Stability analysis of power systems using network decomposition and local gain analysis

We introduce a method for analyzing large-scale power systems by decomposing them into coupled lower order subsystems. This reduces the computational complexity of the analysis and enables us to scale the Sum of Squares programming framework for nonlinear system analysis. The method constructs subsystem Lyapunov functions which are used to estimate the region of attraction pertaining to the equilibrium point of each isolated subsystem. Then a disturbance analysis framework uses the level sets defined by these Lyapunov functions to calculate the stability of pairwise interacting subsystems. This analysis is then used to infer the stability of the entire system when an external disturbance is applied. We demonstrate the application of these techniques to the transient stability analysis of power systems.