CAPACITY

1 Configuración y Carga de Datos

##### UNIVERSIDAD CENTRAL DEL ECUADOR #####
#### AUTOR: MARTIN SARMIENTO ####
### CARRERA: INGENIERÍA EN PETRÓLEOS #####


#### VARIABLE CAPACIDAD ####
## DATASET ##
# Cargar dataset
Datos <- read.csv("Dataset_Mundial_Final.csv", sep = ";", dec = ",", fileEncoding = "latin1")
# Estructura de los datos
str(Datos)

## 'data.frame':    58978 obs. of  29 variables:
##  $ ï..OBJECTID           : int  2 3 4 5 6 7 8 9 10 11 ...
##  $ code                  : chr  "00001-AFG-P" "00002-AFG-P" "00003-AFG-P" "00004-AFG-P" ...
##  $ plant_name            : chr  "Badghis Solar Power Plant" "Balkh solar farm" "Behsood solar farm" "Dab Pal 4 solar farm" ...
##  $ country               : chr  "Afghanistan" "Afghanistan" "Afghanistan" "Afghanistan" ...
##  $ operational_status    : chr  "cancelled - inferred 4 y" "cancelled - inferred 4 y" "cancelled - inferred 4 y" "shelved - inferred 2 y" ...
##  $ longitude             : num  62.9 67.1 70.4 66.2 65.7 ...
##  $ latitude              : num  35.1 36.7 34.4 33.8 31.7 ...
##  $ elevation             : int  918 359 629 2288 1060 1060 1392 398 410 1012 ...
##  $ area                  : num  6.74 10.72 487.73 111.8 1929.96 ...
##  $ size                  : chr  "Small" "Small" "Small" "Small" ...
##  $ slope                 : num  7.38 0.49 1.1 6.16 1.23 ...
##  $ slope_type            : chr  "Moderado" "Plano o casi plano" "Plano o casi plano" "Moderado" ...
##  $ curvature             : num  -0.024 0 0 0.045 -0.005 -0.005 -0.015 0 0 -0.009 ...
##  $ curvature_type        : chr  "Superficies cóncavas / Valles" "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies convexas / Crestas" ...
##  $ aspect                : num  96.8 358.5 36.2 305.8 248.4 ...
##  $ aspect_type           : chr  "East" "North" "Northeast" "Northwest" ...
##  $ dist_to_road          : num  7037.1 92.7 112.1 1705.3 115.8 ...
##  $ ambient_temperature   : num  14.4 17.88 21.32 8.86 19.64 ...
##  $ ghi                   : num  5.82 5.58 5.8 6.75 6.62 ...
##  $ humidity              : num  47.7 42.3 36.4 37.3 24.2 ...
##  $ wind_speed            : num  0.039 0.954 0.234 0.943 0.37 ...
##  $ wind_direction        : num  187.5 207.4 255.6 160.3 97.7 ...
##  $ dt_wind               : chr  "South" "Southwest" "West" "South" ...
##  $ solar_aptitude        : num  0.72 0.635 0.685 0.659 0.819 0.819 0.818 0.642 0.63 0.374 ...
##  $ solar_aptitude_rounded: int  7 6 7 7 8 8 8 6 6 4 ...
##  $ solar_aptittude_class : chr  "Alta" "Alta" "Alta" "Alta" ...
##  $ capacity              : num  32 40 60 3000 100 100 36 50 25 100 ...
##  $ optimal_tilt          : num  30 31 31.1 33 31 ...
##  $ pv_potential          : num  4.61 4.41 4.57 5.42 5.17 ...

# Cargamos las librerias
library(dplyr)

## 
## Adjuntando el paquete: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(gt)
library(e1071)

2 Cálculo de Intervalos y Frecuencias

# Extraer variable
Variable <- na.omit(Datos$capacity)
N <- length(Variable)

# CÁLCULO LÍMITES DECIMALES 
min_dec <- min(Variable)
max_dec <- max(Variable)
k_dec <- floor(1 + 3.322 * log10(N))
rango_dec <- max_dec - min_dec
amplitud_dec <- rango_dec / k_dec

# Cortes exactos 
cortes_dec <- seq(min_dec, max_dec, length.out = k_dec + 1)
cortes_dec[length(cortes_dec)] <- max_dec + 0.0001

# Frecuencias
inter_dec <- cut(Variable, breaks = cortes_dec, include.lowest = TRUE, right = FALSE)
ni_dec <- as.vector(table(inter_dec))

