Fractal antenna inspired EMP power grid mitigation device placement through cycle removal using graph theory

This paper presents a graph theory based method for optimally placing in-series transmission line actively controlled blocking devices for the mitigation of high-altitude electromagnetic pulses (HEMPs), as well as a comparison of controller requirements for global and local optimal control laws. The complexity of the interconnected transmission lines form collections of fractal antennas that readily receive power from HEMP signals. These fractal antennas are described as graph cycles. Placement decisions are achieved by determining all cycles within a graph representing a power grid and counting how often each transmission line appears in these cycles. The transmission lines with the highest occurrences in the cycles are protected first. The cycle blocking method provides a close approximation to the minimum number of required blocking devices (predicted 4 vs. true 3 for the global control solution and 12 vs. true 11 for the local control solution) of the all-permutations baseline test case. In comparison, the genetic algorithm (GA) yields a minimal placement with 5 controllers for the global controller and 13 for the local controller. This is in contrast to the 15 out 15 placements required to meet the bounding case criterion. That is, mitigation of the E 3 HEMP disturbance may be guaranteed if all edges are protected in the system (Lehman et al., 2025). In addition, the required computation time for each method has important consequences. The all-permutations case performs 16 ⋅ 2 15 = 524,288 iterations to find the optimal solution, the GA performs 190,464 iterations for the global control solution and 286,720 iterations for the local control solution while the graph theory method performs 240 iterations for both the global and local control schemes—an iteration reduction of 3 orders of magnitude from the GA and all-permutations solutions.