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Center for Nonlinear Studies |
In 2003 blackout in the large portion of the eastern national powergrid an enviromental uncertainty - falling of a tree branch on a power line -caused a disturbance that propagated dynamically at a rapid pace through the grid causing one power plant after another to fail. The possibility of suchevents occurring frequently becomes large when one starts thinking aboutthe scenario of a power grid with subcomponents providing wildly fluctuatingamounts of power and storage capacity as would be the case if current thinking on the issues such as cogeneration and alternative power sources plays a substantial role in the future power generation network. We are interested in elucidating core causes of instabilities leading to large disturbancesand failure of catastrophic proportions. It turns out that it is the coupling ofarchitecture and dynamics of the system that matter the most. If two partsof the system are completely separated from each other, a big disturbancein one will, of course, not influence the other. But, if the subsystems areconnected, even weakly, and the dynamics is resonant, a small disturbance inone subsystem can grow, spill to the other part and cause the whole system tofail. This is true even if there are controls in place attempting to stabilize oneside - the phenomenon is of the emergent kind, and the only way to control it isto act early at the root cause or provide system-wide regulation that preventscatastrophes. I will discuss the technical aspects of this phenomenon that in the context of power grid we named a "Coherent Swing Instability" (CSI). A simple ring architecture will be presented first, followed by more complex New England Grid model. In order to treat such more complex, large-scale models, we needed to develop new tools, drawing from an operator-theoretic point of view, that also incorporates, in a strong way, the geometric point of view that is so fruitful in low dimensions. This approach leads to a new proposal for model reduction that is rooted in the dynamics of the system rather than in energy-minimization arguments (like in POD). We named the modes that appear in such reduction the "Koopman modes". I will show how this leads to extraction of single-frequency,spatial modes embedded in non-stationary data of short-term,nonlinear swing dynamics, and provides a novel technique foridentification of coherent swings and machines. In addition, I will present a technique for identifying CSI by using Koopman modes, by providing a precursor signal based on their interaction. The set of techniques that we have developed also enables analysis of uncertain and stochastic systems - where initial conditions and/or parameter values are not known exactly - within the same framework. Most of the tools apply equally to discontinuous systems.
Host: Misha Chertkov, chertkov@lanl.gov, 665-8119