Theoretical Foundation of Weight Adjustment for Weighted Least Squares State Estimator

Power system state estimation (SE) is routinely performed in modern energy control centers using the weighted least squares (WLS) method to provide reliable inputs for advanced applications in energy management systems. The accuracy of the SE solution is crucial but can be easily affected by various factors, including gross errors in measurements, among others. In real-time applications, the selection of appropriate weights for measurements is one important factor influencing the accuracy of the WLS method. However, current schemes for weight adjustment may be ad-hoc in nature, lacking substantial theoretical support, which necessitates an iterative process for fine-tuning weight factors. To provide theoretical support and guidance for tuning weight factors in the WLS method, this paper establishes a theoretical foundation for the weight adjustment procedure in SE. A weight adjustment model for the WLS method is proposed by incorporating inequality constraints on uncertain measurements and the performance-driven, residual-based requirements to seek feasible weight adjustment. Given a weight adjustment problem in SE, a necessary and sufficient condition for the existence of a feasible weight adjustment scheme will be established. As a by-product, a weight adjustment scheme is obtained by the proposed method once the existence of feasible adjusted weight vectors is established. Both numerical validation of the derived theoretical results and performance evaluations of an obtained feasible adjustment factor are conducted on the IEEE 14-bus and 118-bus systems to illustrate the derived theorems and the numerical performance of the weight adjustment scheme for the SE problem.