Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems
| dc.contributor.author | González-Zumba, Andrés | |
| dc.contributor.author | Fernández-de-Córdoba, Pedro | |
| dc.contributor.author | Cortés, Juan-Carlos | |
| dc.contributor.author | Mehrmann, Volker | |
| dc.date.accessioned | 2020-12-10T08:54:12Z | |
| dc.date.available | 2020-12-10T08:54:12Z | |
| dc.date.issued | 2020-08-20 | |
| dc.date.updated | 2020-09-03T06:16:01Z | |
| dc.description.abstract | In this paper, we discuss stochastic differential-algebraic equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs). We focus on index-1 SDAEs and their reformulation as ordinary stochastic differential equations (SDEs). Via ergodic theory, it is then feasible to analyze the LEs via the random dynamical system generated by the underlying SDEs. Once the existence of well-defined LEs is guaranteed, we proceed to the use of numerical simulation techniques to determine the LEs numerically. Discrete and continuous QR decomposition-based numerical methods are implemented to compute the fundamental solution matrix and use it in the computation of the LEs. Important computational features of both methods are illustrated via numerical tests. Finally, the methods are applied to two applications from power systems engineering, including the single-machine infinite-bus (SMIB) power system model. | en |
| dc.description.sponsorship | DFG, 239904186, TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken | en |
| dc.description.sponsorship | DFG, 313504828, SPP 1984: Hybride und multimodale Energiesysteme: Systemtheoretische Methoden für die Transformation und den Betrieb komplexer Netze | en |
| dc.identifier.eissn | 2227-7390 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/12169 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-11043 | |
| dc.language.iso | en | en |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject.ddc | 510 Mathematik | de |
| dc.subject.other | stochastic differential-algebraic equations | en |
| dc.subject.other | lyapunov exponent | en |
| dc.subject.other | power system stability | en |
| dc.subject.other | spectral analysis | en |
| dc.subject.other | stochastic systems | en |
| dc.subject.other | numerical methods | en |
| dc.title | Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.articlenumber | 1393 | en |
| dcterms.bibliographicCitation.doi | 10.3390/math8091393 | en |
| dcterms.bibliographicCitation.issue | 9 | en |
| dcterms.bibliographicCitation.journaltitle | Mathematics | en |
| dcterms.bibliographicCitation.originalpublishername | MDPI | en |
| dcterms.bibliographicCitation.originalpublisherplace | Basel | en |
| dcterms.bibliographicCitation.volume | 8 | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.group | FG Numerische Mathematik | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |