The power quality of distributed microgrid (e.g., on-board microgrids) is severely affected by unbalanced loads, and the operation of single-phase loads (unbalanced loads) can lead to a series of imbalance issues in such systems, endangering system reliability and shortening lifespan. Existing control strategies are typically limited to suppressing power fluctuations and do not adequately address issues such as current distortion and point of common coupling (PCC) voltage imbalance. Addressing power fluctuations, this paper optimizes the control layer of the model predictive control (MPC) based on traditional flexible power control, improving the calculation of adaptive coefficients. Building upon this, a dual-flexible model predictive control (DF-MPC) is designed, employing a novel dual-layer flexible computational structure that prioritizes the selection of control vectors with the best voltage balancing effect. This method is tested on a prototype hardware platform with a rated power of 10 kW. Experimental results demonstrate that the proposed DF-MPC method can effectively suppress power fluctuations, reduce the degree of PCC voltage imbalance, and maintain high power quality.