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Optimizac= ión de la compensación reactiva en sistemas eléctricos por el método CRITIC

 

Reactive compensation optimization in electrical systems by the CRITIC method

= 1=

Alvaro Napoleón Chiguano Velasco

https://orcid.org/0000-0002-7651-9728

 

 <= /span>

Maestría en Electricidad, Universidad Técnica de Cotopaxi, Latacunga, Ecuador.

alvaro.chiguano5954@utc.edu.ec= =

= 2=

Jessica Nataly Castillo Fiallos

https://orcid.org/0000-0002-3120-7229

 

 <= /span>

 Facultad de Ciencias de la Ingeniería y Aplicadas, Universidad Técnica de Cotopaxi, Latacunga, Ecuador.

jessica.castillo@utc.edu.ec=

= 3=

Carlos Iván Quinatoa Caiza<= /p>

https://orcid.org/0000-0001-6369-7480

 

 <= /span>

Facultad de Ciencias de la Ingeniería y Aplicadas, Universidad Técnica de Cotopaxi, Latacunga, Ecuador.

carlos.quinatoa7864@utc.edu.ec= =

= 4=

Edison Fabricio Guanochanga Collaguazo

https://orcid.org/0000-0003-4397-9266

 

 <= /span>

Empresa Eléctrica Riobamba, Riobamba, Ecuador.

eguanochanga@eersa.com.ec

 

 

 

 

 =

 

Artículo de Investigación Científica y Tecnológica

Enviado: 10/11/2022

Revisado: 15/12/2022

Aceptado: 23/01/2023

Publicado:05/04/2023

DOI: htt= ps://doi.org/10.33262/cienciadigital.v7i2.2540 <= /span>

 

 =

 

 

 

Cítese:

 

&= nbsp;

Chigu= ano Velasco, A. N., Castillo Fiallos, J. N., Quinatoa Caiza, C. I., & Guanochanga Collaguazo, E. F. (2023). Optimización de la compensación reactiva en sistemas eléctricos por el método CRITIC . Ciencia Digital, 7= (2), 64-81. http= s://doi.org/10.33262/cienciadigital.v7i2.2540

 

 

 

 

CIENCIA DIGITAL<= /b>, es una revista multidisciplinaria, trimestral, que= se publicará en soporte electrónico tiene como misión contr= ibuir a la   formación de profesionales competentes con visión humanística y crítica que sean capaces de exponer sus resultados investigativos y científicos en la misma medida que se promueva mediante = su intervención cambios positivos en la sociedad. = https://cie= nciadigital.org

La revista es editada por la Editorial Ciencia Digital (Editorial = de prestigio registrada en la Cámara Ecuatoriana de Libro con No de Afiliaci= ón 663) www.celibro.org.ec<= /p>

 

 

 

 

Esta revista está protegida bajo una licencia Creative Commons Attribution Non Commercial No Derivatives 4.0 International. Copia de la licencia: http://creativecommons.org/licenses/by-nc-nd/4.= 0/.

 

 

Palabras claves: Ubicación, dimensionamiento, método cri= tic, variable, pesos.<= /span>

&n= bsp;

&n= bsp;

Resumen

Introducción= .  En los sistemas eléctricos AC la inyección de reactivos influye directamente al mejoramiento de parámetros eléctricos c= omo factor de potencia, voltajes, reducción de pérdidas por transporte, cargabilidad de las líneas, etc. En los sistemas eléctricos de potencia l= os estudios de optimización de la compensación reactiva son llevados a cabo mediante diversos métodos heurísticos que se caracterizan por su compleji= dad de programación y por contar con un gran componente de criterio humano, l= os cual influye en gran medida en la evaluación final de los resultados encontrados. Objetivo.  An= alizar los resultados de la aplicación del método Critic a la optimización de la compensación reactiva del sistema de subtransmisión de la Empresa Eléctri= ca Riobamba. Metodología.  In= icialmente se propone un algoritmo para la obtención de la población de escenarios a= ser evaluados y la obtención de los criterios de evaluación, finalmente el análisis estadístico es implementado mediante el uso del método Critic pa= ra la toma de decisión multicriterio. Los algoritmos propuestos y la posteri= or evaluación estadística fueron llevados a cabo en el sistema de 69kV de subtransmisión de la EERSA. Resultados.  De los resultados de la aplicación de = los métodos propuestos a la red de la EERSA se logra el mejoramiento de los perfiles de voltaje mientras se reducen las pérdidas del sistema, todo es= to con los mínimos requerimientos de potencia reactiva inyectada en el siste= ma. Área de estudio especifica: Sistemas Eléctricos.

