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Arnold diffusion in the swing equations of a power system

Salam, Fathi M. A. and Marsden, Jerrold E. and Varaiya, Pravin P. (1984) Arnold diffusion in the swing equations of a power system. IEEE Transactions on Circuits and Systems, 31 (8). pp. 673-688. ISSN 0098-4094.

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We present an application of the theory of Arnold diffusion to interconnected power systems. Using a Hamiltonian formulation, we show that Arnold diffusion arises on certain energy levels of the swing equations model. The occurrence of Arnold diffusion entails complex nonperiodic dynamics and erratic transfer of energy between the subsystems. Conditions under which Arnold diffusion exists in the dynamics of the swing equations are found by using the vector-Melnikov method. These conditions become analytically explicit in the case when some of the subsystems undergo relatively small oscillations. Perturbation and parameter regions are found for which Arnold diffusion occurs. These regions allow for a class of interesting systems from the point of view of power systems engineering.

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Additional Information:© 1984 IEEE. "Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received March 14, 1984. This work was supported in part by DOE Contracts DE-AT03-82 ER 12097 and DE-ASOl-78ER29135, and by the National Science Foundation under Grant ECS-811213. The authors thank Philip Holmes and Nancy Kopell for inspiration. They also thank Felix Wu, Eyad Abed, Aris Arapostathis, Rong Chen, Shankar Sastry, and Nikos Tsolas for valuable discussions.
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Deposited On:31 Oct 2005
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