Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation

Ladislav Zjavka

doi:10.3390/en14227581

Abstract

Forecasting Photovoltaic (PV) energy production, based on the last weather and power data only, can obtain acceptable prediction accuracy in short-time horizons. Numerical Weather Prediction (NWP) systems usually produce free forecasts of the local cloud amount each 6 h. These are considerably delayed by several hours and do not provide sufficient quality. A Differential Polynomial Neural Network (D-PNN) is a recent unconventional soft-computing technique that can model complex weather patterns. D-PNN expands the n-variable kth order Partial Differential Equation (PDE) into selected two-variable node PDEs of the first or second order. Their derivatives are easy to convert into the Laplace transforms and substitute using Operator Calculus (OC). D-PNN proves two-input nodes to insert their PDE components into its gradually expanded sum model. Its PDE representation allows for the variability and uncertainty of specific patterns in the surface layer. The proposed all-day single-model and intra-day several-step PV prediction schemes are compared and interpreted with differential and stochastic machine learning. The statistical models are evolved for the specific data time delay to predict the PV output in complete day sequences or specific hours. Spatial data from a larger territory and the initially recognized daily periods enable models to compute accurate predictions each day and compensate for unexpected pattern variations and different initial conditions. The optimal data samples, determined by the particular time shifts between the model inputs and output, are trained to predict the Clear Sky Index in the defined horizon.

Highlights

Accurate forecasting of hourly or daily solar radiation or direct PV Power (PVP) is challenging, as it is influenced by complex dynamic processes combined with irregular fluctuations resulting in local anomalies [1]
Matlab—Statistics and Machine Learning Toolbox (SMLT) for regression was used with the selected data of 26 input variables to calculate the Clear Sky Index (CSI) output (Figures 2 and 3) which was converted to PVP predictions at the corresponding time, analogous to Differential Polynomial Neural Network (D-Polynomial Neural Network (PNN)) (15)
Persistent benchmarks can rarely obtain the better accuracy on days of changeable weather with unpredictable patterns, where the averaging of single CSI series properly compensates for the PVP uncertainty

Summary

Introduction

Accurate forecasting of hourly or daily solar radiation or direct PV Power (PVP) is challenging, as it is influenced by complex dynamic processes combined with irregular fluctuations resulting in local anomalies [1]. Artificial Intelligence (AI) techniques, using historical time series, attempt to model local patterns and predict intra-day stochastic PVP supplies taking into account the previous case states [3]. This statistical approach can be used to post-process the corresponding NWP output in 24–48 h prediction series [4]. The 24 or 48 h local forecasts of a regional NWP model are processed to compensate for the unavailable observations in the calculation of the PVP output series at the corresponding times [6]. Changeable conditions, unexpected abnormalities or undefined states can result in alterative usefulness and efficiency of both the compared statistical approaches, which can be combined and implemented for various PVP plant specifications and configurations

State of the Art in PVP Forecasting

11 Pr1e2diction h1o3ur 14

Discussion

Conclusions