Submodular Optimization for Power System Control and Stability

Abstract

Due to the increasing demand for electricity and unpredictable supplies from renewable energy, power systems are being operated close to their stability limits. Maintaining power system stability in the presence of disturbances is a challenging task over decades. Power system instability often arises from disturbances and the corrective controls are often combinatorial optimization problems which are NP-hard to solve. Submodularity is a diminishing-return property of set functions which is analogous to the convexity of continuous functions. A combinatorial optimization problem that possesses submodularity can often be solved by greedy algorithms effectively with provable optimality guarantees. The concept of submodularity has been studied in a wide range of areas including sensor placement, feature selection, etc. The submodularity for power system stability problems, however, has not been exploited prior to this work. The goal of this dissertation is to provide novel approaches towards addressing the power system control and stability challenges by exploiting the submodularity. This dissertation covers the voltage control problem, input and output selection problem in wide-area damping control for small signal stability, and controlled islanding problem in cascading failure.