Net Energy Demand Forecasting in France

A statistical modeling project for predicting net electrical energy demand (Net_demand) in France using time series data and machine learning techniques.

Authors:

• @LylianChallier
• @EpsilonFO

Date: March 10, 2025

Overview

This project focuses on forecasting net electrical energy demand in France using historical data up to the end of 2021. The analysis leverages multiple statistical and machine learning approaches including:

• GAM (Generalized Additive Models): For capturing non-linear and cyclical patterns
• Random Forest (RF): For robust prediction with automated feature importance
• Quantile Regression Forest (QRF): For probabilistic forecasts
• Linear Regression: For baseline comparison and variable selection

The primary objective is to accurately predict Net_demand (net energy consumption) by identifying and modeling relationships between energy consumption and various temporal, meteorological, and calendar factors.

Project Structure

.
├── Data/
│   ├── train.csv              # Training dataset (historical data)
│   ├── test.csv               # Test dataset (for predictions)
│   └── sample_submission.csv  # Submission template
├── R/
│   └── score.R                # Custom scoring functions (RMSE, MAPE, Pinball Loss)
├── analyse_explo.r            # Exploratory data analysis
├── select_variables.r         # Variable selection procedures
├── modelisation.R             # Final model training and predictions
└── rapport.Rmd                # Full project report (R Markdown)

Dataset Description

Target Variable

• Net_demand: Net electrical energy demand in France (MW)

Key Features

Temporal Variables:

• Date, Time: Timestamp information
• Year, Month, WeekDays: Calendar components
• toy (time of year): Cyclical annual indicator

Meteorological Variables:

• Temp: Current temperature
• Temp_s95, Temp_s99: Smoothed temperature (95th and 99th percentiles)
• Temp_s95_max, Temp_s95_min: Maximum/minimum smoothed temperatures
• Temp_s99_max, Temp_s99_min: Extreme temperature indicators
• Wind, Wind_weighted: Wind speed and weighted wind
• Nebulosity, Nebulosity_weighted: Cloud cover metrics

Energy Variables:

• Load: Total electrical load
• Load.1, Load.7: Lagged load (1 day, 7 days)
• Solar_power, Wind_power: Renewable energy production
• Net_demand.7: Lagged net demand (7 days)

Calendar Variables:

• BH (Bank Holiday): Public holidays indicator
• BH_before, BH_after: Days before/after holidays
• Summer_break, Christmas_break: Vacation periods
• Holiday, Holiday_zone_a/b/c: Regional vacation zones
• DLS (Daylight Saving Time): Summer time indicator
• BH_Holiday: Combined holiday effect

Key Relationships

Load Decomposition:

Load = Net_demand + Solar_power + Wind_power

Temperature Effect:

• Strong negative correlation between Net_demand and Temp
• U-shaped relationship: high demand in winter (heating) and summer peaks (cooling)

Requirements

R Version

• R >= 4.0.0

Required Packages

install.packages(c(
  "mgcv",          # GAM models
  "corrplot",      # Correlation visualizations
  "gt",            # Table formatting
  "tidyverse",     # Data manipulation
  "ranger",        # Fast Random Forest implementation
  "randomForest",  # Classic Random Forest
  "xgboost",       # Gradient boosting (optional)
  "yarrr"          # Color palettes
))

Installation & Setup

1. Clone the Repository

git clone https://github.com/EpsilonFO/Net-Load_Forecasting.git
cd Net-Load_Forecasting

2. Prepare Data

Ensure the following files are in the Data/ directory:

• train.csv
• test.csv
• sample_submission.csv

3. Install Dependencies

Open R or RStudio and run:

source("install_packages.R")  # Or manually install required packages

Usage

Quick Start: Complete Pipeline

To run the entire modeling pipeline and generate predictions:

# Load and run the main modeling script
source("modelisation.R")

This will:

1. Load and preprocess the data
2. Train GAM and Random Forest models
3. Generate predictions on the test set
4. Save results to Data/submission_rf.csv

Step-by-Step Analysis

1. Exploratory Data Analysis

source("analyse_explo.r")

This script performs:

• Univariate analysis of time series patterns
• Bivariate correlation analysis
• Visualization of temporal, meteorological, and calendar effects
• Identification of key patterns (seasonality, temperature effects, holiday impacts)

Key Findings:

• Clear annual seasonality in net demand
• Strong inverse relationship between demand and temperature
• Significant demand reduction during holidays and summer breaks
• Weekend effect: lower demand on Saturdays and Sundays

2. Variable Selection

source("select_variables.r")

This script implements:

• Linear correlation analysis: Identifies variables with |correlation| > 0.3
• Backward stepwise selection: BIC-based variable selection on linear regression
• Random Forest feature importance: Permutation-based importance ranking

Selection Results:

• Most important variables: Load.1, Temp, Temp_s95_max, Temp_s99_max, WeekDays, BH_Holiday
• Holiday zones (Holiday_zone_a/b/c) found to be non-significant and excluded

3. Model Training and Evaluation

source("modelisation.R")

Models implemented:

GAM Model:

Net_demand ~ s(Time) + s(toy, bs='cc') + ti(Temp) + ti(Temp_s99) + 
             s(Load.1) + s(Load.7) + ti(Temp_s99, Temp) + 
             WeekDays + BH + te(Temp_s95_max, Temp_s99_max) + 
             Summer_break + Christmas_break + ...

