Uncovering Power Transmission Dynamic Model from Incomplete PMU Observations

Proliferation of Phasor Measurement Units (PMUs) that allow for a synchronous and distributed collection of data can be leveraged to obtain reliable information about the power system model. In practice, one has to account for the system being partially observed as not every bus hosts a PMU. We consider the problem of partial recovery of the underlying dynamic state matrix of transmission power grids from time-stamped PMU measurements on a subset of nodes in a network. We propose a data-driven method which does not assume any knowledge of system parameters and only relies on basic assumptions about the system dynamics. The method is based on a least-squares regression with a nuclear norm regularization that accounts for the effect of hidden observations, supplemented with structural physics-informed constraints that enforce the identifiability. Performance of the method is demonstrated on an IEEE test case example.