  The optimal PMU locations to collect voltage phase angle measurements for
detecting line outages in wide-area transmission networks are investigated. The
problem is established as one of maximizing the minimum distance among the
voltage phase angle signatures of the outages, which can be equivalently
formulated as an integer programming problem. Based on a greedy heuristic and a
linear programming relaxation, a branch and bound algorithm is proposed to find
the globally optimal PMU locations. Using this algorithm, the optimal tradeoff
between the number of PMUs and the outage detection performance is
characterized for IEEE 14, 24 and 30 bus systems. The algorithm is shown to
find the globally optimal PMU locations in a small number of iterations. It is
observed that it is sufficient to have roughly one third of the buses providing
PMU measurements in order to achieve the same outage detection performance as
with all the buses providing PMU measurements.
