  Recent work on complex networks compared the topological and electrical
structures of the power grid, taking into account the underlying physical laws
that govern the electrical connectivity between various components in the
network. A distance metric, namely, resistance distance was introduced to
provide a more comprehensive description of interconnections in power systems
compared with the topological structure, which is based only on geographic
connections between network components. Motivated by these studies, in this
paper we revisit the phasor measurement unit (PMU) placement problem by
deriving the connectivity matrix of the network using resistance distances
between buses in the grid, and use it in the integer program formulations for
several standard IEEE bus systems. The main result of this paper is rather
discouraging: more number of PMUs are required, compared with those obtained
using the topological structure, to meet the desired objective of complete
network observability without zero injection measurements. However, in light of
recent advances in the electrical structure of the grid, our study provides a
more realistic perspective of PMU placement in power systems. By further
exploring the connectivity matrix derived using the electrical structure, we
devise a procedure to solve the placement problem without resorting to linear
programming.
