Dynamical model reconstruction and accurate prediction of power-pool time series

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. In this paper, the authors investigate whether the time series of power-pool demand and price can be modeled 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.