An Interval-Probability-based Distribution System State Estimation Quantification Framework Considering Nonlinear Correlations of Uncertain Distributed Generators with Limited Information

The distribution system state estimation (DSSE) is critical for the operation and control of electric distribution systems, but faces significant challenges due to the integration of distributed generators (DGs). The existing uncertain DSSE frameworks struggle with managing correlations, particularly nonlinear correlations among DGs, and it is exacerbated by limited available observations of DGs in practical distribution systems. In light of these problems, initially, this paper utilizes the partition around medoids clustering algorithm and evidence theory to propose a joint Dempster-Shafer (DS) structure for modeling the multiple DGs with limited information, while accounting for their nonlinear correlations. The entire uncertainty hyperspace of DGs is partitioned into a specific number of sub-hyperspaces with corresponding basic probability assignments, according to the limited observations. Subsequently, the uncertainties of DGs are propagated to DSSE outputs by integrating affine arithmetic with evidence theory and multidimensional parallelepiped model, while facilitating further correlation characterization among DGs. Eventually, a probability box (P-box) about each DSSE output, comprising finite intervals with interval probabilities, can be achieved for demonstrating its uncertainty. The proposed interval-probability-based DSSE framework's effectiveness, accuracy, computational efficiency, and scalability are validated through comprehensive tests across various distribution systems.