The uncertainty of distributed photovoltaics poses significant challenges to the stable operation of microgrids. To enhance the microgrid's capability to handle uncertainty and improve overall operational economy, a two-stage distributionally robust economic optimization scheduling model for microgrids based on the Hausdorff distance is proposed.First, an optimization scheduling model for a microgrid with distributed photovoltaics, energy storage, micro gas turbines, conventional loads, and demand response loads is established using the distributionally robust optimization approach. Next, the Hausdorff distance is employed to construct the uncertain scenarios and their associated probability distribution sets within the model. Finally, the model is solved using the column-and-constraint generation (CC&G) algorithm to obtain the optimal scheduling strategy. A simulation is conducted on a residential microgrid as a case study. The results demonstrate that the probability distribution set established using the Hausdorff distance effectively improves the model's economic performance and allows the robustness level to be adjusted by modifying the confidence level. The Monte Carlo simulation validates that the proposed model exhibits good robustness.