Universität zu Köln

Rydin Gorjão, Leonardo ORCID: 0000-0001-5513-0580 (2021). Stochastic timeseries analysis in electric power systems and paleo-climate data. PhD thesis, Universität zu Köln.

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Abstract

In this thesis a data science study of elementary stochastic processes is laid, aided with the development of two numerical software programmes, applied to power-grid frequency studies and Dansgaard--Oeschger events in paleo-climate data. Power-grid frequency is a key measure in power grid studies. It comprises the balance of power in a power grid at any instance. In this thesis an elementary Markovian Langevin-like stochastic process is employed, extending from existent literature, to show the basic elements of power-grid frequency dynamics can be modelled in such manner. Through a data science study of power-grid frequency data, it is shown that fluctuations scale in an inverse square-root relation with their size, alike any other stochastic process, confirming previous theoretical results. A simple Ornstein--Uhlenbeck is offered as a surrogate model for power-grid frequency dynamics, with a versatile input of driving deterministic functions, showing not surprisingly that driven stochastic processes with Gaussian noise do not necessarily show a Gaussian distribution. A study of the correlations between recordings of power-grid frequency in the same power-grid system reveals they are correlated, but a theoretical understanding is yet to be developed. A super-diffusive relaxation of amplitude synchronisation is shown to exist in space in coupled power-grid systems, whereas a linear relation is evidenced for the emergence of phase synchronisation. Two Python software packages are designed, offering the possibility to extract conditional moments for Markovian stochastic processes of any dimension, with a particular application for Markovian jump-diffusion processes for one-dimensional timeseries. Lastly, a study of Dansgaard--Oeschger events in recordings of paleoclimate data under the purview of bivariate Markovian jump-diffusion processes is proposed, augmented by a semi-theoretical study of bivariate stochastic processes, offering an explanation for the discontinuous transitions in these events and showing the existence of deterministic couplings between the recordings of the dust concentration and a proxy for the atmospheric temperature.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Rydin Gorjão, Leonardo leonardo.rydin@gmail.com https://orcid.org/0000-0001-5513-0580 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-357531
Date:	18 February 2021
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Natural sciences and mathematics Mathematics Physics
Uncontrolled Keywords:	Keywords Language Stochastic timeseries English Power-grid systems English Paleo-climate timeseries English
Date of oral exam:	18 February 2021
Referee:	Name Academic Title Witthaut, Dirk J-Prof. Dr. Krug, Joachim Prof. Dr. Bollenbach, Tobias Prof. Dr. Filatrella, Giovanni Prof. Dr. Ansmann, Gerrit Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/35753