ELEVATION

1 Configuración y Carga de Datos

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


#### VARIABLE ELEVACION ####
## DATASET ##
setwd("~/R/ELEVATION")
# Cargar dataset
Datos <- read.csv("Data_Mundial_Final.csv", sep = ";", dec = ",", fileEncoding = "latin1")
# Estructura de los datos
str(Datos)

## 'data.frame':    58771 obs. of  29 variables:
##  $ OBJECTID              : int  127 129 131 132 133 137 138 139 140 145 ...
##  $ code                  : chr  "00127-ARG-P" "00129-ARG-G" "00131-ARG-P" "00132-ARG-P" ...
##  $ plant_name            : chr  "Aconcagua solar farm" "Altiplano 200 Solar Power Plant" "Anchoris solar farm" "Antu Newen solar farm" ...
##  $ country               : chr  "Argentina" "Argentina" "Argentina" "Argentina" ...
##  $ operational_status    : chr  "announced" "operating" "construction" "cancelled - inferred 4 y" ...
##  $ longitude             : num  -68.9 -66.9 -68.9 -70.3 -66.8 ...
##  $ latitude              : num  -33 -24.1 -33.3 -37.4 -28.6 ...
##  $ elevation             : int  929 4000 937 865 858 570 1612 665 3989 2640 ...
##  $ area                  : num  250 4397290 645 241 30 ...
##  $ size                  : chr  "Small" "Big" "Small" "Small" ...
##  $ slope                 : num  0.574 1.603 0.903 1.791 1.872 ...
##  $ slope_type            : chr  "Plano o casi plano" "Plano o casi plano" "Plano o casi plano" "Plano o casi plano" ...
##  $ curvature             : num  0.000795 -0.002781 0.002781 -0.002384 -0.009137 ...
##  $ curvature_type        : chr  "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies planas o intermedias" ...
##  $ aspect                : num  55.1 188.7 108.4 239.3 56.2 ...
##  $ aspect_type           : chr  "Northeast" "South" "East" "Southwest" ...
##  $ dist_to_road          : num  127 56015 336 34 314 ...
##  $ ambient_temperature   : num  12.6 6.8 13.1 11.4 18.8 ...
##  $ ghi                   : num  6.11 8.01 6.12 6.22 6.74 ...
##  $ humidity              : num  53.7 53.7 53.7 53.7 51.5 ...
##  $ wind_speed            : num  3.78 7.02 3.87 6.56 7.19 ...
##  $ wind_direction        : num  55.1 55.1 55.1 55.1 114.8 ...
##  $ dt_wind               : chr  "Northeast" "Northeast" "Northeast" "Northeast" ...
##  $ solar_aptitude        : num  0.746 0.8 0.595 0.657 0.743 ...
##  $ solar_aptitude_rounded: int  7 8 6 7 7 7 8 7 8 6 ...
##  $ solar_aptittude_class : chr  "Alta" "Alta" "Media" "Alta" ...
##  $ capacity              : num  25 101 180 20 50.4 ...
##  $ optimal_tilt          : num  31 26 31 33 30 31 29 31 27 32 ...
##  $ pv_potential          : num  4.98 6.39 4.97 5 5.37 ...

# 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$elevation)
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 <- 10
min_int <- floor(min(Variable) / BASE) * BASE
max_int <- ceiling(max(Variable) / BASE) * BASE
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

cortes_int <- seq(from = min_int, by = Amplitud_int, length.out = k_int_sug + 2)
cortes_int <- cortes_int[cortes_int <= (max_int + Amplitud_int)]

