As the power grid moves towards greater amounts of distributed and renewable generation, there is an increasing need for tools and algorithms that can efficiently and accurately predict safe regions of operation and stability margins, accounting for nonlinear effects. Energy functions, developed primarily in the 1970s-80s, are a useful tool for providing an analytic handle on these phenomena. In this work, we analyze an aspect of energy functions that has previously received little attention: convexity. We prove that the energy function is convex within a convex domain on the voltage magnitudes and phases. This domain corresponds well with typical operational constraints imposed by power system operators. Further, we present several applications of the energy functions beyond transient stability: We show that they can be applied to solving power flow and optimal power flow problems, computing harmful configurations of uncertain injections, model predictive control etc. This is joint work with Misha Chertkov (Los Alamos National Laboratory).
Krishnamurthy Dvijotham is a postdoctoral fellow at the Center for Mathematics of Information, California Institute of Technology. He received his PhD from the University of Washington,Seattle in Computer Science and Engineering. His main research interests are in developing computationally tractable approaches to analyzing dynamical systems and synthesizing controllers, with a particular focus on mechanical and power systems.