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Adaptive Methods for Short-Term Electricity Load Forecasting During COVID-19 Lockdown in France

David Obst, Joseph de Vilmarest, Yannig Goude

arXiv:2009.06527v1stat.APcs.LGstat.ML

TL;DR

Lockdowns changed electricity consumption patterns, making historical-data forecasting models poorly suited to the break and weakening forecasts. This paper adapts GAMs with Kalman filtering and fine-tuning, also transferring information from Italy to France. Its adaptive methods reduce prediction errors against benchmark models, with expert aggregation reducing errors further.

  • Problem

    Lockdown-driven changes in electricity consumption patterns caused historical-data forecasting models to perform poorly, complicating production scheduling and increasing costs for producers and grid operators.

    Source: §I · pp. 1–2

  • Method

    The paper adapts GAMs using Kalman filtering or fine-tuning and transfers information from Italy’s earlier lockdown to anticipate changes in France.

    Source: §I · p. 2, C. Knowledge transfer from Italy · p. 5

  • Results

    Adaptive methods significantly improved predictions over benchmark models, and expert aggregation further reduced errors on both test periods.

    Source: C. Numerical results · p. 7, §V · p. 7

  • Takeaways & Limitations

    The methods produced satisfactory predictions from the first day of France’s stay-at-home order by using Italian data to anticipate behavior changes.

    Source: §I · p. 2, C. Knowledge transfer from Italy · p. 5

Abstract

from arXiv · show

The coronavirus disease 2019 (COVID-19) pandemic has urged many governments in the world to enforce a strict lockdown where all nonessential businesses are closed and citizens are ordered to stay at home. One of the consequences of this policy is a significant change in electricity consumption patterns. Since load forecasting models rely on calendar or meteorological information and are trained on historical data, they fail to capture the significant break caused by the lockdown and have exhibited poor performances since the beginning of the pandemic. This makes the scheduling of the electricity production challenging, and has a high cost for both electricity producers and grid operators. In this paper we introduce adaptive generalized additive models using Kalman filters and fine-tuning to adjust to new electricity consumption patterns. Additionally, knowledge from the lockdown in Italy is transferred to anticipate the change of behavior in France. The proposed methods are applied to forecast the electricity demand during the French lockdown period, where they demonstrate their ability to significantly reduce prediction errors compared to traditional models. Finally expert aggregation is used to leverage the specificities of each predictions and enhance results even further.

I. INTRODUCTION

Lockdowns changed electricity demand patterns, exposing a gap in historical-data forecasting models and motivating adaptive GAM approaches. The paper proposes Kalman-filter and fine-tuning adaptations, including transfer from Italy, to improve forecasts during France’s lockdown.

I. INTRODUCTION

  • Accurate load forecasts support grid balancing and production planning, while forecasting methods range from time-series approaches for horizons under 24 hours to statistical and machine-learning models for longer horizons.GAMs combine flexibility and computational efficiency, and EDF uses them as its lead forecasting tool.Source: §I · p. 1
  • During lockdown, French and Italian demand fell and daily load profiles converged toward Saturday shapes; historical-data models consequently struggled, with French GAM MAPE rising from around 1% to around 5%.Poor forecasts increased costs for producers and system operators and threatened proper functioning of the electrical network.Source: §I · pp. 1–2
  • Earlier studies improved lockdown forecasts using adaptive functional state-space models or mobility-informed multi-task learning, but none examined improving GAMs for the lockdown period.The cited mobility study also reported benefits from joint neural-network training across geographic areas.Source: §I · p. 2
  • The paper proposes Kalman-filter adaptation for rapid response to changing data and GAM fine-tuning that transfers knowledge from pre-lockdown data or an earlier lockdown in another country.It frames adaptation as balancing responsiveness to change with good behavior during stable periods.Source: §I · p. 2
  • The proposed adaptive GAM methods adjust historical models to behavior changes with scarce data, and Italian lockdown data can help anticipate France’s change from the first day.The methods do not require additional features, and reported forecast accuracy was close to pre-pandemic accuracy.Source: §I · p. 2

II. ADAPTATION OF ADDITIVE MODELS

The paper adapts generalized additive models by updating either a reduced set of effect weights or the whole model. Multiplicative correction freezes nonlinear effects while allowing their contributions to change over time.

II. ADAPTATION OF ADDITIVE MODELS

  • A GAM represents the response through additive nonlinear effects of explanatory variables, with each effect expressed using spline basis functions and coefficients.The coefficients are estimated by penalized least squares, with a second-derivative penalty encouraging smooth effects.Source: §II · p. 2
  • The adaptation framework assumes Gaussian i.i.d. residuals initially and considers both updating a linear combination of frozen effects and fine-tuning the whole model.A later experimental variant models residuals with ARIMA.Source: §II · p. 2

A. Multiplicative correction of the effects

  • Multiplicative correction freezes the nonlinear effects and adaptively estimates factors for normalized effects, reducing the number of coefficients from 1 + Σm_j to 1 + d.The authors describe this reduction as a trade-off: a simple model that reacts quickly to breaks while retaining enough complexity to fit nonlinear load patterns.Source: A. Multiplicative correction of the… · p. 3

1) Exponential Least-Squares:

Exponential least-squares adapts effect weights using exponentially decreasing recency weights. The Kalman-filter approach treats those weights as a state that can evolve over time, with a changed state-noise covariance at the lockdown break.

