1 Configuración y Carga de Datos

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


#### VARIABLE APTITUD SOLAR ####
## DATASET ##
setwd("~/R/SOLAR_APTITUDE")
# Cargar dataset
Datos <- read.csv("DataSet_prov.csv", sep = ";", dec = ",", fileEncoding = "latin1")
# Estructura de los datos
str(Datos)
## 'data.frame':    5075 obs. of  30 variables:
##  $ FID_                  : int  0 2 3 4 5 6 10 11 12 13 ...
##  $ OBJECTID              : int  127 129 130 131 132 133 137 138 139 140 ...
##  $ code                  : chr  "00127-ARG-P" "00129-ARG-G" "00130-ARG-P" "00131-ARG-P" ...
##  $ plant_name            : chr  "Aconcagua solar farm" "Altiplano 200 Solar Power Plant" "Altiplano 200 Solar Power Plant" "Anchoris solar farm" ...
##  $ country               : chr  "Argentina" "Argentina" "Argentina" "Argentina" ...
##  $ operational_status    : chr  "announced" "operating" "operating" "construction" ...
##  $ longitude             : num  -68.9 -66.9 -66.9 -68.9 -70.3 ...
##  $ latitude              : num  -33 -24.1 -24.1 -33.3 -37.4 ...
##  $ elevation             : int  929 4000 4000 937 865 858 570 1612 665 3989 ...
##  $ area                  : num  250 4397290 5774 645 241 ...
##  $ size                  : chr  "Pequeña" "Grande" "Pequeña" "Pequeña" ...
##  $ slope                 : num  0.574 1.603 6.243 0.903 1.791 ...
##  $ slope_type            : chr  "Plano o casi plano" "Plano o casi plano" "Moderado" "Plano o casi plano" ...
##  $ curvature             : num  0.000795 -0.002781 -0.043699 0.002781 -0.002384 ...
##  $ curvature_type        : chr  "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies cóncavas / Valles" "Superficies planas o intermedias" ...
##  $ aspect                : num  55.1 188.7 270.9 108.4 239.3 ...
##  $ aspect_type           : chr  "Northeast" "South" "West" "East" ...
##  $ dist_to_road          : num  127 56015 52697 336 34 ...
##  $ ambient_temperature   : num  12.6 6.8 6.8 13.1 11.4 ...
##  $ ghi                   : num  6.11 8.01 7.88 6.12 6.22 ...
##  $ humidity              : num  53.7 53.7 53.7 53.7 53.7 ...
##  $ wind_speed            : num  3.78 7.02 8.33 3.87 6.56 ...
##  $ wind_direction        : num  55.1 55.1 55.1 55.1 55.1 ...
##  $ dt_wind               : chr  "Northeast" "Northeast" "Northeast" "Northeast" ...
##  $ solar_aptitude        : num  0.746 0.8 0.727 0.595 0.657 ...
##  $ solar_aptitude_rounded: int  7 8 7 6 7 7 7 8 7 8 ...
##  $ solar_aptittude_class : chr  "Alta" "Alta" "Alta" "Media" ...
##  $ capacity              : num  25 101 107 180 20 ...
##  $ optimal_tilt          : int  31 26 26 31 33 30 31 29 31 27 ...
##  $ pv_potential          : num  4.98 6.39 6.39 4.97 5 ...
# 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$solar_aptitude)
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(Variable) - min(Variable)
amplitud_dec <- rango_dec / k_dec

# Cortes exactos
cortes_dec <- seq(min(Variable), max(Variable), length.out = k_dec + 1)
cortes_dec[length(cortes_dec)] <- max(Variable) + 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
Amplitud_int <- 0.05
min_int <- floor(min(Variable) / Amplitud_int) * Amplitud_int

cortes_int <- seq(from = min_int, by = Amplitud_int, length.out = 2)
while(max(cortes_int) < max(Variable)) {
  cortes_int <- seq(from = min_int, to = max(cortes_int) + Amplitud_int + 0.0001, by = 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 Aptitud Solar**")) %>%
  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 Aptitud Solar
Lim. Inf Lim. Sup Marca Clase Frec. Abs (ni) Frec. Rel (%) Ni (Asc) Ni (Desc) Hi Asc (%) Hi Desc (%)
0.47 0.51 0.49 1 0.02 1 5075 0.02 100
0.51 0.55 0.53 2 0.04 3 5074 0.06 99.98
0.55 0.58 0.57 92 1.81 95 5072 1.87 99.94
0.58 0.62 0.6 1801 35.49 1896 4980 37.36 98.13
0.62 0.66 0.64 41 0.81 1937 3179 38.17 62.64
0.66 0.7 0.68 811 15.98 2748 3138 54.15 61.83
0.7 0.73 0.71 62 1.22 2810 2327 55.37 45.85
0.73 0.77 0.75 1644 32.39 4454 2265 87.76 44.63
0.77 0.81 0.79 568 11.19 5022 621 98.96 12.24
0.81 0.84 0.82 5 0.1 5027 53 99.05 1.04
0.84 0.88 0.86 13 0.26 5040 48 99.31 0.95
0.88 0.92 0.9 17 0.33 5057 35 99.65 0.69
0.92 0.95 0.93 18 0.35 5075 18 100 0.35
TOTAL - - 5075 100 - - - -

