Short-term prediction of wind power using a hybrid pseudo-inverse Legendre neural network and adaptive firefly algorithm

This paper proposes a low-complexity pseudo-inverse Legendre neural network (PILNNR) with radial basis function (RBF) units in the hidden layer for accurate wind power prediction on a short-term basis varying from 10- to 60-min interval. The random input weights between the expanded input layer using Legendre polynomials and the RBF units in the hidden layer are optimized with a metaheuristic firefly (FF) algorithm for error minimization and improvement of the learning speed. For comparison, two other forecasting models, namely pseudo-inverse RBF (PIRBFNN-FF) neural network and PILNNR [with tanh functions in the hidden layer (PILNNT-FF)] with input-to-hidden layer weights being optimized by FF algorithm, are also presented in this paper. Also the weights between the hidden layer and the output neuron of these neural models are obtained by Moore–Penrose pseudo-inverse algorithm. Further to improve the stability of the weight learning procedure, the L2-norm-regularized least squares (ridge regression) technique is used. A superior predictive ability test is performed on the three proposed wind power forecasting models using bootstrapping procedure in order to identify the best model. Several case studies using wind power data of the wind farms in the states of Wyoming and California in USA and Sotavento wind farm in Spain are presented in this paper.