Algebraic Approach to PMU Placement for Minimum Variance Linear State Estimation in Power Networks

Phasor Measurement Units (PMUs) are used to measure voltages and currents in a power network. Optimal PMU placement in a given network is an important problem since installing PMU at every node of a network is expensive. This paper proposes an algebraic approach to the PMU placement problem with a focus on complete voltage state estimation and PMU measurement noise, with the objective to minimize the variance of the state estimation. The approach determines the minimum number of PMUs needed for full voltage state observability in a network based on the number of buses with known nodal currents. Combined with the information on PMU measurement noise and the network admittance matrix, an optimal PMU placement algorithm is formulated that minimizes the variance of the voltage estimation. This algorithm groups nodes of the network into four different sets based on the nodal voltages and nodal/line currents measured by the PMUs deployed in the network. The proposed placement algorithm considers both single current-channel PMU case and multi-current channel PMU case. This proposed placement algorithm is tested on IEEE 14 bus and IEEE 39 bus network. The results show that optimal placement can significantly reduce the effects of PMU measurement noise on the estimated states.