The accuracy of factored nonlinear weighted least squares state estimation

The factored decomposition technique was recently proposed as a theoretical framework for distributed and hierarchical nonlinear weighted least squares state estimation algorithms for large interconnected power networks. This paper analyses the accuracy of the technique and shows it to be suboptimal when compared to the direct weighted least squares solution commonly used in existing power system state estimation systems. In addition a closed form expression is developed that predicts the expected error in the factored estimate for a given system operating point. A Monte Carlo analysis shows that the theoretical prediction is accurate for a simulated power system. The structure of the prediction is analysed and shown to be proportional to the square of the standard deviation of the measurement noise, suggesting that the error may be insignificant for power systems with reasonably accurate sensors.