With the expansion of renewable energy sources, the stable and high-quality operation of microgrids composed of new energy sources has attracted widespread attention. Among them, the power conversion system (PCS), as an important part of microgrids, plays a crucial role in their operation and management. The PCS operation modes are classified into grid-connected and off-grid modes. However, in off-grid mode, due to the access of nonlinear and unbalanced loads, the output voltage quality of a PCS is worse, and the voltage waveform distortion is serious. To solve these problems, a fast repetitive control (FRC) strategy is proposed for a power conversion system with an Active Neutral Point Clamped (ANPC) architecture of three levels. The voltage loop control strategy can be applied to the voltage/frequency (V/f) mode and the grid-forming mode. The control strategy can effectively realize the suppression of the harmonics of the output voltage and has a 100% capability to carry unbalanced loads. Finally, a 1725 kVA PCS prototype is developed, and the proposed control strategy is verified using the MT3200 HIL semiphysical simulator of ModelingTech in the V/f mode as an example. This practically verifies the feasibility and validity of the proposed control strategy, which has a certain degree of engineering practicability and reference due to the simplicity of the design and the ease of realization.