Impact of system state dynamics on PMU placement in the electric power grid

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.