Random Forest Model:

Net_demand ~ Time + toy + Temp + Temp_s99 + Load.1 + Load.7 + 
             WeekDays + BH + Temp_s95_max * Temp_s99_max + 
             Summer_break + Christmas_break + Wind + ...

Performance Metrics

Models are evaluated using:

• RMSE (Root Mean Square Error): Standard error metric
• MAPE (Mean Absolute Percentage Error): Percentage-based error
• Pinball Loss (quantile=0.8): Asymmetric loss for robust forecasting

Example evaluation results:

# Train/validation split: 2020-2021 for training, 2022+ for evaluation
sel_a <- which(Data0$Year <= 2021)  # Training indices
sel_b <- which(Data0$Year > 2021)   # Evaluation indices

Generating the Report

To compile the full analysis report:

# In RStudio
rmarkdown::render("rapport.Rmd")

This generates a comprehensive HTML/PDF report with:

• Complete exploratory analysis
• Variable selection procedures
• Model comparison tables
• Performance visualizations

Model Details

GAM (Generalized Additive Model)

Advantages:

• Captures non-linear relationships naturally
• Handles cyclical patterns (seasonal effects)
• Interpretable smooth functions
• Built-in regularization with penalization

Key Components:

• s(toy, bs='cc'): Cyclic cubic spline for annual seasonality
• ti(Temp): Tensor product for temperature effects
• te(Temp_s95_max, Temp_s99_max): Temperature interaction terms

Random Forest

Advantages:

• Robust to outliers and non-linearity
• Automatic feature interaction detection
• No need for explicit feature engineering
• Provides feature importance metrics

Variants Tested:

• RF Complete: All available variables
• RF Backward: Variables selected via linear regression backward selection
• RF Mixed: Combines backward selection + RF importance

Quantile Regression Forest (QRF)

Combines GAM predictions with quantile regression for probabilistic forecasts:

# GAM provides base prediction
# QRF models residuals for uncertainty quantification
QRF_prediction = GAM_prediction + QRF_residual_quantile

Custom Scoring Functions

Located in R/score.R:

# Root Mean Square Error
rmse(y, y_hat, digits=0)

# Mean Absolute Percentage Error  
mape(y, y_hat)

# Pinball Loss (for quantile forecasting)
pinball_loss(y, y_hat_quant, quant, output.vect=FALSE)

Results & Submission

Model Performance

Typical performance on validation set (2022 data):

Model	RMSE	MAPE	Pinball Loss (0.8)
GAM	~2000	~5%	~650
RF Complete	~1900	~4.8%	~480
RF Mixed	~1950	~4.9%	~475

Generating Submissions

Final predictions are saved to:

Data/submission_rf.csv

Format:

Date,Net_demand
2022-01-01,45000
2022-01-02,46500
...

Visualization Examples

Time Series Plot

plot(Data0$Date, Data0$Net_demand, type='l', 
     main="Net Demand Over Time")

Temperature Relationship

plot(Data0$Net_demand ~ Data0$Temp, 
     main="Demand vs Temperature")

Model Predictions vs Actual

plot(Data0$Date[sel_b], predictions, type='l', col='red')
lines(Data0$Date[sel_b], Data0$Net_demand[sel_b], col='blue')
legend("topright", c("Predicted", "Actual"), col=c("red", "blue"), lty=1)

Key Insights

Exploratory Analysis

1. Seasonal Pattern: Clear annual cycle with winter peaks (heating) and summer valleys
2. Temperature Effect: Inverse relationship with demand; non-linear with threshold effects
3. Calendar Effects: Significant demand reduction during:
   • Weekends (especially Sundays)
   • Public holidays
   • Summer vacation period
4. Renewable Integration: Load = Net_demand + Solar + Wind (exact relationship verified)

Modeling Insights

1. Most Important Predictors:

   • Historical load (Load.1, Load.7)
   • Temperature (current and smoothed versions)
   • Calendar variables (WeekDays, holidays)

2. Feature Engineering:

   • Lagged variables crucial for time series prediction
   • Temperature extremes (Temp_s95, Temp_s99) capture threshold effects
   • Interaction terms improve non-linear modeling

3. Model Selection:

   • Random Forest generally outperforms linear and GAM models
   • Variable selection improves interpretability without sacrificing performance
   • Ensemble approaches (GAM + QRF) provide robust uncertainty quantification

Troubleshooting

Common Issues

Missing packages:

# Check if package is installed
if (!require("mgcv")) install.packages("mgcv")

Memory issues with large datasets:

# Reduce Random Forest parameters
rf_model <- randomForest(formula, data=train, 
                         ntree=500,        # Reduce trees
                         nodesize=10)      # Increase node size

Date parsing errors:

# Ensure proper date format
Data0$Date <- as.Date(Data0$Date, format="%Y-%m-%d")

Performance Optimization

For faster computation:

• Use ranger instead of randomForest (10-100x faster)
• Reduce ntree parameter for Random Forest
• Use parallel processing with doParallel

Contributing

This is an academic project. For improvements or suggestions, please contact the authors.

License

This project is for educational purposes. Please cite appropriately if using any methodology or code.

References

• GAM: Wood, S. N. (2017). Generalized Additive Models: An Introduction with R
• Random Forest: Breiman, L. (2001). Random Forests. Machine Learning, 45(1), 5-32
• Quantile Regression: Meinshausen, N. (2006). Quantile Regression Forests

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Note: This project analyzes electrical energy demand patterns and builds predictive models for forecasting. The methodology can be adapted to other time series forecasting problems with temporal, meteorological, and calendar features.