This paper considers the control of a 7-leg back-to-back Voltage Source Inverter (VSI) arrangement feeding a 4-wire load from a 3-phase Permanent Magnet Synchronous Generator (PMSG) operating at variable speed. The 7-leg converter is regulated using Resonant Controllers (RCs) at the load side and self-tuning resonant controllers at the generator side. The control system is augmented by a feed-forward compensation algorithm which improves the dynamic performance during transients. Experimental results, obtained from a prototype, are presented and discussed.