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

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 delay...

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Autor principal:	Ladislav Zjavka
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	local weather modeling polynomial network partial differential equation polynomial PDE conversion derivative laplace transformation component model Technology T
Acceso en línea:	https://doaj.org/article/e63eb658a5a846d78eb9bf46a09b1f10
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spelling	oai:doaj.org-article:e63eb658a5a846d78eb9bf46a09b1f102021-11-25T17:26:54ZPhotovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation10.3390/en142275811996-1073https://doaj.org/article/e63eb658a5a846d78eb9bf46a09b1f102021-11-01T00:00:00Zhttps://www.mdpi.com/1996-1073/14/22/7581https://doaj.org/toc/1996-1073Forecasting 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 k<sup>th</sup> 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.Ladislav ZjavkaMDPI AGarticlelocal weather modelingpolynomial networkpartial differential equationpolynomial PDE conversionderivative laplace transformationcomponent modelTechnologyTENEnergies, Vol 14, Iss 7581, p 7581 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	local weather modeling polynomial network partial differential equation polynomial PDE conversion derivative laplace transformation component model Technology T
spellingShingle	local weather modeling polynomial network partial differential equation polynomial PDE conversion derivative laplace transformation component model Technology T Ladislav Zjavka Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation
description	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 k<sup>th</sup> 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.
format	article
author	Ladislav Zjavka
author_facet	Ladislav Zjavka
author_sort	Ladislav Zjavka
title	Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation
title_short	Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation
title_full	Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation
title_fullStr	Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation
title_full_unstemmed	Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation
title_sort	photovoltaic energy all-day and intra-day forecasting using node by node developed polynomial networks forming pde models based on the l-transformation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/e63eb658a5a846d78eb9bf46a09b1f10
work_keys_str_mv	AT ladislavzjavka photovoltaicenergyalldayandintradayforecastingusingnodebynodedevelopedpolynomialnetworksformingpdemodelsbasedontheltransformation
_version_	1718412381879533568

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

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