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

Consideration is given to the local structure of energy functions for electric power networks near points (parameter values) of incipient flutter instability. Previous work by several investigators clearly indicates the subtle nature of energy functions and energylike 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 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 cannot 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