A hybrid ARMA-Legendre polynomial neural network and evolutionary H-infinity filter for the prediction of electricity market clearing price

Abstract

A hybrid adaptive autoregressive moving average (ARMA) and Legendre polynomial neural network trained by an evolutionary H-infinity filter is presented in this paper for predicting short-term electricity prices in a deregulated market. The proposed model comprises a linear autoregressive (AR) part and nonlinear moving average (MA) part obtained through the use of Legendre polynomial basis functions. The Legendre polynomial functional block helps to introduce nonlinearity by expanding the input space to higher dimensional space through basis functions without using any hidden layer like the multilayered perceptron (MLP) network. Instead of using the standard forward-backward (FB-LMS) algorithm for learning the weight parameters of the ARMALEG (hybrid ARMA and Legendre network) a robust H-infinity filter is used which is superior to the widely used extended Kalman filter in terms of handling uncertain noise covariances resulting in fast convergence and tracking. Further to improve the accuracy, the H-infinity filter parameters are optimised using a differential evolution (DE) strategy. The proposed method is tested on PJM electricity market and the residuals (MAPE) are compared with other forecasting methods indicating the improved accuracy of the approach and its suitability to produce a real-time forecast.