# CÁLCULOS MATEMÁTICOS 
hi_dec <- (ni_dec / N) * 100
Ni_asc_dec <- cumsum(ni_dec)
Hi_asc_dec <- cumsum(hi_dec)
Ni_desc_dec <- rev(cumsum(rev(ni_dec)))
Hi_desc_dec <- rev(cumsum(rev(hi_dec)))

# Dataframe Decimal
TDF_Decimal <- data.frame(
  Li = cortes_dec[1:k_dec],
  Ls = cortes_dec[2:(k_dec+1)],
  MC = (cortes_dec[1:k_dec] + cortes_dec[2:(k_dec+1)]) / 2,
  ni = ni_dec,
  hi = hi_dec,
  Ni_asc = Ni_asc_dec,
  Ni_desc = Ni_desc_dec,
  Hi_asc = Hi_asc_dec,
  Hi_desc = Hi_desc_dec)


# CÁLCULO LÍMITES ENTEROS 
min_int <- floor(min(Variable)) 
max_int <- ceiling(max(Variable))
k_int_sug <- floor(1 + 3.322 * log10(N))
Rango_int <- max_int - min_int
Amplitud_raw <- Rango_int / k_int_sug

Amplitud_int <- ceiling(Amplitud_raw / 10) * 10
if(Amplitud_int == 0) Amplitud_int <- 10

min_int <- 0

cortes_int <- seq(from = min_int, by = Amplitud_int, length.out = k_int_sug + 100) # 
cortes_int <- cortes_int[cortes_int <= (max(Variable) + Amplitud_int)]

if(max(cortes_int) < max(Variable)) {
  cortes_int <- c(cortes_int, max(cortes_int) + Amplitud_int)
}

K_real <- length(cortes_int) - 1
lim_inf_int <- cortes_int[1:K_real]
lim_sup_int <- cortes_int[2:(K_real+1)]

# Frecuencias
inter_int <- cut(Variable, breaks = cortes_int, include.lowest = TRUE, right = FALSE)
ni_int <- as.vector(table(inter_int))

# CÁLCULOS MATEMÁTICOS
hi_int <- (ni_int / N) * 100
Ni_asc_int <- cumsum(ni_int)
Hi_asc_int <- cumsum(hi_int)
Ni_desc_int <- rev(cumsum(rev(ni_int)))
Hi_desc_int <- rev(cumsum(rev(hi_int)))

# Dataframe Entero
TDF_Enteros <- data.frame(
  Li = lim_inf_int,
  Ls = lim_sup_int,
  MC = (lim_inf_int + lim_sup_int) / 2,
  ni = ni_int,
  hi = hi_int,
  Ni_asc = Ni_asc_int,
  Ni_desc = Ni_desc_int,
  Hi_asc = Hi_asc_int,
  Hi_desc = Hi_desc_int)

3 Tabla de Distribución de Frecuencias

3.1 Tabla con Límites Decimales

# Crear Dataframe
TDF_Dec_Final <- data.frame(
  Li      = as.character(round(TDF_Decimal$Li, 2)),
  Ls      = as.character(round(TDF_Decimal$Ls, 2)),
  MC      = as.character(round(TDF_Decimal$MC, 2)),
  ni      = as.character(TDF_Decimal$ni),
  hi      = as.character(round(TDF_Decimal$hi, 2)),
  Ni_asc  = as.character(TDF_Decimal$Ni_asc),
  Ni_desc = as.character(TDF_Decimal$Ni_desc),
  Hi_asc  = as.character(round(TDF_Decimal$Hi_asc, 2)),
  Hi_desc = as.character(round(TDF_Decimal$Hi_desc, 2))
)

# Calcular Totales
totales_dec <- c("TOTAL", "-", "-", sum(TDF_Decimal$ni), round(sum(TDF_Decimal$hi), 2), "-", "-", "-", "-")
TDF_Dec_Final <- rbind(TDF_Dec_Final, totales_dec)

# Generar GT
TDF_Dec_Final %>%
  gt() %>%
  tab_header(title = md("**Tabla N°1 de Distribución de Frecuencias de Capacidad (MW)**")) %>%
  tab_source_note(source_note = "Autor: Martin Sarmiento") %>%
  cols_label(
    Li = "Lim. Inf", 
    Ls = "Lim. Sup", 
    MC = "Marca Clase",
    ni = "Frec. Abs (ni)", 
    hi = "Frec. Rel (%)",
    Ni_asc = "Ni (Asc)", 
    Ni_desc = "Ni (Desc)",
    Hi_asc = "Hi Asc (%)", 
    Hi_desc = "Hi Desc (%)"
  ) %>%
  cols_align(align = "center", columns = everything()) %>%
  tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")