 <= /o:p>

 

Keywords: Location, sizing, critic method, variable, weight. =

 

Ab= stract

Introduction. In AC electric systems, the injection of reactive power directly influences the improvement of electrical parameters such as power factor, voltages, loose reduction, line chargeability, etc. In electrical power systems, reactive compensation optimization studies are carried out using various heuristic methods that are characterized by their programming complexity and by a large component of human judgment, which greatly infl= uences the evaluation of the results found.  Objective.  Analyze the results of the application of the Critic method to the optimization of the reactive compensation of the sub-transmission system of the Riobamba Electric Comp= any. Methodology.  Initially, an algorithm to obtain the population of scenarios to be evaluated and the evaluation criteria is proposed, finally the statistical analysis is implemented using the Critic method for multicriteria decision making. The proposed algorithms and the subsequent statistical evaluation were carried out in the EERSA 69kV sub transmission system. Results.  From the results of the application of the proposed methods to the EERSA network, = the improvement of the voltage profiles is achieved while the system losses a= re reduced, all this with the minimum requirements of reactive power injected into the system.

 

 

 

Introdu= cción

En los sistemas eléctricos de distribución el flujo de potencia reactiva a través de las lí= neas de transmisión produce pérdidas de energía, caídas de voltaje, bajo factor = de potencia, e incremento en la cargabilidad en líneas de transmisión provocan= do la insatisfacción del usuario final y el incremento de los costos de operac= ión de las empresas distribuidoras (Okon & Wilkosz, 2018)= .

La tendencia actual dentro de los sistemas eléctricos es la implementación de las nuevas tecnologías y métodos en la búsqueda de la optimización de la operación. In= dicadores como pérdidas, factor de potencia, caída de voltaje son los principales parámetros sujetos a estudio dentro de la operación de los sistemas en esta= do estable. En los sistemas de transmisión la compensación reactiva es uno de = los métodos más efectivos para el control de los parámetros eléctricos antes indicados (Lakra et al., 2017). Por lo cual, se han desarrollado múltiples métodos para solventar el problema de la búsqueda de= las óptimas ubicaciones y capacidades de las compensaciones requeridas en un sistema, donde la complejidad del método usado es relativo a la complejidad= del sistema analizado (Li & Yin, 2019). Es por esto que se consi= dera una evaluación multicriterio en la que se toma en cuenta diferentes criteri= os que dependiendo de su aplicación pueden ser minimizados o maximizados (Abdullahi et al., 2021), la ecuación 1 muestra la estructura básica de la función objetivo más comúnmente usada para la evaluación multicriterio.

           (1)

<= span style=3D'font-size:12.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-f= amily: "Times New Roman",serif;mso-ansi-language:ES-EC'>Diversos trabajos de optimización para compensación de reactivos han sido presentados entorno al= uso de métodos heurísticos como algoritmos genéticos (Arlenny et al., 2019), colonia de hormigas (Elkhidir et al., 2019), optimización por enjambr= e de partículas (Ramadan et al., 2017), entre otros (Bayat & Bagheri, 2019= ). Todos estos métodos de optimización se basan en la evaluación de una función objetivo, la misma que será optimizada de acuerdo con las características de cada método, contando= con diferentes niveles de complejidad para su programación e implementación, así como la aplicación directa sobre la problemática a ser solventada sin considerar los efectos que esta solución pueden conllevar al resto de las variables eléctricas del sistema eléctrico.

