This paper deals with the compensation of magnetic saturation in line frequency transformer coupled, grid-connected power converters. The developed strategy originates from the choice of controlling the actual current injected in the grid (output of the line frequency transformer) instead of the input current of the transformer, as usually proposed. As a matter of fact, better power quality cannot neglect the direct control of the injected grid current. An effective solution providing zero steady-state error at grid frequency and superior disturbance rejection involves the use of a d-q current controller synchronous with the grid voltage. For this reason, the proposed saturation compensation strategy has been implemented inside the d-q reference frame. The downside is that closing the current feedback at the transformer output renders impossible to control the dc current at transformer input, leading to core saturation. A core saturation compensation strategy, based only on the monitoring of the output current distortion around voltage zero crossings, is here presented. Moreover, since the proposed solution does not rely on dc measures, offset problems are avoided. Experimental results confirm the effectiveness of the proposed control architecture and of the strategy adopted to avoid transformer core saturation.