In order to effectively address power quality disturbances (PQDs) such as voltage swells and voltage oscillations caused by the high penetration grid connection of distributed generation, a composite disturbance adaptive sensing method based on a bidirectional long short-term memory (BiLSTM) network integrated with an attention mechanism (AM) is proposed. First, the grey wolf optimizer (GWO) algorithm is employed to optimize the parameters of the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN). The modals of the disturbance signals are decomposed and reconstructed. Subsequently, the features of hierarchical weighted permutation entropy (HWPE) of the disturbance signals are extracted. Finally, a BiLSTM-AM model is constructed to capture the long- and short-term dependencies of multidimensional features for composite PQD recognition. Validation using both simulated and real-world power grid datasets demonstrates excellent identification performance on various disturbance types with the proposed method. Moreover, compared with other deep learning models, the proposed model further demonstrates higher recognition accuracy.