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Smart Grid and Analysis of Large-Scale Interconnected Dynamical Systems

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  • Seminar Series
When Nov 18, 2013
from 01:00 PM to 02:30 PM
Where Engr. IV Bldg., Shannon Room 54-134
Contact Name
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Igor Mezic



In 2003 blackout in the large portion of the eastern national power grid an environmental 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 such events occurring frequently becomes large when one starts thinking about the scenario of a power grid with subcomponents providing wildly fluctuating amounts 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 disturbances and failure of catastrophic proportions. It turns out that it is the coupling of architecture and dynamics of the system that matter the most. If two parts of the system are completely separated from each other, a big disturbance in one will, of course, not influence the other. But, if the subsystems are connected, even weakly, and the dynamics is resonant, a small disturbance in one subsystem can grow, spill to the other part and cause the whole system to fail. This is true even if there are controls in place attempting to stabilize one side - the phenomenon is of the emergent kind, and the only way to control it is to act early at the root cause or provide system-wide regulation that prevents catastrophes. 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 for identification 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.  Finally, the operator-theoretic framework can be used to detect impending instability directly from data obtained from SCADA and PMU.

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.


Professor Mezic works in the field of dynamical systems and control theory and applications to energy efficient design and operations.  He did his Dipl. Ing. in  Mechanical Engineering in 1990 at the University of Rijeka, Croatia and his Ph. D. in Applied Mechanics at the California Institute of Technology. Dr. Mezic was a postdoctoral researcher at the Mathematics Institute, University of Warwick, UK in 1994-95.  From 1995 to 1999 he was a member of Mechanical Engineering Department at the University of California, Santa Barbara where he is currently a Professor.  In 2000-2001 he has worked as an Associate Professor at Harvard University in the Division of Engineering and Applied Sciences.  He won the Alfred P. Sloan Fellowship, NSF CAREER Award from NSF and the George S. Axelby Outstanding Paper Award on "Control of Mixing" from IEEE.  He also won the United Technologies Senior Vice President for Science and Technology Special Achievement Prize in 2007. He was an Editor of Physica D: Nonlinear Phenomena and an Associate Editor of the Journal of Applied Mechanics and SIAM Journal on Control and Optimization. Professor Mezic and his students develop methods to analyze and control nonlinear dynamical systems and apply these methods to understand issues of theoretical and practical relevance in energy efficient design and operations. Dr. Mezic is the Director of the Center for Energy Efficient Design and Head of Buildings and Design Solutions Group at the Institute for Energy Efficiency ay the University of California, Santa Barbara.

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