Photo-Voltaic Power Daily Statistical Predictions Using PDE Models of Stepwise Evolved Polynomial Networks with the Sum PDE Partition and L-transform Substitution

Abstract

Computational methods based on Artificial Intelligence (AI) can convert or post-process data produced by Numerical Weather Prediction (NWP) systems to predict Photo-Voltaic (PV) power in consideration of a plant specific situation. Their statistical models, developed with historical data series, are more precise if they rely on the latest weather observations and PV measurements. NWP models are usually run every 6 h with the prognoses delayed a few hours. Moreover, their accuracy is mostly inadequate for PV plant actual operation. Differential Polynomial Neural Network (D-PNN) is a novel biologically inspired neuro-computing technique which can model complex patterns without reducing significantly the data dimensionality as standard regression or soft-computing does. D-PNN combines appropriate 2-inputs to decompose the n-variable Partial Differential Equation (PDE), being able to describe the atmospheric dynamics, into a set of particular sub-PDEs in its nodes. The selected 2-variable composed PDEs are converted using adapted procedures of Operational Calculus (OC) to obtain the Laplace images of unknown node functions, which are inverse L-transformed to obtain the originals. D-PNN produces applicable sum PDE components in its nodes to extend step by step its composite models towards the optima. The compared AI models are developed with spatial historical data from the estimated optimal daily training periods to process the last day input data series and predict Clear Sky Index (CSI) at the corresponding 24-h horizon.