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Modelo matemático para estimar la producción de la energía primaria en Ecuador.<= /b>

 

 

Mathematical model= to estimate the production of primary energy in Ecuador.

 

Guido Javier Mazón Fierro.[1], = Pablo Ricardo Calderón Limaico.[2],<= /span> Ruffo Neptalí Villa Uvidia.[3] <= /span>& Jenny Margoth Villamarín Padilla.[4]

 

Recibido: 10-03-2019 / Revisado: 15-03-209 /Aceptado: 04-04-2019/ Publicado: 13-05-2019

 

 

 Abstract.                     DOI: https://doi.org/10.33262/cienciadigital.v3i2.2.464<= /span>   

 

In the present paper a series of values of prima= ry energy production in Ecuador was estimated through the multiplicative mathematical model of time series that has as variables the trend, seasonal= ity and noise, it was considered a time lapse of 12 years as of 2015 arriving to obtain estimated values up to the year 2027, as a first step, historical da= ta of the national energy balance of Ecuador 2016 were taken, with these input= s as a starting point the trend was found from a linear extrapolation model, arriving to determine the behavior of the production of primary energy thro= ugh the trend line: T =3D 204.28 + 1.0956 * t where T =3D trend, t =3D time ser= ies, then the seasonality is analyzed which is another of the variables to be conside= red in the model , for this it had to adjust or soften the seasonality to reduce the noise and it was achieved with the technique of the third order moving averages, Finally, the multiplicative model with which estimated values were obtained from 2016 to 2027 was applied, it was possible to predict that for= the last data of the time series the energy production is 241,832 kBEP (Kilo equivalent barrels of oil), being the highest value of registered productio= n.

Keywords: Model, Projection, Mathematics, Energy, Predict, Production.

Resumen.

 <= /span>

En el presente artículo se estimó una serie de valores de producción de energía primaria en Ecuador mediante el modelo matemático multiplicativo de series temporales que tiene como variables la tendencia, estacionalidad y ruido, se consideró un lapso de tiempo de 12 años a partir del 2015 llegando a obtener valores estimados hasta el año 2027, como primer paso se tomaron datos históricos del balance energético nacional de Ecuador 2016, con estos insum= os como punto de partida se encontró la tendencia a partir de un modelo de extrapolación lineal, llegando a determinar el comportamiento de la producc= ión de energía primaria a través de la línea de tendencia:  donde  , , a continuación se analiza la estacionalidad que es otro de las variables a considerar en el modelo, para esto se tuvo que ajustar o suavizar la estacionalidad para disminuir el rui= do y se lo consiguió con la técnica de las medias móviles de tercer orden, se ob= tuvo como resultado el índice de estacionalidad corregido, finalmente se aplica = el modelo multiplicativo con el cual se consiguió valores estimados desde el año 2016 hasta 2027, se pudo predecir que para el último dato de la ser= ie temporal la producción de energía es 241.832 kBEP (Kilo barriles equivalent= es de petróleo),  siendo el valor más = alto de producción registrado.

P= alabras claves: Modelo, Proyección, Matemática, Energía, Predecir, Producción.

Intro= ducción.

La energía es un pila= r en el desarrollo de los países. (Garrido, 2009) menciona que = “Uno de los principales vectores de nuestra evolución ha sido y es, sin lugar a dudas, la energía. Ésta ha hecho posible que el ser humano no solo poblara prácticamente la totalidad de la superficie del planeta, sino que se ha lle= gado al espacio. La energía es fuente de calor, de luz, hace posible que nos desplacemos, que cocinemos nuestros alimentos, que fabriquemos máquinas ent= re otras cosas”.

El modelo actual de desarrollo se sustenta, en gran medida, sobre el consumo de combustibles fósiles: petróleo, gas natural y carbón, que según el Programa de las Nacio= nes Unidas para el desarrollo representan, conjuntamente, más del 80% del suministro de energía primaria a nivel mundial, los combustibles fósiles ti= enen su origen en la fotosíntesis de las plantas, las cuales extraen del sol la energía necesaria para desarrollarse gracias a ella absorben dióxido de car= bono de la atmósfera y se quedan con la parte que les interesa, esto es, el carb= ono, devolviendo el oxígeno al medio ambiente. En definitiva, se podría consider= ar a las plantas como unos captadores y acumuladores de energía solar, transform= ando ésta en carbono. Además, la acumulación de grandes cantidades de materia orgánica en estructuras sedimentarias, sometida a altas presiones y temperaturas, tras un largo periodo de transformación del orden de millones= de años, da lugar a los combustibles fósiles. Normalmente, se considera que el carbón procede de depósitos de materia orgánica vegetal terrestre, mientras= que el petróleo y el gas natural proceden de depósitos de materia orgánica de origen marino, como algas, plancton.(Garrido, 2009).