1) Exponential Least-Squares:

  • Exponential least-squares solves a weighted least-squares problem at each step, with weights decreasing exponentially with the time difference.Its single forgetting factor is selected by minimizing RMSE on a validation set from the final year of training data, then retained for the model trained on the full training set.Source: 1) Exponential Least-Squares · p. 3

2) Kalman Filter:

  • The Kalman formulation recursively estimates the state and its covariance from past observations, yielding the conditional mean and variance of the load.It assumes Gaussian white observation and state noises with variance or covariance σ² and Q.Source: 2) Kalman Filter · p. 3
  • Kalman hyperparameters are selected through likelihood optimization; the authors use a greedy search over diagonal Q* matrices after fixing P*_1 = I.At each iteration, they test matrices differing in one coefficient and choose the likelihood-maximizing candidate.Source: 2) Kalman Filter · p. 3
  • The dynamic Kalman model changes the state-noise covariance at the lockdown start T, using Q* otherwise, to represent a break without imposing an a priori on its form.The static setting uses Q* = 0, reducing the state equation to a constant state.Source: 2) Kalman Filter · p. 3

B. Correction of the full model

The method fine-tunes a previously trained GAM on scarce target data rather than learning a new model from scratch. It uses batch gradient descent, with the number of iterations as the main hyperparameter.

B. Correction of the full model

  • Fine-tuning reuses source-model parameters for a few target instances, addressing behaviors that frozen nonlinear effects with multiplicative adjustment may not capture.The authors avoid training from scratch because few target samples are available.Source: B. Correction of the full model · p. 3
  • Fine-tuning starts from source-trained GAM coefficients and adjusts them with K fixed-step batch-gradient iterations on a penalized linear-regression objective.The adjusted parameters are updated at each time step.Source: B. Correction of the full model · p. 4
  • A sufficiently small step size is considered adequate, with α = α*/5 reported as a practical choice.The cited discussion says step-size choice is not crucial if α is small enough.Source: B. Correction of the full model · p. 4
  • K is the main hyperparameter to tune, and 50–100 gradient iterations often give good results empirically.The paper says this range usually coincides with theoretical guidance.Source: B. Correction of the full model · p. 4

III. DATA AND MODEL PRESENTATION

This section introduces the data and model used for French electricity-consumption forecasting.

III. DATA AND MODEL PRESENTATION

  • The section presents the data and model used to forecast French electricity consumption.Source: §III · p. 4

A. Presentation of the data

The study uses French half-hourly load data and observed temperatures, evaluates distinct pre-lockdown and lockdown periods, and describes an additive model with a short-term ARIMA error correction.

A. Presentation of the data

  • The French load dataset spans January 1, 2012 to June 7, 2020 at 30-minute resolution, with observed national-average temperatures used for reproducible comparisons.Using observed rather than forecast temperatures excludes meteorological-forecast uncertainty from the comparison.Source: A. Presentation of the data · p. 4
  • The crisis evaluation separates March 16–April 15, 2020 from April 16–June 7, 2020, after training on data through August 2019.The first test day is March 16 because consumer behavior had already changed, despite the official lockdown beginning at midday on March 17.Source: A. Presentation of the data · p. 4

B. The additive model

  • The additive-model setup fits separate models for each of the 48 half-hour time slots and includes time-of-year, day-type, daylight-saving, and temperature effects.The model also uses smoothed temperature variables and the previous day’s and week’s loads.Source: B. The additive model · p. 4
  • An ARIMA model selected by AIC captures autocorrelation in errors, and its short-term correction is added to GAM forecasts.The paper searches ARIMA(p,d,q) models with p,q ≤ 100 and d ≤ 1.Source: B. The additive model · p. 4

C. Knowledge transfer from Italy

The method uses Italy’s earlier lockdown to estimate behavioral adjustments for France. It applies a scaled Italian adjustment to French GAM parameters, enabling predictions from the first day of the French lockdown.