while(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 Elevación (m.s.n.m.) de las Plantas Solares**")) %>%
 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 Elevación (m.s.n.m.) de las Plantas Solares
Lim. Inf	Lim. Sup	Marca Clase	Frec. Abs (ni)	Frec. Rel (%)	Ni (Asc)	Ni (Desc)	Hi Asc (%)	Hi Desc (%)
-378	-0.88	-189.44	255	0.43	255	58771	0.43	100
-0.88	376.25	187.69	41914	71.32	42169	58516	71.75	99.57
376.25	753.38	564.81	8716	14.83	50885	16602	86.58	28.25
753.38	1130.5	941.94	3216	5.47	54101	7886	92.05	13.42
1130.5	1507.62	1319.06	2245	3.82	56346	4670	95.87	7.95
1507.62	1884.75	1696.19	1095	1.86	57441	2425	97.74	4.13
1884.75	2261.88	2073.31	461	0.78	57902	1330	98.52	2.26
2261.88	2639	2450.44	270	0.46	58172	869	98.98	1.48
2639	3016.12	2827.56	269	0.46	58441	599	99.44	1.02
3016.12	3393.25	3204.69	124	0.21	58565	330	99.65	0.56
3393.25	3770.38	3581.81	72	0.12	58637	206	99.77	0.35
3770.38	4147.5	3958.94	59	0.1	58696	134	99.87	0.23
4147.5	4524.62	4336.06	39	0.07	58735	75	99.94	0.13
4524.62	4901.75	4713.19	25	0.04	58760	36	99.98	0.06
4901.75	5278.88	5090.31	10	0.02	58770	11	100	0.02
5278.88	5656	5467.44	1	0	58771	1	100	0
TOTAL	-	-	58771	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 Elevación (m.s.n.m.) de las Plantas Solares**")) %>%
 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 Elevación (m.s.n.m.) de las Plantas Solares
Lim. Inf	Lim. Sup	Marca Clase	Frec. Abs (ni)	Frec. Rel (%)	Ni (Asc)	Ni (Desc)	Hi Asc (%)	Hi Desc (%)
-380	0	-190	255	0.43	255	58771	0.43	100
0	380	190	42033	71.52	42288	58516	71.95	99.57
380	760	570	8676	14.76	50964	16483	86.72	28.05
760	1140	950	3185	5.42	54149	7807	92.14	13.28
1140	1520	1330	2241	3.81	56390	4622	95.95	7.86
1520	1900	1710	1076	1.83	57466	2381	97.78	4.05
1900	2280	2090	456	0.78	57922	1305	98.56	2.22
2280	2660	2470	256	0.44	58178	849	98.99	1.44
2660	3040	2850	287	0.49	58465	593	99.48	1.01
3040	3420	3230	103	0.18	58568	306	99.65	0.52
3420	3800	3610	70	0.12	58638	203	99.77	0.35
3800	4180	3990	62	0.11	58700	133	99.88	0.23
4180	4560	4370	37	0.06	58737	71	99.94	0.12
4560	4940	4750	25	0.04	58762	34	99.98	0.06
4940	5320	5130	8	0.01	58770	9	100	0.02
5320	5700	5510	1	0	58771	1	100	0
TOTAL	-	-	58771	100	-	-	-	-

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 = "#FFCC99",
        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("Elevación (m.s.n.m.)", side = 1, line = 4)

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

par(mar = c(8, 7, 4, 2))
barplot(TDF_Enteros$ni, 
        main="",
        xlab = "",
        ylab = "",
        names.arg = TDF_Enteros$MC,
        col = "#FFCC99",
        ylim = c(0, 58771),
        space = 0,
        cex.names = 0.7,
        las = 2) 
mtext("Cantidad", side = 2, line = 4.5, cex = 1, font = 1)
mtext("Elevación (m.s.n.m.)", side = 1, line = 4)

mtext("Gráfica N°2: Distribución de Cantidad de Plantas Solares por Elevación", 
      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$hi, 
        main = "",
        xlab = "",
        ylab = "Porcentaje (%)",
        col = "#FFCC99",
        space = 0,
        names.arg = TDF_Enteros$MC,
        cex.names = 0.7,
        las = 2,
        ylim = c(0, max(TDF_Enteros$hi) * 1.2))
mtext("Elevación (m.s.n.m.)", side = 1, line = 4)

mtext("Gráfica N°3: Distribución Porcentual de las Plantas Solares por Elevación", 
      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$hi, 
        main = "",
        xlab = "",
        ylab = "Porcentaje (%)",
        col = "#FFCC99",
        space = 0,
        names.arg = TDF_Enteros$MC,
        las = 2,
        cex.names = 0.7,
        ylim = c(0, 100))
mtext("Elevación (m.s.n.m.)", side = 1, line = 4)

mtext("Gráfica N°4: Distribución Porcentual de las Plantas Solares por Elevación", 
      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 = "#FFCC99",
        xlab = "Elevación (m.s.n.m.)",
        cex.main = 0.9,
         main = "Gráfica N°5: Distribución de la Elevación 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 = "Elevación (m.s.n.m.)",
     ylab = "Frecuencia acumulada",
     col = "black",
     pch = 19, 
     xlim = c(min(x_desc), max(x_asc)), 
     ylim = c(0, sum(TDF_Enteros$ni)),
     bty = "l")

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

grid()
mtext("Gráfica N°6: Ojivas Ascendentes y Descendentes de la\nDistribución de la Elevación 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", "orange"), 
       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("Elevación (m.s.n.m.)"),
 "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 Elevación 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 Elevación 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]
Elevación (m.s.n.m.)	[-378; 5656]	354.18	156	190	278058.1	527.3121	148.88	3.176571	13.94829	5463 [1015; 5656]
Autor: Martin Sarmiento

6 Conclusiones

La variable “Elevación” fluctúa entre -378 y 5656 m.s.n.m. y sus valores se encuentran alrededor de 156 m.s.n.m., con una desviación estándar de 527.3121, siendo una variable muy heterogénea, cuyos valores se concentran en la parte media baja de la variable con la agregación de valores atípicos de 5463 outliers; por todo lo anterior, el comportamiento de la variable es regular.