VOL. V, N.° 1, 2022 | eISSN: 2697-3243 | pISSN: 2588-0829
Autoridades
Dr. Fernando Sempérteguí Ontaneda, Ph.D
Rector de la Universidad Central del Ecuador
Ing. Diego Paredes Méndez, M.Sc
Decano, Facultad de Ingeniería y Ciencias Aplicadas - FING
Ing. Flavio Arroyo Morocho, Ph.D.
Subdecano, Facultad de Ingeniería y Ciencias Aplicadas – FING
Editor
Flavio Arroyo Morocho
Consejo Editorial
Ing. Diego Paredes Méndez, M. Sc., Presidente, Universidad Central del Ecuador,
Ing. Abel Remache Coyago, M. Sc., Editor académico, Universidad Central del Ecuador,
Ing. Paulina Viera Arroba, M. Sc., Universidad Central del Ecuador,
Dr. Johannes Ritz, ., ., Ph. D. (c ), EU Business School Munich,
Dra. Teresa Magal-Royo, Ph. D, Universidad Politécnica de Valencia,
Dr. Andrés Vivas Albán, Ph. D., Universidad del Cauca,
Dr. Boris Heredia Rojas, Ph. D., Universidad del Norte,
Dr. Jaime Duque Domingo, Ph. D., Universidad de Valladolid,
Dr. Giovanni Herrera Enríquez, Ph. D., Universidad de las Fuerzas Armadas-,
Dr. José Luis Paz, Ph. D., Universidad Nacional Mayor de San Marcos,
Dr. Jesús López Villada, Ph. D., Universidad Internacional ,
Dr. Michel Vargas, Ph. D., Escuela Politécnica Nacional-,
Dr. Andrés Robalino-López, Ph. D., Escuela Politécnica Nacional-,
Consejo Asesor y Evaluador
Ing. Adrián Coello Velásquez, M. Sc. Empresa Eléctrica de Guayaquil,
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Ing. Edison Proaño Ayabaca, Ph. D., Investigador Independiente,
Ing. Holger Santillán, M. Sc., Universidad Politécnica Salesiana ,
Ing. Juan Espinoza Palacios, M. Sc., Escuela Politécnica Nacional ,
Ing. Rogger Peña, M. Sc., Instituto Superior Tecnológico Simón Bolívar,
Ing. Diego Cardona, M. Sc. Ph. D., Red Académica de Docentes e Investigadores en Educación Superior,
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Este número estuvo bajo la coordinación editorial del Ing. Flavio Arroyo, Ph. D., Ing. Abel Remache, M. Sc., y Lic. Tatiana Freire, M. Sc.(c)
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ÍNDICE
Mathematical analysis and simulation in Matlab of dierential protection
in two power transformers Winding ………………...… ................................................................................ 4
Cárdenas D., Chávez C., Morales L., Solís G., Rodríguez J.
Estudio de la incorporación de nano sílice en concreto de alto desempeño () ………………..… ...12
Alvansaz F., Bombón C., Rosero B.
Evaluación del estado de funcionamiento de transformadores de potencia
sumergidos en aceite en las subestaciones eléctricas ……………………………………………..… ......22
Bastidas A., Maquilón J., Chávez C.
Adoquines de hormigón ecoamigables fabricados con la incorporación
de una mezcla de micro-nano sílice ……………………………………………..… .................................. 34
Alvansaz F., Arévalo B., Arévalo J.
Localización óptima de equipos de regulación de voltaje y compensación
de reactivos para alimentadores de medio voltaje, mediante algoritmos evolutivos ……………. ... 43
Carreño C., Avilés J.
Influencias en el ambiente educativo de la carrera de manufactura en Ecuador ………………...…60
Sópalo V., Rocha J., Peralta F., Chichande Y.
Análisis de la integración del diseño en el seno de las MiPymes de la
Zona 9 del DM de Quito -Ecuador que generan productos con valor
agregado para su exportación ………………...… ........................................................................................71
Bravo D.
