  A tri-objective optimal Micro Phasor Measurement Units ({\mu}-PMUs) Placement
method is presented, with a focus on minimizing the following three parameters:
i) the total number of {\mu}-PMU channels, (ii) the maximum state estimation
uncertainty, and (iii) the sensitivity of state estimation to line parameter
tolerances. The suggested formulation takes single-line and {\mu}-PMU failures
into consideration while guaranteeing the complete observability of the system
in the presence and absence of contingencies. It also takes into account the
impact of zero injection nodes and the quantity of {\mu}-PMU channels carried
out at every node. The suggested placement issue is addressed using a
customized version of the nondominated sorting genetic algorithm II (NSGA-II).
According to the results achieved utilizing three test systems of varying
sizes, {\mu}-PMU channels beyond predetermined thresholds only result in higher
costs and negligible further decreases in state estimation uncertainty and
sensitivity to line parameter tolerances. Additionally, we may omit to
instrument between 30 and 40% of buses if {\mu}-PMUs with only two three-phase
channels are utilized, with only a modest negative effect on state estimate
performance even in the event of contingencies.
