A load duration curve displays electrical power demand (MW) sorted from highest to lowest across all hours of a year (8,760 hours), forming a monotonically decreasing curve. It is a fundamental tool in power system planning, revealing the proportion of time that load exceeds a given level. The curve naturally segments into peak, intermediate, and base load regions, helping utilities determine the optimal generation capacity mix. The area under the curve represents total annual energy consumption.
""" anyplot.ai
line-load-duration: Load Duration Curve for Energy Systems
Library: letsplot 4.10.1 | Python 3.13.13
Quality: 90/100 | Updated: 2026-06-10
"""
import os
import shutil
import numpy as np
import pandas as pd
from lets_plot import (
LetsPlot,
aes,
element_blank,
element_line,
element_rect,
element_text,
geom_hline,
geom_line,
geom_ribbon,
geom_text,
ggplot,
ggsize,
labs,
layer_tooltips,
scale_fill_manual,
scale_x_continuous,
scale_y_continuous,
theme,
theme_minimal,
)
from lets_plot.export import ggsave
LetsPlot.setup_html()
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint palette — semantic exception applies for load regions:
# base load (reliable/always-on) → green, intermediate → ochre, peak (costly/intensive) → matte red
COLOR_BASE = "#009E73" # Imprint position 1 — reliable, continuous generation
COLOR_INTER = "#BD8233" # Imprint position 4 — variable middle-tier generation
COLOR_PEAK = "#AE3030" # Imprint position 5 — semantic red for high-cost peak demand
# Data: Synthetic annual hourly load profile for a mid-sized utility
np.random.seed(42)
hours = np.arange(8760)
hour_of_day = hours % 24
day_of_year = hours // 24
base_load = 400
seasonal_component = 450 * np.sin(2 * np.pi * (day_of_year - 30) / 365) ** 2
daily_pattern = 250 * np.sin(np.pi * (hour_of_day - 6) / 16) ** 2
daily_pattern[hour_of_day < 6] = 0
noise = np.random.normal(0, 40, 8760)
hourly_load = base_load + seasonal_component + daily_pattern + noise
hourly_load = np.clip(hourly_load, 350, 1250)
# Sort descending to create the load duration curve
load_sorted = np.sort(hourly_load)[::-1]
rank_hours = np.arange(8760)
peak_threshold = 900
intermediate_threshold = 550
total_energy_gwh = np.sum(load_sorted) / 1000
# Non-overlapping ribbon regions
peak_ymin = np.full(8760, peak_threshold, dtype=float)
peak_ymax = np.where(load_sorted > peak_threshold, load_sorted, peak_threshold)
inter_ymin = np.full(8760, intermediate_threshold, dtype=float)
inter_ymax = np.where(
load_sorted > intermediate_threshold, np.minimum(load_sorted, peak_threshold), intermediate_threshold
)
base_ymin = np.zeros(8760)
base_ymax = np.minimum(load_sorted, intermediate_threshold)
df_peak = pd.DataFrame(
{"hour": rank_hours, "ymin": peak_ymin, "ymax": peak_ymax, "load_mw": load_sorted, "region": "Peak Load"}
)
df_inter = pd.DataFrame(
{"hour": rank_hours, "ymin": inter_ymin, "ymax": inter_ymax, "load_mw": load_sorted, "region": "Intermediate Load"}
)
df_base = pd.DataFrame(
{"hour": rank_hours, "ymin": base_ymin, "ymax": base_ymax, "load_mw": load_sorted, "region": "Base Load"}
)
df_line = pd.DataFrame({"hour": rank_hours, "load_mw": load_sorted})
peak_hours_count = int(np.sum(load_sorted > peak_threshold))
intermediate_hours_count = int(np.sum(load_sorted > intermediate_threshold))
load_factor = np.mean(load_sorted) / np.max(load_sorted) * 100
# Region label positions (center of each shaded band)
df_labels = pd.DataFrame(
{
"hour": [
peak_hours_count / 2,
(peak_hours_count + intermediate_hours_count) / 2,
(intermediate_hours_count + 8760) / 2,
],
"load_mw": [
(np.max(load_sorted) + peak_threshold) / 2,
(peak_threshold + intermediate_threshold) / 2,
intermediate_threshold / 2 + 20,
],
"label": ["Peak\nLoad", "Intermediate\nLoad", "Base\nLoad"],
}
)
