Placement of PMUs Considering Measurement Phase-Angle Mismatch

Phasor measurement units (PMUs) are becoming an important component in the power grid. The PMUs provide time-synchronized measurements of multiple remote measurement points, enabling more accurate and real-time monitoring of the system state. Heuristically, it is difficult to tell how the placement of a PMU at a specific location in the power system would affect the state estimation error, not to say the effect of the PMU synchronization and measurement accuracy. In this paper, we derive the posterior Cramér-Rao bound (PCRB) on the state estimation error based on a measurement model which considers the phase-angle mismatch from PMU measurements. We then propose a PMU placement strategy using the derived PCRB. The greedy algorithm is used to solve the optimization problem. The results are then compared with other heuristics, with the optimal solution through an exhaustive search (for small systems), and with a lower bound on the optimal placement obtained through convex relaxation. For some design criteria, the objective functions are submodular, which guarantees a performance bound on the greedy solution. For other design criteria where the objective functions are not submodular, numerical examples demonstrate the effectiveness of the greedy algorithms.