Linear State Estimator

Linear State Estimation based solely on PMU measurements offers a simplified measurement model, but does not eliminate the fundamental challenges of data quality and model consistency. When only PMU measurements are used, the state estimation problem becomes linear, removing the need for iterative linearization. However, bad data, leverage points, and model inconsistencies can still severely bias the solution. Traditional linear estimators typically rely on least-squares fitting and residual magnitude checks, which remain vulnerable to structured errors and correlated measurement issues—even in a fully linear formulation.

SE+ remains fully applicable in this linear PMU-only setting and retains all of its core advantages. Rather than minimizing residual size, SE+ identifies the most consistent subset of PMU measurements and rejects those that are incompatible with the system model. This consistency-based approach enables robust rejection of bad PMU data, immunity to leverage points, and guaranteed convergence to a feasible solution—without iterative tuning or fragile thresholds. As a result, the SE+-based Linear State Estimator delivers fast, reliable, and unbiased state estimates while preserving the same robustness, explainability, and operational benefits as SE+ in nonlinear state estimation.