To enhance the economic performance of microgrid operations by fully accounting for the uncertainties in wind and solar power generation, a federated learning-based bi-directional gated neuron (FL-BiGRU) model is established for power prediction of renewable energy in loads, which improves the accuracy of power prediction while avoiding the privacy leakage problem of the cooperation of various interested parties in the operation of the power prediction, meanwhile, taking into account the impact of the power prediction results on the scheduling of the microgrids, a two-stage robust optimization model to increase wind energy utilization with simultaneous reduction in microgrid operating expenses. Finally, the validity of the proposed power prediction method and optimal scheduling method is verified through simulation.