Normas para publicar en la revista Ingenio …………..… .............................................................................79
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REVISTA INGENIO
Mathematical analysis and simulation in Matlab of dierential protection in two
power transformers Winding
Análisis matemático y simulación en Matlab de protección diferencial en dos devanados de
transformadores de potencia
David Cárdenas | Universidad Politécnica Salesiana, Guayaquil, Ecuador
Carlos Chávez | Universidad Politécnica Salesiana, Guayaquil, Ecuador
Julio Rodríguez | Universidad Politécnica Salesiana, Guayaquil, Ecuador
Germán Solís | Universidad Politécnica Salesiana, Guayaquil, Ecuador
Luis Morales | Universidad Politécnica Salesiana, Guayaquil, Ecuador
https://doi.org/10.29166/ingenio.v5i1.3785 pISSN 2588-0829
2022 Universidad Central del Ecuador eISSN 2697-3243
CC BY-NC 4.0 —Licencia Creative Commons Reconocimiento-NoComercial 4.0 Internacional ng.revista.ingenio@uce.edu.ec
, (), -, . -
is project deals with the realization of mathematical modeling and simulation in Matlab of dierential
protection in two-winding power transformers, the same one that will be part of the Salesian Polytechnic
University, Guayaquil headquarters; will have the objective of simulating the operating conditions of the
protection equipment (SEL 587) found in a substation, obtaining the equation that governs the dieren-
tial protection operations of said relay, by theoretically analyzing the system conditions, both under nor-
mal conditions and for any fault event (external fault, internal fault) on the primary and / or secondary
side of the transformer, facilitating students who are in the last cycles of the electrical engineering career,
learning the concepts and principles of operation of system protections electric power.
El presente proyecto trata sobre la realización del Modelado Matemático y simulación en MATLAB de la
Protección diferencial en transformadores de potencia de dos devanados, el mismo que formara parte de
la Universidad Politécnica Salesiana, sede Guayaquil. Tendrá como objetivo simular las condiciones de
operación del equipos de protección (SEL 587) encontrado en una subestación, obteniendo la ecuación
que gobierna las operaciones de protección diferencial de dicho relé, al analizar teóricamente las con-
diciones del sistema, tanto en condiciones normales como para cualquier evento de falla (falla externa,
falla interna) en el lado del primario o secundario del transformador, facilitando a los estudiantes que
cursan los últimos ciclos de la carrera de Ingeniería Eléctrica, el aprendizaje de conceptos y principios de
funcionamiento de protecciones de sistema eléctricos de potencia.
.
Within this document you will nd all the information
related to the «Mathematical analysis and simulation in
Matlab of dierential protection in power transformers
with two windings», which consists of making all the
measurements in a dierential protection test module
using the 587 relay, in which all the connections and pos-
sible cases of failure that can occur in an electrical power
system were made, obtaining real data which allowed
analyzing the behavior of the relay for each event.
e rst chapter deals with the demand of the pro-
blems in the electrical power systems based in daily expe-
rience, for which it is proposed to certify the reliability in
Received: 15/06/2021
Accepted: 07/09/2021
Test bench, protection coordination,
dierential relay 587, Matlab program.
Inestabilidad de voltaje, potencias reac-
tivas inductivas, voltajes, ángulos, PV,
QV, factores de participación, colapso
de red.
5
Mathematical analysis and simulation in Matlab of dierential protection in two power transformers windings
the distribution networks through dierential protection.
In the second chapter, the normal operating conditions
were reviewed to electrical systems operating for a nite
or innite time under nominal values. In the third chap-
ter, the respective tests were carried out with the dierent
connections that can be made to a power transformer and
compared through the program in normal condition and
when the internal fault occurs in the transformer. Fina-
lly, in the fourth chapter, the mathematical analysis was
elaborated through equations which was carried out the
structure of the programming in Matlab.
Likewise, the scope of the project and its benets to
society are dened, with the didactic design that allows
to develop real tests where the behavior of the relay is
analyzed through dierential protection, making the di-
erent types of connection of the transformers in which
they evaluated the internal and external faults in the la-
boratory that occur normally.
