The paper presents a new Matlab toolbox called SOStab, which aims to facilitate the use of polynomial optimization for stability analysis of nonlinear power systems.
The key highlights are:
SOStab automates the writing and solving of optimization problems for computing inner and outer approximations of the Region of Attraction (RoA) of power system models. This eliminates the need for users to have expertise in Sum-of-Squares programming.
The toolbox takes minimal input from the user, such as the system dynamics, equilibrium point, state constraints, time horizon, and target set. It then outputs the stability certificates describing the RoA approximations and provides graphical representations.
The authors demonstrate the capabilities of SOStab on two test cases: a Phase Locked Loop (PLL) system and a Single Machine Infinite Bus (SMIB) model with governor and AVR. The results show that SOStab can efficiently compute inner and outer RoA estimates for these nonlinear power system models.
While the current version of SOStab is limited to low-dimensional systems due to the curse of dimensionality in Sum-of-Squares programming, the authors discuss potential future improvements, such as exploiting problem structure to scale the method to higher-dimensional power system models.
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