Statistical Learning Tools for Electricity Load Forecasting

✍ Scribed by Anestis Antoniadis; Jairo Cugliari; Matteo Fasiolo; Yannig Goude; Jean-Michel Poggi

• Year: 2024
• Tongue: English
• Leaves: 232
• Category: Library

✦ Synopsis

This monograph explores a set of statistical and machine learning tools that can be effectively utilized for applied data analysis in the context of electricity load forecasting. Drawing on their substantial research and experience with forecasting electricity demand in industrial settings, the authors guide readers through several modern forecasting methods and tools from both industrial and applied perspectives – generalized additive models (GAMs), probabilistic GAMs, functional time series and wavelets, random forests, aggregation of experts, and mixed effects models. A collection of case studies based on sizable high-resolution datasets, together with relevant R packages, then illustrate the implementation of these techniques. Five real datasets at three different levels of aggregation (nation-wide, region-wide, or individual) from four different countries (UK, France, Ireland, and the USA) are utilized to study five problems: short-term point-wise forecasting, selection of relevant variables for prediction, construction of prediction bands, peak demand prediction, and use of individual consumer data.

This text is intended for practitioners, researchers, and post-graduate students working on electricity load forecasting; it may also be of interest to applied academics or scientists wanting to learn about cutting-edge forecasting tools for application in other areas. Readers are assumed to be familiar with standard statistical concepts such as random variables, probability density functions, and expected values, and to possess some minimal modeling experience.

