The capability of a power plant to operate at a wide range of output power is essential for initial commissioning and normal maintenance. Critical physics issues related to operating a tokamak fusion reactor at fractions of its rated power are explored, and methods for power control are identified. Analysis is carried out with a steady-state, profile-dependent, zero-dimensional power balance model of the plasma, in which several empirical transport scalings appropriate to tokamaks are used. It is found that reactor operation depends strongly on the confinement model, the plasma beta limit, and the effect of alpha power on transport. Parametric calculations indicate that density, auxiliary heating power, and an effective external confinement control mechanism are the key control elements, and burn control is required in most cases. Transition between power plateaus is facilitated by operating in the hybrid transformer mode. In general, the impact of fractional power operation on full-power reactor designs appears to be small.