# Energy summary annotation in upper-right empty space
df_energy = pd.DataFrame(
{
"hour": [5800],
"load_mw": [1170],
"label": [f"Total energy: {total_energy_gwh:,.0f} GWh/yr\nLoad factor: {load_factor:.0f}%"],
}
)
# Capacity threshold labels
df_peak_cap = pd.DataFrame(
{"hour": [6200], "load_mw": [peak_threshold + 38], "label": [f"Peak capacity: {peak_threshold} MW"]}
)
df_inter_cap = pd.DataFrame(
{
"hour": [6200],
"load_mw": [intermediate_threshold + 38],
"label": [f"Intermediate capacity: {intermediate_threshold} MW"],
}
)
REGION_COLORS = {"Peak Load": COLOR_PEAK, "Intermediate Load": COLOR_INTER, "Base Load": COLOR_BASE}
title = "line-load-duration · python · letsplot · anyplot.ai"
n = len(title)
title_fontsize = round(16 * 67 / n) if n > 67 else 16
plot = (
ggplot()
+ geom_ribbon(
data=df_base,
mapping=aes(x="hour", ymin="ymin", ymax="ymax", fill="region"),
alpha=0.72,
tooltips=layer_tooltips()
.format("ymax", ".0f")
.format("@hour", ".0f")
.line("Hour rank: @hour")
.line("Load: @ymax MW")
.line("Region: @region"),
)
+ geom_ribbon(
data=df_inter,
mapping=aes(x="hour", ymin="ymin", ymax="ymax", fill="region"),
alpha=0.72,
tooltips=layer_tooltips()
.format("@load_mw", ".0f")
.format("@hour", ".0f")
.line("Hour rank: @hour")
.line("Load: @load_mw MW")
.line("Region: @region"),
)
+ geom_ribbon(
data=df_peak,
mapping=aes(x="hour", ymin="ymin", ymax="ymax", fill="region"),
alpha=0.72,
tooltips=layer_tooltips()
.format("@load_mw", ".0f")
.format("@hour", ".0f")
.line("Hour rank: @hour")
.line("Load: @load_mw MW")
.line("Region: @region"),
)
+ geom_line(
data=df_line,
mapping=aes(x="hour", y="load_mw"),
color=INK,
size=1.0,
tooltips=layer_tooltips()
.format("@load_mw", ".0f")
.format("@hour", ",d")
.line("Hour: @hour")
.line("Demand: @load_mw MW"),
)
+ geom_hline(yintercept=peak_threshold, linetype="dashed", color=COLOR_PEAK, size=0.8)
+ geom_hline(yintercept=intermediate_threshold, linetype="dashed", color=COLOR_INTER, size=0.8)
+ geom_text(data=df_labels, mapping=aes(x="hour", y="load_mw", label="label"), size=4, color=INK, fontface="bold")
+ geom_text(
data=df_energy, mapping=aes(x="hour", y="load_mw", label="label"), size=3.5, color=INK_MUTED, fontface="italic"
)
+ geom_text(
data=df_peak_cap, mapping=aes(x="hour", y="load_mw", label="label"), size=3.5, color=COLOR_PEAK, fontface="bold"
)
+ geom_text(
data=df_inter_cap,
mapping=aes(x="hour", y="load_mw", label="label"),
size=3.5,
color=COLOR_INTER,
fontface="bold",
)
+ scale_fill_manual(values=REGION_COLORS)
+ scale_x_continuous(
name="Hours of Year (Ranked by Demand)",
breaks=[0, 2000, 4000, 6000, 8000],
labels=["0", "2,000", "4,000", "6,000", "8,000"],
)
+ scale_y_continuous(name="Power Demand (MW)", breaks=[0, 200, 400, 600, 800, 1000, 1200])
+ labs(
title=title,
subtitle=f"Mid-sized utility · Peak {np.max(load_sorted):.0f} MW · {peak_hours_count:,} hours above peak threshold",
)
+ theme_minimal()
+ theme(
plot_title=element_text(size=title_fontsize, face="bold", color=INK),
plot_subtitle=element_text(size=10, color=INK_SOFT),
axis_title=element_text(size=12, color=INK),
axis_text=element_text(size=10, color=INK_SOFT),
panel_grid_major_x=element_blank(),
panel_grid_minor=element_blank(),
panel_grid_major_y=element_line(color=INK_SOFT, size=0.15),
legend_position="none",
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_text=element_text(color=INK_SOFT),
)
+ ggsize(800, 450)
)
# Save PNG and HTML for both themes
# ggsave writes into lets-plot-images/ by default; move to the working directory
ggsave(plot, f"plot-{THEME}.png", scale=4)
ggsave(plot, f"plot-{THEME}.html")
for _ext in ("png", "html"):
_src = os.path.join("lets-plot-images", f"plot-{THEME}.{_ext}")
if os.path.exists(_src):
shutil.move(_src, f"plot-{THEME}.{_ext}")
Part of Load Duration Curve for Energy Systems on anyplot.ai.