As the transportation sector undergoes three major transformations?electrification, shared/on-demand mobility, and automation?there are new challenges to analyzing the impacts of these trends on both the transportation system and the power sector. Most models that analyze the requirements of fleets of shared autonomous electric vehicles (SAEVs) operate at the scale of an urban region, or smaller. A quadratically constrained, quadratic programming problem is formulated, designed to model the requirements of SAEVs at a national scale. The size of the SAEV fleet, the necessary charging infrastructure, the fleet charging schedule, and the dispatch required to serve demand for trips in a region are treated as decision variables. By minimizing both the amortized cost of the fleet and chargers as well as the operational costs of charging, it is possible to explore the coupled interactions between system design and operation. To apply the model at a national scale, key complications about fleet operations are simplified
but a detailed agent-based regional simulation model to parameterize those simplifications is leveraged. Preliminary results are presented, finding that all mobility in the United States (U.S.) currently served by 276 million personally owned vehicles could be served by 12.5 million SAEVs at a cost of $\$ 0.27$/vehicle-mile or $ 0.18/passenger-mile. In conclusion, the energy requirements for this fleet would be 1142 GWh/day (8.5% of 2017 U.S. electricity demand) and the peak charging load 76.7 GW (11% of U.S. power peak). Several model sensitivities are explored, and it is found that sharing is a key factor in the analysis.