A Caltech Library Service

Arnold diffusion in the dynamics of a 4-machine power system undergoing a large fault

Salam, Fathi M. A. and Marsden, Jerrold E. and Varaiya, Pravin P. (1983) Arnold diffusion in the dynamics of a 4-machine power system undergoing a large fault. In: Proceedings of the 22nd IEEE Conference on Decision and Control. IEEE , pp. 1411-1414.

[img] PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


We focus on the seemingly complicated dynamics of a four-machine power system which is undergoing a sudden fault. Adopting a Hamiltonian (energy) formulation, we consider the system as an interconnection of (one degree of freedom) subsystems. Under certain configuration (a star network) and parameter values we establish the presence of Arnold diffusion which entails periodic, almost periodic, and complicated nonperiodic dyanmics all simultaneously present; and erratic transfer of energies between the subsystems. In section 1 we introduce the transient stability problem in a mathematical setting and explain what our results mean in the power systems context. Section 2 provides insights into Arnold diffusion and summarizes its mathematical formulation as in [8], [1]. Section 3 gives conditions for which Arnold diffusion arises on certain energy levels of the swing equations. These conditions are verified analytically in the case when all but one subsystem (machine) undergo relatively small oscillations.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
Additional Information:© 1983 IEEE. Date of Current Version: 02 April 2007. Research is partially supported by DOE Contracts AT03-82ER 12097 and DE-AS01-78ET29135.
Funding AgencyGrant Number
Departemt of Energy (DOE)AT03-82ER 12097
Departemt of Energy (DOE)DE-AS01-78ET29135
Record Number:CaltechAUTHORS:20101027-095131751
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20561
Deposited By: Ruth Sustaita
Deposited On:28 Oct 2010 21:35
Last Modified:09 Nov 2021 00:01

Repository Staff Only: item control page