Citation: Karbowniczak, A.; Latala,
H.; N˛ ecka, K.; Kurpaska, S.; Bergel, T.
Modelling of the Electric Energy
Storage Process in a PCM Battery.
Energies 2022, 15, 735. https://
doi.org/10.3390/en15030735
Academic Editors: Marcin Wójcik,
Justyna Chodkowska-Miszczuk and
Andrea Frazzica
Received: 10 December 2021
Accepted: 11 January 2022
Published: 20 January 2022
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energies
Article
Modelling of the Electric Energy Storage Process in
a PCM Battery
Anna Karbowniczak
1
, Hubert Latala
1,
* , Krzysztof N ˛ ecka
1
, Slawomir Kurpaska
1
and Tomasz Bergel
2
1
Faculty of Production and Power Engineering, University of Agriculture in Krakow, 30-149 Krakow, Poland;
anna.karbowniczak@urk.edu.pl (A.K.); krzysztof.necka@urk.edu.pl (K.N.);
slawomir.kurpaska@urk.edu.pl (S.K.)
2
Faculty of Environmental Engineering and Land Surveying, University of Agriculture in Krakow,
30-059 Krakow, Poland; tomasz.bergel@urk.edu.pl
* Correspondence: hubert.latala@urk.edu.pl
Abstract: The essence of the research was the modeling of a real electric energy storage system in a
phase change battery operating in a foil tunnel. The scope of the work covered the construction of two
partial models, i.e., energy storage in the PCM accumulator and heat losses in the PCM accumulator.
Their construction was based on modeling methods selected on the basis of a literature review and
previous analyses, i.e., artificial neural networks, random forest, enhanced regression trees, MARS
plines, standard multiple regression, standard regression trees, exhaustive for regression trees. Based
on the analysis of the error values, the models of the best quality were selected. The final result of
this study was the construction of such a model of the process of storing electricity in a PCM battery,
characterized by the mean absolute percentage error forecast error of 1–2%. The achievement of
this goal was possible thanks to the use of the artificial neural networks model for which the input
variables were the amount of energy supplied to the accumulator and the temperature of the heat
storage medium.
Keywords: energy storage system; photovoltaic conversion modeling; phase-change battery
1. Introduction
In recent years, we have observed a growing interest in photovoltaic conversion,
which consists in the direct conversion of solar radiation energy into electricity, with the
use of photovoltaic cells. This requires the efficient use of the energy obtained, because
the availability of solar radiation energy is very variable in the daily and annual period.
Therefore, it is necessary to take actions both in the area of forecasting energy yield in
advance of time as well as in the field of effective energy storage [1].
A typical information source for forecasting energy yield is a map of predicted an-
nual electricity production, which may be available free of charge as well as commercially.
Well-known sources of such data in Europe are services such as SoDa using the Helio-
Clim [2], PVGIS [3,4] or METEONORM [5] databases. Commonly used solar bases are
based mainly on satellite measurements from various observation systems (the most pop-
ular are METEOSAT in Europe, GOES in the USA and GMS in Japan), sometimes the
databases are supplemented with information from ground measurements. The result of
the forecast can be defined as an estimate of the annual electricity production from a PV
installation in relation to 1 kWp of installed power for a given geographic location for a
typical meteorological year.
For the current control of the operation of the photovoltaic installation, forecasts are
not required with an annual resolution, but with a daily or hourly resolution. Most often
they are built on the basis of forecasts of meteorological conditions at the location of the
gym. Among the commonly used methods for forecasting electricity yield from a PV
Energies 2022, 15, 735. https://doi.org/10.3390/en15030735 https://www.mdpi.com/journal/energies