El resultado d= e la evaluación de la función objetivo puede presentar diferentes comportamientos para los mismos criterios analizados en dependencia del valor de los pesos = que se le sean asignados. En otras palabras, para priorizar un criterio específ= ico un mayor peso (w) se le debe ser asignado.

El método CRIT= IC para la toma de decisión multivariable provee una metodología para la determinación de los pesos que formaran parte de la función objetivo en don= de cada criterio contará con un mayor peso mientras mayor sea la información q= ue aporte un criterio con relación a los demás  (Lamas et al., 2020). Por lo tanto, la aplicac= ión del método permitirá eludir el uso del criterio personal y determinar matemáticamente los mejores pesos posibles que se le pueden ser asignados a= una función de evaluación multicriterio para la búsqueda de la óptima ubicación= y capacidad para bancos de capacitores en la red de 69 kV de la EERSA. <= /o:p>

Metodología

En sistemas radiales la inyección de reactivos influye directamente sobre el mejoramien= to de los perfiles de voltaje y sobre la inversión económica requerida, sin embargo, su efecto sobre la reducción de pérdidas y cargabilidad en las lín= eas de transporte puede llegar a presentar diversas características dependiendo tanto de las ubicaciones como de las capacidades (Kadom et al., 2020).

<= span style=3D'font-size:12.0pt;mso-bidi-font-size:11.0pt;line-height:115%;font-f= amily: "Times New Roman",serif;mso-ansi-language:ES-EC'>La problemática de la optimización de la compensación capacitiva en sistemas eléctricos puede ser dividido en dos subproblemas, la determinación de las óptimas ubicaciones en las cuales se inyectará potencia reactiva y la determinación de la cantidad óptima de reactivos a inyectar en cada barra (Kamel et al., 2019). En los sistemas de transmisión y subtransmisión el método más común de inyección de potencia reactiva consiste en la conexión de bancos de capacitores por lo que el aná= lisis llevado a cabo a continuación toma en cuenta el uso de bancos de capacitores con un valor mínimo de 0.1MVAr disponible en el mercado.<= /p>

Determinación de la ubicación de bancos de capacitores

<= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se= rif; mso-ansi-language:ES-EC'>En base al análisis de la operación de líneas de transmisión cortas mostrado en la figura 1, se puede deducir el comportamie= nto de los voltajes con modelos de carga de potencias constantes.

Figura 1

Modelo de línea de transmisión corta

<= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se= rif; mso-ansi-language:ES-EC'>Del análisis del sistema de una línea de transmisi= ón corta se obtiene el valor de la potencia reactiva (Q) consumida en la barra= 2 en función de los parámetros de la línea de transmisión (Kersting, 2012).

Q=3D 1x (V1V2cosϕ-V22)                                               (2)

Dado que:

cosϕ≈1                                                 =            (3)

Entonces:

                                                    (4)=

De la ecuación anterior se puede concluir que el valor de la c= aída de voltaje encontrada al final de una línea es proporcional a la reactancia= de la línea y al valor de la potencia reactiva requerida por la carga. Esto de= riva en que el control de potencia reactiva ( ) sería la mejor opción que permitirá la regulación de voltaje= en una barra que no cuente con generación. Dado el análisis anterior cabe indi= car que durante el desarrollo de tomará en cuenta la heurística de que las barr= as con menor voltaje serán las principales candidatas para ubicar bancos de capacitores.

