The interest on weak and micro-grid systems has grown up substantially last time, specially tied up to distributed power generation systems (DPGSs), isolated systems as aircraft, or islanding power systems. These kinds of grids are usually under significant variation in their quantities, specifically in their voltage amplitude and/or frequency. On this line, many studies about synchronization methods have been developed, which may work under variations on the frequency value, unbalanced voltage, and even with harmonic distortion. However, power converters connected to this class of systems are poorly documented-specifically controlled rectifiers. In fact, most of the controlled grid connected converters (GCCs) are defined to work in a fixed frequency and balanced system. This paper deals with a GCC connected to a variable-frequency and unbalanced voltage supply system control through a predictive algorithm with a fixed resolution sampling strategy. Furthermore, the current references are imposed in order to help the weak-grid source subjected to unbalancing, taking more power from the phase with highest voltage amplitude and relaxing the other phases. This issue makes to calculate every phase current reference independently and accordingly the voltage amplitudes keep the dc-link voltage in a desired value. The results show the feasibility of the proposed algorithm, where the performance is highlighted by simulated and experimental waveforms.