Linear analysis for determining and visualizing critical thermal boundaries of power systems

System operators need to constantly assess the security of a power system and take actions in order to maintain safe operation. To do this, they need to quantify the proximity of the security constraints, determine the most critical ones, and then execute a set of actions designed to restore safety margins. A particularly important set of security constraints is thermal overload limits of transformers and transmission lines. However, current thermal security assessment practices typically rely on guessing critical power transfers, require repetitive computer simulations, and are limited to two-dimensional nomograms that are constructed off-line. We present techniques for making this process more efficient and effective that use a linear system model and are based on the analysis of a polyhedron in the space of generator and load powers. These techniques have been tested on three real power networks, one of which has 45k buses.