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This work presents an efficient data-driven method to construct probabilisticvoltage envelopes (PVE) using power flow learning in grids with networkcontingencies. First, a network-aware Gaussian process (GP) termedVertex-Degree Kernel (VDK-GP), developed in prior work, is used to estimatevoltage-power functions for a few network configurations. The paper introducesa novel multi-task vertex degree kernel (MT-VDK) that amalgamates the learnedVDK-GPs to determine power flows for unseen networks, with a significantreduction in the computational complexity and hyperparameter requirementscompared to alternate approaches. Simulations on the IEEE 30-Bus networkdemonstrate the retention and transfer of power flow knowledge in both N-1 andN-2 contingency scenarios. The MT-VDK-GP approach achieves over 50% reductionin mean prediction error for novel N-1 contingency network configurations inlow training data regimes (50-250 samples) over VDK-GP. Additionally, MT-VDK-GPoutperforms a hyper-parameter based transfer learning approach in over 75% ofN-2 contingency network structures, even without historical N-2 outage data.The proposed method demonstrates the ability to achieve PVEs using sixteentimes fewer power flow solutions compared to Monte-Carlo sampling-basedmethods.

Data-Efficient Strategies for Probabilistic Voltage Envelopes under Network Contingencies