Nadie puede desconocer que la energía es el motor que mueve el mundo, sin embargo, involucra probl= emas serios para la humanidad y el planeta, (Cano, 2014) señala que existe una estrecha relación entre desarrollo, energía y entorno ambiental, la n= ecesidad de utilizar combustibles fósiles va acompañado por el deterioro medioambien= tal asociado al cambio climático, es un fenómeno que desafía a todos los modelos estadísticos de predicción energética, esto genera un reto para propiciar el incremento en la actividad científica dirigida a identificar y desarrollar fuentes primarias de energía sustentables, sostenibles y con balance energé= tico positivo.

Es por esto que se pretende realizar un aporte en el sector energético mediante un estudio de = un modelo matemático para estimar la producción de la energía primaria del Ecu= ador debido a la importancia de la energía en el desarrollo de cada país y sus implicaciones en el ambiente, como datos para el estudio, se cuenta con el balance energético de Ecuador del año 2016, el cual describe en detalle la matriz energética de manera global y desglosa datos históricos estadísticos anuales de la oferta de energía primaria y la demanda de energía, en kilo b= arriles equivalentes de petróleo (Kbep), es por ello que el objetivo de este trabaj= o es determinar la producción= de energía primaria en Ecuador al año 2027 para contribuir= a las acertadas toma de decisiones.

Metodología

Marco Teórico Referencial

Para estudiar un sistema, un modelo matemático comienza con la identificación de los aspectos principales o determinantes del sistema y los caracteriza a través de las expresiones matemáticas. La idea en la construc= ción es encontrar un equilibrio entre la simplicidad y una reproducción del comportamiento que permita comprender, analizar y predecir, al cambiar el v= alor de la o las variables que lo describen, la respuesta del sistema en su conjunto.Un modelo matemático es la representación simplificada de la realidad, mediant= e el uso de funciones que describen su comportamiento, o de ecuaciones que representan sus relaciones.(Bocco, 2010).

En el área energética se puede evidenciar varios casos de estudio sob= re las proyecciones a mediano y largo plazo sobre la producción y la demanda de recursos energéticos, se va a citar el estudio realizado en Argentina sobre= el Informe de actualización de prospectiva energética del año 2016 desarrollada por el Área de prospectiva Energía Eléctrica de ese país, en el cual contiene análisis y reflexiones sobre la problemática de la prospectiva energética en argentina y algunas ideas de orientación para el trabajo a desarrollar por = los grupos de investigación para hacer pronósticos  en series de tiempo, se ha trabajado en colaboración con la Universi= dad Tecnológica Nacional – Facultad Regional General Pacheco y con destacados especialistas, con el propósito de asociar el trabajo de investigación con = las necesidades genuinas de la sociedad, entendiendo el concepto de planeamiento energético como un conjunto de actividades específicas orientadas no a pred= ecir el futuro sino a emitir hipótesis razonables fundadas en el análisis y el conocimiento, acciones capaces de trasformar y modificar el sector energéti= co.(Canabal & Marcel, 2009)

Otro caso de estudio = es el desarrollado en México el cual lleva por título Consumo de electricidad y crecimiento económico en México análisis de series de tiempo y prospectiva = en donde se considera el desarrollo de algoritmos de diagnóstico y predicción de activos en el sector energético, con la finalid= ad de conocer su estado real y, analizar la operatividad y vida útil de los mi= smos en el futuro.(Recalde, 2010)

Por serie de tiempo nos referimos a datos estadísticos que se recopilan, observ= an o registran en intervalos de tiempo regulares diario, semanal, semestral, anu= al, entre otros. Las componentes de la serie de tiempo son tres tipos básicos de variación, los cuales sobrepuestos o actuando en conjunto, contribuyen a los cambios observados en un período de tiempo y dan a la serie su aspecto cara= cterístico. Estas tres componentes son: Tendencia, estacionalidad, y variación irregula= r.(Peña, 2010)

