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("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$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**")) %>%
  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 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	58978	0.43	100
-0.88	376.25	187.69	42089	71.36	42344	58723	71.8	99.57
376.25	753.38	564.81	8740	14.82	51084	16634	86.62	28.2
753.38	1130.5	941.94	3224	5.47	54308	7894	92.08	13.38
1130.5	1507.62	1319.06	2245	3.81	56553	4670	95.89	7.92
1507.62	1884.75	1696.19	1095	1.86	57648	2425	97.74	4.11
1884.75	2261.88	2073.31	461	0.78	58109	1330	98.53	2.26
2261.88	2639	2450.44	270	0.46	58379	869	98.98	1.47
2639	3016.12	2827.56	269	0.46	58648	599	99.44	1.02
3016.12	3393.25	3204.69	124	0.21	58772	330	99.65	0.56
3393.25	3770.38	3581.81	72	0.12	58844	206	99.77	0.35
3770.38	4147.5	3958.94	59	0.1	58903	134	99.87	0.23
4147.5	4524.62	4336.06	39	0.07	58942	75	99.94	0.13
4524.62	4901.75	4713.19	25	0.04	58967	36	99.98	0.06
4901.75	5278.88	5090.31	10	0.02	58977	11	100	0.02
5278.88	5656	5467.44	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 Elevación (m.s.n.m.) de las Plantas Solares**")) %>%
  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 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	58978	0.43	100
0	380	190	42208	71.57	42463	58723	72	99.57
380	760	570	8700	14.75	51163	16515	86.75	28
760	1140	950	3193	5.41	54356	7815	92.16	13.25
1140	1520	1330	2241	3.8	56597	4622	95.96	7.84
1520	1900	1710	1076	1.82	57673	2381	97.79	4.04
1900	2280	2090	456	0.77	58129	1305	98.56	2.21
2280	2660	2470	256	0.43	58385	849	98.99	1.44
2660	3040	2850	287	0.49	58672	593	99.48	1.01
3040	3420	3230	103	0.17	58775	306	99.66	0.52
3420	3800	3610	70	0.12	58845	203	99.77	0.34
3800	4180	3990	62	0.11	58907	133	99.88	0.23
4180	4560	4370	37	0.06	58944	71	99.94	0.12
4560	4940	4750	25	0.04	58969	34	99.98	0.06
4940	5320	5130	8	0.01	58977	9	100	0.02
5320	5700	5510	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 = "#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, 2), "%"), 
     pos = 3, cex = 0.6, col = "black")

par(mar = c(8, 5, 5, 2))
bp4 <- barplot(TDF_Enteros$hi, 
        main = "",
        xlab = "",
        ylab = "Porcentaje (%)",
        col = "#FFCC99",
        space = 0,
        names.arg = TDF_Enteros$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, 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 = "#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]	353.62	156	190	277349.6	526.6399	148.93	3.180583	13.98931	5459 [1017; 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 526.6399, siendo una variable muy heterogénea, cuyos valores se concentran en la parte media baja de la variable con la agregación de valores atípicos de 5459 outliers; por todo lo anterior, el comportamiento de la variable es muy irregular.