The prediction of electricity demand is of much interest to the electricity supply industry, both to aid long term planning strategies, involving the forecasting of seasonal peak demands, and for use in the short term (up to 24 hours) operation of generating plant. Many different techniques have been tried, with work ranging from the earlier methods of regression to the more recent, optimal estimation (Kalman filtering) techniques.
In this project, we exploit and extend the Unobserved Components (UC) approach developed at Lancaster University over the last ten years and implemented both in a computer program called microCAPTAIN and in the Matlab software environment .
The UC model is considered in two basic versions: a univariate Dynamic Harmonic Regression (DHR) form, where the series is represented by the usual sum of low frequency trend, cyclical, seasonal and irregular components, but with the seasonal component modelled by a non-standard, time variable parameter, harmonic regression relationship; and a more comprehensive Data-Based Mechanistic model form, where these components are expanded to allow for linear or non-linear effects arising from the variations in measured input or exogenous variables. In electricity demand it is common to considere weather variables (like temperature, relative humidity, wind speed, etc.); socio economic indicators (prices, general economic context, etc.); etc.
In the case of a model with inputs incorporated, the exogenous effects can take the form of static (possibly nonlinear) regression relationships involving the exogenous variables; or they may arise from dynamic influences, with the exogenous variables affecting the series through (possibly nonlinear) dynamic models. In both versions, however, the recursive Kalman Filter and Fixed Interval Smoothing algorithms are exploited to estimate the various components, making the model particularly useful for adaptive seasonal adjustment, signal extraction, interpolation over gaps, and forecasting (or backcasting) of fairly general, nonstationary time series.
Optimisation of the "hyper-parameters" in the UC models (e.g. the noise variance ratio and other parameters in the stochastic state-space models of the various components) is carried in a variety of ways, depending upon the nature of the model. In the univariate case, the exceptional spectral properties of the DHR model allows for the development of a novel method of estimation in the frequency domain, where the logarithm of the model pseudo-spectrum is fitted to the logarithm of the empirical AutoRegressive (AR) spectrum. In all the applications considered, this cost function seems better defined than the equivalent likelihood function and yields both improved convergence properties and reduced numerical requirements. In the case where the exogenous input effects are taken into account, the optimisation is normally carried out in an iterative manner, sometimes involving more conventional maximum Likelihood estimation based on prediction error decomposition, but sometimes exploiting alternative procedures.
This overall approach to UC modelling has proven successful in the analysis, forecasting and seasonal adjustment of many different kinds of nonstationary and nonlinear time series in a variety of different areas. Apart from electricity load demand forecasting in UK the approach has proven very useful in analysing tourism demand in Spain; phone calls offered by a UK credit card company; unemployment in the US over the past 50 years; seasonal adjustment of the UK Labour Force Survey data; long term temperature variations in a US river catchment; and nonlinear rainfall-flow modelling in a variety of Countries.
The whole methodology has been coded into Matlab and a Graphical User Interface (GUI) has been developed to allow for an easy way to go along the process of identification, estimation and forecasting. Here there is a snapshot of one window of the GUI environment for one week ahead forecasts (hourly data):
Bunn, D and Farmer, E D, 1985, Comparative Models for Electrical Load Forecasting, New York: John Wiley.
Engle, R. F., Granger, C. W. J., Rice, J. and Weiss, A. (1986), Semiparametric Estimates of the Relation Between Weather and Electricity Sales, Journal of the Amer. Stat. Assoc., 81, No. 394.
Engle, R. F., Mustafa, C. and Rice, J. (1992), Modelling peak electricity demand, Journal of Forecasting, 11, 2241-2251.
Harvey, A. C. and Koopman, S. J. (1993), Forecasting Hourly Electricity Demand Using Time-varying Splines, Journal of the Amer. Stat. Assoc., 88, No. 424.
Irisarri, G. D., Windergren, S. E. and Yehsakul, P. D. (1982), On Line Load Forecasting for Energy Control Center Application, IEEE Transact. on Power Apparatus and Systems, Vol. PAS-101, No. 1.
Magd, M A Abu-El, and Sinha, N K, 1982 Short-term demand modelling and forecasting: a review. IEEE Trans on Systems. Man. and Cybernetics, SMC-12, 3.
Ng, C N and Young, P C, 1990, Recursive Estimation and Forecasting of Nonstationary Time Series, Journal of Forecasting, 9, 173-204.
Peirson, J. and Henley, A. (1993), Electricity load and temperature: Issues in dynamic specification, in Recent studies of the Demand for Energy in the UK, David Hawdon (ed.), Surrey Energy Economics Discussion Paper Series (SEEDS), Department of Economics, University of Surrey, Surrey
Young, P C, 1994, Time-variable Parameter and Trend Estimation in Non-stationary Economic Time Series. Journal of Forecasting, 13, 179-210.
Young, P C and Benner, S, 1991, microCAPTAIN Handbook: Version 2.0.
