  While the uncertainty in generation and demand increases, accurately
estimating the dynamic characteristics of power systems becomes crucial for
employing the appropriate control actions to maintain their stability. In our
previous work, we have shown that Bayesian Physics-informed Neural Networks
(BPINNs) outperform conventional system identification methods in identifying
the power system dynamic behavior under measurement noise. This paper takes the
next natural step and addresses the more significant challenge, exploring how
BPINN perform in estimating power system dynamics under increasing uncertainty
from many Inverter-based Resources (IBRs) connected to the grid. These
introduce a different type of uncertainty, compared to noisy measurements. The
BPINN combines the advantages of Physics-informed Neural Networks (PINNs), such
as inverse problem applicability, with Bayesian approaches for uncertainty
quantification. We explore the BPINN performance on a wide range of systems,
starting from a single machine infinite bus (SMIB) system and 3-bus system to
extract important insights, to the 14-bus CIGRE distribution grid, and the
large IEEE 118-bus system. We also investigate approaches that can accelerate
the BPINN training, such as pretraining and transfer learning. Throughout this
paper, we show that in presence of uncertainty, the BPINN achieves orders of
magnitude lower errors than the widely popular method for system identification
SINDy and significantly lower errors than PINN, while transfer learning helps
reduce training time by up to 80 %.
