Contingency-Constrained Optimal Placement of Micro-PMUs and Smart Meters in Microgrids

This paper investigates the optimal placement of micro-phasor measurement units ( $\boldsymbol {\mu }$ PMUs) and smart meters (SMs) in microgrids ( $\boldsymbol {\mu }$ Gs). The optimal placement problem is formulated as a mixed-integer linear programming problem in which the major constraint is to maintain the observability at steady state and contingencies. We apply the Benders decomposition to this optimization problem in which a master problem and two subproblems are considered in order to lessen the dimensional and computational complexities of the proposed optimization model. The master problem identifies the optimal locations of SMs and $\boldsymbol {\mu }$ PMUs. Subproblems I and II satisfy $\boldsymbol {\mu }\text{G}$ observability constraints at steady state and contingency conditions, respectively. In the case of any subproblem violations, appropriate infeasibility cuts are produced and added to the master problem. The steady state observability analysis using SM data is a nonlinear model which is linearized in $\boldsymbol {\mu }\text{G}$ studies for accommodating SM and $\boldsymbol {\mu }$ PMU data. For the observability assessment in contingencies, a linear model which considers $\boldsymbol {\mu }$ PMU locations is developed. The proposed method is tested on a 33-bus test $\boldsymbol {\mu }\text{G}$ and comprehensive simulation studies are presented for validating the effectiveness of the proposed method for various $\boldsymbol {\mu }\text{G}$ configurations.