Tabla N°1 de Distribución de Frecuencias de Capacidad (MW)
Lim. Inf	Lim. Sup	Marca Clase	Frec. Abs (ni)	Frec. Rel (%)	Ni (Asc)	Ni (Desc)	Hi Asc (%)	Hi Desc (%)
1	1563.44	782.22	58881	99.84	58881	58978	99.84	100
1563.44	3125.88	2344.66	66	0.11	58947	97	99.95	0.16
3125.88	4688.31	3907.09	11	0.02	58958	31	99.97	0.05
4688.31	6250.75	5469.53	5	0.01	58963	20	99.97	0.03
6250.75	7813.19	7031.97	8	0.01	58971	15	99.99	0.03
7813.19	9375.62	8594.41	2	0	58973	7	99.99	0.01
9375.62	10938.06	10156.84	2	0	58975	5	99.99	0.01
10938.06	12500.5	11719.28	2	0	58977	3	100	0.01
12500.5	14062.94	13281.72	0	0	58977	1	100	0
14062.94	15625.38	14844.16	0	0	58977	1	100	0
15625.38	17187.81	16406.59	0	0	58977	1	100	0
17187.81	18750.25	17969.03	0	0	58977	1	100	0
18750.25	20312.69	19531.47	0	0	58977	1	100	0
20312.69	21875.12	21093.91	0	0	58977	1	100	0
21875.12	23437.56	22656.34	0	0	58977	1	100	0
23437.56	25000	24218.78	1	0	58978	1	100	0
TOTAL	-	-	58978	100	-	-	-	-
Autor: Martin Sarmiento

3.2 Tabla con Límites Enteros

# Crear Dataframe
TDF_Int_Final <- data.frame(
  Li      = as.character(TDF_Enteros$Li),
  Ls      = as.character(TDF_Enteros$Ls),
  MC      = as.character(TDF_Enteros$MC),
  ni      = as.character(TDF_Enteros$ni),
  hi      = as.character(round(TDF_Enteros$hi, 2)),
  Ni_asc  = as.character(TDF_Enteros$Ni_asc),
  Ni_desc = as.character(TDF_Enteros$Ni_desc),
  Hi_asc  = as.character(round(TDF_Enteros$Hi_asc, 2)),
  Hi_desc = as.character(round(TDF_Enteros$Hi_desc, 2))
)

# Calcular Totales
totales_int <- c("TOTAL", "-", "-", sum(TDF_Enteros$ni), round(sum(TDF_Enteros$hi), 2), "-", "-", "-", "-")
TDF_Int_Final <- rbind(TDF_Int_Final, totales_int)

# Generar GT
TDF_Int_Final %>%
  gt() %>%
  tab_header(title = md("**Tabla N°2 de Distribución de Frecuencias de Capacidad (MW)**")) %>%
  tab_source_note(source_note = "Autor: Martin Sarmiento") %>%
  cols_label(
    Li = "Lim. Inf", 
    Ls = "Lim. Sup", 
    MC = "Marca Clase",
    ni = "Frec. Abs (ni)", 
    hi = "Frec. Rel (%)",
    Ni_asc = "Ni (Asc)", 
    Ni_desc = "Ni (Desc)",
    Hi_asc = "Hi Asc (%)", 
    Hi_desc = "Hi Desc (%)"
  ) %>%
  cols_align(align = "center", columns = everything()) %>%
  tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")

Tabla N°2 de Distribución de Frecuencias de Capacidad (MW)
Lim. Inf	Lim. Sup	Marca Clase	Frec. Abs (ni)	Frec. Rel (%)	Ni (Asc)	Ni (Desc)	Hi Asc (%)	Hi Desc (%)
0	1570	785	58881	99.84	58881	58978	99.84	100
1570	3140	2355	66	0.11	58947	97	99.95	0.16
3140	4710	3925	11	0.02	58958	31	99.97	0.05
4710	6280	5495	5	0.01	58963	20	99.97	0.03
6280	7850	7065	8	0.01	58971	15	99.99	0.03
7850	9420	8635	2	0	58973	7	99.99	0.01
9420	10990	10205	2	0	58975	5	99.99	0.01
10990	12560	11775	2	0	58977	3	100	0.01
12560	14130	13345	0	0	58977	1	100	0
14130	15700	14915	0	0	58977	1	100	0
15700	17270	16485	0	0	58977	1	100	0
17270	18840	18055	0	0	58977	1	100	0
18840	20410	19625	0	0	58977	1	100	0
20410	21980	21195	0	0	58977	1	100	0
21980	23550	22765	0	0	58977	1	100	0
23550	25120	24335	1	0	58978	1	100	0
TOTAL	-	-	58978	100	-	-	-	-
Autor: Martin Sarmiento

