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

The authors study undamped power systems at points of incipient flutter instability, i.e., at equilibria characterized by a conjugate pair of purely imaginary eigenvalues of algebraic multiplicity 2 (the simplest case). They show that such systems can be associated with four nonequivalent energy functions (Hamiltonians). They derive the universal perturbations of these Hamiltonians and show that they are generic in one- or three-parameter families of Hamiltonians. They also show that systems associated with these Hamiltonians behave qualitatively differently from each other under perturbations. In particular, it is possible for systems characterized by three of these Hamiltonians (those of mixed signature) to lose stability under perturbations, while the single Hamiltonian of positive signature is not associated with a system which will lose stability under perturbations. The authors also note that the Hamiltonians of mixed signature associated with perturbations of these systems cannot be used as Liapunov functions (because they are indefinite) even if the system is stable