This work is a continuation of our research on high-performance (6-phase) permanent-magnet faulttolerant synchronous generator (HPHSG). It focuses on interfacing the HPHSG source to the electrical distribution network via a matrix converter (MC) whose indirect topology (IMC) has six phases on the generator side and three phases on the grid side. In the literature, the most common MCs are three-phase and publication on multi-input converters with (N>3) are quite rare. The main objective of this paper is to develop a hexaphase IMC structure and its corresponding SVM control law. A closed-loop simulation of the system feeding a 1.35MW inductive load is carried out, and provides an overall evaluation of the system's performance.