C. Knowledge transfer from Italy

  • Italy’s total lockdown began March 9, 2020, seven days before France’s, providing an earlier period of lockdown observations.Source: C. Knowledge transfer from Italy · p. 4
  • The transfer assumes similar responses to stay-at-home orders and uses Italian load and weather data to estimate coefficient adjustments from February 28 onward.The Italian data are hourly and span January 2015 to June 28, 2020; the source model is trained on 2015–2019 data.Source: C. Knowledge transfer from Italy · p. 5
  • GAM-δ adds a scaled Italian adjustment to French source parameters while leaving the French time-of-year coefficients unadjusted.The scale factor accounts for differing load levels between France and Italy.Source: C. Knowledge transfer from Italy · p. 5
  • GAM-δ can reduce prediction error from the first French lockdown day, and can be followed by fine-tuning on French data as it becomes available.Source: C. Knowledge transfer from Italy · p. 5

IV. EXPERIMENTS

The experiments examine French load forecasting and model behavior during lockdown. Model dynamics show how the adaptive variants respond to the demand change over time.

A. Model dynamics

  • Adaptive methods, notably Kalman with dynamic break and GAM fine-tuned, reduce lockdown overprediction, while regular GAM keeps overpredicting; GAM-δ helps early but later drifts.GAM-δ drifts as Italian consumption recovers faster than French consumption during the second lockdown month.Source: Figure 3 · p. 5, A. Model dynamics · p. 5
  • GAM-δ uses Italian lockdown patterns for an initial performance boost, but its predictions drift as Italian consumption recovers faster than French consumption.The method is intended to help during the first couple of weeks while other models adjust.Source: A. Model dynamics · p. 5
  • A break covariance matrix lets Kalman variants adapt faster at lockdown; the dynamic setting evolves faster than the static setting, whose state is assumed constant.The state-coefficient trajectories are shown relative to September 1, 2019.Source: A. Model dynamics · pp. 5–6, Figure 4 · p. 6
  • Fine-tuning changes the lagged-load coefficients: working-day terms fall, especially Monday, while weekend terms rise, notably Saturday.The paper relates these shifts to lockdown days becoming more alike and closer to Saturday profiles, and to declining demand in the first weeks.Source: Figure 5 · p. 6, A. Model dynamics · p. 6

B. Aggregation

The section combines 11 forecasting candidates so the forecast can benefit from the most useful expert over time. At lockdown, weights shift toward Saturday-shaped and Italy-informed predictions early, then toward adaptive methods as they adjust.

B. Aggregation

  • The 11 candidates include adapted ARIMA and GAM models plus GAM Saturday, which applies regular GAM as if every day were Saturday.The Saturday expert is motivated by daily profiles converging toward the Saturday shape during lockdown.Source: B. Aggregation · p. 6
  • Online aggregation combines expert forecasts and updates weights according to past performance using ML-Poly, without tuning a learning-rate parameter.ML-Poly uses a gradient-descent-like strategy with a time-varying step based on experts’ past performances.Source: B. Aggregation · p. 6
  • At lockdown, transfer-learning, break-model, and Saturday experts are introduced with uniform weight 1/12, while existing experts share the remaining weight proportionally.Source: B. Aggregation · p. 6
  • At lockdown, GAM Saturday and GAM-δ receive high weight, while adaptive Kalman and fine-tuning experts become more competitive as they gather data.GAM-δ has 1984 MW RMSE on the first two lockdown days, compared with 2674 for Dynamic Break and 3005 for regular GAM.Source: B. Aggregation · pp. 6–7, Figure 6 · p. 7

C. Numerical results

The adaptive methods reduce both error metrics relative to standard GAM+ARIMA on both COVID-19 test sets; Kalman with Dynamic Break performs best, while expert aggregation further reduces errors.

C. Numerical results

  • Performance is assessed using RMSE in MW and MAPE in percent, computed over the test-set instances.The test set contains n instances.Source: C. Numerical results · p. 7
  • Both COVID-19 test sets show significantly lower RMSE and MAPE than standard GAM+ARIMA, with Kalman with Dynamic Break best on both metrics and fine-tuned methods close behind.The supplied passage gives no numerical values for these comparisons.Source: C. Numerical results · p. 7
  • Expert aggregation further reduces errors on both test periods, with GAM Saturday offsetting other experts’ tendency to overestimate demand during the first period.GAM Saturday underestimates demand, compensating for the other experts’ bias despite its weak standalone performance.Source: C. Numerical results · p. 7

V. CONCLUSION

The paper concludes that Kalman-filter adaptation and GAM fine-tuning improve French lockdown forecasts, with Italian data helping anticipate the lockdown effect. It identifies broader models, inputs, regions, and countries as directions for further work.

V. CONCLUSION

  • Kalman filtering and GAM fine-tuning improve French lockdown forecasts versus benchmark models without adding exogenous features, and Italian data helps anticipate the lockdown effect.Expert aggregation further improves results by leveraging individual experts’ specificities.Source: §V · p. 7
  • The proposed adaptation framework could extend beyond GAM; neural networks are identified as a future direction.The paper notes neural networks’ high performance in load forecasting.Source: §V · p. 7
  • Future work includes mobility or macroeconomic inputs, regional load data, and more countries, with transfer and adaptation approaches remaining relevant.The authors note that pandemic propagation and consumption impacts differed by region in France and Italy, and that exogenous-variable effects may vary over time.Source: §V · p. 7
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