To address the shortcomings of the existing deep learning-based Non-Intrusive Load Monitoring （NILM） methods in capturing long-term dependencies and complex nonlinear dynamic features， an NILM method combining BiLSTM-Transformer and Kolmogorov-Arnold Network （KAN） was proposed， and a mix model BT-KAN was constructed. Firstly， the BiLSTM-Transformer module was designed to combine the advantage of the Bidirectional Long Short-Term Memory （BiLSTM） network in modeling bidirectional sequence dependencies with the capability of Transformer in modeling global context， and a multi-head attention mechanism was employed to capture long-term dependencies of power load effectively， thereby improving the disaggregation accuracy long-cycle appliances. Then， the KAN module was used to capture nonlinear dynamic features of power load signals more accurately through a hierarchical nonlinear mapping mechanism based on the Kolmogorov-Arnold representation theorem， thereby improving the disaggregation accuracy for complex load modes. Experimental results on the REDD （Reference Energy Disaggregation Dataset） and UK-DALE （UK Domestic Appliance-Level Electricity） datasets show that compared with four Transformer-based similar models， the proposed model achieves reduction of at least 1.6% and 5.5% in Mean Absolute Error （MAE）， the improvement of at least 8.3% and 0.7% in F1-score. It can be seen that the proposed method captures long-term dependencies and nonlinear dynamic features in power load signals more accurately and improves the disaggregation effect of complex appliance operating modes.