  We consider the problem of reconstructing the dynamic state matrix of
transmission power grids from time-stamped PMU measurements in the regime of
ambient fluctuations. Using a maximum likelihood based approach, we construct a
family of convex estimators that adapt to the structure of the problem
depending on the available prior information. The proposed method is fully
data-driven and does not assume any knowledge of system parameters. It can be
implemented in near real-time and requires a small amount of data. Our learning
algorithms can be used for model validation and calibration, and can also be
applied to related problems of system stability, detection of forced
oscillations, generation re-dispatch, as well as to the estimation of the
system state.
