State estimation with sampling offsets in wide area measurement systems

An implicit assumption made in studies on state estimation is that the time and frequency at which these measurements are taken is consistent across all the distributed sensing sites. For instance, in the literatures on Wide Area Measurement Systems (WAMS) deployed in the power grid, where the sensors equipped with Global Positioning Signals (GPS), the sensing sites are deemed capable to provide perfectly synchronous readings at the various sampling sites. The validity of the assumption may need to be re-examined with the recent advancements in decentralized state estimation algorithms. Importantly, when there are timing offsets between sampling devices, the effects on the measurement system's performance can be catastrophic. The prevalent point of view is to either study the resulting error, or to resort to Kalman filtering for aligning the measurements. Taking on this view typically requires additional information about the underlying state. In this paper, we revisit the problem of state estimation and propose a new model for data acquisition under asynchronous sampling. The key idea is to apply sampling theory and to exploit the redundancy in the spatial sampling to interpolate the system state. We provide a necessary and sufficient condition for identifiability of the time offsets and propose an algorithm for the joint regression on state and timing offsets. The efficacy of the proposed algorithm is shown by numerical simulations.