1 Configuración y Carga de Datos

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


#### VARIABLE TEMPERATURA AMBIENTE ####
## DATASET ##
setwd("~/R/AMBIENT_TEMPERATURE")
# 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  "Small" "Big" "Small" "Small" ...
##  $ 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                   : chr  "6,11" "8,012" "7,878" "6,119" ...
##  $ 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$ambient_temperature)
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
BASE <- 2
min_int <- floor(min(Variable) / BASE) * BASE
max_int <- ceiling(max(Variable) / BASE) * BASE

Amplitud_int <- 2

cortes_int <- seq(from = min_int, by = Amplitud_int, length.out = 20)
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 Temperatura Ambiente (°C)**")) %>%
  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 Temperatura Ambiente (°C)
Lim. Inf Lim. Sup Marca Clase Frec. Abs (ni) Frec. Rel (%) Ni (Asc) Ni (Desc) Hi Asc (%) Hi Desc (%)
3.7 5.74 4.72 5 0.1 5 5075 0.1 100
5.74 7.78 6.76 9 0.18 14 5070 0.28 99.9
7.78 9.82 8.8 5 0.1 19 5061 0.37 99.72
9.82 11.85 10.83 6 0.12 25 5056 0.49 99.63
11.85 13.89 12.87 52 1.02 77 5050 1.52 99.51
13.89 15.93 14.91 179 3.53 256 4998 5.04 98.48
15.93 17.97 16.95 142 2.8 398 4819 7.84 94.96
17.97 20.01 18.99 229 4.51 627 4677 12.35 92.16
20.01 22.05 21.03 297 5.85 924 4448 18.21 87.65
22.05 24.08 23.07 743 14.64 1667 4151 32.85 81.79
24.08 26.12 25.1 1307 25.75 2974 3408 58.6 67.15
26.12 28.16 27.14 1626 32.04 4600 2101 90.64 41.4
28.16 30.2 29.18 475 9.36 5075 475 100 9.36
TOTAL - - 5075 100 - - - -

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 Temperatura Ambiente (°C)**")) %>%
  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 Temperatura Ambiente (°C)
Lim. Inf Lim. Sup Marca Clase Frec. Abs (ni) Frec. Rel (%) Ni (Asc) Ni (Desc) Hi Asc (%) Hi Desc (%)
2 4 3 1 0.02 1 5075 0.02 100
4 6 5 4 0.08 5 5074 0.1 99.98
6 8 7 11 0.22 16 5070 0.32 99.9
8 10 9 3 0.06 19 5059 0.37 99.68
10 12 11 7 0.14 26 5056 0.51 99.63
12 14 13 57 1.12 83 5049 1.64 99.49
14 16 15 173 3.41 256 4992 5.04 98.36
16 18 17 142 2.8 398 4819 7.84 94.96
18 20 19 220 4.33 618 4677 12.18 92.16
20 22 21 298 5.87 916 4457 18.05 87.82
22 24 23 731 14.4 1647 4159 32.45 81.95
24 26 25 1249 24.61 2896 3428 57.06 67.55
26 28 27 1493 29.42 4389 2179 86.48 42.94
28 30 29 684 13.48 5073 686 99.96 13.52
30 32 31 2 0.04 5075 2 100 0.04
TOTAL - - 5075 100 - - - -

4 Análisis Gráfico

4.1 Histogramas de Cantidad

par(mar = c(8, 5, 5, 2)) 
barplot(TDF_Enteros$ni, 
        names.arg = TDF_Enteros$MC,
        main = "",
        xlab = "", 
        ylab = "Cantidad",
        col = "#EE5C42",
        space = 0, 
        las = 2, 
        cex.names = 0.7)
mtext("Temperatura (°C)", side = 1, line = 4)

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

par(mar = c(8, 5, 5, 2))
barplot(TDF_Enteros$ni, 
        main="",
        xlab = "",
        ylab = "Cantidad",
        names.arg = TDF_Enteros$MC,
        col = "#EE5C42",
        space = 0,
        cex.names = 0.7,
        las = 2,
        ylim = c(0, sum(TDF_Enteros$ni))) 
mtext("Temperatura (°C)", side = 1, line = 4)

mtext("Gráfica N°2: Distribución de Cantidad de Plantas Solares por Temperatura", 
      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$hi, 
        main = "", 
        xlab = "", 
        ylab = "Porcentaje (%)", 
        col = "#EE5C42", 
        space = 0, 
        names.arg = TDF_Enteros$MC, 
        cex.names = 0.7, 
        las = 2, 
        ylim = c(0, max(TDF_Enteros$hi) * 1.2))
mtext("Temperatura (°C)", side = 1, line = 4)

mtext("Gráfica N°3: Distribución Porcentual de las Plantas Solares por Temperatura", 
      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$hi, 
        main = "", 
        xlab = "", 
        ylab = "Porcentaje (%)", 
        col = "#EE5C42", 
        space = 0, 
        names.arg = TDF_Enteros$MC, 
        las = 2, 
        cex.names = 0.7, 
        ylim = c(0, 100)) 
mtext("Temperatura (°C)", side = 1, line = 4)

mtext("Gráfica N°4: Distribución Porcentual Global de las Plantas Solares por Temperatura", 
      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 = "#EE5C42",
        xlab = "Temperatura (°C)",
        cex.main = 0.9,
        main = "Gráfica N°5: Distribución de la Temperatura Ambiente en las Plantas Solares")

4.4 Ojivas

par(mar = c(5, 5, 4, 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 = "Temperatura (°C)",
     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 = "#8B3626", type = "b", pch = 19)

grid()
mtext("Gráfica N°6: Ojivas Ascendentes y Descendentes de la\nDistribución de la Temperatura 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", "#8B3626"), 
       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("Temperatura Ambiente (°C)"),
 "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 Temperatura Ambiente 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 Temperatura Ambiente 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]
Temperatura Ambiente (°C) [3.7; 30.2] 24.49 25.4 27 13.86032 3.722945 15.2 -1.53991 2.667926 333 [3.7; 17]
Autor: Martin Sarmiento

6 Conclusiones

La variable “Temperatura Ambiente” fluctúa entre 3.7 y 30.2 °C y sus valores se encuentran alrededor de 25.4 °C, con una desviación estándar de 3.722945, siendo una variable homogénea, cuyos valores se concentran en la parte media alta de la variable con la agregación de valores atípicos de 333 outliers; por todo lo anterior, el comportamiento de la variable es perjudicial.