An optimal joint placement of PMUs and flow measurements for ensuring power system observability under N-2 transmission contingencies

This paper discusses an optimal joint placement of phasor measurement units (PMUs) and flow measurement devices for ensuring observability of power systems under N-2 transmission contingencies while excluding single-bus islanding situations. Previous studies mainly focus on system observability under N-1 contingencies, and consider the PMU placement only or the joint placement while restricting PMUs and flow measurements to be adjacent. In comparison, this paper first proposes a single-stage optimal joint placement model which minimizes the total investment cost of PMUs and flow measurements for achieving system observability under N-2 transmission contingencies while excluding single-bus islanding situations. Different topologies corresponding to double-line outage situations and the effect of zero power injection nodes are accurately considered, and system disintegration is adequately addressed for guaranteeing system observability under N-2 transmission contingencies. Moreover, the proposed model allows a flow measurement on a branch to observe one terminal node even if the other terminal is not adjacent to a PMU. The proposed single-stage optimal joint placement model is formulated as a mixed-integer nonlinear programming (MINLP) problem, and is equivalently transformed into a mixed-integer linear programming (MILP) problem and solved via a decomposition algorithm. Furthermore, as system operators may prefer a multi-stage placement plan so as to well spread limited financial budgets among multiple years, the proposed single-stage joint placement model is further extended to a three-stage strategy for incrementally ensuring system observability with respect to the original topology, N-1 contingencies, and N-2 contingencies. Both models are verified via several IEEE power systems. Numerical results show that, as compared to previous studies, the proposed optimal joint placement approaches are advantageous in reducing total investment cost while ensuring system observability, and the three-stage placement model presents an effective strategy to handle limited financial budgets among multiple years. In addition, impacts of other factors on the proposed model, including single PMU failure, substation based optimization, branch PMU based optimization, single-bus islanding inclusion, and zero power injection effect verification, are analyzed and discussed via extensive case studies.