Convexity of Structure Preserving Energy Functions in Power Transmission: Novel Results and Applications
It is well-known in the power systems literature that the behavior of the transmission power system (under certain simplifying assumptions) can be used to study the post-fault dynamics of a power system and provide principled estimates on dynamic stability margins. In this paper, we study a special feature of the energy function that has previously received little attention: convexity. We prove that the energy function for structure preserving models of power systems is convex under certain reasonable conditions on phases and voltages. Beyond stability analysis, these convexity results have a number of applications, noticeably, building a provably convergent PF solver, which we discuss in detail in this paper. We also outline potential applications to reformulating Optimum Power Flow (OPF), Model Predictive Control (MPC) and identifying the most probable failure (instanton) as convex optimization problems.
© 2015 AACC. This work has emerged from discussions in July of 2014 at Los Alamos with Scott Backhaus and Ian Hiskens, whom the authors are thankful for guidance, comments, encouragement and criticism. The work at LANL was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. This material is based upon work partially supported by the National Science Foundation award # 1128501, EECS Collaborative Research "Power Grid Spectroscopy" under NMC.