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_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$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 0.06 0.03 76 0.13 76 58978 0.13 100
0.06 0.12 0.09 81 0.14 157 58902 0.27 99.87
0.12 0.18 0.15 182 0.31 339 58821 0.57 99.73
0.18 0.24 0.21 276 0.47 615 58639 1.04 99.43
0.24 0.29 0.26 352 0.6 967 58363 1.64 98.96
0.29 0.35 0.32 517 0.88 1484 58011 2.52 98.36
0.35 0.41 0.38 487 0.83 1971 57494 3.34 97.48
0.41 0.47 0.44 865 1.47 2836 57007 4.81 96.66
0.47 0.53 0.5 3502 5.94 6338 56142 10.75 95.19
0.53 0.59 0.56 5404 9.16 11742 52640 19.91 89.25
0.59 0.65 0.62 8835 14.98 20577 47236 34.89 80.09
0.65 0.71 0.68 10817 18.34 31394 38401 53.23 65.11
0.71 0.77 0.74 11337 19.22 42731 27584 72.45 46.77
0.77 0.82 0.79 8140 13.8 50871 16247 86.25 27.55
0.82 0.88 0.85 5630 9.55 56501 8107 95.8 13.75
0.88 0.94 0.91 2477 4.2 58978 2477 100 4.2
TOTAL - - 58978 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 0.05 0.03 71 0.12 71 58978 0.12 100
0.05 0.1 0.08 41 0.07 112 58907 0.19 99.88
0.1 0.15 0.12 147 0.25 259 58866 0.44 99.81
0.15 0.2 0.18 168 0.28 427 58719 0.72 99.56
0.2 0.25 0.22 267 0.45 694 58551 1.18 99.28
0.25 0.3 0.28 315 0.53 1009 58284 1.71 98.82
0.3 0.35 0.33 443 0.75 1452 57969 2.46 98.29
0.35 0.4 0.38 436 0.74 1888 57526 3.2 97.54
0.4 0.45 0.43 370 0.63 2258 57090 3.83 96.8
0.45 0.5 0.48 2370 4.02 4628 56720 7.85 96.17
0.5 0.55 0.52 3985 6.76 8613 54350 14.6 92.15
0.55 0.6 0.58 6337 10.74 14950 50365 25.35 85.4
0.6 0.65 0.62 5889 9.99 20839 44028 35.33 74.65
0.65 0.7 0.68 9612 16.3 30451 38139 51.63 64.67
0.7 0.75 0.73 9762 16.55 40213 28527 68.18 48.37
0.75 0.8 0.78 7606 12.9 47819 18765 81.08 31.82
0.8 0.85 0.83 5696 9.66 53515 11159 90.74 18.92
0.85 0.9 0.88 4154 7.04 57669 5463 97.78 9.26
0.9 0.95 0.92 1309 2.22 58978 1309 100 2.22
TOTAL - - 58978 100 - - - -

4 Análisis Gráfico

4.1 Histogramas de Cantidad

par(mar = c(8, 7, 5, 2)) 
barplot(TDF_Enteros$ni, 
        names.arg = round(TDF_Enteros$MC, 2), 
        main = "",
        xlab = "", 
        ylab = "",
        col = "#FFA07A",
        space = 0, 
        las = 2, 
        cex.names = 0.7,
        ylim = c(0, max(TDF_Enteros$ni) * 1.2))
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
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, 7, 5, 2))
barplot(TDF_Enteros$ni, 
        main="",
        xlab = "",
        ylab = "",
        names.arg = round(TDF_Enteros$MC, 2),
        col = "#FFA07A",
        space = 0,
        cex.names = 0.7,
        las = 2,
        ylim = c(0, 58978)) 
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
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, 2), "%"), 
     pos = 3, cex = 0.6, col = "black")

par(mar = c(8, 5, 5, 2))
bp4 <- barplot(TDF_Enteros$hi, 
        main = "",
        xlab = "",
        ylab = "Porcentaje (%)",
        col = "#FFA07A",
        space = 0,
        names.arg = round(TDF_Enteros$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, 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 = "#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("left", 
       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; 0.94] 0.68 0.69 0.73 0.01822424 0.1349972 19.85 -0.9593403 2.061074 1317 [0; 0.34]
Autor: Martin Sarmiento

6 Conclusiones

La variable “Aptitud Solar” fluctúa entre 0 y 0.94 y sus valores se encuentran alrededor de 0.69, con una desviación estándar de 0.01822424, siendo una variable muy homogénea, cuyos valores se concentran en la parte media alta de la variable con la agregación de valores atípicos de 1317 outliers; por todo lo anterior, el comportamiento de la variable es muy bueno.