Teniendo en cuenta el enfoque de compensación capacitiva para = el control de voltaje, las ubicaciones especificadas para la instalación de ba= ncos de capacitores serán determinadas mediante el sondeo de la barra con menor voltaje. Sin embargo, tanto en la barra Slack como PV no es posible realiza= r el control de voltaje médiate compensación capacitiva dado que estas cuentan c= on un control propio el que por lo general ajusta su potencia reactiva generad= a ( ) para llegar a un voltaje especificado (X. Li et al., 2017)<= /span>. Por lo tanto, el uso de compensación capacitiva para control= de voltaje únicamente será usada en barras tipo PQ.

 

Determinación de la capacidad de bancos de capacitores

La búsqueda de las máximas capacidades a instalar en cada barr= a de un SEP puede ser analizado mediante una búsqueda discreta al incrementar sucesivamente la capacidad de los bancos de capacitores en las ubicaciones determinadas. Cada paso de incremento (  deberá ser evaluado p= or la función objetivo ( ) la cual permitirá determinar si se ha llegado o no a la mejor solución.

La función objetivo a maximizar corresponde a la ecuación indi= cada a continuación:

<= !--[if gte msEquation 12]>FO=3D w1.Vmin+ w2.P+w3.CTotal=                                  (5)=

Donde:

: Peso de cada criterio.

: Mínimo volta= je del sistema.

 : Pérdidas totales del sistema por trans= porte.

: Total de potencia reactiva instalada en el sistema ( ).<= /span>

Esta función objetivo será optimizada mediante la aplicación d= el método CRITIC mostrada en Yepes (2022), la cual se resume en 5 pasos:

1.   Crear la matriz de decisión: Se crea una matriz con todos los posibles valores de ,  y  obtenidos de cada uno= de los posibles conjuntos de los bancos de capacitores a instalar. =

Tabla 1

 = Ejemplo matriz de decisión

 

2.      Normalizar por el rango los valores de cada uno de los criteri= os: En base a los valores de la matriz de decisión estos se transforman a p.u. =

Tabla 2

 = Criterio para transformación a p.u. la matriz de decisión

Beneficio

Costo

 

3.      Calcular la desviación típica de cada criterio.

=                                                 =            (6)

4.      Calcular la correlación entre cada par de criterios.

= <= ![if !msEquation]>                                                 =                         (7)

5.      Calcular el peso de cada criterio.

wj=3Dσj <= /span>k=3D1n(1-rjk<= /m:sub>)=                                                 =             (8)

Resultados

En el presente trabajo primeramente se realizó el análisis de la metodología de búsqueda de la óptima compensación reactiva mediante bancos de capacitores para el mejoramiento de los perfiles de volt= aje y la reducción de las pérdidas por transporte en la red de 69kV de la Empre= sa Eléctrica Riobamba (figura 2). La función de optimización fue valorada medi= ante el uso del método CRITIC para el análisis multivariable.<= /p>

La red de Subtransmisión de 69kV de la EERSA está compuesta por 14 barras, la barra 1 representa la conexión al SNI, las barr= as 11 y 12 son barras de conexión a las centrales de generación Alao (10.2 MVA= ) y Rio Blanco (3MVA) respectivamente, mientras que las barras restantes corresponden a subestaciones de carga.

 

 

Figura 2

Red de 69kVde la EERSA

 

La figura 3 presenta los perfiles de voltaje a la hora pico (1= 9:00 horas) en cada barra de la red presentada.

Figura 3

Perfil de voltajes de la red de subtransmisión de la EERSA a la hora pico

<= v:shape id=3D"Imagen_x0020_67" o:spid=3D"_x0000_i1031" type=3D"#_x0000_t75" style= =3D'width:277.5pt; height:207.75pt;visibility:visible;mso-wrap-style:square'>

Según el criterio previamente indicado en el cual = las ubicaciones de los bancos de capacitores serán determinadas de acuerdo con = la barra que presente el menor voltaje, la ubicación inicial correspondería a = la barra 14. Además, es importante notar que las barras de la EERSA que presen= tan equipamientos de generación operan a manera de barras de carga volviendo posible el control de voltaje mediante compensación capacitiva.<= /span>

Por lo dicho anteriormente, se indica que la ubica= ción de bancos de capacitores será únicamente tomada en barras de carga, por lo = que para el caso del sistema de la figura 2 se iniciaría la ubicación de capacitores en la barra 14.

