The use of distributed maximum power point tracking (DMPPT) algorithms is spreading because of their higher efficiency in the case of partial shading. The possibility of integrating photovoltaic (PV) modules in a modular multilevel converter (MMC) connected to the grid has been proposed in recent literature with the advantage of integrating DMPPT algorithms. In the case of partial shading, circulating currents control is necessary to extract the maximum available power and inject symmetric currents in the grid. Novel control strategies for both the ac and dc circulating current components of a three-phase MMC-based PV were proposed and analyzed in this work. Thanks to the presence of a capacitor connected to the dc-side of the MMC, the ac circulating currents could freely be controlled to extract the maximum power from all the PV modules in any irradiance condition while maintaining low power losses. Moreover, in contrast to previous works, instead of measuring the active power of legs and compensating for their imbalance using open-loop control, the power leg mismatches are compensated exploiting the dc loop currents generated through closed loop controls. The effectiveness of the proposed control strategy was proved by simulations performed using MATLAB Simulink.