Instability results in loss of synchronism leading
to separation of generators that are protected by out-of-step relays. Large
excursions in the rotor angles imply it is not possible to apply linear system
theory. Since nonlinear system analysis is not generally feasible, numerical
methods are used to simulate the system to predict system stability for
accurate results. However, transient energy function methods have been
developed in last 30 years that are fast, reasonably accurate and can handle
the presence of FACTS and HVDC controllers by preserving the structure
of the system network.