Transportation is the fastest-growing source of greenhouse gas (GHG) emissions and energy consumption globally. While the convergence of shared mobility, vehicle automation, and electrification has the potential to drastically reduce transportation impacts, it requires careful integration with rapidly evolving electricity systems. Here, we examine these interactions using a U.S.-wide simulation framework encompassing private electric vehicles (EVs), shared automated EVs (SAEVs), charging infrastructure, controlled EV charging, and a grid economic dispatch model to simulate personal mobility exclusively using EVs. We find that private EVs with uncontrolled charging would reduce GHG emissions by 46% compared to gasoline vehicles. Private EVs with fleetwide controlled charging would achieve a 49% reduction in emissions from baseline and reduce peak charging demand by 53% from the uncontrolled scenario. We also find that an SAEV fleet 9% the size of today's active vehicle fleet can satisfy trip demand with only 2.6 million chargers (0.2 per EV). Such an SAEV fleet would achieve a 70% reduction in GHG emissions at 41% of the lifecycle cost as a private EV fleet with controlled charging. The emissions and cost advantage of SAEVs is primarily due to reduced vehicle manufacturing compared with private EVs.