4 Análisis Gráfico

4.1 Histogramas de Cantidad

par(mar = c(8, 7, 5, 2)) 
barplot(TDF_Enteros$ni, 
        names.arg = TDF_Enteros$MC,
        main = "",
        xlab = "", 
        ylab = "",
        col = "#EED5D2",
        ylim = c(0, max(TDF_Enteros$ni) * 1.2),
        space = 0, 
        las = 2, 
        cex.names = 0.7)
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
mtext("Capacidad (MW)", side = 1, line = 4)

mtext("Gráfica N°1: Distribución de Cantidad de Plantas Solares por Capacidad", 
      side = 3, 
      line = 2, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

par(mar = c(8, 7, 5, 2))
barplot(TDF_Enteros$ni, 
        main="",
        xlab = "",
        ylab = "",
        names.arg = TDF_Enteros$MC,
        col = "#EED5D2",
        space = 0,
        cex.names = 0.7,
        las = 2,
        ylim = c(0, 58978)) 
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
mtext("Capacidad (MW)", side = 1, line = 4)

mtext("Gráfica N°2: Distribución de Cantidad de Plantas Solares por Capacidad", 
      side = 3, 
      line = 2, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

4.2 Histogramas Porcentuales

par(mar = c(8, 5, 5, 2))
bp3 <- barplot(TDF_Enteros$hi, 
        main = "", 
        xlab = "", 
        ylab = "Porcentaje (%)", 
        col = "#EED5D2", 
        space = 0, 
        names.arg = TDF_Enteros$MC, 
        cex.names = 0.7, 
        las = 2, 
        ylim = c(0, max(TDF_Enteros$hi) * 1.2))
mtext("Capacidad (MW)", side = 1, line = 4)

mtext("Gráfica N°3: Distribución Porcentual de las Plantas Solares por Capacidad", 
      side = 3, 
      line = 2, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

text(x = bp3, 
     y = TDF_Enteros$hi, 
     labels = paste0(round(TDF_Enteros$hi, 2), "%"), 
     pos = 3, cex = 0.6, col = "black")

par(mar = c(8, 5, 5, 2))
bp4 <- barplot(TDF_Enteros$hi, 
        main = "", 
        xlab = "", 
        ylab = "Porcentaje (%)", 
        col = "#EED5D2", 
        space = 0, 
        names.arg = TDF_Enteros$MC, 
        las = 2, 
        cex.names = 0.7, 
        ylim = c(0, 110)) 
mtext("Capacidad (MW)", side = 1, line = 4)

mtext("Gráfica N°4: Distribución Porcentual de las Plantas Solares por Capacidad", 
      side = 3, 
      line = 2, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

text(x = bp4, 
     y = TDF_Enteros$hi, 
     labels = paste0(round(TDF_Enteros$hi, 2), "%"), 
     pos = 3, cex = 0.6, col = "black")

4.3 Diagrama de Cajas (Boxplot)

par(mar = c(5, 5, 4, 2))
boxplot(Variable, 
        horizontal = TRUE,
        col = "#EED5D2",
        xlab = "Capacidad (MW)",
        cex.main = 0.9,
        main = "Gráfica N°5: Distribución de la Capacidad en las Plantas Solares")

4.4 Ojivas

par(mar = c(5, 5, 7, 10), xpd = TRUE)

# Coordenadas
x_asc <- TDF_Enteros$Ls
x_desc <- TDF_Enteros$Li
y_asc <- TDF_Enteros$Ni_asc
y_desc <- TDF_Enteros$Ni_desc

# 1. Dibujar la Ascendente 
plot(x_asc, y_asc,
     type = "b", 
     main = "",
     xlab = "Capacidad (MW)",
     ylab = "Frecuencia acumulada",
     col = "black",
     pch = 19, 
     xlim = c(min(TDF_Enteros$Li), max(x_asc)), 
     ylim = c(0, sum(TDF_Enteros$ni)),
     bty = "l"
)

