Probabilistic Interval State Estimation for Distribution System With Correlation Probability Box Depicting Stochastic Uncertainties of DG

Stochastic uncertainty, comprising both aleatory and epistemic uncertainties, is intrinsic in the distributed generation (DG). However, existing distribution system state estimation (DSSE) methods lack a unified modeling framework to characterize both uncertainties and struggle to provide estimation results that are both probabilistically informative and interval-bounded. To bridge this gap, a novel probabilistic interval forecasting-aided state estimation (PI-FASE) framework is proposed. First, a PI-FASE problem is formulated grounded on the probabilistic interval state-space model, where uncertainties are reflected and quantified by probabilistic intervals of state variables. Second, the correlation probability box (CP-box) is constructed to depict both aleatory and epistemic uncertainties, considering intrinsic correlations among DG units. Third, a probabilistic interval extended Kalman filter (PI-EKF) algorithm is developed to achieve highly efficient and low conservative PI-FASE. Within PI-EKF, probabilistic intervals are generated from the CP-box via Sobol–Copula sampling, propagated through state prediction, and then updated using interval measurements. The final state estimates are expressed as P-boxes, offering both interval bounds and probabilistic insight into the system states. Numerical simulations on the IEEE 13-bus, IEEE 33-bus, and IEEE 123-bus unbalanced distribution systems validate the superiority of the proposed PI-FASE.