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

This paper investigates the optimal placement of micro-phasor measurement units (<inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mu }$ </tex-math></inline-formula>PMUs) and smart meters (SMs) in microgrids (<inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mu }$ </tex-math></inline-formula>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 <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mu }$ </tex-math></inline-formula>PMUs. Subproblems I and II satisfy <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mu }\text{G}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mu }\text{G}$ </tex-math></inline-formula> studies for accommodating SM and <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mu }$ </tex-math></inline-formula>PMU data. For the observability assessment in contingencies, a linear model which considers <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mu }$ </tex-math></inline-formula>PMU locations is developed. The proposed method is tested on a 33-bus test <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mu }\text{G}$ </tex-math></inline-formula> and comprehensive simulation studies are presented for validating the effectiveness of the proposed method for various <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {\mu }\text{G}$ </tex-math></inline-formula> configurations.