Optimum lyapunov functions and stability regions for multimachine power systems

The paper is a contribution to the application of Lyapunov´s theory to the analysis of transient power-system stability. The technique of the paper originates with a theorem introduced by Anderson to prove the generalised Popov criterion for multivaiable fedback systems. Explicit expressions of the Lyapunov functions and the transient-stability regions are computed for multimachine power systems. It is shown that the obtained Lyapunov functions yield better estimates of the stability regions than the energy function which was used in some recent papers. The dependence of the stability regions on the damping torques is investigated. It is shown that optimum-stability results are obtained if particular relationships between damping torques and inertial constants are satisfied.