Abstract
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.
Highlights
Synchronous generators in interconnected AC electric power systems exhibit electro-mechanical oscillations
As a matter of fact, power system stabilizers installed on conventional synchronous generators have so far been the main source of damping against inter-area oscillations [1] and substituting new renewable sources of energy for conventional synchronous machines reduces the availability of these resources
There is a vast literature on damping of inter-area oscillations in power systems with large penetrations of new renewable generation, see e.g. [3]
Summary
Synchronous generators in interconnected AC electric power systems exhibit electro-mechanical oscillations. When μ is not small, the theory loses its validity, yet inter-area oscillations are observed even in networks with large μ Our purpose in this manuscript is to connect the standard singular perturbation theory approach to inter-area oscillations to this modal point of view, valid regardless of interarea coupling. Where we grouped the voltage angle deviations into a vector δθ, and introduced the diagonal inertia and damping matrices, M = diag(mi) (with mi = 0 on load nodes), D = diag(di) as well as the network Laplacian matrix L, Lij =. From Eqs. (4) and (6), they are determined by the Laplacian, the inertia, and the damping matrices
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