On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems

Yijun Chen; Kanghong Shi; Ian R. Petersen; Elizabeth L. Ratnam

doi:10.1016/j.ifacol.2024.10.169

On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems

Yijun Chen, Kanghong Shi, Ian R. Petersen, Elizabeth L. Ratnam

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

Abstract

In this paper, we propose employing battery-based feedback control and nonlinear negative imaginary (NI) systems theory to reduce the need for such expansion. By formulating a novel Luré-Postnikov-like Lyapunov function, stability results are presented for the feedback interconnection of two single nonlinear NI systems, while output feedback consensus results are established for the feedback interconnection of two networked nonlinear NI systems based on a network topology. This theoretical framework underpins our design of battery-based control in power transmission systems. We demonstrate that the power grid can be gradually transitioned into the proposed NI systems, one transmission line at a time.

Original language	English
Title of host publication	26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024
Editors	Rodolphe Sepulchre, Malcolm C. Smith
Place of Publication	Cambridge UK
Publisher	Elsevier
Pages	220-225
Number of pages	6
Volume	58
Edition	17
DOIs	https://doi.org/10.1016/j.ifacol.2024.10.169
Publication status	Published - 2024
Externally published	Yes
Event	International Symposium on Mathematical Theory of Networks and Systems 2024 - Cambridge, United Kingdom Duration: 19 Aug 2024 → 23 Aug 2024 Conference number: 26th https://www.sciencedirect.com/journal/ifac-papersonline/vol/58/issue/17 (Proceedings) https://mtns2024.eng.cam.ac.uk/ (Website)

Publication series

Name	IFAC-PapersOnLine
Publisher	Elsevier - International Federation of Automatic Control (IFAC)
ISSN (Print)	2405-8971
ISSN (Electronic)	2405-8963

Conference

Conference	International Symposium on Mathematical Theory of Networks and Systems 2024
Abbreviated title	MTNS 2024
Country/Territory	United Kingdom
City	Cambridge
Period	19/08/24 → 23/08/24
Internet address	https://www.sciencedirect.com/journal/ifac-papersonline/vol/58/issue/17 (Proceedings) https://mtns2024.eng.cam.ac.uk/ (Website)

Keywords

consensus
electrical power systems
Nonlinear negative imaginary systems
stability

Access to Document

10.1016/j.ifacol.2024.10.169Licence: CC BY-NC-ND

650877007-oaFinal published version, 380 KBLicence: CC BY-NC-ND

Cite this

Chen, Y., Shi, K., Petersen, I. R., & Ratnam, E. L. (2024). On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems. In R. Sepulchre, & M. C. Smith (Eds.), 26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024 (17 ed., Vol. 58, pp. 220-225). (IFAC-PapersOnLine). Elsevier. https://doi.org/10.1016/j.ifacol.2024.10.169

Chen, Yijun ; Shi, Kanghong ; Petersen, Ian R. et al. / On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems. 26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024. editor / Rodolphe Sepulchre ; Malcolm C. Smith. Vol. 58 17. ed. Cambridge UK : Elsevier, 2024. pp. 220-225 (IFAC-PapersOnLine).

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title = "On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems",

abstract = "In this paper, we propose employing battery-based feedback control and nonlinear negative imaginary (NI) systems theory to reduce the need for such expansion. By formulating a novel Lur{\'e}-Postnikov-like Lyapunov function, stability results are presented for the feedback interconnection of two single nonlinear NI systems, while output feedback consensus results are established for the feedback interconnection of two networked nonlinear NI systems based on a network topology. This theoretical framework underpins our design of battery-based control in power transmission systems. We demonstrate that the power grid can be gradually transitioned into the proposed NI systems, one transmission line at a time.",

keywords = "consensus, electrical power systems, Nonlinear negative imaginary systems, stability",

author = "Yijun Chen and Kanghong Shi and Petersen, \{Ian R.\} and Ratnam, \{Elizabeth L.\}",

note = "Publisher Copyright: Copyright {\textcopyright} 2024 The Authors.; International Symposium on Mathematical Theory of Networks and Systems 2024, MTNS 2024 ; Conference date: 19-08-2024 Through 23-08-2024",

year = "2024",

doi = "10.1016/j.ifacol.2024.10.169",

language = "English",

volume = "58",

series = "IFAC-PapersOnLine",

publisher = "Elsevier",

pages = "220--225",

editor = "Rodolphe Sepulchre and \{C. Smith\}, Malcolm",

booktitle = "26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024",

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Chen, Y, Shi, K, Petersen, IR & Ratnam, EL 2024, On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems. in R Sepulchre & M C. Smith (eds), 26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024. 17 edn, vol. 58, IFAC-PapersOnLine, Elsevier, Cambridge UK, pp. 220-225, International Symposium on Mathematical Theory of Networks and Systems 2024, Cambridge, United Kingdom, 19/08/24. https://doi.org/10.1016/j.ifacol.2024.10.169

On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems. / Chen, Yijun; Shi, Kanghong; Petersen, Ian R. et al.
26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024. ed. / Rodolphe Sepulchre; Malcolm C. Smith. Vol. 58 17. ed. Cambridge UK: Elsevier, 2024. p. 220-225 (IFAC-PapersOnLine).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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AB - In this paper, we propose employing battery-based feedback control and nonlinear negative imaginary (NI) systems theory to reduce the need for such expansion. By formulating a novel Luré-Postnikov-like Lyapunov function, stability results are presented for the feedback interconnection of two single nonlinear NI systems, while output feedback consensus results are established for the feedback interconnection of two networked nonlinear NI systems based on a network topology. This theoretical framework underpins our design of battery-based control in power transmission systems. We demonstrate that the power grid can be gradually transitioned into the proposed NI systems, one transmission line at a time.

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Chen Y, Shi K, Petersen IR, Ratnam EL. On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems. In Sepulchre R, C. Smith M, editors, 26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024. 17 ed. Vol. 58. Cambridge UK: Elsevier. 2024. p. 220-225. (IFAC-PapersOnLine). doi: 10.1016/j.ifacol.2024.10.169

On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems

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Keywords

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