✦ Table of Contents

Contents
1 Introduction
1.1 Industrial Motivation
1.2 Data Sets
1.2.1 General Considerations
1.2.2 Salient Features of Electricity Demand
1.2.3 Irish Individual Electrical Demand Data
1.2.3.1 Data Presentation
1.2.3.2 Data Processing
1.2.3.3 Getting the Data
1.2.4 French National Demand Data
1.2.4.1 Data Presentation
1.2.4.2 Data Processing
1.2.4.3 Getting the Data
1.2.5 US Regional Demand Data from the GEFCOM 2014 Competition
1.2.5.1 Data Presentation
1.2.5.2 Data Processing
1.2.5.3 Getting the Data
1.3 Problems
1.3.1 Short-Term Point Forecasting
1.3.2 Probabilistic Forecasting
1.3.3 Selection of Relevant Variables for Prediction
1.3.4 Peak Demand Forecasting
1.3.5 Adaptive Forecasting
1.3.6 Bottom-up and Hierarchical Forecasting
1.4 Assessment and Validation
1.4.1 Assessment Scores
1.4.1.1 Pointwise Forecasting
1.4.1.2 Probabilistic Forecasting
1.4.2 Validation Procedures
1.4.2.1 Cross-Validation
1.4.2.2 Bootstrapping
Part I A Toolbox of Models
2 Additive Modelling of Electricity Demand with mgcv
2.1 Introducing GAMs
2.1.1 GAM Model Structure
2.1.2 GAM Model Fitting in a Bayesian Framework
2.1.3 Basic Smooth Effects and Penalties
2.1.3.1 Thin Plate Splines and Derivative-Based Penalties
2.1.3.2 Smooth Effects in mgcv
2.1.4 Model Selection
2.1.4.1 Model Selection via Smoothing Parameter Estimation
2.1.4.2 Performing AIC-Based Model Selection Under Penalization
2.1.4.3 Choosing the Type and the Basis Dimension of a Smooth Effect
2.1.5 Example: Modelling Aggregated Irish Smart Meter Data
2.2 More Smooth Effects and Big Data Methods
2.2.1 Tensor-Product and By-variable Smooths
2.2.2 GAM Methods for Large Data Sets
2.2.3 Example: Modelling Aggregate Irish Smart Meter Data (Continued)
2.2.4 Alternatives to mgcv for GAM Modelling
2.2.5 Summary
3 Probabilistic GAMs: Beyond Mean Modelling
3.1 Introduction to GAMLSS Modelling in mgcv
3.1.1 Probabilistic GAM Modelling of GEFCom 2014 Data
3.2 Introducing QGAM Models
3.2.1 QGAM Model Structure
3.2.2 Fitting QGAM Models with qgam
3.2.3 Distribution-Free QGAM Modelling of GEFCom 2014 Data
3.2.4 Alternatives to mgcv and qgam for GAMLSS and QGAM Modelling
3.3 Summary
4 Functional Time Series
4.1 Functional Data
4.2 Wavelets
4.3 KWF: A Nonparametric Regression for Stationary FTS
4.4 Prediction Interval
4.4.1 Bootstrap Generation
4.4.2 Two Variants from the KWF Method
4.5 Clustering Functional Data
4.5.1 Clustering by Feature Extraction
4.5.2 Clustering Using a Dissimilarity Measure
5 Random Forests
5.1 Random Forests: An Ensemble Based Method
5.1.1 CART Trees
5.1.2 Principle of Random Forests
5.1.3 OOB Error
5.2 Variable Importance Measures and Marginal Effects
5.2.1 Permutation Variable Importance
5.2.2 Group Variable Importance
5.2.3 Marginal Effects
5.3 Tuning Meta-Parameters
5.3.1 Tuning for Prediction
5.3.2 Tuning for Computing VI
5.4 Theoretical Results
5.5 A Variant Adapted to Time Series
5.6 Electricity Data Modeling Using Random Forests
5.6.1 CART Trees
5.6.1.1 Nested Sequence of Pruned Subtrees
5.6.1.2 Optimal and Suboptimal CART Trees
5.6.2 Random Forests
6 Aggregation of Experts
6.1 Introduction
6.2 Online Forecasting of Arbitrary Sequence with a Set of Experts
6.3 The Notion of Regret
6.4 Aggregation with Exponential Weights
6.5 Gradient Trick
6.6 Aggregation with Adaptive Learning Rates
6.7 Specialized Experts
6.8 Nonconvex Aggregation
6.8.1 Ridge
6.8.2 Tricks
6.8.2.1 Constant Bias
6.8.2.2 Random Walk
6.9 Dealing with Breaks
6.9.1 Shifting Oracle
6.9.2 Fixed Share
7 Mixed Effects Models for Electricity Load Forecasting
7.1 Introduction
7.2 The Standard Linear Mixed Effects Model
7.2.1 Classical Linear Model
7.2.2 Random Effects
7.2.3 A Simple Example of a LME Model
7.3 Stochastic Linear Mixed Models for Longitudinal Data
7.4 Regression Trees for Mixed Effects Longitudinal Data
7.4.1 The RE-EM Tree Algorithm
7.5 Functional Mixed Effects Models
7.5.1 A Penalized Spline Approach to Functional Mixed Effects Model Analysis
7.6 Predicting Time Series of Electricity Consumption
Part II Case Studies: Models in Action on Specific Applications
Case Studies Organization
8 Disaggregated Forecasting of the Total Consumption of a Given Subset of Customers
8.1 Data
8.1.1 Original Data Set
8.1.2 Other Data Sets
8.2 Problems
8.3 Modeling and Results
8.3.1 From Individual Curves to a Hierarchy of Partitions for Forecasting
8.3.2 Numerical Experiments
8.4 Validation
8.5 Interpretation
8.6 Complements and Discussion
8.6.1 Upscaling
8.6.2 Discussion
9 Aggregation of Multiscale Experts for Bottom-Up Load Forecasting
9.1 Data
9.2 Problem
9.3 Methods
9.4 Numerical Results
9.5 Discussions
10 Short-Term Electricity Load Forecasting for Fine-Grained Data with PLAM
10.1 Data
10.1.1 Data Transformation
10.1.2 Generation of Aggregates
10.2 Problem
10.3 Modelling
10.3.1 Estimation and Model Selection in PLAMs
10.4 Analysis and Results
10.5 Discussion and Conclusion
11 Functional State Space Models
11.1 Data
11.2 Problems
11.3 Modelling
11.4 Model Construction
11.5 Prediction Performances
11.6 Supplements and Discussion
12 Forecasting Daily Peak Demand Using GAMs
12.1 Forecasting Problem
12.2 Modelling
12.2.1 A High-Resolution Approach
12.2.2 A Multiresolution Approach
12.3 Results on GEFCom 2014 Data
12.4 Conclusion
13 Forecasting During the Lockdown Period
13.1 Data
13.2 Problem
13.3 Methods
13.3.1 GAM and Adaptive GAM
13.3.2 RF and Adaptive RF
13.3.3 Stacking GAM and RF
13.3.4 Aggregation Algorithms
13.4 Numerical Results
13.5 Discussions
References