  This work presents an efficient data-driven method to learn power flows in
grids with network contingencies and to estimate corresponding probabilistic
voltage envelopes (PVE). First, a network-aware Gaussian process (GP) termed
Vertex-Degree Kernel (VDK-GP), developed in prior work, is used to estimate
voltage-power functions for a few network configurations. The paper introduces
a novel multi-task vertex degree kernel (MT-VDK) that amalgamates the learned
VDK-GPs to determine power flows for unseen networks, with a significant
reduction in the computational complexity and hyperparameter requirements
compared to alternate approaches. Simulations on the IEEE 30-Bus network
demonstrate the retention and transfer of power flow knowledge in both N-1 and
N-2 contingency scenarios. The MT-VDK-GP approach achieves over 50% reduction
in mean prediction error for novel N-1 contingency network configurations in
low training data regimes (50-250 samples) over VDK-GP. Additionally, MT-VDK-GP
outperforms a hyper-parameter based transfer learning approach in over 75% of
N-2 contingency network structures, even without historical N-2 outage data.
The proposed method demonstrates the ability to achieve PVEs using sixteen
times fewer power flow solutions compared to Monte-Carlo sampling-based
methods.

Machine Learning;Systems and Control;Systems and Control