Uncertainty sensitivity analysis of WLS-based grid state estimators

Fine-grained state estimation is expected to play a key role in smart grid monitoring and control. The most common class of state estimators at both transmission and distribution level relies on the so-called Weighted Least Squares (WLS) approach. While various, well-established implementations of WLS-based state estimators exist, all solutions typically exploit redundant data to assure full state observability and to build well conditioned matrices. At the moment, in the specific case of distribution networks just a few “true” measurement points are usually available. Therefore, the current distribution system state estimation (DSSE) techniques heavily rely on “pseudo” measurements based on historical load data. However, in future the traditional distinction between transmission and distribution systems is expected to blur and a larger number of heterogeneous instruments (e.g. the PMUs) could be deployed for real-time smart grid monitoring. In this respect, the purpose of this paper is twofold, i.e. i) to analyze in general how the uncertainty of different types of measurements may affect WLS-based state estimation accuracy when a minimum number of measurements is considered and ii) to identify a criterion for minimizing the sensitivity to measurement uncertainty. In the paper, the results of the theoretical analysis are validated through simulations in a case study.