Earlier papers have shown that the use of line current magnitude measu
rements may lead to non-uniquely observable systems. This paper studie
s the bad data identification problem under these conditions. The defi
nition of measurement criticality is revised in order to account for t
he non-uniquely observable cases. The problem of bad data identificati
on is investigated both as a post estimation problem when using the le
ast squares estimation method and as an outlier rejection problem when
using the least absolute value estimation method. Modifications to th
e existing bad data processing methods are proposed in order to accoun
t for the current magnitude measurements.