OPTIMAL_TILT
MARTIN SARMIENTO
2025-12-02
1 Configuración y Carga de Datos
##### UNIVERSIDAD CENTRAL DEL ECUADOR #####
#### AUTOR: MARTIN SARMIENTO ####
### CARRERA: INGENIERÍA EN PETRÓLEOS #####
#### VARIABLE INCLINACIÓN ÓPTIMA ####
## DATASET ##
setwd("~/R/OPTIMAL_TILT")
# 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 ...##
## 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, union2 Cálculo de Intervalos y Frecuencias
#Extraer variable
Variable <- na.omit(Datos$optimal_tilt)
N <- length(Variable)
# Cálculo Límites Decimales #
# Cálculos básicos
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
# Generamos los 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))
hi_dec <- (ni_dec/N)*100
# Cálculos de Frecuencias
sum_ni <- sum(ni_dec)
hi_dec <- (ni_dec / sum_ni) * 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)))
# Construcción del Dataframe Decimal
TDF_Decimal <- data.frame(
Li = round(cortes_dec[1:k_dec], 2),
Ls = round(cortes_dec[2:(k_dec+1)], 2),
MC = round((cortes_dec[1:k_dec] + cortes_dec[2:(k_dec+1)]) / 2, 2),
ni = ni_dec,
hi = round(hi_dec, 2),
Ni_asc = cumsum(ni_dec),
Ni_desc = rev(cumsum(rev(ni_dec))),
Hi_asc = cumsum(round(hi_dec, 2)),
Hi_desc = rev(cumsum(rev(round(hi_dec, 2)))))
# Cálculo Límites Enteros #
BASE <- 10
# Cálculos básicos
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
# Generar cortes enteros
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)]
# Asegurar cobertura del máximo
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 de Frecuencias
hi_int <- (ni_int / N) * 100
Ni_asc_int <- cumsum(ni_int)
Ni_desc_int <- rev(cumsum(rev(ni_int)))
Hi_asc_int <- cumsum(hi_int)
Hi_desc_int <- rev(cumsum(rev(hi_int)))
# Construcción del 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 = round(hi_int, 2),
Ni_asc = Ni_asc_int,
Ni_desc = Ni_desc_int,
Hi_asc = round(Hi_asc_int, 2),
Hi_desc = round(Hi_desc_int, 2))3 Tabla de Distribución de Frecuencias
3.1 Tabla con Límites Decimales
#### Crear de fila de totales ####
totales_dec <- c("TOTAL", "-", "-", sum(TDF_Decimal$ni), 100, "-", "-", "-", "-")
TDF_Dec_Final <- rbind(mutate(TDF_Decimal, across(everything(), as.character)), totales_dec)
# Generar GT Decimal
TDF_Dec_Final %>%
gt() %>%
tab_header(title = md("**Tabla N°1 de Distribución de Frecuencias de Inclinación Óptima (°) 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 (%)"
) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°1 de Distribución de Frecuencias de Inclinación Óptima (°) de las Plantas Solares | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| 1 | 4.23 | 2.62 | 63 | 1.24 | 63 | 5075 | 1.24 | 100 |
| 4.23 | 7.46 | 5.85 | 637 | 12.55 | 700 | 5012 | 13.79 | 98.76 |
| 7.46 | 10.69 | 9.08 | 962 | 18.96 | 1662 | 4375 | 32.75 | 86.21 |
| 10.69 | 13.92 | 12.31 | 498 | 9.81 | 2160 | 3413 | 42.56 | 67.25 |
| 13.92 | 17.15 | 15.54 | 589 | 11.61 | 2749 | 2915 | 54.17 | 57.44 |
