Fault current limiters (FCL) in electrical power systems offer the opportunity to reduce short-circuit stresses to the system in the case of faults. But as electrical power systems are normally operated without faults most of the time, FCLs must not have negative effects during these periods of normal operation. The FCL investigated in this paper is based on a 6-pulse current converter. As every other current converter this type of FCL can introduce additional system perturbations in form of higher harmonics. The aim of this work is to develop appropriate strategies to control the FCL in a way that virtually no additional system perturbations are introduced by the FCL under normal no-fault conditions. In electrical three-phase systems this means simply, the controller has to provide sinusoidal current waveforms.