Qualitative methods to solve qualitative problems in power system state estimation

An effort is made to show that a mathematically consistent combinatorial theory which has been previously used for topological observability analysis can be extended to deal with other qualitative problems in power system state estimation. In particular, the problems of critical measurement and critical set identification are addressed. The interest in investigating these questions lies in the fact that, when contaminated by gross errors, critical measurements are undetectable, whereas measurements in critical sets are unidentifiable. The performance of the proposed combinatorial methods is appraised by means of several tests, using the IEEE-14 and 30 bus systems and two realistic systems of Brazilian utilities. The results show that the critical measurement identification method is very fast, with execution times compatible with real time applications. The technique for identification of critical sets has also exhibited a better computational performance than the improved enumerative method