This paper investigates methods to achieve a wide constant power speed range (CPSR) in electric drives using hybrid excitation synchronous machines; five strategies are presented and compared. These range from state-of-the-art flux weakening based on demagnetizing armature current injection, to algorithms based on wound excitation (WE) current regulation, all the way to techniques involving both armature and WE current regulation. It is shown that one of these latter strategies allows a theoretically infinite CPSR and unity power factor operation throughout. This result is also verified experimentally, and a 10:1 range is demonstrated. Finally, a discussion is presented on practical limiting issues such as harmonic flux linkage components, inductance variations, and high-speed iron losses.