 =

En ambos casos se realizan análisis de pronóstico a futuro, Ahora bien, qué se entiende por pronóstico y cuál es su diferenciación con proyección y perspectivas, térmi= nos que se confunde frecuentemente. Por pronóstico se entiende una afirmación s= obre el futuro, la cual informa que, bajo determinadas condiciones, en un moment= o y lugar determinados sucederá un acontecimiento o acontecimientos con una probabilidad muy próxima a la seguridad. Por lo que todo pronóstico signifi= ca una afirmación basada en una teoría perfecta, según la moderna lógica científica. En la práctica muy raras veces puede establecerse un pronóstico= en el sentido exacto del término, ya que las teorías ni son perfectas ni lo suficientemente amplias para que puedan abarcar todos los factores endógeno= s y exógenos. Por consiguiente, en la práctica, no se trata de definir con el t= érmino pronóstico ninguna predicción cuya certeza esté vinculada al máximo grado de probabilidad o cuyas hipótesis no tengan contenido informativo o sean meras tautologías. En la práctica, sin embargo, sería más adecuado en la mayoría = de los casos hablar de proyección y no de pronóstico. Por proyección se entien= de una afirmación sobre el futuro desarrollo condicionando a determinadas prem= isas que sólo posee una probabilidad limitada. Por consiguiente, las predicciones son, hoy por hoy, proyecciones y no pronósticos, aunque si bien se utilizan ambos términos. Se puede distinguir las proyecciones de puntos y las de intervalos. El término perspectivas se utiliza más en casos de previsiones a largo plazo, basándose en magnitudes futuras y no en meras extrapolaciones tendenciales. (Martínez et al., 2012)

Marco Metodológico = ;

En el presente trabajo se va = a utilizar un modelo matemático para obtener una proyección o estimación a futuro de la energía primaria en Ecuador, en base a lo mencionado se considera como punt= o de partida el balance energético nacional del Ecuador año 2016, el cual cuenta= con datos históricos de la producción primaria de energía, los mismos que son la base para poder hacer la predicción en el futuro, en el modelo se han considerado dos parámetros como son la tendencia y la estacionalidad, para = obtener una confiable proyección de la variable a analizar se utilizó el modelo de secuencia temporal.

Como primer paso se represent= an los datos años y producción primaria de energía mediante un gráfico de líne= as Gráfico 1, en el cual se describe la relación que ha sucedido en pasados añ= os con los datos, después de este paso se utiliza un modelo de extrapolación lineal para obtener una línea de tendencia de los datos esto para proyectar patrones establecidos del pasado hacia el futuro.

Una vez obtenida la línea de tendencia, esta servirá para proyectar o extrapolar la variable producción = de energía primaria, se necesita utilizar una serie de tiempo en años para predecir los valores con un modelo de extrapolación lineal.

A continuación, para que el modelo brinde un nivel de confianza y se pueda aceptar su predicción se va ajustar el modelo a partir de dos componentes tendencia y estacionalidad se= analizan los datos históricos a ver si responden a un modelo aditivo o un modelo multiplicativo para esto se calcula la serie de diferencias y de cocientes consecutivos con  estos dos conjunt= os de datos se procede a encontrar su desviación estándar y la media, la relación entre estas dos medidas estadísticas permiten encontrar el coeficiente de variación (CV), siendo el discrimínate para determinar a qué modelo obedecen los datos de producción de energía primaria, como el resultado de CV es men= or en la serie de cocientes consecutivos se establece que el modelo multiplica= tivo es el idóneo para ser utilizado.

Modelo multiplicativo:         Ecuación 1

Donde= :

=

=

=

De la ecuación 1 se despeja el producto estacionalidad y ruido obteniendo:

                            Ecuación 2

Como se puede apreciar la estacionalidad se encuentra interferida por el ruido para aislar y disipar = la variable ruido y obtener un modelo óptimo, se utilizó las medias móviles de orden tres, para hallar un índice de estacionalidad con el menor ruido posi= ble se dividió la estacionalidad con ruido por las medias móviles y se multipli= co por cien.

                  Ecuación 3<= /p>

Donde= :

=

=

=

Se prosigue con la sumatoria = de  este v= alor tiene que ser igual a 1200 puesto que tenemos 12 datos originales y estamos utilizando un índice de estacionalidad, como el resultado excede al esperad= o se lo corrigió mediante la siguiente razón:

      Ecuación 4

Finalmente se hace uso del mo= delo matemático multiplicativo para la estimación o predicción de la energía primaria a partir de las componentes de tendencia y estacionalidad:

                        Ecuación 5= =

Donde= :

=

=

Estos valores estimados se los calcula para 12 años que es considerado como plazo de tiempo medio, como se poseen datos originales del año 2004 al 2015 se extrapola el mismo número de datos originales empleando la ecuación 5, mediante este procedimiento que s= e obtienen valores futuros de la producción de energía primaria en Ecuador hasta el año 2027.

 

 

 

Análisis de los Resultados.

