  Assessing small-signal stability of power systems composed of thousands of
interacting generators is a computationally challenging task. To reduce the
computational burden, this paper introduces a novel condition to assess and
certify small-signal stability. Using this certificate, we can see the impact
of network topology and system parameters (generators' damping and inertia) on
the eigenvalues of the system. The proposed certificate is derived from
rigorous analysis of the classical structure-preserving swing equation model
and has a physically insightful interpretation related to the generators'
parameters and reactive power. To develop the certificate, we use singular
perturbation techniques, and in the process, we establish the relationship
between the structure-preserving model and its singular perturbation
counterpart. As the proposed method is fully distributed and uses only local
measurements, its computational cost does not increase with the size of the
system. The effectiveness of the scheme is numerically illustrated on the WSCC
system.
