A theoretical framework for qualitative problems in power system state estimation

The qualitative problems of observability analysis and identification of critical measurements and critical sets are topics highly addressed in the literature. The analysis of such problems allows one to qualify the available measurements and predicts the extent of the benefits provided by the state estimator. Nevertheless, due to the lack of a concise theoretical approach, important concepts are often overlooked, so one cannot directly relate the existing numerical methods. Thus, based on the Jacobian's fundamental subspaces, this paper presents a unified theoretical framework for qualitative analysis. This approach along with a comprehensive literature review enables a categorization of the existing numerical methods, which are shown to be closely related. Given bases for the subspaces, unified alternative methods are conceived. These methods are independent of the decompositions required to obtain the bases for the subspaces. This paper also proposes a method to estimate the Jacobian's rank, which is used to identify cases prone to be pathological avoiding unnecessary iterations required by numerical observability analysis algorithms. An example shows that in 99.8% of cases the iterations can be dispensed with. Case studies with small systems of 6 and 14 buses are used to present the proposed approaches in a didactic way.