A multivariate forecasting method for short‐term load using chaotic features and RBF neural network

Abstract

SUMMARYThis paper presents a multivariate forecasting method for electric short-term load using chaos theory and radial basis function (RBF) neural networks. To apply the method, the largest Lyapunov exponent and correlation dimension are firstly calculated which show the electric load series is essentially a chaotic time series. Then, a multivariate chaotic prediction method is proposed taking historical load and temperature into account. Phase space reconstruction of a univariate time series is extended to construct a multivariate time series. Delay time and embedding dimension of the historical load series and temperature series are determined by mutual information and minimal forecasting error, respectively. Finally, a three-layer RBF neural network is employed to forecast the load of one day ahead and one week ahead. Real load data of Chongqing Power Grid are tested. Daily and weekly forecasting results show that the proposed multivariate approach improves the accuracy of forecasting significantly comparing with the univariate methods. Discussion of forecasting error and future work are also presented. As an efficient and effective alternative for STLF, the chaos theory based multivariate forecasting is feasible for potential application.

Soft Measurement Modeling Based on Chaos Theory for Biochemical Oxygen Demand (BOD)

“…The above method for univariate chaotic time series can realize the single variable short-term prediction based on the history value [17,[24][25][26]. It is worth noting that the soft measurement method is a multivariate modeling process.…”

“…In order to select an appropriate delay time τ, there are several methods to choose from, such as mutual information (MI) [17], autocorrelation function [25] and C-C method [30]. Because it can reflect the nonlinear correlation between the two time series, MI method is adopted broadly.…”

“…Chaos is a widely existing phenomenon in nature and is a specific behavior for the nonlinear dynamic system. With the rapid development of chaos theory, the chaotic time series analysis and prediction are widely studied and have been widespread concerned in the research fields such as electric short-term load [17], economics [18], industrial manufacture [19], signal processing [20] and medical diagnosis [21]. A multivariate prediction method was presented for electric short-term load using chaos theory and radial basis function (RBF) neural networks.…”

“…A multivariate prediction method was presented for electric short-term load using chaos theory and radial basis function (RBF) neural networks. The proposed method improves the precision of forecasting significantly comparing with the univariate methods [17]. Multilayer perceptron (MLP) neural network model based on phase space reconstruction (PSR) in chaos theory was proposed to predict the carbon price.…”

“…PSR in chaos theory can memorize all of the properties of a chaotic attractor and clearly recover the motion trace of a time series, thus PSR provides more information for modeling and makes more accurate forecasting possible [17][18][19][20]. Therefore, we suppose that the WWTP is a chaotic system, but this has not been demonstrated yet.…”