  Interconnecting power systems has a number of advantages such as better
electric power quality, increased reliability of power supply, economies of
scales through production and reserve pooling and so forth. Simultaneously, it
may jeopardize the overall system stability with the emergence of so-called
inter-area oscillations, which are coherent oscillations involving groups of
rotating machines separated by large distances up to thousands of kilometers.
These often weakly damped modes may have harmful consequences for grid
operation, yet despite decades of investigations, the mechanisms that generate
them are still poorly understood, and the existing theories are based on
assumptions that are not satisfied in real power grids where such modes are
observed. Here we construct a matrix perturbation theory of large
interconnected power systems that clarifies the origin and the conditions for
the emergence of inter-area oscillations. We show that coherent inter-area
oscillations emerge from the zero-modes of a multi-area network Laplacian
matrix, which hybridize only weakly with other modes, even under significant
capacity of the inter-area tie-lines, i.e. even when the standard assumption of
area partitioning is not satisfied. The general theory is illustrated on a
two-area system, and numerically applied to the well-connected PanTaGruEl model
of the synchronous grid of continental Europe.
