Current control based on hysteresis algorithms are widely used in different applications, such as motion control, active filtering or active/reactive power delivery control in distributed generation systems. The hysteresis current control provides to the system a fast and robust dynamic response, and requires a simple implementation in standard digital signal platforms. On the other hand, the main drawback of classical hysteresis current control lies in the fact that the switching frequency is variable, as the hysteresis band is fixed. In this paper a variable band hysteresis control algorithm will be presented. As it will be shown, this variable band permits overcoming the aforementioned problem giving rise to an almost constant switching frequency. The performance of this algorithm, together with classical hysteresis controls and proportional resonant (PR) controllers, has been evaluated in three different single-phase PV inverter topologies, by means of simulations performed with PSIM. In addition, the behavior of the thermal losses when using each control structure in such converters has been studied as well.