Tabla= 1. Producción de energía primaria por años en Ecuador.=

Año=

Pro= ducción Energía Primaria en kBEP (Kilo barriles equivalentes de petróleo)

2004

207.509

2005

214.974

2006

216.811

2007

208.488

2008

207.577

2009

198.677

2010

197.970

2011

205.250

2012

208.894

2013

216.074

2014

229.587

2015

225.021

Fuente: Balance energético nacional del Ecuador año 2016= .

=  

Gráfi= co 1. Producción de energía primaria por años en Ecuador y su línea de tendencia.=

Fuente: Elaboración propia tomado datos= del balance energético nacional del Ecuador año 2016.

Con l= os datos de la Tabla 1 se aplica un modelo de extrapolación lineal para obtener una línea de tendencia:          Ecuación 6

Donde= :

=

=

=  

Tabla= 2. Ten= dencia de la producción de energía primaria por años en Ecuador.=

Año

 

Tiempo

Tendencia

2004

 

01

205.3756

2005

 

02

206.4712

2006

 

03

207.5668

2007

 

04

208.6624

2008

 

05

209.7580

2009

 

06

210.8536

2010

 

07

211.9492

2011

 

08

213.0448

2012

 

09

214.1404

2013

 

10

215.2360

2014

 

11

216.3316

2015

 

12

217.4272

Fuente= : Elaboración propia.

El an= álisis de datos históricos mediante la serie de diferencias y de cocientes consecutivos nos arroga los siguientes resultados.=

Tabla= 3. Serie= de diferencias y de cocientes consecutivos.

Año

Producción Energía Primaria kBEP

Serie diferencias consecutivas<= /o:p>

Serie cocientes consecutivos

2004

207.509 7.465

1.03597

2005

214.974

1.837

1.00855

2006

216.811

-8.323

0.96161

2007

208.488

-0.911

0.99563

2008

207.577

-8.900

0.95712

2009

198.677

-0.707

0.99644

2010

197.970

7.280

1.03677

2011

205.250

3.644

1.01775

2012

208.894

7.180

1.03437

2013

216.074

13.513

1.06254

2014

229.587

-4.566

0.98011

2015

225.021

 

 

 

Media

1.59200

1.00790

Desviación estándar sd

6.75757

0.03188

Coeficiente de variación CV

4.24471

0.03163

Fuente= : Balance energético nacional del Ecuador año 2016.

El coeficiente de variación (= CV), determina a qué modelo obedecen los datos de producción de energía primaria= :

como el resultado de CV es me= nor en la serie de cocientes consecutivos se establece que el modelo multiplica= tivo es el idóneo para ser utilizado.

Posteriormente en la Tabla 4 = se presentan valores de estacionalidad con ruido o fluctuaciones. <= /span>

Tabla= 4. Estac= ionalidad con ruido.

Año

Producción Energía Primaria kBEP

Tendencia

Estacionalidad con Ruido<= /span>

2004

207.509

205.3756

1.010388

2005

214.974

206.4712

1.041182

2006

216.811

207.5668

1.044536

2007

208.488

208.6624

0.999164

2008

207.577

209.7580

0.989602

2009

198.677

210.8536

0.942251

2010

197.970

211.9492

0.934045

2011

205.250

213.0448

0.963412

2012

208.894

214.1404

0.975500

2013

216.074

215.2360

1.003893

2014

229.587

216.3316

1.061274

2015

225.021

217.4272

1.034926

Fuente= : Balance energético nacional del Ecuador año 2016.

Para ajustar o modelizar la Estacionalidad y disipar el ruido se calcula el Índi= ce de estacionalidad corregido cuyas soluciones se indican en la siguiente tab= la:

Tabla= 5. Índic= e de estacionalidad corregido.

Año

Estacionalidad con Ruido<= /span>

Medias Móviles de grado 3

Índice de estacionalidad

Índice de estacionalidad corregido

2004

1.010388

 

99.929478

99.340571

2005

1.041182

1.032035

100.886250

100.291704

2006

1.044536

1.028294

101.579520

100.980888

2007

0.999164

1.011101

98.819441

98.237075

2008

0.989602

0.977006

101.289296

100.692374

2009

0.942251

0.955299

98.634110

98.052836

2010

0.934045

0.946569

98.676830

98.095304

2011

0.963412

0.957652

100.601472

100.008604

2012

0.975500

0.980935

99.445923

98.859865

2013

1.003893

1.013556

99.046692

98.462987

2014

1.061274

1.033364

102.700821

102.095581

2015

1.034926

 

