This article presents an optimal circulating current reference generator to perform the intercluster capacitor voltage balancing in modular multilevel matrix converters (M3C) under branch fault conditions. The proposed reference generator is directly introduced in the original reference frame, enabling a straightforward formulation of the optimal control problem for fault-tolerant operations. This approach allows the reference generator to efficiently provide the optimal circulating current in each branch, thereby balancing the energies of the converter's clusters even during open-circuit branch fault operation. Experimental results on an M3C prototype of 36 submodules are provided to validate the effectiveness and high-quality performance of the proposed strategy.