Optimal Placement of Phasor Measurement Unit in Smart Grids Considering Multiple Constraints

The distribution of measurement noise is usually assumed to be Gaussian in the optimal phasor measurement unit (PMU) placement (OPP) problem. However, this is not always accurate in practice. This paper proposes a new OPP method for smart grids in which the effects of conventional measurements, limited channels of PMUs, zero-injection buses (ZIBs), single PMU loss contingency, state estimation error (SEE), and the maximum SEE variance (MSEEV) are considered. The SEE and MSEEV are both obtained using a robust $t$-distribution maximum likelihood estimator (MLE) because $t$-distribution is more flexible for modeling both Gaussian and non-Gaussian noises. The A- and G-optimal experimental criteria are utilized to form the SEE and MSEEV constraints. This allows the optimization problem to be converted into a linear objective function subject to linear matrix inequality observability constraints. The performance of the proposed OPP method is verified by the simulations of the IEEE 14-bus, 30-bus, and 118-bus systems as well as the 188-bus practical distribution system in China.