https://doi.org/10.1140/epjp/s13360-023-04008-y
Regular Article
Storage size estimation for volatile renewable power generation: an application of the Fokker–Planck equation
Karl Ahlborn Maschinenfabrik KG, Vor dem Scheuerchen 17, 37247, Grossalmerode, Germany
Received:
25
April
2022
Accepted:
11
April
2023
Published online:
10
May
2023
The time series of the volatile wind and solar power production in Germany are analysed with regard to a storage system with a finite capacity. The dimensions of this system are estimated in such a way that the storage is available at any time with a certain probability of failure. It is shown that, under simplifying assumptions, the storage filling equation belongs to the equations describing the Brownian motion of particles in the viscous limit. Using the associated Fokker–Planck equation, we show that the storage content is exponentially distributed in a first approximation and the failure probability is calculated from the distribution function. It is shown that the wind and solar power production together with a storage facility is in principle capable of providing a safe base load for longer periods of time if the mean inflow of the storage facility is more than 20% larger than the mean outflow.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
