IMSE lunchtime seminar: November 6, at noon

We meet in Grainger Libraryroom 329.

Alejandro Dominguez-Garcia, ECE, talks on Analysis of Power System Dynamics Subject to Stochastic Power Injections

 We propose a framework to study the impact of stochastic active/reactive power injections on power system dynamics with a focus on time scales involving electromechanical phenomena. In this framework the active/reactive power injections evolve according to a continuous-time Markov chain (CTMC), while the power system dynamics are described by the standard differential algebraic equation (DAE) model. The DAE model is linearized around a nominal set of active/reactive power injections; and the combination of the linearized DAE model and the CTMC forms a stochastic process known as a Stochastic Hybrid System (SHS). The extended generator of the SHS yields a system of ordinary differential equations that governs the evolution of the power system dynamic and algebraic state moments. We illustrate the application of the framework through numerical case studies. We close by discussing several extensions to the SHS model that allow capturing additional phenomena of interest, but make
the analysis of the resulting SHS substantially harder.

This work is joint with Lee DeVille, Sairaj Dhople, and Jiangmeng Zhang.

followed by Lee DeVille, Math, speaking about
Moment closure for stochastic hybrid systems in equilibrium

We consider the formalism of stochastic hybrid systems (SHS) in general, and some specific problems motivated by applications. We seek to uncover the evolution of the moments of the process when it is at equilibrium or approaching equilibrium. We present a family of such processes for which classical techniques are ineffective and present a few differing perspectives on how to attack such problems, using both maximum entropy and renewal process ideas. We show that even when every component of the system is linear, the dynamics can be quite complex, and some surprising challenges arise.

This work is joint with Sairaj Dhople, Alejandro Dominguez-Garcia, and Jiangmeng Zhang.

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