3.2 Tabla con Límites Enteros

# Crear Dataframe
TDF_Int_Final <- data.frame(
  Li      = as.character(round(TDF_Enteros$Li, 2)),
  Ls      = as.character(round(TDF_Enteros$Ls, 2)),
  MC      = as.character(round(TDF_Enteros$MC, 2)),
  ni      = as.character(TDF_Enteros$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 Aptitud Solar**")) %>%
  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 Aptitud Solar
Lim. Inf Lim. Sup Marca Clase Frec. Abs (ni) Frec. Rel (%) Ni (Asc) Ni (Desc) Hi Asc (%) Hi Desc (%)
0.45 0.5 0.48 1 0.02 1 5075 0.02 100
0.5 0.55 0.52 2 0.04 3 5074 0.06 99.98
0.55 0.6 0.58 1891 37.26 1894 5072 37.32 99.94
0.6 0.65 0.62 21 0.41 1915 3181 37.73 62.68
0.65 0.7 0.68 838 16.51 2753 3160 54.25 62.27
0.7 0.75 0.72 1693 33.36 4446 2322 87.61 45.75
0.75 0.8 0.78 476 9.38 4922 629 96.99 12.39
0.8 0.85 0.83 105 2.07 5027 153 99.05 3.01
0.85 0.9 0.88 21 0.41 5048 48 99.47 0.95
0.9 0.95 0.92 26 0.51 5074 27 99.98 0.53
0.95 1 0.98 1 0.02 5075 1 100 0.02
TOTAL - - 5075 100 - - - -

4 Análisis Gráfico

4.1 Histogramas de Cantidad

par(mar = c(8, 5, 5, 2)) 
barplot(TDF_Enteros$ni, 
        names.arg = round(TDF_Enteros$MC, 3), 
        main = "",
        xlab = "", 
        ylab = "Cantidad",
        col = "#FFA07A",
        space = 0, 
        las = 2, 
        cex.names = 0.7,
        ylim = c(0, 2000))
mtext("Aptitud Solar", side = 1, line = 4)

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

par(mar = c(8, 5, 5, 2))
barplot(TDF_Enteros$ni, 
        main="",
        xlab = "",
        ylab = "Cantidad",
        names.arg = round(TDF_Enteros$MC, 3),
        col = "#FFA07A",
        space = 0,
        cex.names = 0.7,
        las = 2,
        ylim = c(0, sum(TDF_Enteros$ni))) 
mtext("Aptitud Solar", side = 1, line = 4)

mtext("Gráfica N°2: Distribución de Cantidad Global de Plantas Solares por Aptitud Solar", 
      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$hi, 
        main = "",
        xlab = "",
        ylab = "Porcentaje (%)",
        col = "#FFA07A",
        space = 0,
        names.arg = round(TDF_Enteros$MC, 2),
        cex.names = 0.7,
        las = 2,
        ylim = c(0, max(TDF_Enteros$hi) * 1.2))
mtext("Aptitud Solar", side = 1, line = 4)

mtext("Gráfica N°3: Distribución Porcentual de las Plantas Solares por Aptitud Solar", 
      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, 1), "%"), 
     pos = 3, cex = 0.6, col = "black")

par(mar = c(8, 5, 5, 2))
bp4 <- barplot(TDF_Enteros$hi, 
        main = "",
        xlab = "",
        ylab = "Porcentaje (%)",
        col = "#FFA07A",
        space = 0,
        names.arg = round(TDF_Enteros$MC, 2),
        las = 2,
        cex.names = 0.7,
        ylim = c(0, 100))
mtext("Aptitud Solar", side = 1, line = 4)

mtext("Gráfica N°4: Distribución Porcentual de las Plantas Solares por Aptitud Solar",
      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, 1), "%"), 
     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 = "#FFA07A",
        xlab = "Aptitud Solar",
        cex.main = 0.9,
        main = "Gráfica N°5: Distribución de la Aptitud Solar 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 = "Aptitud Solar",
     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 = "#D35400", type = "b", pch = 19)

grid()
mtext("Gráfica N°6: Ojivas Ascendentes y Descendentes de la\nDistribución de la Aptitud Solar 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", "#D35400"), 
       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("Aptitud Solar"),
 "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 Aptitud Solar 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 Aptitud Solar 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]
Aptitud Solar [0.47; 0.95] 0.68 0.67 0.58 0.006204596 0.07876926 11.58 0.1682415 -1.106004 0 [Sin Outliers]
Autor: Martin Sarmiento

6 Conclusiones

La variable “Aptitud Solar” fluctúa entre 0.47 y 0.8 y sus valores se encuentran alrededor de 0.67, con una desviación estándar de 0.07876926, siendo una variable muy homogénea, cuyos valores se concentran en la parte media baja de la variable con la agregación de no presencia de valores atípicos; por todo lo anterior, el comportamiento de la variable es muy bueno.