Quantifying Uncertainty in State Estimation: The MoK-FoBS Method via Interval Analysis

The Bayesian framework is conventionally adopted in power system static state estimation (SSE) to quantify uncertainty via probability density functions (PDFs). However, the reliability of such PDFs is frequently undermined by the complex nature of noise in measurement systems, potentially leading to significant estimation inaccuracies. To address this problem, this paper proposes a modified Krawczyk-forward-backward synthesis (MoK-FoBS) method to quantify uncertainty in SSE through interval analysis. The proposed MoK-FoBS method combines the strengths of the modified forward-backward propagation (FBP) method with the modified Krawczyk method to mitigate the overestimation problem. Employing simulation data derived from IEEE testing systems, it is verified through the Monte Carlo method that the MoK-FoBS method can estimate hard boundaries that invariably contain the true state values. In contrast, the true state values may lie outside the uncertainty boundaries estimated by the weighted least squares approach. A comparative analysis reveals that the MoK-FoBS method can achieve narrower state boundaries than the FBP method, thereby improving estimation precision.