A Two-Stage Mixed Integer Programming Model for Distributionally Robust State-Based Non-Intrusive Load Monitoring

This paper presents a non-intrusive load monitoring (NILM) model based on two-stage mixed-integer linear programming theory. Compared with other mixed integer optimization-based models, this paper model introduces fewer integer variables and richer absolute error function of load decomposition, which makes the power state selection of each device more accurate and the power consumption more accurate fitting. First, to tackle the issues related to noisy load data, an innovative load feature extraction model based on Kullback-Leibler distributionally robust optimization principles is introduced. Then the key features (power boundary/fluctuation features) of each device identified through this robust model are integrated into the constraints of the two-stage NILM model. The two-stage complementary framework includes: the determination of device state interval in the first stage; and the accurate fitting of device power consumption within the device state interval in the second stage. Comparative validation against existing optimization-based models on the AMPds, REFIT, and actual laboratory data sets demonstrate that our proposed model significantly enhances power decomposition accuracy and computational efficiency. In addition, the two-stage complementary framework and load feature extraction model can be applied to other optimization-based models of NILM to improve the computational efficiency of each model and the accuracy of load decomposition.