# 2. Agregar la Descendente 
lines(x_desc, y_desc, col = "#CDB7B5", type = "b", pch = 19)

grid()
mtext("Gráfica N°6: Ojivas Ascendentes y Descendentes de la\nDistribución de la Capacidad en las Plantas Solares", 
      side = 3, 
      line = 3, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

legend("right", 
       legend = c("Ascendente", "Descendente"), 
       col = c("black", "#CDB7B5"), 
       lty = 1, 
       pch = 1, 
       cex = 0.6, 
       inset = c(0.05, 0.05),
       bty = "n")

5 Indicadores Estadísticos

## INDICADORES DE TENDENCIA CENTRAL
# Media aritmética
media <- round(mean(Variable), 2)

# Mediana
mediana <- round(median(Variable), 2)

# Moda
max_frecuencia <- max(TDF_Enteros$ni)
moda_vals <- TDF_Enteros$MC[TDF_Enteros$ni == max_frecuencia]
moda_txt <- paste(round(moda_vals, 2), collapse = ", ")

## INDICADORES DE DISPERSIÓN
# Varianza
varianza <- var(Variable)

# Desviación Estándar
sd_val <- sd(Variable)

# Coeficiente de Variación
cv <- round((sd_val / abs(media)) * 100, 2)

## INDICADORES DE FORMA
# Coeficiente de Asimetría
asimetria <- skewness(Variable, type = 2)

# Curtosis
curtosis <- kurtosis(Variable)

# Outliers
Q1 <- quantile(Variable, 0.25)
Q3 <- quantile(Variable, 0.75)
IQR_val <- Q3 - Q1
lim_inf <- Q1 - 1.5 * IQR_val
lim_sup <- Q3 + 1.5 * IQR_val

outliers_data <- Variable[Variable < lim_inf | Variable > lim_sup]
num_outliers <- length(outliers_data)

if(num_outliers > 0){
  rango_outliers <- paste0(num_outliers, " [", round(min(outliers_data), 2), "; ", round(max(outliers_data), 2), "]")
} else {
  rango_outliers <- "0 [Sin Outliers]"
}

tabla_indicadores <- data.frame(
 "Variable" = c("Capacidad (MW)"),
 "Rango_MinMax" = paste0("[", round(min(Variable), 2), "; ", round(max(Variable), 2), "]"),
 "X" = c(media),
 "Me" = c(mediana),
 "Mo" = c(moda_txt),
 "V" = c(varianza),
 "Sd" = c(sd_val),
 "Cv" = c(cv),
 "As" = c(asimetria),
 "K" = c(curtosis),
 "Outliers" = rango_outliers)

# Generar Tabla GT
tabla_conclusiones_gt <- tabla_indicadores %>%
 gt() %>%
 tab_header(title = md("**Tabla N°3 de Conclusiones de Capacidad de las Plantas Solares**")) %>%
 tab_source_note(source_note = "Autor: Martin Sarmiento") %>%
 cols_label(
  Variable = "Variable",
  Rango_MinMax = "Rango",
  X = "Media (X)",
  Me = "Mediana (Me)",
 Mo = "Moda (Mo)",
  V = "Varianza (V)",
  Sd = "Desv. Est. (Sd)",
  Cv = "C.V. (%)",
  As = "Asimetría (As)",
  K = "Curtosis (K)",
  Outliers = "Outliers [Intervalo]"
 ) %>%
 tab_options(
  heading.title.font.size = px(16),
  column_labels.background.color = "#F0F0F0"
 )

tabla_conclusiones_gt

Tabla N°3 de Conclusiones de Capacidad de las Plantas Solares
Variable	Rango	Media (X)	Mediana (Me)	Moda (Mo)	Varianza (V)	Desv. Est. (Sd)	C.V. (%)	Asimetría (As)	Curtosis (K)	Outliers [Intervalo]
Capacidad (MW)	[1; 25000]	39.17	4.6	785	46202.11	214.9468	548.75	46.58015	3867.768	8383 [57.5; 25000]
Autor: Martin Sarmiento

6 Conclusiones

La variable “Capacidad” fluctúa entre 1 y 25000 MW y sus valores se encuentran alrededor de 39.17 MW, con una desviación estándar de 214.9468, siendo una variable muy heterogénea, cuyos valores se concentran en la parte media baja de la variable con la agregación de valores atípicos de 8383 outliers; por todo lo anterior, el comportamiento de la variable es muy perjudicial.