Due to the different losses caused by various photovoltaic (PV) array faults, accurate diagnosis of fault types is becoming increasingly important. Compared with a single one, multiple PV stations collect sufficient fault samples, but their data is not allowed to be shared directly due to potential conflicts of interest. Therefore, federated learning can be exploited to train a collaborative fault diagnosis model. However, the modeling efficiency is seriously affected by the model update mechanism since each PV station has a different computing capability and amount of data. Moreover, for the safe and stable operation of the PV system, the robustness of collaborative modeling must be guaranteed rather than simply being processed on a central server. To address these challenges, a novel asynchronous decentralized federated learning (ADFL) framework is proposed. Each PV station not only trains its local model but also participates in collaborative fault diagnosis by exchanging model parameters to improve the generalization without losing accuracy. The global model is aggregated distributedly to avoid central node failure. By designing the asynchronous update scheme, the communication overhead and training time are greatly reduced. Both the experiments and numerical simulations are carried out to verify the effectiveness of the proposed method.