  The goal of this paper is to study the impact of the dynamic nature of bus
voltage magnitudes and phase angles, which constitute the state of the power
system, on the phasor measurement unit (PMU) placement problem. To facilitate
this study, the placement problem is addressed from the perspective of the
electrical structure which, unlike existing work on PMU placement, accounts for
the sensitivity between power injections and nodal phase angle differences
between various buses in the power network. A linear dynamic model captures the
time evolution of system states, and a simple procedure is devised to estimate
the state transition function at each time instant. The placement problem is
formulated as a series (time steps) of binary integer programs, with the goal
to obtain the minimum number of PMUs at each time step for complete network
observability in the absence of zero injection measurements. Experiments are
conducted on several standard IEEE test bus systems. The main thesis of this
study is that, owing to the dynamic nature of the system states, for optimal
power system operation the best one could do is to install a PMU on each bus of
the given network, though it is undesirable from an economic standpoint.
