  The paper presents a Gaussian/kernel process regression method for real-time
state estimation and forecasting of phase angle and angular speed in systems
with a high penetration of solar generation units, operating under a sparse
measurements regime on both sunny and cloudy days. The method treats unknown
terms in the swing equations, such as solar power, as random processes, thereby
transforming these equations into stochastic differential equations. The
proposed method accurately forecasts and estimates both observed and unobserved
operating states, delivering forecasts comparable to those of the standard
data-driven Gaussian/kernel process for observed system states. Additionally,
the method demonstrates improved accuracy with increased observation frequency
and reduced measurement errors in the IEEE 14-bus test system.