Los criterios seleccionados para el análisis multivariable aplicado a la compensación de reactivos en el sistema analiza= do corresponden a voltaje mínimo, pérdidas por transporte y reactivos totales = a inyectar, los valores numéricos de cada caso se muestran en la tabla 3.

Tabla 3

 = Matriz de decisión para compensación en la red de la EERSA

V min

Pérdidas MW

MVAr

V min

Pérdidas MW

MVAr

0.9668

8.32

0

0.9842

8.31

1.7

0.9677

8.31

0.1

0.9852

8.32

1.8

0.9688

8.30

0.2

0.9862

8.34

1.9

0.9698

8.29

0.3

0.9872

8.35

2

0.9709

8.28

0.4

0.9882

8.37

2.1

0.9719

8.27

0.5

0.9892

8.39

2.2

0.973

8.27

0.6

0.9902

8.41

2.3

0.974

8.26

0.7

0.9912

8.43

2.4

0.9751

8.26

0.8

0.9922

8.46

2.5

0.9761

8.26

0.9

0.9932

8.48

2.6

0.9771

8.26

1

0.9941

8.51

2.7

0.9781

8.26

1.1

0.9951

8.53

2.8

0.9791

8.26

1.2

0.9961

8.56

2.9

0.9802

8.27

1.3

0.9971

8.59

3

0.9812

8.28

1.4

0.9981

8.62

3.1

0.9822

8.29

1.5

0.999

8.65

3.2

0.9832

8.30

1.6

1

8.68

3.3

Las figuras 4 y 5 muestran las variaciones del vol= taje p.u. en la barra 14 y las pérdidas por transporte del sistema de subtransmi= sión ante incrementos paulatinos de potencia reactiva capacitiva de 0.1 MVAr en = la barra 14.

 

 

Figura 4

MVAr inyectados vs voltaje en la barra 14

Figura 5

MVAr inyectados en la barra 14 vs pérdidas del sistema <= /o:p>

Como se observa en las figuras anteriores, la rela= ción entre la potencia reactiva capacitiva y el voltaje en la barra 14 es directamente proporcional mientras que la relación entre la potencia reacti= va inyectada y las pérdidas del sistema no es del todo clara. Si bien se obser= va que inicialmente la conexión de pequeños bancos de capacitores ayuda en elevación de voltajes y la reducción de pérdidas, se presenta un límite lue= go del cual las pérdidas del sistema se incrementan requiriéndose que se reali= ce una evaluación entre la inyección de potencia reactiva capacitiva, sus beneficios sobre el control de voltaje y su perjuicio en el incremento de l= as pérdidas del sistema.

La figura 6 muestra los valores normalizados de la matriz de decisión, el cual corresponde al segundo paso del flujo de proceso para el cálculo de los pesos y sobre los cuales se realiza el análisis de selección del valor óptimo de inyección de reactivos.

Figura 6

Casos posibles vs valores normalizados

 

Las tablas 4 y 5 presentan los valores determinados de manera estadística para la desviación estándar y la correla= ción entre los criterios de decisión analizados.

Tabla 4

Desviación estándar de valores analiza= dos

V min

Pérdidas

kVAr

0.3023

0.3054

0.3018

 

Tabla 5

 = Correlación entre valores analizados

 

V min

Pérdidas

kVAr

V min

1

-0.8598

-0.9999

Pérdidas

-0.8598

1

0.8656

kVAr

-0.9999

0.8656

1

Finalmente se calcula los pesos de cada criterio relacionando los datos de las tablas 4 y 5 de acuerdo con lo mostrado en la ecuación 8. La tabla 6 muestra los pesos finales determinados para el caso de incremento de reactancia capacitiva en la barra 14.

