Nodal elimination for E3 HEMP mitigation: A physics-informed graph theory approach

This paper presents a comparison of methods to determine the minimum number of placement locations for neutral blocking, global linear quadratic regulator (G-LQR), and local linear quadratic regulator (L-LQR) controllers throughout a power grid to prevent transformer saturation during the onset of an E 3 high-altitude electromagnetic pulse (HEMP) disturbance. Different device placement configurations yield different efficacies in E 3 HEMP mitigation. The first placement method discussed is a genetic algorithm (GA), which serves as a baseline optimizer test case. The scaling and run time of the GA depend on the complexity of the objective function and often times becomes intractable as the count of transformers on the grid increases. As a scalable alternative, this paper introduces the novel nodal elimination method, where a power grid is represented as a graph and critical nodes based on node degree are removed one at a time. Unlike the GA, which may run anywhere from O ( 1 ) to O ( n n ) depending on function complexity, the nodal elimination method is guaranteed to run in O ( n ) . The novelty of this method is in its application to the power grid for HEMP E 3 mitigation. The nodal elimination method identifies optimal placement locations with three orders of magnitude fewer iterations than the GA, demonstrating its viability and computational efficiency for optimal neutral blocking device placements. It is shown that with centralized and decentralized LQR controllers on a 20-bus and 150-bus grid, the nodal elimination method also finds solutions that require fewer controllers than the GA solutions.