Bounding Case Requirements for Power Grid Protection Against High-Altitude Electromagnetic Pulses

Securing the power grid is of extreme concern to many nations as power infrastructure has become integral to modern life and society. A high-altitude electromagnetic pulse (HEMP) is generated by a nuclear detonation high in the atmosphere, producing a powerful electromagnetic field that can damage or destroy electronic devices over a wide area. Protecting against HEMP attacks (insults) requires knowledge of the problem’s bounds before the problem can be appropriately solved. This paper presents a collection of analyses to determine the basic requirements for controller placements on a power grid. Two primary analyses are conducted. The first is an inverted controllability analysis in which the HEMP event is treated as an unbounded control input to the system. Considering the HEMP insult as a controller, we can break down controllability to reduce its influence on the system. The analysis indicates that either all but one neutral path to ground must be protected or that all transmission lines should be secured. However, further exploration of the controllability definition suggests that fewer blocking devices are sufficient for effective HEMP mitigation. The second analysis involves observability to identify the minimum number of sensors needed for full-state feedback. The results show that only one state sensor is required to achieve full-state feedback for the system. These requirements suggest that there is room to optimize controller design and placement to minimize total controller count on a power grid to ensure HEMP mitigation. As an example, the Horton et al. system model with 15 transformers and 15 transmission lines is used to provide a baseline comparison for future optimization studies by running all permutations of neutral and transmission line blocking cases. The minimum number of neutral controllers is 8, which is approximately half of the bounding solution of 14. The minimum number of transmission line controllers is 3, which is one-fifth of the bounding solution of 15 and less than half of the required neutral controllers.