Tabla 6

 = Pesos determinados para cada criterio analizado

W1

W2

W3

V min

Pérdidas

kVAr

1.1668

0.6091

0.6441

La relación matemática entre los valores normalizados y los pesos determinados es evaluada de acuerdo con lo mostrado en la ecuación 9.

                                   (9)

Donde:

: Peso de cada criterio.

<= span lang=3DES-MX style=3D'font-size:11.0pt;line-height:107%;font-family:"Calibr= i",sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareas= t-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times Ne= w Roman"; mso-bidi-theme-font:minor-bidi;position:relative;top:4.0pt;mso-text-raise:-= 4.0pt; mso-ansi-language:ES-MX;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'= > : Mínimo voltaje del sistema.

 : Pérdidas totales del sis= tema por transporte.

: Total de potencia reactiva instalada en el sistema ( ).

 La figura= 7 muestra gráficamente los valores puntuales de la función de optimización an= te cada caso de incremento de la potencia reactiva inyectada en la barra 14.

Figura 7

Casos posibles vs Función de optimización

La maximización de la función objetivo permite determinar la condición de operación que cuente con la mejor relación entre elevación de voltaje, reducción de pérdidas y menor requerimiento de potenc= ia reactiva.

Para el ejemplo evaluado se determina que la mejor condición de operación se alcanza en el caso 17 en el cual se requiere la inyección de 1.6 MVAr en la barra 14.  La tabla 7 permite hacer una evaluación numérica entre los valores obtenidos a condiciones normales de operación de la red de 69kV de la EERSA y la condic= ión óptima de compensación determinada mediante el método Critic.

Tabla 7

 = Condición y operación inicial y compensada

 

V min p. u

Pérdidas MW

MVAr inyectados

inicial

0.9668

8.32

0

compensado

0.9832

8.29

1.6

 

Si bien el análisis anterior fue realizado para un instante particular de tiempo (19:00 horas), un análisis similar puede ser realizado para cualquier instante a lo largo del día. La figura 8 muestra l= os resultados del análisis para la óptima compensación de reactivos en la barr= a 14 para un rango de estudio de 24 horas.

Figura 8

Voltajes y pérdidas iniciales vs compensados

 

 

Discusión

Los resultados obtenidos muestran que el método implementado logra un notorio mejoramiento de los perfiles de voltaje a la = vez que se reduce las pérdidas por transporte del sistema. Por otro lado, se demuestran que el modelo de optimización implementado adapta su respuesta de forma dinámica ante las distintas condiciones de operación presentes en la = red de la EERSA.

La aplicación del modelo de optimización propuesto aplicado a las 24 horas del día permitirá generar un cronograma de conexión= y desconexión de los bancos de capacitores en la red de la EERSA. La figura 9 muestra gráficamente los valores horarios de inyección de reactivos requeri= dos para las barras del sistema. Los resultados demuestran que para la condición base de estudio únicamente se requiere compensación para las barras 12 y 14= de la red de la EERSA

Figura 9

Resultados compensación requerida

La metodología empleada demuestra ser de fácil programación e implementación, sin embargo, el tiempo de ejecución del algoritmo es proporcional al tamaño del sistema analizado e inversamente proporcional al tamaño del paso de VAr a inyectar utilizado.

Por otro lado, es importante notar que el éxito de= los resultados al aplicar el método CRITIC depende en gran medida de los criter= ios utilizados para la evaluación. Esto le permite que pueda este ser implement= ado para todo análisis en el cual se pueda crear un conjunto de eventos, como e= n el caso de ubicación de equipos de protección para redes de medio voltaje (Zeinalzadeh et al., 2019) cuyo algoritmo de validación podría ser simplific= ado mediante la técnica utilizada en el este trabajo.

