Increasingly, experts are forecasting the future of transportation to be shared, autonomous and electric. As shared autonomous electric vehicle (SAEV) fleets roll out to the market, the electricity consumed by the fleet will have significant impacts on energy demand and, in turn, drive variation in energy cost and reliability, especially if the charging is unmanaged. This research proposes a smart charging (SC) framework to identify benefits of active SAEV charging management that strategically shifts electricity demand away from high-priced peak hours or towards renewable generation periods. Time of use (TOU), real time pricing (RTP), and solar generation electricity scenarios are tested using an agent-based simulation to study (1) the impact of battery capacity and charging infrastructure type on SAEV fleet performance and operational costs under SC management; (2) the cost reduction potential of SC considering energy price fluctuation, uncertainty, and seasonal variation; (3) the charging infrastructure requirements; and (4) the system efficiency of powering SAEVs with solar generation. A case study from the Puget Sound region demonstrates the proposed SC algorithm using trip patterns from the regional travel demand model and local energy prices. Results suggest that in the absence of electricity price signals, SAEV charging demand is likely to peak the evening, when regional electricity use patterns already indicate high demand. Under SC management, EVs with larger battery sizes are more responsive to low-electricity cost charging opportunities, and have greater potential to reduce total energy related costs (electricity plus charging infrastructure) for a SAEV fleet, especially under RTP structure.