This paper proposes a novel two-level model predictive control (MPC) speed control algorithm for autonomous vehicles as a successive convex optimization problem focused on both energy use and arrival time. Internal losses such as detailed motor/inverter efficiency and battery loss, as well as external losses, such as wind and grade, are considered. The effect of the higher accessory energy usage of autonomous vehicles on the energy-optimal speed profile is considered in the algorithm and investigated in the paper. The proposed successive convex approach produces a highly accurate optimal speed profile while also being solvable in real-time with the vehicle on-board computing resources. An electric vehicle model is created in MATLAB/Simulink and validated to real-world logged driving data. This vehicle model is used to perform a variety of simulated test cases, which show an energy savings potential of about 1% to 20% for different driving conditions, compared to a non-energy-optimal driving profile.