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Keywords:

  • hierarchical dynamic linear model;
  • state-space model;
  • periodic spline;
  • price elasticity

We propose a model of the daily load curve for residential electricity usage, including in particular the effects of dynamic price incentives on the demand response, a topic of considerable interest in the emerging Smart Grid. The model is based on a time series and stochastic regression framework in which the observed daily load curve is represented in terms of a set of periodic smoothing-spline basis functions, with the basis function coefficients evolving according to a linear Gaussian state-space model that incorporates level shifts, day of the week and holiday adjustments, and weather effects, as well as the dynamic price-incentive effects mentioned earlier. Model parameters are estimated from observational time-series data using maximum-likelihood methods, with the computations being efficiently carried out using Kalman filtering recursions. The resulting fitted model can be used for short-term load forecasting by providing a forward sequence of price-incentive signals and weather projections over the forecast period. This proposed modeling and forecasting methodology have many advantages over competing methods in the literature, including the ability to model intraday load-substitution effects that are induced by the specified dynamic pricing schedules, the ability to use fine-grained (5–15 min interval) observational data without greatly increasing the computational cost of the estimation and forecasting procedures, the ability to use informative prior distributions for any model parameters that cannot be reliably estimated from the available observational data, and the ability to update model forecasts based on the latest sequence of partial observational data without having to store the entire time-series history. Copyright © 2013 John Wiley & Sons, Ltd.