses of copper
(Pcopper) and total (Ptotal). The first one is calculated by
multiplying the coil resistivity (Rf) by any current (
) that
passes through the motor. The total losses are copper losses
in all wire turns.
= . (23)
= . (24)
At the resistive losses (or copper losses), as in the total
losses, the results are estimates that can work as a good
comparison between analytical and simulated values.
III. M
ETHODOLOGY
A literature review over mathematical models for
electrical motors design will be used for modeling the single-
phase VRMs. With these models, a PSO algorithm will be
executed under the assumptions of the finite element method.
The main aim with this procedure is to reduce the copper loss
inside this equipment.
Therefore, the simulations will happen through a software
that develops numerical models by using electromagnetism
concepts. For better understanding about purposes of this text,
some items must be highlighted:
1. Set the main parameters for the motor design;
2. Define the necessary equations to model the motor;
ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024
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DOI:
LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 1, January 2024
10.5281/zenodo.10402205
D. Schumanski, D.de Oliveira Macedo, J. Almansa Malagoli and C. Schimith Silva Coelho,
“Single-Phase Variable Reluctance Motor Design using Particle Swarm Optimization”,
Latin-American Journal of Computing (LAJC), vol. 11, no. 1, 2024.
3. Study and run the particle swarm optimization
algorithm;
4. Write the objective function and the vector
parameters to generate the copper loss minimization;
5. Use FEMM software to model, discretize and
generate the post processing from before and after
the optimization;
6. Verify and compare results between the traditional
methodology of electromagnetic device design and
the data generated after minimizing the objective
function;
7. Generate the motor magnetic flow density and verify
the copper loss before and after using the PSO.
In this context, the intention is to write the necessary
equations to minimize the single-phase variable reluctance
motor copper loss and, later, evaluate through FEMM
software the magnetic flow density in order to achieve the
research objectives.
IV. D
EVELOPMENT AND
D
ISCUSSION
In this section, discussions and results will be presented in
three parts: original motor, optimization and optimum motor.
A. Original Motor
To start comprehending the problem, a single-phase motor
with 6 poles was chosen, with the specifications listed on
Table I. This is a model by WEG that has characteristics of an
induction motor.
TABLE I. O
RIGINAL MOTOR
’
S VARIABLES
Parameter
Values
Parameter
Values
Constant k1
1.4363
Efficiency
0.8
Set per engine
volume TRV
16000 Voltage 220V
Power CV 7.5
Magnetic flow density
before saturation
1.5T
RPM 1760
Magnetic flow density
for saturation point
2.2T
Number of
stator poles
6 Magnetic permeability 4∗10
−7
/
Input power
5500W
Current density
6 A/m²
Therefore, a MATLAB algorithm was developed to
generate the dimensions of the 6 poles variable reluctance
motor stator and rotor, as well as its coils, which took to the
construction of the motor via AUTOCAD with a few adjusts,
and later exporting this model to FEMM, setting materials
and borders. In this way, just enter the file menu and click
import .dxf finally open the CAD Drawing file and the
drawing will be imported into FEMM. After developing the
motor project equations and running the algorithm, the main
parameters were found, as shown in Table II.
TABLE II. D
IMENSIONS OF THE ORIGINAL MOTOR
Parameter
Values
Parameter
Values
Dr
118.4 mm
Tr
31.34mm
L
170mm
Br
31º
Bs
30º
Dr
15.39mm
g
0.3077mm
Yr
18.8mm
Ys
16.9mm
Ds
33.16mm
Ds
215.2mm
Ne
20
ts
30.78mm
ac
5.133mm²
In order to verify the electromagnetic device, the peak
current of 53.34 A is considered, this current was obtained by
the sum of the nominal current with the efficient nominal
current. This means that the magnetic flow density applied to
the peak current (Ip) must not have a module superior to the
material magnetic flow saturation density.
The steel saturation is, approximately, of 2.2T. Figures 3
and 4 represent the motor magnetic flow density and the
highest value is close to 2.2T, although inferior. In general,
single-phase VRMs work close to saturation, if compared to
other motors, besides that, the motor performance is still good.
Fig. 3. Original motor aligned
Fig. 4. Original motor misaligned
After computational simulation through FEMM software,
the total copper loss was found for a peak current of 190.54W,
with the analytical solution, the result is 194.52W. Therefore,
the error between methods was of 2.04 %. It is concluded that
with the increase of input current, the magnetic flow density
is increased inside the motor air gap with a proportional
relation.
The total losses had a significant scale value, which means
specific optimizations will be required to reduce the power
loss in the windings.
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DOI:
LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 1, January 2024
10.5281/zenodo.10402205
LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 1, January - June 2024
B. Optimization
Following the PSO steps and considering the Equation 24
as the objective function (OF) of the problem, the objective
becomes minimizing the single-phase variable reluctance
motor copper losses. Some of the variables, parameters and
limits were listed on Table III.
