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LANS Informal Seminar: Dvijotham Krishnamurthy
July 1, 2015 @ 15:00 CDT
Seminar Title: A differential analysis of the Power Flow Equations
Speaker: Dvijotham Krishnamurthy, Postdoctoral fellow, CMI, Information Science and Technology, California Institute of Technology
Date/Time: 2015-07-01 15:00
Location: Building 240, Room 1404-1405
Description:
The AC Power Flow Equations are fundamental to several aspects of power systems operations. However, they constitute a system of multivariate quadratic equations and are hard to deal with in a theoretically sound manner. In this work, we study the power flow equations from a differential perspective. By analyzing regions over which the power flow Jacobian is non-singular, we develop techniques to find operationally relevant solutions to the power flow equations, or certify the non-existence of these solutions (a red flag for the system operator). Further, we obtain conditions on the injections that guarantee the existence of a solution to the power flow equations satisfying operational constraints. We discuss various applications of these results to power systems operations and present numerical results on a set of IEEE benchmark networks.
(Joint work with Steven Low, Michael Chertkov and Konstantin Turitsyn)