To enhance early electrical fire warning in power IoT systems, we propose a residual current modeling method combining grey correlation and neural networks. By analyzing 27985 sets of data from an intelligent fire monitoring system, effective data collection and processing with advanced sensor technology in an IoT context were demonstrated. The model, derived from correlation analysis and grey prediction algorithms, uses a trained neural network for predicting residual current. This method not only augments the efficiency and accuracy of data processing in IoT but also underscores the significance of sensor technology in electrical monitoring and fire prevention. The comparative analysis of predicted and actual residual currents, showing an error range of 0.18 to 3.21%, validates the accuracy of the model and the utility of sensor-driven methods in IoT applications.