| 17.15 | 20.38 | 18.77 | 651 | 12.83 | 3400 | 2326 | 67 | 45.83 |
| 20.38 | 23.62 | 22 | 904 | 17.81 | 4304 | 1675 | 84.81 | 33 |
| 23.62 | 26.85 | 25.23 | 452 | 8.91 | 4756 | 771 | 93.72 | 15.19 |
| 26.85 | 30.08 | 28.46 | 288 | 5.67 | 5044 | 319 | 99.39 | 6.28 |
| 30.08 | 33.31 | 31.69 | 29 | 0.57 | 5073 | 31 | 99.96 | 0.61 |
| 33.31 | 36.54 | 34.92 | 1 | 0.02 | 5074 | 2 | 99.98 | 0.04 |
| 36.54 | 39.77 | 38.15 | 0 | 0 | 5074 | 1 | 99.98 | 0.02 |
| 39.77 | 43 | 41.38 | 1 | 0.02 | 5075 | 1 | 100 | 0.02 |
| TOTAL | - | - | 5075 | 100 | - | - | - | - |
3.2 Tabla con Límites Enteros
#### Crear de fila de totales ####
totales_int <- c("TOTAL", "-", "-", sum(TDF_Enteros$ni), 100, "-", "-", "-", "-")
TDF_Int_Final <- rbind(mutate(TDF_Enteros, across(everything(), as.character)), totales_int)
# Generar GT Enteros
TDF_Int_Final %>%
gt() %>%
tab_header(
title = md("**Tabla N°2 de Distribución de Frecuencias de Inclinación Óptima (°) de las Plantas Solares**")) %>%
cols_label(
Li = "Lim. Inf",
Ls = "Lim. Sup",
MC = "Marca Clase",
ni = "Frec. Abs (ni)",
hi = "Frec. Rel (%)",
Ni_asc = "Ni (Asc)",
Ni_desc = "Ni (Desc)",
Hi_asc = "Hi Asc (%)",
Hi_desc = "Hi Desc (%)"
) %>%
fmt_number(columns = c(Li, Ls), decimals = 0) %>%
fmt_number(columns = c(hi, Hi_asc, Hi_desc), decimals = 2) %>%
tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")| Tabla N°2 de Distribución de Frecuencias de Inclinación Óptima (°) de las Plantas Solares | ||||||||
| Lim. Inf | Lim. Sup | Marca Clase | Frec. Abs (ni) | Frec. Rel (%) | Ni (Asc) | Ni (Desc) | Hi Asc (%) | Hi Desc (%) |
|---|---|---|---|---|---|---|---|---|
| 0 | 10 | 5 | 1545 | 30.44 | 1545 | 5075 | 30.44 | 100 |
| 10 | 20 | 15 | 1508 | 29.71 | 3053 | 3530 | 60.16 | 69.56 |
| 20 | 30 | 25 | 1957 | 38.56 | 5010 | 2022 | 98.72 | 39.84 |
| 30 | 40 | 35 | 64 | 1.26 | 5074 | 65 | 99.98 | 1.28 |
| 40 | 50 | 45 | 1 | 0.02 | 5075 | 1 | 100 | 0.02 |
| 50 | 60 | 55 | 0 | 0 | 5075 | 0 | 100 | 0 |
| TOTAL | - | - | 5075 | 100 | - | - | - | - |
4 Análisis Gráfico
4.1 Histogramas de Cantidad
par(mar = c(8, 5, 5, 2))
barplot(TDF_Enteros$ni,
names.arg = TDF_Enteros$MC,
main = "",
xlab = "",
ylab = "Cantidad",
col = "#C6E2FF",
space = 0,
las = 2,
cex.names = 0.7)
mtext("Inclinación Óptima (°)", side = 1, line = 4)
mtext("Gráfica N°1: Distribución de Cantidad de Plantas Solares por Inclinación Óptima",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
par(mar = c(8, 5, 4, 2))
barplot(TDF_Enteros$ni,
main="",
xlab = "",
ylab = "Cantidad",
names.arg = TDF_Enteros$MC,
col = "#C6E2FF",
space = 0,
cex.names = 0.7,
las = 2,
ylim = c(0, sum(TDF_Enteros$ni)))
mtext("Inclinación Óptima (°)", side = 1, line = 4)
mtext("Gráfica N°2: Distribución de Cantidad de Plantas Solares por Inclinación Óptima",
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$hi,
main = "",
xlab = "",
ylab = "Porcentaje (%)",
col = "#C6E2FF",
space = 0,
names.arg = TDF_Enteros$MC,