Conclusiones

·         Tal como se muestra en el apartado de compensación capacitiva, los criterios heurísticos para la ubicación de las localizaciones a instalar bancos de capacitores acompañados con la técnica estadística CRITIC para el análisis multivariable presentaría una nueva propuesta para la óptima compensación capacitiva en sistemas eléctricos, así como también la solución de diversos problemas de optimización en los que l= as posibles soluciones puedan ser divididas en escenarios finitos.<= /span>

·         La implementación del análisis estadís= tico permitirá determinar la correcta capacidad de reactivos a ser inyectados, la cual permitirá lograr la máxima corrección de los perfiles de voltaje sin incrementar las pérdidas por transporte en las líneas de transmisión.<= /o:p>

·      =    Se observa que el modelo de optimizaci= ón para compensación reactiva aplicado al sistema de 69kV de la EERSA presenta= muy buenos resultados para el control de local de voltaje, sin embargo, no se aprecian mejoras considerables en cuanto a reducción de pérdidas del sistem= a.

Conflicto de intere= ses

Los autores del presente artículo científico de revisión bibliográfica manifiestan que no poseen ningún tipo de conflicto de interés en relación con la presente investigación.

<= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se= rif'> 

Referencias Bibliográficas

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Bayat, A., & Bagheri, A. (2019). Optimal active and reactive power allocation in distribution networks using a novel heuris= tic approach. Applied Energy, 233234, 71–85. https://doi.org/10.1016/J.APENERGY.2018.10.030

Elkhidir, L., Hassan, A., & Khalid, M. (2019). SVC-based controller design via ant colony optimization algorithm. 8th International Conference on Renewable Energy Research and Applications, ICR= ERA 2019, 301–308. https://doi.org/10.1109/ICRERA47325.2019.8996883

Kadom, H. F., Hussain, A. N., & Al-Jubori, W. = K. S. (2020). Optimal dual design based on capacitor placement and reconfigura= tion techniques for loss reduction and voltage enhancement. IOP Conference Series: Materials Science and Engineering, 745(1), 012003. https://doi.org/10.1088/1757-899X/745/1/012003

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Li, X., Wang, Y., Li, N., Han, M., Tang, Y., & Liu, F. (2017). Optimal fractional order PID controller design for automatic voltage regulator system based on reference model using particle swarm optimization. International Journal of Machine Learning and Cybernetics<= /i>, 8(5), 1595–1605. https://doi.org/10.1007/S13042-016-0530-2/METRICS

Okon, T., & Wilkosz, K. (2018). Diagnostics of Reactive Power Flow in a Power Network. 2018 International Conference on Diagnostics in Electrical Engineering, Diagnostika 2018. https://doi.org/10.1109/DIAGNOSTIKA.2018.8526090

Ramadan, H. S., Bendary, A. F., & Nagy, S. (20= 17). Particle swarm optimization algorithm for capacitor allocation problem in d= istribution systems with wind turbine generators. International Journal of Electrical Power and Energy Systems, 84, 143–152. https://doi.org/10.1016/j.ijepes.2016.04.041

Yepes Piqueras, V. (2022, January). Método CRITIC de toma de decisión multicriterio. Poli blogs. Universidad Politécnica de Valencia. https:/= /victoryepes.blogs.upv.es/2022/01/13/metodo-critic-de-toma-de-decision-mult= icriterio/

Zeinalzadeh, A., Estebsari, A., & Bahmanyar, A. (2019). Multi-Objective Optimal Placement of Recloser and = Sectionalized in Electricity Distribution Feeders. Proceedings - 2019 IEEE Internation= al Conference on Environment and Electrical Engineering and 2019 IEEE Industri= al and Commercial Power Systems Europe, EEEIC/I and CPS Europe 2019. https://doi.org/10.1109/EEEIC.2019.8783430

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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ISSN: 2602-8= 085

Vol. 7 No. 2,  pp. 64 – 81 , abril – junio 2023

 

 

 

 

                  Optimización & Eficiencia         Página 64 | 81

 

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