Optimal PMU Placement by an Equivalent Linear Formulation for Exhaustive Search

Observability of bulk power transmission network by means of minimum number of phasor measurement units (PMUs), with the aid of the network topology, is a great challenge. This paper presents a novel equivalent integer linear programming method (EILPM) for the exhaustive search-based PMU placement. The state estimation implemented based on such a placement is completely linear, thereby eliminating drawbacks of the conventional SCADA-based state estimation. Additional constraints for observability preservation following single PMU or line outages can easily be implemented in the proposed EILPM. Furthermore, the limitation of communication channels is dealt with by translation of nonlinear terms into linear ones. Optimal PMU placement is carried out on the IEEE 118-bus test system in different scenarios. The comparison between obtained results of EILPM and those of other methods reveals optimality of the solutions. Moreover, the proposed method is successfully applied on the Iranian National Grid, which demonstrates it can effectively be employed for practical power networks.

Nomenclature

Binary connectivity parameter between buses and .

Binary variable which is equal to 1 if the PMU installed at bus measures the voltage of bus for , or the current of line for ; and 0 otherwise.

Indices of bus.

Superscript denoting value of the associated variable or parameter when line is out.

Binary variable whose value of 1 indicates that the current of line for or the voltage of bus for can be measured if a PMU is installed at bus .

Index of line.

Number of network lines.

Number of zero injection buses in the power network.

Number of network buses.

Observability function of bus .

Binary decision variable that is equal to 1 if a PMU is installed at bus and 0 otherwise.

Vector of PMUs combination .

Superscript denoting the value of the associated variable or parameter, when influence of the PMU installed at bus (if any) on observability is neglected.

Installation cost of PMU at bus .

Binary auxiliary variable indicating calculation of unknown state of bus is assigned to the equation resulted from the zero injection .

Bus index for zero injection .

Binary parameter whose value is 0 if is equal to , and 1 otherwise.