TABLE III. V
ARIABLE
,
PARAMETER AND LIMITS
Variable
Parameter
Minimum limit
Maximum limit
x(1)
Dr(mm)
110
130
x(2)
Ys(mm)
15
20
x(3)
Yr(mm)
17
22
x(4)
Deix(mm)
30
60
x(5)
g(mm)
0.3
0.6
The Objective Function will be Equation 24, in addition,
we used lateral constraints that delimit a range of variation for
each design variable. It is worth mentioning some settings of
the PSO algorithm, such as:
• Population size: 50;
• Generations number: 50;
• Inertia weight: 1;
• Inertia weight damping ratio: 0.99;
• Personal learning coefficient: 1.5;
• Global learning: 2.0.
Thus, the processing time was less than five minutes and
the computational cost was also low, followed the settings of
the notebook used in the optimization: i5, 10GB and SSD
256GB.
TABLE IV. P
ARAMETER
V
ALUES AFTER THE
PSO
A
LGORITHM IS RUN
Parameter
Optimal value
x(1)
114 (mm)
x(2)
18.4 (mm)
x(3)
20 (mm)
x(4)
45.0 (mm)
x(5)
0.305 (mm)
OF
45.2 (W)
After executing the algorithm, other two parameters were
described, as well as the objective function, as seen on Table
IV, where a saturation current of 27.65A and the copper losses
were considered as 58.59W.
Fig. 5. Minimization of Losses in VRM Copper through PSO
In general lines, the problem is based on a mono-objective
function, that with the optimization, reduced the copper loss
in 29.62% when using the saturation current, as can be seen in
Figure 5.
C. Optimum Motor
After running the algorithm 10 times in the test, it was
possible to observe the standard deviation and mean of the
design variables and the objective function. Table V shows
the details of the executions, showing the optimum motor
parameters.
TABLE V. P
ARAMETER
V
ALUES AFTER THE
PSO
A
LGORITHM IS RUN
Tests
OF
x(1)
x(2)
x(3)
x(4)
x(5)
1
45.0
113.8
18.3
20
45,2
0,305
2
45.2
114.0
18.4
20
44,9
0,305
3
45.3
114.2
18.3
20,1
44,9
0,305
4
45.6
114.0
18.3
20
45
0,305
5
45.3
114.0
18.4
19,9
45,2
0,304
6
45.2
114.1
18.4
19,8
45,3
0,304
7
45.3
114.0
18.3
20,1
45,1
0,306
8
45.2
114
18,2
20
44,8
0,305
9
45.1
114,2
18,5
20
44,9
0,306
10
45.0
114,1
18,4
20
45,1
0,305
Standard
Deviation
0.175 0,117 0,085 0,087 0,164 0,305
Average
45.2
114,0
18,4
20,0
45,0
0,305
An interesting observation is that the measures were
reduced, except for the parameters (Yr) and (Ys), the rotor and
stator breeches had a measurement increase.
Fig. 6. Optimum motor aligned
Figures 6 and 7 indicate the magnetic flow density inside
the VRM with the peak current after the optimization process.
Fig. 7. Optimum motor misaligned
ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024
49
DOI:
LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 1, January 2024
10.5281/zenodo.10402205
D. Schumanski, D.de Oliveira Macedo, J. Almansa Malagoli and C. Schimith Silva Coelho,
“Single-Phase Variable Reluctance Motor Design using Particle Swarm Optimization”,
Latin-American Journal of Computing (LAJC), vol. 11, no. 1, 2024.
After the optimum motor computational simulation with
FEMM software, a total copper loss for a peak current of
183.63W was found. With analytic calculus, the value was
180.78W. This means that the error between analytical and
simulated results for the optimum motor is of 1.57%. It can
be concluded that the magnetic flow density on the motor
after the optimization reduced, what means they are under the
material saturation of 2.2T. In this context, it can be observed
that the PSO algorithm is effective for the convergence of the
mono-objective functions, what means that the total copper
loss was successfully reduced.
D. Magnetic Flow Density Analysis
The single-phase variable reluctance motors, in general,
work close to the saturation, when compared to other motors,
even so, their performance is good. Figures 8 and 9 represent
the total airgap length when submitted to the peak current, in
the original and the optimized motor.
Fig. 8. Magnetic flux density for peak current of original motor
Fig. 9. Magnetic flux density for peak current of optimal motor
As the magnetic flow density in the airgap to a motor on
its original and optimal unalignment, the flow density is low,
therefore the data was not proven through graphics, but the
flow gets thinner on the gap between stator and rotor. It can
be concluded that with the increase of the input current, there
is an increase to the magnetic flow inside the airgap of the
single phase VRM, therefore, they have a directly
proportional relation. The same behavior can be observed
with the copper losses. In general, simulations stay under the
iron saturation value of 2.2T, when simulated until the peak
current. During the optimization procedure, the copper loss
was reduced and the magnetic flow density in the airgap was
under the saturation point.