cex.names = 0.7,
las = 2,
ylim = c(0, max(TDF_Enteros$hi) * 1.2))
mtext("Inclinación Óptima (°)", side = 1, line = 4)
mtext("Gráfica N°3: Distribución Porcentual de las Plantas Solares por Inclinación Óptima",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
text(x = bp3,
y = TDF_Enteros$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 = "#C6E2FF",
space = 0,
names.arg = TDF_Enteros$MC,
las = 2,
cex.names = 0.7,
ylim = c(0, 100))
mtext("Inclinación Óptima(°)", side = 1, line = 4)
mtext("Gráfica N°4: Distribución Porcentual de las Plantas Solares por Inclinación",
side = 3,
line = 2,
adj = 0.5,
cex = 0.9,
font = 2)
text(x = bp4,
y = TDF_Enteros$hi,
labels = paste0(round(TDF_Enteros$hi, 1), "%"),
pos = 3, cex = 0.6, col = "black")
4.3 Diagrama de Cajas (Boxplot)
par(mar = c(5, 5, 4, 2))
boxplot(Variable,
horizontal = TRUE,
col = "#C6E2FF",
xlab = "Inclinación Óptima (°)",
cex.main = 0.9,
main = "Gráfica N°5: Distribución de la Inclinación Óptima en las Plantas Solares")
4.4 Ojivas
par(mar = c(5, 5, 7, 10), xpd = TRUE)
# Coordenadas
x_asc <- TDF_Enteros$Ls
x_desc <- TDF_Enteros$Li
y_asc <- TDF_Enteros$Ni_asc
y_desc <- TDF_Enteros$Ni_desc
# 1. Dibujar la Ascendente
plot(x_asc, y_asc,
type = "b",
main = "",
xlab = "Inclinación Óptima (°)",
ylab = "Frecuencia acumulada",
col = "black",
pch = 19,
xlim = c(min(TDF_Enteros$Li), max(x_asc)),
ylim = c(0, sum(TDF_Enteros$ni)),
bty = "l"
)
# 2. Agregar la Descendente
lines(x_desc, y_desc, col = "#9FB6CD", type = "b", pch = 19)
grid()
mtext("Gráfica N°6: Ojivas Ascendentes y Descendentes de la\nDistribución de la Inclinación Óptima en las Plantas Solares",
side = 3,
line = 3,
adj = 0.5,
cex = 0.9,
font = 2)
legend("left",
legend = c("Ascendente", "Descendente"),
col = c("black", "#9FB6CD"),
lty = 1,
pch = 1,
cex = 0.6,
inset = c(0.05, 0.05),
bty = "n")
5 Indicadores Estadísticos
## INDICADORES DE TENDENCIA CENTRAL
# Media aritmética
media <- round(mean(Variable), 2)
# Mediana
mediana <- round(median(Variable), 2)
# Moda
max_frecuencia <- max(TDF_Enteros$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("Inclinación Óptima (°)"),
"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 Inclinación Óptima 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 Inclinación Óptima 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] |
|---|---|---|---|---|---|---|---|---|---|---|
| Inclinación Óptima (°) | [1; 43] | 15.93 | 17 | 25 | 50.04666 | 7.074366 | 44.41 | 0.07502187 | -1.181107 | 1 [43; 43] |
| Autor: Martin Sarmiento | ||||||||||
6 Conclusiones
La variable “Inclinación Óptima” fluctúa entre 1° y 43° y sus valores se encuentran alrededor de 17°, con una desviación estándar de 7.074366, siendo una variable muy heterogénea, cuyos valores se concentran en la parte media alta de la variable con la agregación de valores atípicos de 1 outlier; por todo lo anterior, el comportamiento de la variable es regular.