For the understanding and total perception of the
subject, books, previous technical projects, papers and
web sources were reviewed, in order to consolidate the
knowledge regarding the case study.
S
e experiments were implement using 1 test module,
three single-phase transformers each one of 1500
120 / 240 to form three-phase banks with dierent
connections Star-Star (υυ), Star-Delta (Υ∆), Delta-Delta
(∆∆), Delta-Star (∆Υ), located in the Circuits laboratory
of the Politécnica Salesiana University (see Figure 1).
Figure 2 shows a 0-100 variable resistive load
three-phase bank, with a maximum current of 2,5. e
measuring equipment that we use to perform all the tests
is the ideal 61-746 (see Figure 2).
is measuring instrument that is displayed in gure
3 was used as a reference to be able to make comparisons
of voltages and currents (see Figure 3), allowing you to
perform load studies and check the capacity of the elec-
trical systems before adding the load (see Table 1).
D
For a transformer with two winding, the dierential relay
will detect the faults that occur both inside the protected
area and its external connections to the current trans-
formers associated with this protection. is will act as
Figure 1. Module for transformer protection
Source: Politécnica Salesiana University.
Figure 2. Variable resistive load from 0-100, 2,5A
Sources: Politécnica Salesiana University.
Table 1.
Nomenclature
ree-phase Star-Star system
ree-phase Star-Delta system
ree-phase Delta-Delta system
ree-phase Delta-Star system
Ohm, unit of electrical resistance
Eective value
voltage
Volts
Amps
Volt-amperes, unit of apparent power
6
Cárdenas D., et al.
a protection with absolute selectivity; the instantaneous
current, modules and phases will be compared.
Figure 4 shows the current ows that circulate throu-
gh the Tc’s which send information to the dierential re-
lay, these being governed by the following equations for
non-fault and fault-free conditions (see Figure 4):
Dierential current = Id = I1 + I2
Equation 1: Dierential current.
Source: [7, p. 23]
I1=I2 Id=0
Equation 2: Equipment without failure
Source: [7, p. 23]
I1≠I2 Id≠0
Equation 3: Equipment failed
Source: [7, p. 23].
e dierential protection characteristic can be set ei-
ther as a percentage dierential characteristic as a slo-
pe or as a variable percentage dierential characteristic
with double slope (see Figure 5); the element’s operation
is determined by the operating () and holding ()
quantities, calculated from the input currents of the win-
dings [7, p. 21].
e gure shows the operating current and a res-
training current and an 087 setting or a minimum
level required for the operation and two operating slo-
pes called 1 with their operating limit 1 which is an
initial curve starting at the origin and with its intersec-
tion 087 and a second curve 2 which, if used, must
be greater than or equal to 1 and its entire upper area
is a region of operation of the relay and the internal area
of the gure shows a region of the relay where this does
not operate [7, p. 21].
Triggering occurs if the operation amount is greater
than the minimum pickup level and is greater than the
curve value, for a particular holding amount. Four set-
tings dene the characteristic [7, p. 21].
With careful selection of these settings, the user can
closely emulate the characteristics of existing dierential
current relays [7, p. 21].
Dierential protection responds to design criteria ba-
sed on reliability, speed, selectivity, safety, sensitivity, eco-
nomy and simplicity [7, p. 21].
Figure 4.
Protection of transformers with two winding
Figure 6.
Equivalent circuit of the transformer
Figure 3.
Ideal 61-746
Figure 5.
Slope of dierential operation
Source: [7, p. 22].
7
Mathematical analysis and simulation in Matlab of dierential protection in two power transformers windings
II.
To nd the currents of the ’s, the analysis of the trans-
former is performed, we begin from the equivalent cir-
cuit of the transformer where (see Figure 6):
Vrn = Input voltage.
R1 = Hysteresis resistance and heat losses.
Lm1 = Inductance necessary to produce magnetic ux
from the transformer.
Rcc1 = Short circuit resistance
Lcc1 = Short circuit inductance
Rc = Load resistance
I1 = Primary current
Io = Vacuum current
Im = Magnetizing current
Irh = hysteresis current
I2 = Secondary current
Using Kirchho’s laws, we obtain the following dieren-
tial equations that dene the modeling of the single-pha-
se transformers in gure 6:
Single phase transformer 1
e voltage over time is dened by the following formula:
Vrn(t)=Vp Sen(wt+0º) (1)
From Kirchho’s law, we dene the current of the pri-
mary of the transformer T1 as a function of the no-load
current and of the secondary:
I1T1=Io+I2 (2)
Knowing that the voltage over time of the inductor is de-
ned as:
(3)
Applying Ohm’s law we draw hysteresis current from the
single-phase transformer T1.
(4)
Secondary current of single-phase transformer T1.
(5)
Primary current of a single-phase transformer.
(6)
Single phase transformer 2
e voltage over time is dened by the following formula:
Vsn(t) = Vp * Sen(wt + 120°) (7)
From Kirchho’s law, we dene that the current of the
primary of the transformer T2 as a function of the no-
load current and of the secondary:
I1T2 = Io + I2 (8)
Knowing that the voltage at time of the inductor is de-
ned as:
(9)
Applying Ohm’s law, we draw hysteresis current from the
single-phase transformer T2.
(10)
Secondary current of single-phase transformer T2.
(11)
Primary current of a single-phase transformer.
(12)
Single phase transformer 3
e voltage over time is dened by the following formula:
Vtn(t) = Vp * Sen(wt - 120°) (13)
From Kirchho’s law, we dene that the primary current
of the transformer T3 as a function of the no-load cu-
rrent and the secondary current:
I1T3 = Io + I2 (14)
Knowing that the voltage at time of the inductor is de-
ned as:
(15)
Applying Ohm’s law we draw hysteresis current from the
single-phase transformer T3.
(16)
Secondary current of single-phase transformer T3.
(17)
8
Cárdenas D., et al.
Primary current of a single-phase transformer.
(18)
Single phase transformer 1
Primary current of transformer T1, seen from the secon-
dary of ’.
(19)
Secondary current of transformer T1, seen from the se-
condary of ’.
(20)
Single phase transformer 2
Primary current of transformer T1, seen from the secon-
dary of ’.
(21)
Secondary current of transformer T1, seen from the se-
condary of ’.
(22)
Single phase transformer 3
Primary current of the transformer T1, seen from the se-
condary of ’.
(23)
Secondary current of transformer T1, seen from the se-
condary of ’ (see Figure ).
(23)
1 of a dierential relay.
(24)
2 of a dierential relay.
(25)
Aer nding the currents of said which we dene
with the following formulas:
Figure 7.
Block diagram of protection relay operation.
Figure 9.
Parameter entry graph window
Figure 8.
Compensation matrix
9
Mathematical analysis and simulation in Matlab of dierential protection in two power transformers windings
TRANSFORMER 1
Primary phase current, aer passing through 1.
(26)
Secondary phase current, aer passing through 2.
(27)
TRANSFORMER 2
Primary phase current, aer passing through 1.
(28)
Secondary phase current, aer passing through 2.
(29)
TRANSFORMER 3
Current of phase of the primary, aer passing through
1.
ICw1F = ICw1
Tap1 (30)
Secondary phase current, aer passing through
2.
(31)
en go to the block of compensation matrices depen-
ding on the transformer connections and their phase di-
erence that was chosen internally in the program and
in turn the dierential relay relates them through pre-
viously adjusted parameters, the matrices are as follows
(see Figure 8).
Example:
Protection relay operation through compensation matrix.
Primary current in each of the phases, from the com-
pensation matrix.
(32)
Secondary current in each of the phases, from the com-
pensation matrix.
(33)
Aer having had all these currents, the relay proceeds
to calculate the operating currents (Iop) and restriction
(Irst) for which the following equation is used:
Operating current in phase .
IopA=IA
W1FC1 + IA W2 FC1 (34)
Operating current in phase .
IopB=IBW1FC1 + IB W2 FC1 (35)
Operating current in phase .
Figure 10.
Results graph window
Figure 11.
Simulink blocks