Transcript slides
DESIGNING AND AGGREGATING EXPERTS
FOR ENERGY DEMAND FORECASTING
SESO 2014 International Thematic Week
“Smart Energy and Stochastic Optimization''
June 23 to 27, 2014
Yannig Goude
Georges Oppenheim
Pierre Gaillard
Gilles Stoltz
EDF R&D
UPEM & Paris 11
EDF R&D, HEC Paris-CNRS
HEC Paris-CNRS
INDUSTRIAL CHALLENGES
Smart grids
More and more « real time » data (ex: linky, 1million meters in 2016)
Demand response (new tariffs, real time pricing…)
New communication tools with customers (webservice, on-line reporting….)
Renewables energy development
A more and more probabilistic context
Opening of the electricity market:
Losses/gains of customers
Sensors data:
Production/consumption sites
Smart home, internet of things
New usages/tariffs:
Electric cars
Heat pumps, smart phones, battery charge, computers, flat screens….
Demand response, special tariffs (time varying…)
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STATISTICAL CHALLENGES
Large scale data sets
Parallelizing statistical algorithms
Complex data analysing: heteregonous spatial/temporal sampling, different sources/nature of data
Adaptivity
Non-parametric models, fonctional data analysis
Model selection, data driven penalty…
Sequential estimation
Break detection
On-line update, sequential data treatment (data flow, connection to big data)
Aggregation with on-line weigths
Multi-scale models
Multi-horizon models
Multi level data on the grid
Data mining of time series
Large scale simulations
Simulation platform, parallel processing
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CONTRIBUTIONS
Large scale data sets
GAM parallel processing
EDF R&D/IBM simulation platform
Adaptivity
GAM models, automatic GAM selection
functional data analysis (CLR: curve linear regression, KWF: kernel wavelet fonctional)
Sequential learning:
Adaptive GAM
Combining forecasts
Spatio temporal/multi-scale models, complex data
« Downscaling » electricity consumption: link INSEE (socio-demographic, census) data to local electricity
consumption (meters, grid data) and meteo data
EDF R&D/IBM simulation platform
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LOAD FORECASTING
Electricity consumption is the main entry for optimizing the production units
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ELECTRICITY CONSUMPTION DATA
Trend
Yearly, Weekly, Daily cycles
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ELECTRICITY CONSUMPTION DATA
Meteorological events
Special days
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GAM (GENERALIZED ADDITIVE MODELS)
A good trade-off complexity/adaptivity
Publications
Application on load forecasting
• A. Pierrot and Y. Goude, Short-Term Electricity Load Forecasting With Generalized Additive Models Proceedings of
ISAP power, pp 593-600, 2011.
• R. Nédellec, J. Cugliari and Y. Goude, GEFCom2012: Electricity Load Forecasting and Backcasting with SemiParametric Models, International Journal of Forecasting , 2014, 30, 375 - 381.
GAM « parallel »: BAM (Big Additive Models)
• S.N. Wood, Goude, Y. and S. Shaw, Generalized additive models for large datasets, Journal of Royal Statistical
Society-C, 2014.
Adaptive GAM (forgetting factor)
• A. Ba, M. Sinn, Y. Goude and P. Pompey, Adaptive Learning of Smoothing Functions: Application to Electricity Load
Forecasting Advances in Neural Information Processing Systems 25, 2012, 2519-2527.
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GAM
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GEFCOM COMPETITION
20 substations on the US grid
11 temperature series
hourly data from january 2004 to june
2008
9 weeks to predict : 8 from 2005 to
2006, and the one following the train set
(no temperature forecast available)
105 teams
?
One issue : no localisation information
http://www.kaggle.com/c/global-energy-forecasting-competition-2012-load-forecasting
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GEFCOM COMPETITION
Nedellec, R.; Cugliari, J. & Goude, Y.
