Energy analysis of load-induced flutter instability in classical models of electric power networks

Journal Article · Fri Dec 01 00:00:00 EST 1989 · IEEE Transactions on Circuits and Systems (Institute of Electrical and Electronics Engineers); (USA)

DOI:https://doi.org/10.1109/31.41318· OSTI ID:6908441

Kwatny, H G; Yu, X M ^[1]

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1. Dept. of Mechanical Engineering and Mechanics, Drexel Univ., Philadelphia, PA (US)

In this paper, the authors consider the local structure of energy functions for electric power networks near points (parameter values) of incipient flutter instability. Previous work by several investigators clearly indicate the subtle nature of energy functions and energy- like Lyapunov functions when the system exhibits such an instability mechanism. In fact the question of existence of an energy function under these circumstances has been raised. The issue is important because it is now well known that power systems with loads contain such bifurcation points. It is shown, herein, that a local energy function does exist in a sense consistent with the inverse problem of analytical mechanics. However, sufficiently near points of flutter instability the energy function for both stable and unstable systems is not sign definite. Such an energy function can not be used as a Lyapunov function. Nevertheless, it is possible to obtain natural Lyapunov functions by combining the energy function with one or more additional first integrals. The analysis is based on the association of the linearized undamped power system with loads with a quadratic Hamiltonian system. General (universal) perturbations of the normal forms of the degenerate quadratic Hamiltonians at such bifurcation points are derived and lead to the stated conclusions. An example is included.

• OSTI ID: 6908441
• Journal Information: IEEE Transactions on Circuits and Systems (Institute of Electrical and Electronics Engineers); (USA), Vol. 36:12; ISSN 0098-4094
• Country of Publication: United States
• Language: English

Related Subjects

24 POWER TRANSMISSION AND DISTRIBUTION
29 ENERGY PLANNING
POLICY AND ECONOMY
ELECTRIC POWER INDUSTRY
ENERGY ANALYSIS
DISTURBANCES
HAMILTONIANS
LOAD MANAGEMENT
LYAPUNOV METHOD
POWER SYSTEMS
ENERGY SYSTEMS
INDUSTRY
MANAGEMENT
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
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