This paper explores the use of a solid state transformer (SST) to mitigate the $E_{3A}$ component of a high-altitude electromagnetic pulse (HEMP) insult using external energy storage optimal control techniques. In lieu of conventional passive blocking devices or feedback-controlled energy storage devices, a novel implementation of Hamiltonian error tracking is utilized to develop a feedback control law for the variable converter ratio in an SST. The findings of the simulations performed in this paper suggest that additional energy storage is not necessary to protect an individual load from a HEMP insult. The simulations performed examine the response of a single-phase SST connected to a single voltage source on a long transmission line on the one side and a single linear resistor on the other. The control law is specifically developed for the late-time, low-frequency portion of a HEMP insult, namely the $E_{3A}$ components. The Hamiltonian error-based converter ratio control law is compared with nonlinear optimal feedforward controls to show that the HSSPFC is an external energy storage optimal controller.

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.

This paper explores the feasibility of implementing a flywheel energy storage system designed to generate voltage for the purpose of mitigating current flow through the transformer neutral path to ground, which is induced by a high-altitude electromagnetic pulse (HEMP) event. The active flywheel system presents the advantage of employing custom optimal control laws, in contrast to the conventional approach of utilizing passive blocking capacitors. A Hamiltonian-based optimal control law for energy storage is derived and integrated into models of both the transformer and the flywheel energy storage system. This Hamiltonian-based feedback control law is subsequently compared against an energy-optimal feedforward control law to validate its optimality. The analysis reveals that the required energy storage capacity is $13\mathrm{Wh}$, the necessary power output is less than $5\mathrm{kW}$ at any given time during the insult, and the required bandwidth for the controller is around $5\mathrm{Hz}$. These specifications can be met by commercially available flywheel devices. This methodology can be extended to other energy storage devices to ensure that their specifications adequately address the requirements for HEMP mitigation.

This paper introduces a novel control archetype designed to mitigate high-altitude electromagnetic pulse (HEMP) $E_3$ disturbances on the power grid, as well as information on performance and specifications of different control laws for the controller archetype. This method of protection has been overlooked in the literature until now. A controlled voltage supply is placed on the load-side of a transformer, diverting unwanted power from the transformer core to prevent saturation. The controlled voltage source is modeled using four control laws: an integral controller (capacitor), Linear Quadratic Regulator (LQR), an energy storage minimized feedforward control law, and a Hamiltonian feedback law. Results show that the Hamiltonian feedback law and the energy storage minimization feedforward control law both flat-line magnetic flux with similar actuator requirements. The LQR approach requires less energy storage than the other two laws, depending on control tuning, as it allows greater exogenous current flow through the neutral path to ground. This leads to further optimization opportunities based on acceptable exogenous current levels. A sweep of different LQR gains revealed a reduction of approximately $32\%$ in minimum control effort, $47\%$ in minimum power to maintain saturation bounds, $20\%$ in energy storage requirements, and $59\%$ in required controller bandwidth. Voltage and bandwidth requirements of the load-side controller are comparable to neutral blocking requirements with energy and power requirements being higher for the load-side controller. This, however, comes with the benefit of being able to use pre-existing assets—neutral blocking devices have not been deployed. Additionally, the load-side blocking capacitor degrades transformer performance compared to the unmitigated system.