GEFCom2012: Electric load forecasting and backcasting with semi-parametric models
International Journal of Forecasting , 2014, 30, 375 - 381
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GEFCOM COMPETITION
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CURVE LINEAR REGRESSION
Regressing curves on curves
Dimension reduction, SVD of cov(Y,X) , selection with penalised model selection
Scale to big data sets (SVD+linear regression)
Publications
Application on electricity load forecasting
• H. Cho, Y. Goude, X. Brossat & Q. Yao, Modeling and Forecasting Daily Electricity Load Curves: A Hybrid Approach
Journal of the American Statistical Association, 2013, 108, 7-21.
• Cho, H.; Goude, Y.; Brossat, X. & Yao, Q, Modelling and forecasting daily electricity load using curve linear regression
submitted to Lecture Notes in Statistics: Modeling and Stochastic Learning for Forecasting in High Dimension.
Clusturing functional data
• H. Cho, Y. Goude, X. Brossat & Q. Yao, Clusturing for curve linear regression, technical report, 2013.
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CURVE LINEAR REGRESSION
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OTHER MODELS
Random forest: a popular machine learning method for classification/regression
• Breiman, L., . Random Forests, Machine Learning, 45 (1), 2001.
yes
Bank Holiday
<6°C
no
Temperature
<55GW
>6°C
Lag Load
>55GW
http://luc.devroye.org/BRUCE/brucepics.html
KWF (Kernel Wavelet Functional): another approach for functional data forecasts
• See: Antoniadis, A., Brossat, X., Cugliari, J., Poggi, J., Clustering functional data using wavelets. In: Proceedings of
the Nineteenth International Conference on Computational Statistics(COMPSTAT), 2010.
• Antoniadis, A., Paparoditis, E., Sapatinas, T., A functional wavelet–kernel approach for time series prediction.
Journal of the Royal Statistical Society: Series B 68(5), 837–857, 2006.
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SEQUENTIAL AGREGATION OF EXPERTS
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SEQUENTIAL AGREGATION OF EXPERTS
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SEQUENTIAL AGREGATION OF EXPERTS
Cesa-Bianchi, N., Lugosi, G.: Prediction, Learning, and Games. Cambridge University Press (2006)
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EXPONENTIALLY WEIGHTED AVERAGE FORECASTER (EWA)
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EXPONENTIATED GRADIENT FORECASTER (EG)
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OTHER ALGORITHMS
Theoretical calibration
Works well in practice
Gaillard, P., Stoltz, G., van Erven, T.:
A second-order bound with excess
losses (2014).
ArXiv:1402.2044
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APPLICATION ON LOAD FORECASTING
initial « heterogenous » experts:
GAM
Kernel Wavelet Functional
Curve Linear Regression
Random Forest
Designing a set of experts from the original ones: 4 « home made » tricks
Bagging: 60 experts
Boosting:Boosting: trained on
45 experts
such that
Specializing: focus on cold/warm days, some periods of the year… 24 experts
Time scaling: MD with GAM, ST with the 3 initial experts
performs well
Publications
• M. Devaine, P. Gaillard, Y. Goude & G. Stoltz, Forecasting electricity consumption by aggregating specialized experts A review of the sequential aggregation of specialized experts, with an application to Slovakian and French countrywide one-day-ahead (half-)hourly predictions Machine Learning, 2013, 90, 231-260.
• Gaillard, P. & Goude, Y., Forecasting electricity consumption by aggregating experts; how to design a good set of
experts to appear in Lecture Notes in Statistics: Modeling and Stochastic Learning for Forecasting in High
Dimension, 2013.
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COMBINING FORECASTS
combining
Designing experts
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ANOTHER DATA SET: HEAT DEMAND
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PERSPECTIVES
Forecasting methods:
Industrial implementation on the way (national, substations, cogeneration central in Poland: 30%
better with GAM)
CLR: improve automatic clusturing, forecasting the clusters (HMM)
Combining:
publication of the R package OPERA (Online Prediction through ExpeRts Aggregation) coming soon
application on other data sets
derive probabilistic forecasts from a set of experts
Probabilistic forecasts
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