Explicit formulas for the Variance of the State of a Linearized Power System driven by Gaussian stochastic disturbances Article Swipe

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Xian Wu , Kaihua Xi , Aijie Cheng , Hai Xiang Lin , Jan H. van Schuppen , Chenghui Zhang ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2302.06326

We look into the fluctuations caused by disturbances in power systems. In the linearized system of the power systems, the disturbance is modeled by a Brownian motion process, and the fluctuations are described by the covariance matrix of the associated stochastic process at the invariant probability distribution. We derive explicit formulas for the covariance matrix for the system with a uniform damping-inertia ratio. The variance of the frequency at the node with the disturbance is significantly bigger than the sum of those at all the other nodes, indicating the disturbance effects the node most, according to research on the variances in complete graphs and star graphs. Additionally, it is shown that adding new nodes typically does not aid in reducing the variations at the disturbance's source node. Finally, it is shown by the explicit formulas that the line capacity affect the variation of the frequency and the inertia affects the variance of the phase differences.

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Mathematics Covariance Variance (accounting) Disturbance (geology) Gaussian Node (physics) Inertia Brownian motion Applied mathematics Covariance matrix Control theory (sociology) Invariant (physics) Statistical physics Statistics Physics Computer science Classical mechanics Control (management) Biology Accounting Paleontology Mathematical physics Artificial intelligence Quantum mechanics Business

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2302.06326
PDF: https://arxiv.org/pdf/2302.06326
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Title: Explicit formulas for the Variance of the State of a Linearized Power System driven by Gaussian stochastic disturbances

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Publication year: 2023

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Publication date: 2023-02-13

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Authors: Xian Wu, Kaihua Xi, Aijie Cheng, Hai Xiang Lin, Jan H. van Schuppen, Chenghui Zhang

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Concepts: Mathematics, Covariance, Variance (accounting), Disturbance (geology), Gaussian, Node (physics), Inertia, Brownian motion, Applied mathematics, Covariance matrix, Control theory (sociology), Invariant (physics), Statistical physics, Statistics, Physics, Computer science, Classical mechanics, Control (management), Biology, Accounting, Paleontology, Mathematical physics, Artificial intelligence, Quantum mechanics, Business

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abstract_inverted_index.research	96
abstract_inverted_index.systems,	18
abstract_inverted_index.systems.	10
abstract_inverted_index.variance	64, 150
abstract_inverted_index.according	94
abstract_inverted_index.described	32
abstract_inverted_index.frequency	67, 144
abstract_inverted_index.invariant	44
abstract_inverted_index.typically	114
abstract_inverted_index.variances	99
abstract_inverted_index.variation	141
abstract_inverted_index.associated	39
abstract_inverted_index.covariance	35, 53
abstract_inverted_index.indicating	87
abstract_inverted_index.linearized	13
abstract_inverted_index.stochastic	40
abstract_inverted_index.variations	121
abstract_inverted_index.disturbance	20, 73, 89
abstract_inverted_index.probability	45
abstract_inverted_index.differences.	154
abstract_inverted_index.disturbances	7
abstract_inverted_index.fluctuations	4, 30
abstract_inverted_index.Additionally,	106
abstract_inverted_index.distribution.	46
abstract_inverted_index.disturbance's	124
abstract_inverted_index.significantly	75
abstract_inverted_index.damping-inertia	61
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	6
citation_normalized_percentile