  The increasing development of the electric power grid, the largest engineered
system ever, to an even more complicated and larger system requires a new
generation of stability assessment methods that are computationally tractable
and feasible in real-time. In this paper we first extend the recently
introduced Lyapunov Functions Family (LFF) transient stability assessment
approach, that has potential to reduce the computational cost on large scale
power grids, to structure-preserving power grids. Then, we introduce a new
geometry-based method to construct the stability region estimate of power
systems. Our conceptual demonstration shows that this new method can certify
stability of a broader set of initial conditions compared to the
minimization-based LFF method and the energy methods (closest UEP and
controlling UEP methods).
