Security is a critical issue in modern power system operation. With the aid of analytic tools for large-scale and hybrid systems, this paper proposes two new safety verification methods for power systems. The first method is based on barrier certificates and passivity. This method provides a general safety verification framework for power systems with the port-Hamiltonian structure. The energy shaping technique is also exploited to attain safety conditions for controlled port-Hamiltonian systems. The second method, based on positive invariance, yields exact safety verification for power systems based on linearized models, particularly linear Hamiltonian systems. Decidability of exact safety verification is established via algebraic and positive invariance approaches; other analytic and numerical issues are addressed from the positive invariance perspective.

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