  In this paper, phasor measurement unit (PMU) placement for power grid state
estimation under different degrees of observability is studied. Observability
degree is the depth of the buses' reachability by the placed PMUs and thus
constitutes an important characteristic for PMU placement. However, the sole
observability as addressed in many works still does not guarantee a good
estimate for the grid state. Some existing works also considered the PMU
placement for minimizing the mean squared error or maximizing the mutual
information between the measurement output and grid state. However, they ignore
the observability requirements for computational tractability and thus
potentially lead to artificial results such as acceptance of the estimate for
an unobserved state component as its unconditional mean. In this work, the PMU
placement optimization problem is considered by minimizing the mean squared
error or maximizing the mutual information between the measurement output and
grid state, under grid observability constraints. The provided solution is free
from the mentioned fundamental drawbacks in the existing PMU placement designs.
The problems are posed as binary nonlinear optimization problems, for which
this paper develops efficient algorithms for computational solutions. The
performance of the proposed algorithms is analyzed in detail through numerical
examples on large-scale IEEE power networks.