V. C
ONCLUSIONS
Reducing the copper loss and reducing magnetic flow
density, guarantees efficiency improvement during the motor
operation, in a way that the equipment can convert energy
more efficiently. Comparing the properties between both
motors: the original and the optimum, it can be considered
that the optimization was successful, once the main objective
of reducing copper loss was achieved, as well as the ideal
measures were presented. It might be necessary to take into
consideration the optimization of other parameters, since not
all the motor measures were reduced, but some even had
some increase. This is an important factor for further
research.
A
CKNOWLEDGMENT
The authors thank the Institutional Program of Scientific
Initiation Scholarships of the Federal University of Paraná and
the National Council for Scientific and Technological
Development (CNPq) for their support for the development of
this research and Coordination for the Improvement of Higher
Education Personnel (CAPES).
R
EFERENCES
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0 50 100 150 200 250 300 350 400
Leght(mm)
0
0.5
1
1.5
2
2.5
Magnetic Flux Density (T)
Original
0 50 100 150 200 250 300 350 400
Leght(mm)
0
0.5
1
1.5
2
2.5
Magnetic Flux Density (T)
Optimal
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AUTHORS
Danyelle Schumanski is a civil engineer graduated by the Federal
University of Paraná at the Campus Pontal do Paraná-Center for
Marine Studies (CPP-CEM UFPR) and is master's degree student at
the Graduate Program in Electrical Engineering at the same institution
(PPGEE-UFPR). During her academic life, she has published articles in
the fields of electrical engineering with magnetic field optimizations
and materials science with polymeric mortars and quality analysis
evaluations.
Dullian is a Civil Engineering student at the Federal University of
Paraná (UFPR), who currently performs scientific initiation (PIBIC-
CNPq) under the topic of PSO algorithm optimization of a 6x6
monophase motor's airgap copper loss and magnetic flow. He's a
student representative at the Civil Engineering course's collegiate at
UFPR and has got a scholarship at the geoprocessing data laboratory
(LAGEAMB-UFPR). Dullian is also a technitian in eletromechanics by
the Federal Institute of Santa Catarina (IFSC-SC) with emphasis in
procedures and projects.
Danyelle Schumanski
Dullian Carly de Oliveira Macedo
D. Schumanski, D.de Oliveira Macedo, J. Almansa Malagoli and C. Schimith Silva Coelho,
“Single-Phase Variable Reluctance Motor Design using Particle Swarm Optimization”,
Latin-American Journal of Computing (LAJC), vol. 11, no. 1, 2024
ISSN:1390-9266 e-ISSN:1390-9134 LAJC 2024
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LATIN-AMERICAN JOURNAL OF COMPUTING (LAJC), Vol XI, Issue 2, July 2024
AUTHORS
Juliana Almansa Malagoli was born in Uberlândia (Minas Gerais) and is
graduated in Electrical Engineering with emphasis in computing by the
Federal University of Uberlândia (UFU). Became a master in Electrical
Engineering by UFU in 2012, same year when she started her doctorate
thesis on the field of energy systems at the same university. In 2016
she has accomplished her doctorate degree in Electrical Engineering.
Juliana has participated of the Electromagnetic Device Design and
Analysis Group of the Federal University of Santa Catarina (GRUCAD-
UFSC) during the period of 2012-13 and is now the lead researcher of the
Study Group on Modeling, Environmental and Intelligent Systems of the
Federal University of Paraná (GEMSAI-UFPR), where she is a professor
of higher education at the Pontal do Paraná Campus – Center for Marine
Studies (CPP-CEM UFPR) and a collaborative professor at the Graduate
Program in Electrical Engineering (PPGEE-UFPR) in Curitiba.
Has a bachelor's degree in Industrial Electrical Engineering from the
Universidade Tecnologica Federal do Paraná (2013) and a master's
degree in Electrical Engineering from the Universidade Federal do
Paraná (2017). She is currently a professor in the Department of
Electrical Engineering at the Pontifical Catholic University of Paraná.
She has experience in the field of Electrical Engineering, with emphasis
on Electrical and Industrial Installations, working on electrical projects
for hydroelectric power plants, dams, airports, and other industrial and
infrastructure facilities. Her main areas of expertise include electrical
installations, lightning protection systems (SPDA), power flow, and state
estimator.
Juliana Almansa Malagoli
Cinthia Schimith Silva Coelho
D. Schumanski, D.de Oliveira Macedo, J. Almansa Malagoli and C. Schimith Silva Coelho,
“Single-Phase Variable Reluctance Motor Design using Particle Swarm Optimization”,
Latin-American Journal of Computing (LAJC), vol. 11, no. 1, 2024
