ISyE Department Seminar - Daniel Molzahn

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Convex Relaxations of the Power Flow Equations: Overview and Selected Applications


Electric power systems are critical infrastructure that underlie almost all aspects of modern society. With rapidly increasing quantities of renewable generation and the continuing expansion of electricity markets, electric power systems are undergoing significant changes. New algorithms for optimizing the design and operation of electric power systems are needed in order to enable these transformational changes.

This presentation focuses on the "power flow equations" which model the physical relationships that exist on electric transmission and distribution systems. The nonlinearity of the power flow equations results in a variety of algorithmic and theoretical challenges, including non-convex feasible spaces for optimization problems constrained by these equations. Many convex relaxation techniques have recently been applied to simplify the power flow representations used in a variety of power system optimization and control problems. This presentation first overviews various convex relaxation techniques that have been applied to the power flow equations, with a focus on semidefinite programming and second-order cone programming formulations as well as techniques for tightening the relaxations. This presentation then summarizes several applications of convex relaxations in a variety of power systems contexts.


Daniel Molzahn is an assistant professor in the School of Electrical and Computer Engineering at the Georgia Institute of Technology. Daniel also holds an appointment as a computational engineer in the Energy Systems Division at Argonne National Laboratory. Daniel was a Dow postdoctoral fellow at the University of Michigan. He completed the B.S., M.S., and Ph.D. degrees in Electrical Engineering and the Masters of Public Affairs degree from the University of Wisconsin–Madison, where he was a National Science Foundation Graduate Research Fellow. His research interests are in the application of optimization techniques to electric power systems.


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