105.503970

104.882211

Sumatoria

1207.1138

1200

Fuente= : Elaboración propia.=

Tabla= 6. Estimación de la producción de la energía primaria en Ecuador.=

Año=

Tie= mpo

Ten= dencia

Índ= ice de estacionalidad corregido

Val= ores Estimados

<= span style=3D'font-size:11.0pt;line-height:115%;font-family:"Calibri",sans-ser= if; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:"Times New Roman= "; mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi; mso-ansi-language:ES;mso-fareast-language:ES;mso-bidi-language:AR-SA'>

2004

1

205.3756

99.340571

204.021

2005

2

206.4712<= o:p>

100.29170= 4

207.073

2006

3

207.5668

100.980888

209.603

2007

4

208.6624<= o:p>

98.237075=

204.984

2008

5

209.758

100.692374

211.210

2009

6

210.8536<= o:p>

98.052836=

206.748

2010

7

211.9492

98.095304

207.912

2011

8

213.0448<= o:p>

100.00860= 4

213.063

2012

9

214.1404

98.859865

211.699

2013

10

215.236

98.462987=

211.928

2014

11

216.3316

102.095581

220.865

2015

12

217.4272<= o:p>

104.88221= 1

228.042

2016

13

218.5228

99.340571

217.082

2017

14

219.6184<= o:p>

100.29170= 4

220.259

2018

15

220.714

100.980888

222.879

2019

16

221.8096<= o:p>

98.237075=

217.899

2020

17

222.9052

100.692374

224.449

2021

18

224.0008<= o:p>

98.052836=

219.639

2022

19

225.0964

98.095304

220.809

2023

20

226.192

100.00860= 4

226.211

2024

21

227.2876

98.859865

224.696

2025

22

228.3832<= o:p>

98.462987=

224.873

2026

23

229.4788

102.095581

234.288

2027

24

230.5744<= o:p>

104.88221= 1

241.832

Fuente= : Elaboración propia.

=  

&nbs= p;

&nbs= p;

&nbs= p;

Gráfi= co 2. Val= ores estimados de Producción de energía primaria en Ecuador.

Fuente= : Elaboración propia.<= /span>

Conclusiones.

·      =    Se ha estimado mediante un modelo matemático multiplicativo una serie de valor= es de la producción de energía primaria en Ecuador a mediano plazo en 12 años,= se puede predecir que para el año 2027 aumentara la producción de energía a 24= 1.832 kBEP (Kilo barriles equivalentes de petróleo),  siendo el valor más alto de producción que se tiene que generar para llegar a este requerimiento, esto anuncia que se debe desarrollar otras fue= ntes de energía posiblemente renovables para cubrir los kBEP que se necesitan a mediano plazo.  <= /p>

·      =    El modelo matemático para la naturaleza de los datos que se analizaron se comp= robó que cumple con un modelo multiplicativo y se lo considera como confiable de= bido a que relaciona la tendencia, estacionalidad y el ruido, que son los factor= es de mayor influencia en una serie temporal, aplicando un modelo de extrapola= ción lineal se estudió la tendencia llegando a determinar mediante los datos históricos que la  es igual a

·      =    Mediante medias móviles de grado tres se ha realizado el suavizado o ajuste o los parámetros de estacionalidad y ruido para que la estimación sea aceptada y = los valores calculados se los considere dentro del margen de tolerancia, es por eso que= se tiene en el modelo encontrado el índice de estacionalidad corregido =
 .

 

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PARA CITAR EL ARTÍCULO INDEXADO.

=  

Mazón Fierro, G., Calderón Limaico, P., Villa Uvidia, R., & Villamarín Padill= a, J. (2019). Modelo matemático para estimar la producción de la energía prima= ria en Ecuador. Ciencia Digital3(2.2), 118-131. https://doi.org/10.33262/cienciadigital.v3i2.2.464

 


 

 

 

 

El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revista Ciencia Digital.

 

El artículo qu= eda en propiedad de la revista y, por tanto, su publicación parcial y/o total en otro medio tiene que ser autorizado por el director de la Revista Ciencia Digital.

 

 

 



[1] Escue= la Superior Politécnica de Chimborazo, Facultad de Administración de Empresas. Riobamba, Ecuador. guido.mazon@espoch.edu.ec

[2] Escuela Superior Politécnica de Chimborazo, Facultad de Administración de Empresas. Riobamba, Ecuador. pablo.calderon@espoch.edu.ec<= /span>

[3] Escuela Superior Politécnica de Chimborazo, Facultad de Administraci= ón de Empresas. Riobamba, Ecuador. ruffo.villa@espoch.edu.ec

[4] Escuela Superior Politécnica de Chimborazo, Facultad de Administraci= ón de Empresas. Riobamba, Ecuador. jenny.villamarin@espoch.edu.ec

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