  We investigate coherent oscillations in large scale transmission power grids,
where large groups of generators respond in unison to a distant disturbance.
Such long wavelength coherent phenomena are known as inter-area oscillations.
Their existence in networks of weakly connected areas is well captured by
singular perturbation theory. However, they are also observed in strongly
connected networks without time-scale separation, where applying singular
perturbation theory is not justified. We show that the occurrence of these
oscillations is actually generic. Applying matrix perturbation theory, we show
that, because these modes have the lowest oscillation frequencies of the
system, they are only moderately sensitive to increased network connectivity
between well chosen, initially weakly connected areas, and that their general
structure remains the same, regardless of the strength of the inter-area
coupling. This is qualitatively understood by bringing together the standard
singular perturbation theory and Courant's nodal domain theorem.
