Seminar Details
2020-12-01 (14h) : Applications of Convex Restriction Techniques to Electric Power System Optimization Problems
At MS Teams
Organized by Mathematical Engineering
Speaker :
Daniel Molzahn (Georgia Institute of Technology, USA)
Abstract :
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.
Power system optimization problems are constrained by the so-called “power flow” equations which relate the voltages and power injections. Due to the nonlinearity of these equations, power system optimization problems are nonconvex, resulting in a variety of algorithmic and theoretical challenges. Over the last decade, the research community has developed many new techniques for addressing the nonlinearities associated with the power flow equations. These techniques can be categorized as approximations, convex relaxations (outer approximations of the feasible space), and convex restrictions (inner approximations of the feasible space). After overviewing each of these categories of techniques, this presentation details recent progress in the development of convex restrictions of power system optimization problems. This presentation then describes two algorithms that use convex restrictions to 1) compute paths between operating points such that all points on the paths are feasible with respect to both the power flow equations and the operational constraints, and 2) solve robust optimization problems that ensure constraint satisfaction despite uncertain perturbations from renewable generators.
This is joint work with Dongchan Lee, Line Roald, and Kostya Turitsyn.