Dynamical model reconstruction and accurate prediction
of power-pool time series
IEEE Transactions on Instrumentation and Measurement, 55 (1):
327--336 (February 2006)DOI: doi:10.1109/TIM.2005.861492
Abstract
The emergence of the power pool as a popular
institution for trading of power in different countries
has led to increased interest in the prediction of
power demand and price. We investigate whether the time
series of power-pool demand and price can be modelled
as the output of a low-dimensional chaotic dynamical
system by using delay embedding and estimation of the
embedding dimension, attractor-dimension or
correlation-dimension calculation, Lyapunov-spectrum
and Lyapunov-dimension calculation, stationarity and
nonlinearity tests, as well as prediction analysis.
Different dimension estimates are consistent and show
close similarity, thus increasing the credibility of
the fractal-dimension estimates. The Lyapunov spectrum
consistently shows one positive Lyapunov exponent and
one zero exponent with the rest being negative,
pointing to the existence of chaos. The authors then
propose a least squares genetic programming (LS-GP) to
reconstruct the nonlinear dynamics from the power-pool
time series. Compared to some standard predictors
including the radial basis function (RBF) neural
network and the local state-space predictor, the
proposed method does not only achieve good prediction
of the power-pool time series but also accurately
predicts the peaks in the power price and demand based
on the data sets used in the present study.