Linear State Estimation in Presence of Bounded Uncertainties: A Comparative Analysis

TL;DR

PMU-based linear state estimation is challenged by bounded uncertainties in both data and line parameters, which can deviate up to $\pm 30\%$ from nominal values. The paper compares interval arithmetic, convex optimization, and GLFP for robust LSE under these bounded perturbations, using MATPOWER-generated data on IEEE test systems. Results show interval arithmetic delivers ultrafast bounds and small computation times, convex optimization provides accurate state estimates with reasonable time for larger systems, and GLFP incurs high computational burden and sensitivity to matrix elements. These findings offer practical paths for robust PMU-based LSE in real-time settings and indicate future work will explore machine learning-enabled approaches and hardware validation.

Abstract

A variety of algorithms have been proposed to address the power system state estimation problem in the presence of uncertainties in the data. However, less emphasis has been given to handling perturbations in the model. In the context of linear state estimation (LSE), which is the focus of this paper, perturbations in the model come from variations in the line parameters. Since the actual values of the line parameters can be different from the values stored in a power utility's database, we investigate three approaches in this paper to estimate the states in the presence of bounded uncertainties in the data and the model. The first approach is based on interval arithmetic, the second is based on convex optimization, and the third is based on generalized linear fractional programming. The three algorithms are applied to multiple IEEE test systems and compared in terms of their speed and accuracy. The results indicate that the first two algorithms are extremely fast and give expected results, while the third suffers from scalability issues and is unsuitable for LSE.

Figures (5)

• Figure 1: Estimated voltages for 5-bus system. The voltages estimated using GLFP approach lie outside the bounds, while the actual voltages lie within the bounds obtained using interval arithmetic approach.
• Figure 2: Estimated voltages for 14-bus system. For the real part as well as the imaginary parts, the actual voltages and the voltages estimated using convex optimization approach, lie within the bounds obtained using interval arithmetic approach.
• Figure 3: Estimated voltages for 30-bus system. For real part, all actual voltages and most of the voltages estimated using convex optimization approach lie within the bounds obtained using interval arithmetic approach. For imaginary part, most of the actual voltages and all of the voltages estimated using convex optimization approach lie within the bounds obtained using interval arithmetic approach.
• Figure 4: Estimated voltages for 57-bus system. For real part, actual voltages lie within the bounds obtained using interval arithmetic approach, while voltages estimated using convex optimization approach lie mostly below the lower bound. For imaginary part, all actual voltages and most of the voltages estimated using convex optimization approach lie within the bounds obtained using interval arithmetic approach.
• Figure 5: Estimated voltages for 118-bus system. For real part, actual voltages lie within the bounds obtained using interval arithmetic approach, while the voltages estimated using convex optimization approach lie mostly below the lower bound. For imaginary part, all actual voltages and most of the voltages estimated using convex optimization approach lie within the bounds obtained using interval arithmetic approach.