Modeling and Forecasting Daily Electricity Load Curves: A Hybrid Approach

We propose a hybrid approach for the modeling and the short-term forecasting of electricity loads. Two building blocks of our approach are (1) modeling the overall trend and seasonality by fitting a generalized additive model to the weekly averages of the load and (2) modeling the dependence structure across consecutive daily loads via curve linear regression. For the latter, a new methodology is proposed for linear regression with both curve response and curve regressors. The key idea behind the proposed methodology is dimension reduction based on a singular value decomposition in a Hilbert space, which reduces the curve regression problem to several ordinary (i.e., scalar) linear regression problems. We illustrate the hybrid method using French electricity loads between 1996 and 2009, on which we also compare our method with other available models including the Électricité de France operational model. Supplementary materials for this article are available online.

[1]  S. Wood.  Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models , 2011 .

[2]  Jairo Cugliari,et al.  Prévision non paramétrique de processus à valeurs fonctionnelles : application à la consommation d’électricité , 2011 .

[3]  S. Wood.  Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models , 2004 .

[4]  A. Dawid.  Spherical Matrix Distributions and a Multivariate Model , 1977 .

[5]  Peter Hall,et al.  Assessing the finite dimensionality of functional data , 2006 .

[6]  Anestis Antoniadis,et al.  Clustering Functional Data using Wavelets , 2010, Int. J. Wavelets Multiresolution Inf. Process..

[7]  P. McSharry,et al.  Short-Term Load Forecasting Methods: An Evaluation Based on European Data , 2007, IEEE Transactions on Power Systems.

[8]  G. He,et al.  EXTENDING CORRELATION AND REGRESSION FROM MULTIVARIATE TO FUNCTIONAL DATA , 2000 .

[9]  Jianqing Fan.  Nonlinear Time Series , 2003 .

[10]  H. Müller,et al.  FUNCTIONAL RESPONSE MODELS , 2004 .

[11]  J. Ramsay,et al.  Some Tools for Functional Data Analysis , 1991 .

[12]  Jeng-Min Chiou,et al.  Functional clustering and identifying substructures of longitudinal data , 2007 .

[13]  S. Wood.  Generalized Additive Models: An Introduction with R , 2006 .

[14]  L. Wasserman,et al.  CATS , 2005 .

[15]  A. Harvey,et al.  Forecasting Hourly Electricity Demand Using Time-Varying Splines , 1993 .

[16]  M. Hallin,et al.  Determining the Number of Factors in the General Dynamic Factor Model , 2007 .

[17]  Catherine A. Sugar,et al.  Clustering for Sparsely Sampled Functional Data , 2003 .

[18]  David S. Gilliam,et al.  Some properties of canonical correlations and variates in infinite dimensions , 2008 .

[19]  Joel L. Horowitz,et al.  Methodology and convergence rates for functional linear regression , 2007, 0708.0466.

[20]  B. Silverman,et al.  Smoothed functional principal components analysis by choice of norm , 1996 .

[21]  Clifford Lam,et al.  Factor modeling for high-dimensional time series: inference for the number of factors , 2012, 1206.0613.

[22]  Clive W. J. Granger,et al.  Short-run forecasts of electricity loads and peaks , 2001 .

[23]  Rob J Hyndman,et al.  Short-Term Load Forecasting Based on a Semi-Parametric Additive Model , 2012, IEEE Transactions on Power Systems.

[24]  B. Mallick,et al.  Functional clustering by Bayesian wavelet methods , 2006 .

[25]  Anestis Antoniadis,et al.  A Functional Wavelet-Kernel Approach for Continuous-time Prediction , 2005 .

[26]  Alan Y. Chiang,et al.  Generalized Additive Models: An Introduction With R , 2007, Technometrics.

[27]  James W. Taylor,et al.  Triple seasonal methods for short-term electricity demand forecasting , 2010, Eur. J. Oper. Res..

[28]  Ulrich Stadtmüller,et al.  Functional singular component analysis , 2011 .

[29]  F. Smithies.  The Eigen‐Values and Singular Values of Integral Equations† , 1938 .

[30]  Carlo Novara,et al.  Nonlinear Time Series , 2003 .

[31]  A. Antoniadis,et al.  A functional wavelet–kernel approach for time series prediction , 2006 .

[32]  Suhartono,et al.  Short-term electricity load forecasting , 2011 .

[33]  Siem Jan Koopman,et al.  Dynamic factors in periodic time-varying regressions with an application to hourly electricity load modelling , 2012, Comput. Stat. Data Anal..

[34]  Anestis Antoniadis,et al.  Functional Clustering using Wavelets , 2010 .

[35]  R. Buizza,et al.  Neural Network Load Forecasting with Weather Ensemble Predictions , 2002, IEEE Power Engineering Review.

[36]  Remy Cottet,et al.  Bayesian Modeling and Forecasting of Intraday Electricity Load , 2003 .

[37]  Hans-Georg Müller,et al.  Functional Data Analysis , 2016 .

[38]  Clive W. J. Granger,et al.  Semiparametric estimates of the relation between weather and electricity sales , 1986 .

[39]  Rob J Hyndman,et al.  A state space framework for automatic forecasting using exponential smoothing methods , 2002 .

[40]  Qiwei Yao,et al.  Identifying the finite dimensionality of curve time series , 2010, 1211.2522.

[41]  Jane-Ling Wang,et al.  Functional canonical analysis for square integrable stochastic processes , 2003 .

[42]  T. Hsing,et al.  Canonical correlation for stochastic processes , 2008 .

[43]  S. Koopman,et al.  An Hourly Periodic State Space Model for Modelling French National Electricity Load , 2007 .

[44]  P. McSharry,et al.  A comparison of univariate methods for forecasting electricity demand up to a day ahead , 2006 .

[45]  E. Hannan.  The general theory of canonical correlation and its relation to functional analysis , 1961, Journal of the Australian Mathematical Society.

[46]  H. Müller,et al.  Functional Data Analysis for Sparse Longitudinal Data , 2005 .