Abstract: Aiming at the collaborative optimization operation problem of the microgrid cluster composed of microgrids belonging to different stakeholders under privacy protection, this paper proposes a multi-agent collaborative optimization operation and strategy evolution method of microgrid cluster based on federated learning. First, each microgrid trains its own equivalent package model locally and uploads it to the cloud. Then, the cloud collects the equivalent package model of each microgrid, performs scenario deduction and global strategy search, and issues strategies to each microgrid. Finally, each microgrid learns new strategies through the distributed joint training of vertical federated neural networks to realize the collaborative optimization operation and strategy evolution of microgrid clusters under privacy protection. The simulation results of the collaborative operation of microgrid clusters with different scales show that this method realizes the collaborative optimization operation of multi-agent microgrid cluster under privacy protection. Compared with autonomous control, non-cooperative game as well as the multi-agent deep reinforcement learning method, the proposed method improves the overall economic benefits of the microgrid cluster and ensures the reasonable distribution of the interests of each participant.