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^*

^*Corresponding author for this work

School of Engineering

Research output: Contribution to journal › Conference article › 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
Pages (from-to)	220-225
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	58
Issue number	17
DOIs	https://doi.org/10.1016/j.ifacol.2024.10.169
Publication status	Published - 1 Aug 2024
Event	26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024 - Cambridge, United Kingdom Duration: 19 Aug 2024 → 23 Aug 2024

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10.1016/j.ifacol.2024.10.169

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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.; 26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024 ; Conference date: 19-08-2024 Through 23-08-2024",

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

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AU - Chen, Yijun

AU - Shi, Kanghong

AU - Petersen, Ian R.

AU - Ratnam, Elizabeth L.

PY - 2024/8/1

Y1 - 2024/8/1

N2 - 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.

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.

KW - consensus

KW - electrical power systems

KW - Nonlinear negative imaginary systems

KW - stability

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DO - 10.1016/j.ifacol.2024.10.169

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AN - SCOPUS:85210323564

SN - 2405-8971

VL - 58

SP - 220

EP - 225

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 17

T2 - 26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024

Y2 - 19 August 2024 through 23 August 2024

ER -

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

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