Hamiltonian energy-balance method for direct analysis of power systems transient stability

This paper outlines a Hamiltonian energy-balance function for computing stable and unstable regions of power systems. Once the generator model is defined, a certain number of variables (holonomic constraints) specifies its state properties (prefault, fault-on, and postfault) entirely. The change between the postfault (final) and prefault (initial) states is expressed by an energy balance equation (crucial for solving many dynamical problems). State equations (instead of swing equation) with the properties (or functions) of the system are built using the prefault and postfault energies (kinetic and potential) of the generators. When a large disturbance occurs, the 'migration' from one state to another is computed using concepts of least action principle, conservation, and dissipation of energy, perturbation theory and calculus of variations. The method is tested with two electric power systems, where the classical model represents the synchronous generators. Prefault, fault-on, and postfault regions are clearly characterised on 3D energy surfaces indicating whether the generators remain (or not) stable after a fault in the power system. The trajectories of the Hamiltonian energies of the generators are projected on 2D planar projection maps. The results provided important insights into transient stability problems not seen so far.