Photo-voltaic power intra-day and daily statistical predictions using sum models composed from L-transformed PDE compone
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ORIGINAL PAPER
Photo-voltaic power intra-day and daily statistical predictions using sum models composed from L-transformed PDE components in nodes of step by step developed polynomial neural networks Ladislav Zjavka1 Received: 19 July 2019 / Accepted: 7 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2021
Abstract Precise forecasts of photo-voltaic (PV) energy production are necessary for its planning, utilization and integration into the electrical grid. Intra-day or daily statistical models, using only the latest weather observations and power data measurements, can predict PV power for a plant-specific location and condition on time. Numerical weather prediction (NWP) systems are run every 6 h to produce free prognoses of local cloudiness with a considerable delay and usually not in operational quality. Differential polynomial neural network (D-PNN) is a novel neuro-computing technique able to model complex weather patterns. D-PNN decomposes the n-variable partial differential equation (PDE), allowing complex representation of the nearground atmospheric dynamics, into a set of 2-input node sub-PDEs. These are converted and substituted using the Laplace transformation according to operational calculus. D-PNN produces applicable PDE components which extend, one by one, its composite models using the selected optimal inputs. The models are developed with historical spatial data from estimated daily training periods for a specific inputs- > output time-shift to predict clear-sky index. Multi-step 1–9 h and one-step 24-h PV power predictions using machine learning and regression are compared to assess the performance of their models for both of the approaches. The presented spatial models obtain a better prediction accuracy than those post-processing NWP data, using a few variables only. The daily statistical models allow prediction of full PVP cycles in one step with an adequate accuracy in the morning and afternoon hours. This is inevitable in management of PV plant energy production and consumption. Keywords Uncertainty modeling · Partial differential equation · Polynomial neural network · Operational calculus PDE conversion · Laplace transformation
1 Introduction Solar radiation variability is caused by many uncertain factors possible to describe by differential equations. Weather prediction methods can be broadly classified into 3 main approaches: • NWP systems using physical consideration; • statistical regression or soft-computing approach using historical data; • hybrid or ensemble models based on combined methods.
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Ladislav Zjavka [email protected] Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VŠB-Technical University of Ostrava, 17. listopadu 15/2172, Ostrava, Czech Republic
NWP systems simplify the atmospheric circulation, solving sets of primitive physical equations for the ideal gas flow. Their deterministic NWP models are unable to recognize detailed physical events at the surface level as they use a fixed grid scale for the
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