Bálint Hartmann, Géza Ódor, Kristóf Benedek, István Papp
{"title":"Power-grid modelling via gradual improvement of parameters","authors":"Bálint Hartmann, Géza Ódor, Kristóf Benedek, István Papp","doi":"arxiv-2409.02758","DOIUrl":null,"url":null,"abstract":"The dynamics of electric power systems are widely studied through the phase\nsynchronization of oscillators, typically with the use of the Kuramoto\nequation. While there are numerous well-known order parameters to characterize\nthese dynamics, shortcoming of these metrics are also recognized. To capture\nall transitions from phase disordered states over phase locking to fully\nsynchronized systems, new metrics were proposed and demonstrated on homogeneous\nmodels. In this paper we aim to address a gap in the literature, namely, to\nexamine how gradual improvement of power grid models affect the goodness of\ncertain metrics. To study how the details of models are perceived by the\ndifferent metrics, 12 variations of a power grid model were created,\nintroducing varying level of heterogeneity through the coupling strength, the\nnodal powers and the moment of inertia. The grid models were compared using a\nsecond-order Kuramoto equation and adaptive Runge-Kutta solver, measuring the\nvalues of the phase, the frequency and the universal order parameters. Finally,\nfrequency results of the models were compared to grid measurements. We found\nthat the universal order parameter was able to capture more details of the grid\nmodels, especially in cases of decreasing moment of inertia. The most\nheterogeneous models showed very low synchronization and thus suggest a\nlimitation of the second-order Kuramoto equation. Finally, we show local\nfrequency results related to the multi-peaks of static models, which implies\nthat spatial heterogeneity can also induce such multi-peak behavior.","PeriodicalId":501043,"journal":{"name":"arXiv - PHYS - Physics and Society","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Physics and Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02758","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The dynamics of electric power systems are widely studied through the phase
synchronization of oscillators, typically with the use of the Kuramoto
equation. While there are numerous well-known order parameters to characterize
these dynamics, shortcoming of these metrics are also recognized. To capture
all transitions from phase disordered states over phase locking to fully
synchronized systems, new metrics were proposed and demonstrated on homogeneous
models. In this paper we aim to address a gap in the literature, namely, to
examine how gradual improvement of power grid models affect the goodness of
certain metrics. To study how the details of models are perceived by the
different metrics, 12 variations of a power grid model were created,
introducing varying level of heterogeneity through the coupling strength, the
nodal powers and the moment of inertia. The grid models were compared using a
second-order Kuramoto equation and adaptive Runge-Kutta solver, measuring the
values of the phase, the frequency and the universal order parameters. Finally,
frequency results of the models were compared to grid measurements. We found
that the universal order parameter was able to capture more details of the grid
models, especially in cases of decreasing moment of inertia. The most
heterogeneous models showed very low synchronization and thus suggest a
limitation of the second-order Kuramoto equation. Finally, we show local
frequency results related to the multi-peaks of static models, which implies
that spatial heterogeneity can also induce such multi-peak behavior.