Bearingless ac homopolar machines combine magnetic bearing and motor/generator functionality into a single electric machine which features variable excitation, high power density at high rotational speed, a simple and robust rotor structure, and magnet-less excitation. These features make the bearingless ac homopolar machine a promising machine for highspeed flywheel energy storage systems (FESS). The variable excitation of the bearingless ac homopolar machine has the potential to increase the FESS's efficiency by allowing for low excitation during periods of free-wheeling and high-speed operation. However, the magnetic suspension's position stiffness and current stiffness depend upon the excitation level. This dependency must be taken into account in the suspension controller or the magnetic suspension may become unstable at certain excitation levels. A technique for modeling this dependence is presented in this paper and explored through 3D finite element simulation. A prototype design is analyzed for two rotor structures: one with a square airgap length profile and one with an inverted sinusoidal airgap length profile.